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A brick is a type of construction material used to build walls, pavements and other elements in masonry construction. Properly, the term brick denotes a unit primarily composed of clay, but is now also used informally to denote units made of other materials or other chemically cured construction blocks. Bricks can be joined using mortar, adhesives or by interlocking. Bricks are usually produced at brickworks in numerous classes, types, materials, and sizes which vary with region, and are produced in bulk quantities.
Block is a similar term referring to a rectangular building unit composed of clay or concrete, but is usually larger than a brick. Lightweight bricks (also called lightweight blocks) are made from expanded clay aggregate.
Fired bricks are one of the longest-lasting and strongest building materials, sometimes referred to as artificial stone, and have been used since . Air-dried bricks, also known as mudbricks, have a history older than fired bricks, and have an additional ingredient of a mechanical binder such as straw.
Bricks are laid in courses and numerous patterns known as bonds, collectively known as brickwork, and may be laid in various kinds of mortar to hold the bricks together to make a durable structure.
History
Middle East and South Asia
The earliest bricks were dried mudbricks, meaning that they were formed from clay-bearing earth or mud and dried (usually in the sun) until they were strong enough for use. The oldest discovered bricks, originally made from shaped mud and dating before 7500 BC, were found at Tell Aswad, in the upper Tigris region and in southeast Anatolia close to Diyarbakir.
Mudbrick construction was used at Çatalhöyük, from c. 7,400 BC.
Mudbrick structures, dating to c. 7,200 BC have been located in Jericho, Jordan Valley. These structures were made up of the first bricks with dimension 400x150x100 mm.
Between 5000 and 4500 BC, Mesopotamia had discovered fired brick. The standard brick sizes in Mesopotamia followed a general rule: the width of the dried or burned brick would be twice its thickness, and its length would be double its width.
The South Asian inhabitants of Mehrgarh also constructed air-dried mudbrick structures between 7000 and 3300 BC and later the ancient Indus Valley cities of Mohenjo-daro, Harappa, and Mehrgarh. Ceramic, or fired brick was used as early as 3000 BC in early Indus Valley cities like Kalibangan. | Brick | Wikipedia | 500 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
In the middle of the third millennium BC, there was a rise in monumental baked brick architecture in Indus cities. Examples included the Great Bath at Mohenjo-daro, the fire altars of Kaalibangan, and the granary of Harappa. There was a uniformity to the brick sizes throughout the Indus Valley region, conforming to the 1:2:4, thickness, width, and length ratio. As the Indus civilization began its decline at the start of the second millennium BC, Harappans migrated east, spreading their knowledge of brickmaking technology. This led to the rise of cities like Pataliputra, Kausambi, and Ujjain, where there was an enormous demand for kiln-made bricks.
By 604 BC, bricks were the construction materials for architectural wonders such as the Hanging Gardens of Babylon, where glazed fired bricks were put into practice.
China
The earliest fired bricks appeared in Neolithic China around 4400 BC at Chengtoushan, a walled settlement of the Daxi culture. These bricks were made of red clay, fired on all sides to above 600 °C, and used as flooring for houses. By the Qujialing period (3300 BC), fired bricks were being used to pave roads and as building foundations at Chengtoushan.
According to Lukas Nickel, the use of ceramic pieces for protecting and decorating floors and walls dates back at various cultural sites to 3000-2000 BC and perhaps even before, but these elements should be rather qualified as tiles. For the longest time builders relied on wood, mud and rammed earth, while fired brick and mudbrick played no structural role in architecture. Proper brick construction, for erecting walls and vaults, finally emerges in the third century BC, when baked bricks of regular shape began to be employed for vaulting underground tombs. Hollow brick tomb chambers rose in popularity as builders were forced to adapt due to a lack of readily available wood or stone. The oldest extant brick building above ground is possibly Songyue Pagoda, dated to 523 AD. | Brick | Wikipedia | 415 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
By the end of the third century BC in China, both hollow and small bricks were available for use in building walls and ceilings. Fired bricks were first mass-produced during the construction of the tomb of China's first Emperor, Qin Shi Huangdi. The floors of the three pits of the terracotta army were paved with an estimated 230,000 bricks, with the majority measuring 28x14x7 cm, following a 4:2:1 ratio. The use of fired bricks in Chinese city walls first appeared in the Eastern Han dynasty (25 AD-220 AD). Up until the Middle Ages, buildings in Central Asia were typically built with unbaked bricks. It was only starting in the ninth century CE when buildings were entirely constructed using fired bricks.
The carpenter's manual Yingzao Fashi, published in 1103 at the time of the Song dynasty described the brick making process and glazing techniques then in use. Using the 17th-century encyclopaedic text Tiangong Kaiwu, historian Timothy Brook outlined the brick production process of Ming dynasty China:
Europe
Early civilisations around the Mediterranean, including the Ancient Greeks and Romans, adopted the use of fired bricks. By the early first century CE, standardised fired bricks were being heavily produced in Rome. The Roman legions operated mobile kilns, and built large brick structures throughout the Roman Empire, stamping the bricks with the seal of the legion. The Romans used brick for walls, arches, forts, aqueducts, etc. Notable mentions of Roman brick structures are the Herculaneum gate of Pompeii and the baths of Caracalla.
During the Early Middle Ages the use of bricks in construction became popular in Northern Europe, after being introduced there from Northwestern Italy. An independent style of brick architecture, known as brick Gothic (similar to Gothic architecture) flourished in places that lacked indigenous sources of rocks. Examples of this architectural style can be found in modern-day Denmark, Germany, Poland, and Kaliningrad (former East Prussia).
This style evolved into the Brick Renaissance as the stylistic changes associated with the Italian Renaissance spread to northern Europe, leading to the adoption of Renaissance elements into brick building. Identifiable attributes included a low-pitched hipped or flat roof, symmetrical facade, round arch entrances and windows, columns and pilasters, and more. | Brick | Wikipedia | 474 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
A clear distinction between the two styles only developed at the transition to Baroque architecture. In Lübeck, for example, Brick Renaissance is clearly recognisable in buildings equipped with terracotta reliefs by the artist Statius von Düren, who was also active at Schwerin (Schwerin Castle) and Wismar (Fürstenhof).
Long-distance bulk transport of bricks and other construction equipment remained prohibitively expensive until the development of modern transportation infrastructure, with the construction of canal, roads, and railways.
Industrial era
Production of bricks increased massively with the onset of the Industrial Revolution and the rise in factory building in England. For reasons of speed and economy, bricks were increasingly preferred as building material to stone, even in areas where the stone was readily available. It was at this time in London that bright red brick was chosen for construction to make the buildings more visible in the heavy fog and to help prevent traffic accidents.
The transition from the traditional method of production known as hand-moulding to a mechanised form of mass-production slowly took place during the first half of the nineteenth century. The first brick-making machine was patented by Richard A. Ver Valen of Haverstraw, New York, in 1852. The Bradley & Craven Ltd 'Stiff-Plastic Brickmaking Machine' was patented in 1853. Bradley & Craven went on to be a dominant manufacturer of brickmaking machinery. Henry Clayton, employed at the Atlas Works in Middlesex, England, in 1855, patented a brick-making machine that was capable of producing up to 25,000 bricks daily with minimal supervision. His mechanical apparatus soon achieved widespread attention after it was adopted for use by the South Eastern Railway Company for brick-making at their factory near Folkestone.
At the end of the 19th century, the Hudson River region of New York State would become the world's largest brick manufacturing region, with 130 brickyards lining the shores of the Hudson River from Mechanicsville to Haverstraw and employing 8,000 people. At its peak, about 1 billion bricks were produced a year, with many being sent to New York City for use in its construction industry. | Brick | Wikipedia | 440 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
The demand for high office building construction at the turn of the 20th century led to a much greater use of cast and wrought iron, and later, steel and concrete. The use of brick for skyscraper construction severely limited the size of the building – the Monadnock Building, built in 1896 in Chicago, required exceptionally thick walls to maintain the structural integrity of its 17 storeys.
Following pioneering work in the 1950s at the Swiss Federal Institute of Technology and the Building Research Establishment in Watford, UK, the use of improved masonry for the construction of tall structures up to 18 storeys high was made viable. However, the use of brick has largely remained restricted to small to medium-sized buildings, as steel and concrete remain superior materials for high-rise construction.
Methods of manufacture
Four basic types of brick are un-fired, fired, chemically set bricks, and compressed earth blocks. Each type is manufactured differently for various purposes.
Mudbrick
Unfired bricks, also known as mudbrick, are made from a mixture of silt, clay, sand and other earth materials like gravel and stone, combined with tempers and binding agents such as chopped straw, grasses, tree bark, or dung. Since these bricks are made up of natural materials and only require heat from the Sun to bake, mudbricks have a relatively low embodied energy and carbon footprint.
The ingredients are first harvested and added together, with clay content ranging from 30% to 70%. The mixture is broken up with hoes or adzes, and stirred with water to form a homogenous blend. Next, the tempers and binding agents are added in a ratio, roughly one part straw to five parts earth to reduce weight and reinforce the brick by helping reduce shrinkage. However, additional clay could be added to reduce the need for straw, which would prevent the likelihood of insects deteriorating the organic material of the bricks, subsequently weakening the structure. These ingredients are thoroughly mixed together by hand or by treading and are then left to ferment for about a day. | Brick | Wikipedia | 409 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
The mix is then kneaded with water and molded into rectangular prisms of a desired size. Bricks are lined up and left to dry in the sun for three days on both sides. After the six days, the bricks continue drying until required for use. Typically, longer drying times are preferred, but the average is eight to nine days spanning from initial stages to its application in structures. Unfired bricks could be made in the spring months and left to dry over the summer for use in the autumn. Mudbricks are commonly employed in arid environments to allow for adequate air drying.
Fired brick
Fired bricks are baked in a kiln which makes them durable. Modern, fired, clay bricks are formed in one of three processes – soft mud, dry press, or extruded. Depending on the country, either the extruded or soft mud method is the most common, since they are the most economical.
Clay and shale are the raw ingredients in the recipe for a fired brick. They are the product of thousands of years of decomposition and erosion of rocks, such as pegmatite and granite, leading to a material that has properties of being highly chemically stable and inert. Within the clays and shales are the materials of aluminosilicate (pure clay), free silica (quartz), and decomposed rock.
One proposed optimal mix is:
Silica (sand) – 50% to 60% by weight
Alumina (clay) – 20% to 30% by weight
Lime – 2 to 5% by weight
Iron oxide – ≤ 7% by weight
Magnesia – less than 1% by weight
Shaping methods
Three main methods are used for shaping the raw materials into bricks to be fired: | Brick | Wikipedia | 349 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
Moulded bricks – These bricks start with raw clay, preferably in a mix with 25–30% sand to reduce shrinkage. The clay is first ground and mixed with water to the desired consistency. The clay is then pressed into steel moulds with a hydraulic press. The shaped clay is then fired at to achieve strength.
Dry-pressed bricks – The dry-press method is similar to the soft-mud moulded method, but starts with a much thicker clay mix, so it forms more accurate, sharper-edged bricks. The greater force in pressing and the longer firing time make this method more expensive.
Extruded bricks – For extruded bricks the clay is mixed with 10–15% water (stiff extrusion) or 20–25% water (soft extrusion) in a pugmill. This mixture is forced through a die to create a long cable of material of the desired width and depth. This mass is then cut into bricks of the desired length by a wall of wires. Most structural bricks are made by this method as it produces hard, dense bricks, and suitable dies can produce perforations as well. The introduction of such holes reduces the volume of clay needed, and hence the cost. Hollow bricks are lighter and easier to handle, and have different thermal properties from solid bricks. The cut bricks are hardened by drying for 20 to 40 hours at before being fired. The heat for drying is often waste heat from the kiln.
Kilns
In many modern brickworks, bricks are usually fired in a continuously fired tunnel kiln, in which the bricks are fired as they move slowly through the kiln on conveyors, rails, or kiln cars, which achieves a more consistent brick product. The bricks often have lime, ash, and organic matter added, which accelerates the burning process.
The other major kiln type is the Bull's Trench Kiln (BTK), based on a design developed by British engineer W. Bull in the late 19th century.
An oval or circular trench is dug, wide, deep, and in circumference. A tall exhaust chimney is constructed in the centre. Half or more of the trench is filled with "green" (unfired) bricks which are stacked in an open lattice pattern to allow airflow. The lattice is capped with a roofing layer of finished brick. | Brick | Wikipedia | 485 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
In operation, new green bricks, along with roofing bricks, are stacked at one end of the brick pile. Historically, a stack of unfired bricks covered for protection from the weather was called a "hack". Cooled finished bricks are removed from the other end for transport to their destinations. In the middle, the brick workers create a firing zone by dropping fuel (coal, wood, oil, debris, etc.) through access holes in the roof above the trench. The constant source of fuel maybe grown on the woodlots.
The advantage of the BTK design is a much greater energy efficiency compared with clamp or scove kilns. Sheet metal or boards are used to route the airflow through the brick lattice so that fresh air flows first through the recently burned bricks, heating the air, then through the active burning zone. The air continues through the green brick zone (pre-heating and drying the bricks), and finally out the chimney, where the rising gases create suction that pulls air through the system. The reuse of heated air yields savings in fuel cost.
As with the rail process, the BTK process is continuous. A half-dozen labourers working around the clock can fire approximately 15,000–25,000 bricks a day. Unlike the rail process, in the BTK process the bricks do not move. Instead, the locations at which the bricks are loaded, fired, and unloaded gradually rotate through the trench.
Influences on colour
The colour of fired clay bricks is influenced by the chemical and mineral content of the raw materials, the firing temperature, and the atmosphere in the kiln. For example, pink bricks are the result of a high iron content, white or yellow bricks have a higher lime content. Most bricks burn to various red hues; as the temperature is increased the colour moves through dark red, purple, and then to brown or grey at around . The names of bricks may reflect their origin and colour, such as London stock brick and Cambridgeshire White. Brick tinting may be performed to change the colour of bricks to blend-in areas of brickwork with the surrounding masonry.
An impervious and ornamental surface may be laid on brick either by salt glazing, in which salt is added during the burning process, or by the use of a slip, which is a glaze material into which the bricks are dipped. Subsequent reheating in the kiln fuses the slip into a glazed surface integral with the brick base. | Brick | Wikipedia | 502 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
Chemically set bricks
Chemically set bricks are not fired but may have the curing process accelerated by the application of heat and pressure in an autoclave.
Calcium-silicate bricks
Calcium-silicate bricks are also called sandlime or flintlime bricks, depending on their ingredients. Rather than being made with clay they are made with lime binding the silicate material. The raw materials for calcium-silicate bricks include lime mixed in a proportion of about 1 to 10 with sand, quartz, crushed flint, or crushed siliceous rock together with mineral colourants. The materials are mixed and left until the lime is completely hydrated; the mixture is then pressed into moulds and cured in an autoclave for three to fourteen hours to speed the chemical hardening. The finished bricks are very accurate and uniform, although the sharp arrises need careful handling to avoid damage to brick and bricklayer. The bricks can be made in a variety of colours; white, black, buff, and grey-blues are common, and pastel shades can be achieved. This type of brick is common in Sweden as well as Russia and other post-Soviet countries, especially in houses built or renovated in the 1970s. A version known as fly ash bricks, manufactured using fly ash, lime, and gypsum (known as the FaL-G process) are common in South Asia. Calcium-silicate bricks are also manufactured in Canada and the United States, and meet the criteria set forth in ASTM C73 – 10 Standard Specification for Calcium Silicate Brick (Sand-Lime Brick).
Concrete bricks
Bricks formed from concrete are usually termed as blocks or concrete masonry unit, and are typically pale grey. They are made from a dry, small aggregate concrete which is formed in steel moulds by vibration and compaction in either an "egglayer" or static machine. The finished blocks are cured, rather than fired, using low-pressure steam. Concrete bricks and blocks are manufactured in a wide range of shapes, sizes and face treatments – a number of which simulate the appearance of clay bricks. | Brick | Wikipedia | 429 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
Concrete bricks are available in many colours and as an engineering brick made with sulfate-resisting Portland cement or equivalent. When made with adequate amount of cement they are suitable for harsh environments such as wet conditions and retaining walls. They are made to standards BS 6073, EN 771-3 or ASTM C55. Concrete bricks contract or shrink so they need movement joints every 5 to 6 metres, but are similar to other bricks of similar density in thermal and sound resistance and fire resistance.
Compressed earth blocks
Compressed earth blocks are made mostly from slightly moistened local soils compressed with a mechanical hydraulic press or manual lever press. A small amount of a cement binder may be added, resulting in a stabilised compressed earth block.
Types
There are thousands of types of bricks that are named for their use, size, forming method, origin, quality, texture, and/or materials.
Categorized by manufacture method:
Extruded – made by being forced through an opening in a steel die, with a very consistent size and shape.
Wire-cut – cut to size after extrusion with a tensioned wire which may leave drag marks
Moulded – shaped in moulds rather than being extruded
Machine-moulded – clay is forced into moulds using pressure
Handmade – clay is forced into moulds by a person
Dry-pressed – similar to soft mud method, but starts with a much thicker clay mix and is compressed with great force.
Categorized by use:
Common or building – A brick not intended to be visible, used for internal structure
Face – A brick used on exterior surfaces to present a clean appearance
Hollow – not solid, the holes are less than 25% of the brick volume
Perforated – holes greater than 25% of the brick volume
Keyed – indentations in at least one face and end to be used with rendering and plastering
Paving – brick intended to be in ground contact as a walkway or roadway
Thin – brick with normal height and length but thin width to be used as a veneer | Brick | Wikipedia | 409 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
Specialized use bricks:
Chemically resistant – bricks made with resistance to chemical reactions
Acid brick – acid resistant bricks
Engineering – a type of hard, dense, brick used where strength, low water porosity or acid (flue gas) resistance are needed. Further classified as type A and type B based on their compressive strength
Accrington – a type of engineering brick from England
Fire or refractory – highly heat-resistant bricks
Clinker – a vitrified brick
Ceramic glazed – fire bricks with a decorative glazing
Bricks named for place of origin:
Chicago common brick - a soft brick made near Chicago, Illinois with a range of colors, like buff yellow, salmon pink, or deep red
Cream City brick – a light yellow brick made in Milwaukee, Wisconsin
Dutch brick – a hard light coloured brick originally from the Netherlands
Fareham red brick – a type of construction brick
London stock brick – type of handmade brick which was used for the majority of building work in London and South East England until the growth in the use of machine-made bricks
Nanak Shahi bricks – a type of decorative brick in India
Roman brick – a long, flat brick typically used by the Romans
Staffordshire blue brick – a type of construction brick from England
Optimal dimensions, characteristics, and strength
For efficient handling and laying, bricks must be small enough and light enough to be picked up by the bricklayer using one hand (leaving the other hand free for the trowel). Bricks are usually laid flat, and as a result, the effective limit on the width of a brick is set by the distance which can conveniently be spanned between the thumb and fingers of one hand, normally about . In most cases, the length of a brick is twice its width plus the width of a mortar joint, about or slightly more. This allows bricks to be laid bonded in a structure which increases stability and strength (for an example, see the illustration of bricks laid in English bond, at the head of this article). The wall is built using alternating courses of stretchers, bricks laid longways, and headers, bricks laid crossways. The headers tie the wall together over its width. In fact, this wall is built in a variation of English bond called English cross bond where the successive layers of stretchers are displaced horizontally from each other by half a brick length. In true English bond, the perpendicular lines of the stretcher courses are in line with each other. | Brick | Wikipedia | 491 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
A bigger brick makes for a thicker (and thus more insulating) wall. Historically, this meant that bigger bricks were necessary in colder climates (see for instance the slightly larger size of the Russian brick in table below), while a smaller brick was adequate, and more economical, in warmer regions. A notable illustration of this correlation is the Green Gate in Gdansk; built in 1571 of imported Dutch brick, too small for the colder climate of Gdansk, it was notorious for being a chilly and drafty residence. Nowadays this is no longer an issue, as modern walls typically incorporate specialised insulation materials.
The correct brick for a job can be selected from a choice of colour, surface texture, density, weight, absorption, and pore structure, thermal characteristics, thermal and moisture movement, and fire resistance.
In England, the length and width of the common brick remained fairly constant from 1625 when the size was regulated by statute at 9 x x 3 inches (but see brick tax), but the depth has varied from about or smaller in earlier times to about more recently. In the United Kingdom, the usual size of a modern brick (from 1965) is , which, with a nominal mortar joint, forms a unit size of , for a ratio of 6:3:2.
In the United States, modern standard bricks are specified for various uses; The most commonly used is the modular brick has the actual dimensions of × × inches (194 × 92 × 57 mm). With the standard inch mortar joint, this gives the nominal dimensions of 8 x 4 x inches which eases the calculation of the number of bricks in a given wall. The 2:1 ratio of modular bricks means that when they turn corners, a 1/2 running bond is formed without needing to cut the brick down or fill the gap with a cut brick; and the height of modular bricks means that a soldier course matches the height of three modular running courses, or one standard CMU course.
Some brickmakers create innovative sizes and shapes for bricks used for plastering (and therefore not visible on the inside of the building) where their inherent mechanical properties are more important than their visual ones. These bricks are usually slightly larger, but not as large as blocks and offer the following advantages:
A slightly larger brick requires less mortar and handling (fewer bricks), which reduces cost
Their ribbed exterior aids plastering
More complex interior cavities allow improved insulation, while maintaining strength. | Brick | Wikipedia | 490 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
Blocks have a much greater range of sizes. Standard co-ordinating sizes in length and height (in mm) include 400×200, 450×150, 450×200, 450×225, 450×300, 600×150, 600×200, and 600×225; depths (work size, mm) include 60, 75, 90, 100, 115, 140, 150, 190, 200, 225, and 250. They are usable across this range as they are lighter than clay bricks. The density of solid clay bricks is around 2000 kg/m3: this is reduced by frogging, hollow bricks, and so on, but aerated autoclaved concrete, even as a solid brick, can have densities in the range of 450–850 kg/m3.
Bricks may also be classified as solid (less than 25% perforations by volume, although the brick may be "frogged," having indentations on one of the longer faces), perforated (containing a pattern of small holes through the brick, removing no more than 25% of the volume), cellular (containing a pattern of holes removing more than 20% of the volume, but closed on one face), or hollow (containing a pattern of large holes removing more than 25% of the brick's volume). Blocks may be solid, cellular or hollow.
The term "frog" can refer to the indentation or the implement used to make it. Modern brickmakers usually use plastic frogs but in the past they were made of wood.
The compressive strength of bricks produced in the United States ranges from about , varying according to the use to which the brick are to be put. In England clay bricks can have strengths of up to 100 MPa, although a common house brick is likely to show a range of 20–40 MPa.
Uses
Bricks are a versatile building material, able to participate in a wide variety of applications, including:
Structural walls, exterior and interior walls
Bearing and non-bearing sound proof partitions
The fireproofing of structural-steel members in the form of firewalls, party walls, enclosures and fire towers
Foundations for stucco
Chimneys and fireplaces
Porches and terraces
Outdoor steps, brick walks and paved floors
Swimming pools | Brick | Wikipedia | 462 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
In the United States, bricks have been used for both buildings and pavement. Examples of brick use in buildings can be seen in colonial era buildings and other notable structures around the country. Bricks have been used in paving roads and sidewalks especially during the late 19th century and early 20th century. The introduction of asphalt and concrete reduced the use of brick for paving, but they are still sometimes installed as a method of traffic calming or as a decorative surface in pedestrian precincts. For example, in the early 1900s, most of the streets in the city of Grand Rapids, Michigan, were paved with bricks. Today, there are only about 20 blocks of brick-paved streets remaining (totalling less than 0.5 percent of all the streets in the city limits). Much like in Grand Rapids, municipalities across the United States began replacing brick streets with inexpensive asphalt concrete by the mid-20th century.
In Northwest Europe, bricks have been used in construction for centuries. Until recently, almost all houses were built almost entirely from bricks. Although many houses are now built using a mixture of concrete blocks and other materials, many houses are skinned with a layer of bricks on the outside for aesthetic appeal.
Bricks in the metallurgy and glass industries are often used for lining furnaces, in particular refractory bricks such as silica, magnesia, chamotte and neutral (chromomagnesite) refractory bricks. This type of brick must have good thermal shock resistance, refractoriness under load, high melting point, and satisfactory porosity. There is a large refractory brick industry, especially in the United Kingdom, Japan, the United States, Belgium and the Netherlands.
Engineering bricks are used where strength, low water porosity or acid (flue gas) resistance are needed.
In the UK a red brick university is one founded in the late 19th or early 20th century. The term is used to refer to such institutions collectively to distinguish them from the older Oxbridge institutions, and refers to the use of bricks, as opposed to stone, in their buildings.
Colombian architect Rogelio Salmona was noted for his extensive use of red bricks in his buildings and for using natural shapes like spirals, radial geometry and curves in his designs. | Brick | Wikipedia | 452 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
Limitations
Starting in the 20th century, the use of brickwork declined in some areas due to concerns about earthquakes. Earthquakes such as the San Francisco earthquake of 1906 and the 1933 Long Beach earthquake revealed the weaknesses of unreinforced brick masonry in earthquake-prone areas. During seismic events, the mortar cracks and crumbles, so that the bricks are no longer held together. Brick masonry with steel reinforcement, which helps hold the masonry together during earthquakes, has been used to replace unreinforced bricks in many buildings. Retrofitting older unreinforced masonry structures has been mandated in many jurisdictions. However, similar to steel corrosion in reinforced concrete, rebar rusting will compromise the structural integrity of reinforced brick and ultimately limit the expected lifetime, so there is a trade-off between earthquake safety and longevity to a certain extent.
Accessibility
The United States Access Board does not specify which materials a sidewalk must be made of in order to be ADA compliant, but states that sidewalks must not have surface variances of greater than one inch. Due to the accessibility challenges of bricks, the Federal Highway Administration recommends against the use of bricks as well as cobblestones in its accessibility guide for sidewalks and crosswalks. The Brick Industry Association maintains standards for making brick more accessible for disabled people, with proper and regular maintenance being necessary to keep brick accessible.
Some US jurisdictions, such as San Francisco, have taken steps to remove brick sidewalks from certain areas such as Market Street in order to improve accessibility.
Gallery | Brick | Wikipedia | 302 | 4526 | https://en.wikipedia.org/wiki/Brick | Technology | Building materials | null |
Bipolar disorder, previously known as manic depression, is a mental disorder characterized by periods of depression and periods of abnormally elevated mood that each last from days to weeks. If the elevated mood is severe or associated with psychosis, it is called mania; if it is less severe and does not significantly affect functioning, it is called hypomania. During mania, an individual behaves or feels abnormally energetic, happy, or irritable, and they often make impulsive decisions with little regard for the consequences. There is usually, but not always, a reduced need for sleep during manic phases. During periods of depression, the individual may experience crying, have a negative outlook on life, and demonstrate poor eye contact with others. The risk of suicide is high. Over a period of 20 years, 6% of those with bipolar disorder died by suicide. 40-50% overall and 78% of adolescents engaged in self-harm. Other mental health issues, such as anxiety disorders and substance use disorders, are commonly associated with bipolar disorder. The global prevalence of bipolar disorder is estimated to be between 1–5% of the world's population.
While the causes of this mood disorder are not clearly understood, both genetic and environmental factors are thought to play a role. Genetic factors may account for up to 70–90% of the risk of developing bipolar disorder. Many genes, each with small effects, may contribute to the development of the disorder. Environmental risk factors include a history of childhood abuse and long-term stress. The condition is classified as bipolar I disorder if there has been at least one manic episode, with or without depressive episodes, and as bipolar II disorder if there has been at least one hypomanic episode (but no full manic episodes) and one major depressive episode. It is classified as cyclothymia if there are hypomanic episodes with periods of depression that do not meet the criteria for major depressive episodes.
If these symptoms are due to drugs or medical problems, they are not diagnosed as bipolar disorder. Other conditions that have overlapping symptoms with bipolar disorder include attention deficit hyperactivity disorder, personality disorders, schizophrenia, and substance use disorder as well as many other medical conditions. Medical testing is not required for a diagnosis, though blood tests or medical imaging can rule out other problems. | Bipolar disorder | Wikipedia | 472 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Mood stabilizers, particularly lithium, and certain anticonvulsants, such as lamotrigine and valproate, as well as atypical antipsychotics, including quetiapine, olanzapine, and aripiprazole are the mainstay of long-term pharmacologic relapse prevention. Antipsychotics are additionally given during acute manic episodes as well as in cases where mood stabilizers are poorly tolerated or ineffective. In patients where compliance is of concern, long-acting injectable formulations are available. There is some evidence that psychotherapy improves the course of this disorder. The use of antidepressants in depressive episodes is controversial: they can be effective but certain classes of antidepressants increase the risk of mania. The treatment of depressive episodes, therefore, is often difficult. Electroconvulsive therapy (ECT) is effective in acute manic and depressive episodes, especially with psychosis or catatonia. Admission to a psychiatric hospital may be required if a person is a risk to themselves or others; involuntary treatment is sometimes necessary if the affected person refuses treatment.
Bipolar disorder occurs in approximately 2% of the global population. In the United States, about 3% are estimated to be affected at some point in their life; rates appear to be similar in females and males. Symptoms most commonly begin between the ages of 20 and 25 years old; an earlier onset in life is associated with a worse prognosis. Interest in functioning in the assessment of patients with bipolar disorder is growing, with an emphasis on specific domains such as work, education, social life, family, and cognition. Around one-quarter to one-third of people with bipolar disorder have financial, social or work-related problems due to the illness. Bipolar disorder is among the top 20 causes of disability worldwide and leads to substantial costs for society. Due to lifestyle choices and the side effects of medications, the risk of death from natural causes such as coronary heart disease in people with bipolar disorder is twice that of the general population.
Signs and symptoms | Bipolar disorder | Wikipedia | 427 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Late adolescence and early adulthood are peak years for the onset of bipolar disorder. The condition is characterized by intermittent episodes of mania, commonly (but not in every patient) alternating with bouts of depression, with an absence of symptoms in between. During these episodes, people with bipolar disorder exhibit disruptions in normal mood, psychomotor activity (the level of physical activity that is influenced by mood)—e.g. constant fidgeting during mania or slowed movements during depression—circadian rhythm and cognition. Mania can present with varying levels of mood disturbance, ranging from euphoria, which is associated with "classic mania", to dysphoria and irritability. Psychotic symptoms such as delusions or hallucinations may occur in both manic and depressive episodes; their content and nature are consistent with the person's prevailing mood. In some people with bipolar disorder, depressive symptoms predominate, and the episodes of mania are always the more subdued hypomania type.
According to the DSM-5 criteria, mania is distinguished from hypomania by the duration: hypomania is present if elevated mood symptoms persist for at least four consecutive days, while mania is present if such symptoms persist for more than a week. Unlike mania, hypomania is not always associated with impaired functioning. The biological mechanisms responsible for switching from a manic or hypomanic episode to a depressive episode, or vice versa, remain poorly understood.
Manic episodes
Also known as a manic episode, mania is a distinct period of at least one week of elevated or irritable mood, which can range from euphoria to delirium. The core symptom of mania involves an increase in energy of psychomotor activity. Mania can also present with increased self-esteem or grandiosity, racing thoughts, pressured speech that is difficult to interrupt, decreased need for sleep, disinhibited social behavior, increased goal-oriented activities and impaired judgement, which can lead to exhibition of behaviors characterized as impulsive or high-risk, such as hypersexuality or excessive spending. To fit the definition of a manic episode, these behaviors must impair the individual's ability to socialize or work. If untreated, a manic episode usually lasts three to six months. | Bipolar disorder | Wikipedia | 474 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
In severe manic episodes, a person can experience psychotic symptoms, where thought content is affected along with mood. They may feel unstoppable, persecuted, or as if they have a special relationship with God, a great mission to accomplish, or other grandiose or delusional ideas. This may lead to violent behavior and, sometimes, hospitalization in an inpatient psychiatric hospital. The severity of manic symptoms can be measured by rating scales such as the Young Mania Rating Scale, though questions remain about the reliability of these scales.
The onset of a manic or depressive episode is often foreshadowed by sleep disturbance. Manic individuals often have a history of substance use disorder developed over years as a form of "self-medication".
Hypomanic episodes
Hypomania is the milder form of mania, defined as at least four days of the same criteria as mania, but which does not cause a significant decrease in the individual's ability to socialize or work, lacks psychotic features such as delusions or hallucinations, and does not require psychiatric hospitalization. Overall functioning may actually increase during episodes of hypomania and is thought to serve as a defense mechanism against depression by some. Hypomanic episodes rarely progress to full-blown manic episodes. Some people who experience hypomania show increased creativity, while others are irritable or demonstrate poor judgment.
Hypomania may feel good to some individuals who experience it, though most people who experience hypomania state that the stress of the experience is very painful. People with bipolar disorder who experience hypomania tend to forget the effects of their actions on those around them. Even when family and friends recognize mood swings, the individual will often deny that anything is wrong. If not accompanied by depressive episodes, hypomanic episodes are often not deemed problematic unless the mood changes are uncontrollable or volatile. Most commonly, symptoms continue for time periods from a few weeks to a few months.
Depressive episodes | Bipolar disorder | Wikipedia | 414 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Symptoms of the depressive phase of bipolar disorder include persistent feelings of sadness, irritability or anger, loss of interest in previously enjoyed activities, excessive or inappropriate guilt, hopelessness, sleeping too much or not enough, changes in appetite or weight, fatigue, problems concentrating, self-loathing or feelings of worthlessness, and thoughts of death or suicide. Although the DSM-5 criteria for diagnosing unipolar and bipolar episodes are the same, some clinical features are more common in the latter, including increased sleep, sudden onset and resolution of symptoms, significant weight gain or loss, and severe episodes after childbirth.
The earlier the age of onset, the more likely the first few episodes are to be depressive. For most people with bipolar types 1 and 2, the depressive episodes are much longer than the manic or hypomanic episodes. Since a diagnosis of bipolar disorder requires a manic or hypomanic episode, many affected individuals are initially misdiagnosed as having major depression and treated with prescribed antidepressants.
Mixed affective episodes
In bipolar disorder, a mixed state is an episode during which symptoms of both mania and depression occur simultaneously. Individuals experiencing a mixed state may have manic symptoms such as grandiose thoughts while simultaneously experiencing depressive symptoms such as excessive guilt or feeling suicidal. They are considered to have a higher risk for suicidal behavior as depressive emotions such as hopelessness are often paired with mood swings or difficulties with impulse control. Anxiety disorders occur more frequently as a comorbidity in mixed bipolar episodes than in non-mixed bipolar depression or mania. Substance (including alcohol) use also follows this trend, thereby appearing to depict bipolar symptoms as no more than a consequence of substance use. | Bipolar disorder | Wikipedia | 351 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Comorbid conditions
People with bipolar disorder often have other co-existing psychiatric conditions such as anxiety (present in about 71% of people with bipolar disorder), substance abuse (56%), personality disorders (36%) and attention deficit hyperactivity disorder (10–20%) which can add to the burden of illness and worsen the prognosis. Certain medical conditions are also more common in people with bipolar disorder as compared to the general population. This includes increased rates of metabolic syndrome (present in 37% of people with bipolar disorder), migraine headaches (35%), obesity (21%) and type 2 diabetes (14%). This contributes to a risk of death that is two times higher in those with bipolar disorder as compared to the general population. Hypothyroidism is also common regardless of drug choice.
Substance use disorder is a common comorbidity in bipolar disorder; the subject has been widely reviewed.
Causes
The causes of bipolar disorder likely vary between individuals and the exact mechanism underlying the disorder remains unclear. Genetic influences are believed to account for 73–93% of the risk of developing the disorder indicating a strong hereditary component. The overall heritability of the bipolar spectrum has been estimated at 0.71. Twin studies have been limited by relatively small sample sizes but have indicated a substantial genetic contribution, as well as environmental influence. For bipolar I disorder, the rate at which identical twins (same genes) will both have bipolar I disorder (concordance) is around 40%, compared to about 5% in fraternal twins. A combination of bipolar I, II, and cyclothymia similarly produced rates of 42% and 11% (identical and fraternal twins, respectively). The rates of bipolar II combinations without bipolar I are lowerbipolar II at 23 and 17%, and bipolar II combining with cyclothymia at 33 and 14%which may reflect relatively higher genetic heterogeneity.
The cause of bipolar disorders overlaps with major depressive disorder. When defining concordance as the co-twins having either bipolar disorder or major depression, then the concordance rate rises to 67% in identical twins and 19% in fraternal twins. The relatively low concordance between fraternal twins brought up together suggests that shared family environmental effects are limited, although the ability to detect them has been limited by small sample sizes. | Bipolar disorder | Wikipedia | 487 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Genetic
Behavioral genetic studies have suggested that many chromosomal regions and candidate genes are related to bipolar disorder susceptibility with each gene exerting a mild to moderate effect. The risk of bipolar disorder is nearly ten-fold higher in first-degree relatives of those with bipolar disorder than in the general population; similarly, the risk of major depressive disorder is three times higher in relatives of those with bipolar disorder than in the general population.
Although the first genetic linkage finding for mania was in 1969, linkage studies have been inconsistent. Findings point strongly to heterogeneity, with different genes implicated in different families. Robust and replicable genome-wide significant associations showed several common single-nucleotide polymorphisms (SNPs) are associated with bipolar disorder, including variants within the genes CACNA1C, ODZ4, and NCAN. The largest and most recent genome-wide association study failed to find any locus that exerts a large effect, reinforcing the idea that no single gene is responsible for bipolar disorder in most cases. Polymorphisms in BDNF, DRD4, DAO, and TPH1 have been frequently associated with bipolar disorder and were initially associated in a meta-analysis, but this association disappeared after correction for multiple testing. On the other hand, two polymorphisms in TPH2 were identified as being associated with bipolar disorder.
Due to the inconsistent findings in a genome-wide association study, multiple studies have undertaken the approach of analyzing SNPs in biological pathways. Signaling pathways traditionally associated with bipolar disorder that have been supported by these studies include corticotropin-releasing hormone signaling, cardiac β-adrenergic signaling, phospholipase C signaling, glutamate receptor signaling, cardiac hypertrophy signaling, Wnt signaling, Notch signaling, and endothelin 1 signaling. Of the 16 genes identified in these pathways, three were found to be dysregulated in the dorsolateral prefrontal cortex portion of the brain in post-mortem studies: CACNA1C, GNG2, and ITPR2.
Bipolar disorder is associated with reduced expression of specific DNA repair enzymes and increased levels of oxidative DNA damages. | Bipolar disorder | Wikipedia | 462 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Environmental
Psychosocial factors play a significant role in the development and course of bipolar disorder, and individual psychosocial variables may interact with genetic dispositions. Recent life events and interpersonal relationships likely contribute to the onset and recurrence of bipolar mood episodes, just as they do for unipolar depression. In surveys, 30–50% of adults diagnosed with bipolar disorder report traumatic/abusive experiences in childhood, which is associated with earlier onset, a higher rate of suicide attempts, and more co-occurring disorders such as post-traumatic stress disorder. Subtypes of abuse, such as sexual and emotional abuse, also contribute to violent behaviors seen in patients with bipolar disorder. The number of reported stressful events in childhood is higher in those with an adult diagnosis of bipolar spectrum disorder than in those without, particularly events stemming from a harsh environment rather than from the child's own behavior. Acutely, mania can be induced by sleep deprivation in around 30% of people with bipolar disorder.
Neurological
Less commonly, bipolar disorder or a bipolar-like disorder may occur as a result of or in association with a neurological condition or injury including stroke, traumatic brain injury, HIV infection, multiple sclerosis, porphyria, and rarely temporal lobe epilepsy.
Proposed mechanisms
The precise mechanisms that cause bipolar disorder are not well understood. Bipolar disorder is thought to be associated with abnormalities in the structure and function of certain brain areas responsible for cognitive tasks and the processing of emotions. A neurologic model for bipolar disorder proposes that the emotional circuitry of the brain can be divided into two main parts. The ventral system (regulates emotional perception) includes brain structures such as the amygdala, insula, ventral striatum, ventral anterior cingulate cortex, and the prefrontal cortex. The dorsal system (responsible for emotional regulation) includes the hippocampus, dorsal anterior cingulate cortex, and other parts of the prefrontal cortex. The model hypothesizes that bipolar disorder may occur when the ventral system is overactivated and the dorsal system is underactivated. Other models suggest the ability to regulate emotions is disrupted in people with bipolar disorder and that dysfunction of the ventricular prefrontal cortex is crucial to this disruption. | Bipolar disorder | Wikipedia | 456 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Meta-analyses of structural MRI studies have shown that certain brain regions (e.g., the left rostral anterior cingulate cortex, fronto-insular cortex, ventral prefrontal cortex, and claustrum) are smaller in people with bipolar disorder, whereas other regions are larger (lateral ventricles, globus pallidus, subgenual anterior cingulate, and the amygdala). Additionally, these meta-analyses found that people with bipolar disorder have higher rates of deep white matter hyperintensities.
Functional MRI findings suggest that the ventricular prefrontal cortex regulates the limbic system, especially the amygdala. In people with bipolar disorder, decreased ventricular prefrontal cortex activity allows for the dysregulated activity of the amygdala, which likely contributes to labile mood and poor emotional regulation. Consistent with this, pharmacological treatment of mania returns ventricular prefrontal cortex activity to the levels in non-manic people, suggesting that ventricular prefrontal cortex activity is an indicator of mood state. However, while pharmacological treatment of mania reduces amygdala hyperactivity, it remains more active than the amygdala of those without bipolar disorder, suggesting amygdala activity may be a marker of the disorder rather than the current mood state. Manic and depressive episodes tend to be characterized by dysfunction in different regions of the ventricular prefrontal cortex. Manic episodes appear to be associated with decreased activation of the right ventricular prefrontal cortex whereas depressive episodes are associated with decreased activation of the left ventricular prefrontal cortex. These disruptions often occur during development linked with synaptic pruning dysfunction. | Bipolar disorder | Wikipedia | 366 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
People with bipolar disorder who are in a euthymic mood state show decreased activity in the lingual gyrus compared to people without bipolar disorder. In contrast, they demonstrate decreased activity in the inferior frontal cortex during manic episodes compared to people without the disorder. Similar studies examining the differences in brain activity between people with bipolar disorder and those without did not find a consistent area in the brain that was more or less active when comparing these two groups. People with bipolar have increased activation of left hemisphere ventral limbic areaswhich mediate emotional experiences and generation of emotional responsesand decreased activation of right hemisphere cortical structures related to cognitionstructures associated with the regulation of emotions. However, further research is needed to consolidate neuroimaging findings, which are often heterogeneous and not consistently reported according to a common standard.
Neuroscientists have proposed additional models to try to explain the cause of bipolar disorder. One proposed model for bipolar disorder suggests that hypersensitivity of reward circuits consisting of frontostriatal circuits causes mania, and decreased sensitivity of these circuits causes depression. According to the "kindling" hypothesis, when people who are genetically predisposed toward bipolar disorder experience stressful events, the stress threshold at which mood changes occur becomes progressively lower, until the episodes eventually start (and recur) spontaneously. There is evidence supporting an association between early-life stress and dysfunction of the hypothalamic-pituitary-adrenal axis leading to its overactivation, which may play a role in the pathogenesis of bipolar disorder. Other brain components that have been proposed to play a role in bipolar disorder are the mitochondria and a sodium ATPase pump. Circadian rhythms and regulation of the hormone melatonin also seem to be altered.
Dopamine, a neurotransmitter responsible for mood cycling, has increased transmission during the manic phase. The dopamine hypothesis states that the increase in dopamine results in secondary homeostatic downregulation of key system elements and receptors such as lower sensitivity of dopaminergic receptors. This results in decreased dopamine transmission characteristic of the depressive phase. The depressive phase ends with homeostatic upregulation potentially restarting the cycle over again. Glutamate is significantly increased within the left dorsolateral prefrontal cortex during the manic phase of bipolar disorder, and returns to normal levels once the phase is over. | Bipolar disorder | Wikipedia | 504 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Medications used to treat bipolar may exert their effect by modulating intracellular signaling, such as through depleting myo-inositol levels, inhibition of cAMP signaling, and through altering subunits of the dopamine-associated G-protein. Consistent with this, elevated levels of Gαi, Gαs, and Gαq/11 have been reported in brain and blood samples, along with increased protein kinase A (PKA) expression and sensitivity; typically, PKA activates as part of the intracellular signalling cascade downstream from the detachment of Gαs subunit from the G protein complex.
Decreased levels of 5-hydroxyindoleacetic acid, a byproduct of serotonin, are present in the cerebrospinal fluid of persons with bipolar disorder during both the depressed and manic phases. Increased dopaminergic activity has been hypothesized in manic states due to the ability of dopamine agonists to stimulate mania in people with bipolar disorder. Decreased sensitivity of regulatory α2 adrenergic receptors as well as increased cell counts in the locus coeruleus indicated increased noradrenergic activity in manic people. Low plasma GABA levels on both sides of the mood spectrum have been found. One review found no difference in monoamine levels, but found abnormal norepinephrine turnover in people with bipolar disorder. Tyrosine depletion was found to reduce the effects of methamphetamine in people with bipolar disorder as well as symptoms of mania, implicating dopamine in mania. VMAT2 binding was found to be increased in one study of people with bipolar mania.
Diagnosis
Bipolar disorder is commonly diagnosed during adolescence or early adulthood, but onset can occur throughout life. Its diagnosis is based on the self-reported experiences of the individual, abnormal behavior reported by family members, friends or co-workers, observable signs of illness as assessed by a clinician, and ideally a medical work-up to rule out other causes. Caregiver-scored rating scales, specifically from the mother, have shown to be more accurate than teacher and youth-scored reports in identifying youths with bipolar disorder. Assessment is usually done on an outpatient basis; admission to an inpatient facility is considered if there is a risk to oneself or others. | Bipolar disorder | Wikipedia | 478 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
The most widely used criteria for diagnosing bipolar disorder are from the American Psychiatric Association's (APA) Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5) and the World Health Organization's (WHO) International Statistical Classification of Diseases and Related Health Problems, 10th Edition (ICD-10). The ICD-10 criteria are used more often in clinical settings outside of the U.S. while the DSM criteria are used within the U.S. and are the prevailing criteria used internationally in research studies. The DSM-5, published in 2013, includes further and more accurate specifiers compared to its predecessor, the DSM-IV-TR. This work has influenced the eleventh revision of the ICD, which includes the various diagnoses within the bipolar spectrum of the DSM-V.
Several rating scales for the screening and evaluation of bipolar disorder exist, including the Bipolar spectrum diagnostic scale, Mood Disorder Questionnaire, the General Behavior Inventory and the Hypomania Checklist. The use of evaluation scales cannot substitute a full clinical interview but they serve to systematize the recollection of symptoms. On the other hand, instruments for screening bipolar disorder tend to have lower sensitivity.
Differential diagnosis
Bipolar disorder is classified by the International Classification of Diseases as a mental and behavioural disorder. Mental disorders that can have symptoms similar to those seen in bipolar disorder include schizophrenia, major depressive disorder, attention deficit hyperactivity disorder (ADHD), and certain personality disorders, such as borderline personality disorder. A key difference between bipolar disorder and borderline personality disorder is the nature of the mood swings; in contrast to the sustained changes to mood over days to weeks or longer, those of the latter condition (more accurately called emotional dysregulation) are sudden and often short-lived, and secondary to social stressors. | Bipolar disorder | Wikipedia | 380 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Although there are no biological tests that are diagnostic of bipolar disorder, blood tests and/or imaging are carried out to investigate whether medical illnesses with clinical presentations similar to that of bipolar disorder are present before making a definitive diagnosis. Neurologic diseases such as multiple sclerosis, complex partial seizures, strokes, brain tumors, Wilson's disease, traumatic brain injury, Huntington's disease, and complex migraines can mimic features of bipolar disorder. An EEG may be used to exclude neurological disorders such as epilepsy, and a CT scan or MRI of the head may be used to exclude brain lesions. Additionally, disorders of the endocrine system such as hypothyroidism, hyperthyroidism, and Cushing's disease are in the differential as is the connective tissue disease systemic lupus erythematosus. Infectious causes of mania that may appear similar to bipolar mania include herpes encephalitis, HIV, influenza, or neurosyphilis. Certain vitamin deficiencies such as pellagra (niacin deficiency), vitamin B12 deficiency, folate deficiency, and Wernicke–Korsakoff syndrome (thiamine deficiency) can also lead to mania. Common medications that can cause manic symptoms include antidepressants, prednisone, Parkinson's disease medications, thyroid hormone, stimulants (including cocaine and methamphetamine), and certain antibiotics.
Bipolar spectrum
Bipolar spectrum disorders include: bipolar I disorder, bipolar II disorder, cyclothymic disorder and cases where subthreshold symptoms are found to cause clinically significant impairment or distress. These disorders involve major depressive episodes that alternate with manic or hypomanic episodes, or with mixed episodes that feature symptoms of both mood states. The concept of the bipolar spectrum is similar to that of Emil Kraepelin's original concept of manic depressive illness. Bipolar II disorder was established as a diagnosis in 1994 within DSM IV; though debate continues over whether it is a distinct entity, part of a spectrum, or exists at all.
Criteria and subtypes | Bipolar disorder | Wikipedia | 435 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
The DSM and the ICD characterize bipolar disorder as a spectrum of disorders occurring on a continuum. The DSM-5 and ICD-11 lists three specific subtypes:
Bipolar I disorder: At least one manic episode is necessary to make the diagnosis; depressive episodes are common in the vast majority of cases with bipolar disorder I, but are unnecessary for the diagnosis. Specifiers such as "mild, moderate, moderate-severe, severe" and "with psychotic features" should be added as applicable to indicate the presentation and course of the disorder.
Bipolar II disorder: No manic episodes and one or more hypomanic episodes and one or more major depressive episodes. Hypomanic episodes do not go to the full extremes of mania (i.e., do not usually cause severe social or occupational impairment, and are without psychosis), and this can make bipolar II more difficult to diagnose, since the hypomanic episodes may simply appear as periods of successful high productivity and are reported less frequently than a distressing, crippling depression.
Cyclothymia: A history of hypomanic episodes with periods of depression that do not meet criteria for major depressive episodes.
When relevant, specifiers for peripartum onset and with rapid cycling should be used with any subtype. Individuals who have subthreshold symptoms that cause clinically significant distress or impairment, but do not meet full criteria for one of the three subtypes may be diagnosed with other specified or unspecified bipolar disorder. Other specified bipolar disorder is used when a clinician chooses to explain why the full criteria were not met (e.g., hypomania without a prior major depressive episode). If the condition is thought to have a non-psychiatric medical cause, the diagnosis of bipolar and related disorder due to another medical condition is made, while substance/medication-induced bipolar and related disorder is used if a medication is thought to have triggered the condition. | Bipolar disorder | Wikipedia | 405 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Rapid cycling
Most people who meet criteria for bipolar disorder experience a number of episodes, on average 0.4 to 0.7 per year, lasting three to six months. Rapid cycling, however, is a course specifier that may be applied to any bipolar subtype. It is defined as having four or more mood disturbance episodes within a one-year span. Rapid cycling is usually temporary but is common amongst people with bipolar disorder and affects 25.8–45.3% of them at some point in their life. These episodes are separated from each other by a remission (partial or full) for at least two months or a switch in mood polarity (i.e., from a depressive episode to a manic episode or vice versa). The definition of rapid cycling most frequently cited in the literature (including the DSM-V and ICD-11) is that of Dunner and Fieve: at least four major depressive, manic, hypomanic or mixed episodes during a 12-month period. The literature examining the pharmacological treatment of rapid cycling is sparse and there is no clear consensus with respect to its optimal pharmacological management. "Ultra rapid" and "ultradian" have been applied to faster-cycling types of bipolar disorder. People with the rapid cycling or faster-cycling subtypes of bipolar disorder tend to be more difficult to treat and less responsive to medications than other people with bipolar disorder.
Coexisting psychiatric conditions
The diagnosis of bipolar disorder can be complicated by coexisting (comorbid) psychiatric conditions including obsessive–compulsive disorder, substance-use disorder, eating disorders, attention deficit hyperactivity disorder, social phobia, premenstrual syndrome (including premenstrual dysphoric disorder), or panic disorder. A thorough longitudinal analysis of symptoms and episodes, assisted if possible by discussions with friends and family members, is crucial to establishing a treatment plan where these comorbidities exist. Children of parents with bipolar disorder more frequently have other mental health problems.
Children | Bipolar disorder | Wikipedia | 425 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
In the 1920s, Kraepelin noted that manic episodes are rare before puberty. In general, bipolar disorder in children was not recognized in the first half of the twentieth century. This issue diminished with an increased following of the DSM criteria in the last part of the twentieth century. The diagnosis of childhood bipolar disorder, while formerly controversial, has gained greater acceptance among childhood and adolescent psychiatrists. American children and adolescents diagnosed with bipolar disorder in community hospitals increased 4-fold reaching rates of up to 40% in 10 years around the beginning of the 21st century, while in outpatient clinics it doubled reaching 6%. Studies using DSM criteria show that up to 1% of youth may have bipolar disorder. The DSM-5 has established a diagnosis—disruptive mood dysregulation disorder—that covers children with long-term, persistent irritability that had at times been misdiagnosed as having bipolar disorder, distinct from irritability in bipolar disorder that is restricted to discrete mood episodes.
Adults
Bipolar on average, starts during adulthood. Bipolar 1, on average, starts at the age of 18 years old, and Bipolar 2 starts at age 22 years old on average. However, most delay seeking treatment for an average of 8 years after symptoms start. Bipolar is often misdiagnosed with other psychiatric disorders. There is no definitive association between race, ethnicity, or Socioeconomic status (SES). Adults with Bipolar report having a lower quality of life, even outside of a manic or depressive episode. Bipolar can put strain on marriage and other relationships, having a job, and everyday functioning. Bipolar is associated with having higher rates of unemployment. Most have trouble keeping a job, leading to trouble with healthcare access, leading to more decline in their mental health due to not receiving treatment such as medicine and therapy. | Bipolar disorder | Wikipedia | 371 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Elderly
Bipolar disorder is uncommon in older patients, with a measured lifetime prevalence of 1% in over 60s and a 12-month prevalence of 0.10.5% in people over 65. Despite this, it is overrepresented in psychiatric admissions, making up 48% of inpatient admission to aged care psychiatry units, and the incidence of mood disorders is increasing overall with the aging population. Depressive episodes more commonly present with sleep disturbance, fatigue, hopelessness about the future, slowed thinking, and poor concentration and memory; the last three symptoms are seen in what is known as pseudodementia. Clinical features also differ between those with late-onset bipolar disorder and those who developed it early in life; the former group present with milder manic episodes, more prominent cognitive changes and have a background of worse psychosocial functioning, while the latter present more commonly with mixed affective episodes, and have a stronger family history of illness. Older people with bipolar disorder experience cognitive changes, particularly in executive functions such as abstract thinking and switching cognitive sets, as well as concentrating for long periods and decision-making.
Prevention
Attempts at prevention of bipolar disorder have focused on stress (such as childhood adversity or highly conflictual families) which, although not a diagnostically specific causal agent for bipolar, does place genetically and biologically vulnerable individuals at risk for a more severe course of illness. Longitudinal studies have indicated that full-blown manic stages are often preceded by a variety of prodromal clinical features, providing support for the occurrence of an at-risk state of the disorder when an early intervention might prevent its further development and/or improve its outcome.
Management | Bipolar disorder | Wikipedia | 334 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
The aim of management is to treat acute episodes safely with medication and work with the patient in long-term maintenance to prevent further episodes and optimise function using a combination of pharmacological and psychotherapeutic techniques. Hospitalization may be required especially with the manic episodes present in bipolar I. This can be voluntary or (local legislation permitting) involuntary. Long-term inpatient stays are now less common due to deinstitutionalization, although these can still occur. Following (or in lieu of) a hospital admission, support services available can include drop-in centers, visits from members of a community mental health team or an Assertive Community Treatment team, supported employment, patient-led support groups, and intensive outpatient programs. These are sometimes referred to as partial-inpatient programs. Compared to the general population, people with bipolar disorder are less likely to frequently engage in physical exercise. Exercise may have physical and mental benefits for people with bipolar disorder, but there is a lack of research.
Psychosocial
Psychotherapy aims to assist a person with bipolar disorder in accepting and understanding their diagnosis, coping with various types of stress, improving their interpersonal relationships, and recognizing prodromal symptoms before full-blown recurrence. Cognitive behavioral therapy (CBT), family-focused therapy, and psychoeducation have the most evidence for efficacy in regard to relapse prevention, while interpersonal and social rhythm therapy and cognitive-behavioral therapy appear the most effective in regard to residual depressive symptoms. Most studies have been based only on bipolar I, however, and treatment during the acute phase can be a particular challenge. Some clinicians emphasize the need to talk with individuals experiencing mania, to develop a therapeutic alliance in support of recovery.
Medication
Medications are often prescribed to help improve symptoms of bipolar disorder. Medications approved for treating bipolar disorder including mood stabilizers, antipsychotics, and certain antidepressants. Sometimes a combination of medications may also be suggested. The choice of medications may differ depending on the bipolar disorder episode type or if the person is experiencing unipolar or bipolar depression. Other factors to consider when deciding on an appropriate treatment approach includes if the person has any comorbidities, their response to previous therapies, adverse effects, and the desire of the person to be treated. | Bipolar disorder | Wikipedia | 471 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Mood stabilizers
Lithium and the anticonvulsants carbamazepine, lamotrigine, and valproic acid are classed as mood stabilizers due to their effect on the mood states in bipolar disorder. Lithium has the best overall evidence and is considered an effective treatment for acute manic episodes, preventing relapses, and bipolar depression. Lithium reduces the risk of suicide, self-harm, and death in people with bipolar disorder. Lithium is preferred for long-term mood stabilization. Lithium treatment is also associated with adverse effects and it has been shown to erode kidney and thyroid function over extended periods. Valproate has become a commonly prescribed treatment and effectively treats manic episodes. Carbamazepine is less effective in preventing relapse than lithium or valproate. Lamotrigine has some efficacy in treating depression, and this benefit is greatest in more severe depression. Lamotrigine may have a similar effectiveness to lithium for treating bipolar disorder, however, there is evidence to suggest that lamotrigine is less effective at preventing recurrent mania episodes. Lamotrigine treatment has been shown to be safer compared to lithium treatment, with less adverse effects. Valproate and carbamazepine are teratogenic and should be avoided as a treatment in women of childbearing age, but discontinuation of these medications during pregnancy is associated with a high risk of relapse. The effectiveness of topiramate is unknown. Carbamazepine effectively treats manic episodes, with some evidence it has greater benefit in rapid-cycling bipolar disorder, or those with more psychotic symptoms or more symptoms similar to that of schizoaffective disorder.
Mood stabilizers are used for long-term maintenance but have not demonstrated the ability to quickly treat acute bipolar depression. | Bipolar disorder | Wikipedia | 374 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Antipsychotics
Antipsychotic medications are effective for short-term treatment of bipolar manic episodes and appear to be superior to lithium and anticonvulsants for this purpose. Atypical antipsychotics are also indicated for bipolar depression refractory to treatment with mood stabilizers. Olanzapine is effective in preventing relapses, although the supporting evidence is weaker than the evidence for lithium. A 2006 review found that haloperidol was an effective treatment for acute mania, limited data supported no difference in overall efficacy between haloperidol, olanzapine or risperidone, and that it could be less effective than aripiprazole.
Antidepressants
Antidepressant monotherapy is not recommended in the treatment of bipolar disorder and does not provide any benefit over mood stabilizers. Atypical antipsychotic medications (e.g., aripiprazole) are preferred over antidepressants to augment the effects of mood stabilizers due to the lack of efficacy of antidepressants in bipolar disorder. Treatment of bipolar disorder using antidepressants may carry a risk of affective switches where a person switches from depression to manic or hypomanic phases or mixed states. There may also be a risk of accelerating cycling between phases when antidepressants are used in bipolar disorder. The risk of affective switches is higher in bipolar I depression; antidepressants are generally avoided in bipolar I disorder or only used with mood stabilizers when they are deemed necessary.
Whether modern antidepressants cause mania or cycle acceleration in bipolar disorder is highly controversial, as is whether antidepressants provide any benefit over mood stabilizers alone.
Combined treatment approaches
Antipsychotics and mood stabilizers used together are quicker and more effective at treating mania than either class of drug used alone. Some analyses indicate antipsychotics alone are also more effective at treating acute mania. A first-line treatment for depression in bipolar disorder is a combination of olanzapine and fluoxetine. | Bipolar disorder | Wikipedia | 418 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Other drugs
Short courses of benzodiazepines are used in addition to other medications for calming effect until mood stabilizing become effective. Electroconvulsive therapy (ECT) is an effective form of treatment for acute mood disturbances in those with bipolar disorder, especially when psychotic or catatonic features are displayed. ECT is also recommended for use in pregnant women with bipolar disorder. It is unclear if ketamine (a common general dissociative anesthetic used in surgery) is useful in bipolar disorder. Gabapentin and pregabalin are not proven to be effective for treating bipolar disorder.
Children
Treating bipolar disorder in children involves medication and psychotherapy. The literature and research on the effects of psychosocial therapy on bipolar spectrum disorders are scarce, making it difficult to determine the efficacy of various therapies. Mood stabilizers and atypical antipsychotics are commonly prescribed. Among the former, lithium is the only compound approved by the FDA for children. Psychological treatment combines normally education on the disease, group therapy, and cognitive behavioral therapy. Long-term medication is often needed.
Resistance to treatment
The poor response from some bipolar patients to treatment has given evidence to the concept of treatment-resistant bipolar disorder. Guidelines to the definition of treatment-resistant bipolar disorder and evidence-based options for its management were reviewed in 2020.
Management of obesity
A large proportion (approximately 68%) of people who seek treatment for bipolar disorder are obese or overweight and managing obesity is important for reducing the risk of other health conditions that are associated with obesity. Management approaches include non-pharmacological, pharmacological, and surgical. Examples of non-pharmacological include dietary interventions, exercise, behavioral therapies, or combined approaches. Pharmacological approaches include weight-loss medications or changing medications already being prescribed. Some people with bipolar disorder who have obesity may also be eligible for bariatric surgery. The effectiveness of these various approaches to improving or managing obesity in people with bipolar disorder is not clear. | Bipolar disorder | Wikipedia | 416 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Prognosis
A lifelong condition with periods of partial or full recovery in between recurrent episodes of relapse, bipolar disorder is considered to be a major health problem worldwide because of the increased rates of disability and premature mortality. It is also associated with co-occurring psychiatric and medical problems, higher rates of death from natural causes (e.g., cardiovascular disease), and high rates of initial under- or misdiagnosis, causing a delay in appropriate treatment and contributing to poorer prognoses. When compared to the general population, people with bipolar disorder also have higher rates of other serious medical comorbidities including diabetes mellitus, respiratory diseases, HIV, and hepatitis C virus infection. After a diagnosis is made, it remains difficult to achieve complete remission of all symptoms with the currently available psychiatric medications and symptoms often become progressively more severe over time.
Compliance with medications is one of the most significant factors that can decrease the rate and severity of relapse and have a positive impact on overall prognosis. However, the types of medications used in treating BD commonly cause side effects and more than 75% of individuals with BD inconsistently take their medications for various reasons. Of the various types of the disorder, rapid cycling (four or more episodes in one year) is associated with the worst prognosis due to higher rates of self-harm and suicide. Individuals diagnosed with bipolar who have a family history of bipolar disorder are at a greater risk for more frequent manic/hypomanic episodes. Early onset and psychotic features are also associated with worse outcomes, as well as subtypes that are nonresponsive to lithium.
Early recognition and intervention also improve prognosis as the symptoms in earlier stages are less severe and more responsive to treatment. Onset after adolescence is connected to better prognoses for both genders, and being male is a protective factor against higher levels of depression. For women, better social functioning before developing bipolar disorder and being a parent are protective towards suicide attempts. | Bipolar disorder | Wikipedia | 407 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Functioning
Changes in cognitive processes and abilities are seen in mood disorders, with those of bipolar disorder being greater than those in major depressive disorder. These include reduced attentional and executive capabilities and impaired memory. People with bipolar disorder often experience a decline in cognitive functioning during (or possibly before) their first episode, after which a certain degree of cognitive dysfunction typically becomes permanent, with more severe impairment during acute phases and moderate impairment during periods of remission. As a result, two-thirds of people with BD continue to experience impaired psychosocial functioning in between episodes even when their mood symptoms are in full remission. A similar pattern is seen in both BD-I and BD-II, but people with BD-II experience a lesser degree of impairment.
When bipolar disorder occurs in children, it severely and adversely affects their psychosocial development. Children and adolescents with bipolar disorder have higher rates of significant difficulties with substance use disorders, psychosis, academic difficulties, behavioral problems, social difficulties, and legal problems. Cognitive deficits typically increase over the course of the illness. Higher degrees of impairment correlate with the number of previous manic episodes and hospitalizations, and with the presence of psychotic symptoms. Early intervention can slow the progression of cognitive impairment, while treatment at later stages can help reduce distress and negative consequences related to cognitive dysfunction.
Despite the overly ambitious goals that are frequently part of manic episodes, symptoms of mania undermine the ability to achieve these goals and often interfere with an individual's social and occupational functioning. One-third of people with BD remain unemployed for one year following a hospitalization for mania. Depressive symptoms during and between episodes, which occur much more frequently for most people than hypomanic or manic symptoms over the course of illness, are associated with lower functional recovery in between episodes, including unemployment or underemployment for both BD-I and BD-II. However, the course of illness (duration, age of onset, number of hospitalizations, and the presence or not of rapid cycling) and cognitive performance are the best predictors of employment outcomes in individuals with bipolar disorder, followed by symptoms of depression and years of education. | Bipolar disorder | Wikipedia | 444 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Recovery and recurrence
A naturalistic study in 2003 by Tohen and coworkers from the first admission for mania or mixed episode (representing the hospitalized and therefore most severe cases) found that 50% achieved syndromal recovery (no longer meeting criteria for the diagnosis) within six weeks and 98% within two years. Within two years, 72% achieved symptomatic recovery (no symptoms at all) and 43% achieved functional recovery (regaining of prior occupational and residential status). However, 40% went on to experience a new episode of mania or depression within 2 years of syndromal recovery, and 19% switched phases without recovery.
Symptoms preceding a relapse (prodromal), especially those related to mania, can be reliably identified by people with bipolar disorder. There have been intents to teach patients coping strategies when noticing such symptoms with encouraging results.
Suicide
Bipolar disorder can cause suicidal ideation that leads to suicide attempts. Individuals whose bipolar disorder begins with a depressive or mixed affective episode seem to have a poorer prognosis and an increased risk of suicide. One out of two people with bipolar disorder attempt suicide at least once during their lifetime and many attempts are successfully completed. The annual average suicide rate is 0.4%-1.4%, which is 30 to 60 times greater than that of the general population. The number of deaths from suicide in bipolar disorder is between 18 and 25 times higher than would be expected in similarly aged people without bipolar disorder. The lifetime risk of suicide is much higher in those with bipolar disorder, with an estimated 34% of people attempting suicide and 15–20% dying by suicide.
Risk factors for suicide attempts and death from suicide in people with bipolar disorder include older age, prior suicide attempts, a depressive or mixed index episode (first episode), a manic index episode with psychotic symptoms, hopelessness or psychomotor agitation present during the episodes, co-existing anxiety disorder, a first degree relative with a mood disorder or suicide, interpersonal conflicts, occupational problems, bereavement or social isolation.
Epidemiology | Bipolar disorder | Wikipedia | 426 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Bipolar disorder is the sixth leading cause of disability worldwide and has a lifetime prevalence of about 1 to 3% in the general population. However, a reanalysis of data from the National Epidemiological Catchment Area survey in the United States suggested that 0.8% of the population experience a manic episode at least once (the diagnostic threshold for bipolar I) and a further 0.5% have a hypomanic episode (the diagnostic threshold for bipolar II or cyclothymia). Including sub-threshold diagnostic criteria, such as one or two symptoms over a short time-period, an additional 5.1% of the population, adding up to a total of 6.4%, were classified as having a bipolar spectrum disorder. A more recent analysis of data from a second US National Comorbidity Survey found that 1% met lifetime prevalence criteria for bipolar I, 1.1% for bipolar II, and 2.4% for subthreshold symptoms. Estimates vary about how many children and young adults have bipolar disorder. These estimates range from 0.6 to 15% depending on differing settings, methods, and referral settings, raising suspicions of overdiagnosis. One meta-analysis of bipolar disorder in young people worldwide estimated that about 1.8% of people between the ages of seven and 21 have bipolar disorder. Similar to adults, bipolar disorder in children and adolescents is thought to occur at a similar frequency in boys and girls.
There are conceptual and methodological limitations and variations in the findings. Prevalence studies of bipolar disorder are typically carried out by lay interviewers who follow fully structured/fixed interview schemes; responses to single items from such interviews may have limited validity. In addition, diagnoses (and therefore estimates of prevalence) vary depending on whether a categorical or spectrum approach is used. This consideration has led to concerns about the potential for both underdiagnosis and overdiagnosis. | Bipolar disorder | Wikipedia | 389 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
The incidence of bipolar disorder is similar in men and women as well as across different cultures and ethnic groups. A 2000 study by the World Health Organization found that prevalence and incidence of bipolar disorder are very similar across the world. Age-standardized prevalence per 100,000 ranged from 421.0 in South Asia to 481.7 in Africa and Europe for men and from 450.3 in Africa and Europe to 491.6 in Oceania for women. However, severity may differ widely across the globe. Disability-adjusted life year rates, for example, appear to be higher in developing countries, where medical coverage may be poorer and medication less available. Within the United States, Asian Americans have significantly lower rates than their African American and European American counterparts. In 2017, the Global Burden of Disease Study estimated there were 4.5 million new cases and a total of 45.5 million cases globally.
History
In the early 1800s, French psychiatrist Jean-Étienne Dominique Esquirol's lypemania, one of his affective monomanias, was the first elaboration on what was to become modern depression. The basis of the current conceptualization of bipolar illness can be traced back to the 1850s. In 1850, Jean-Pierre Falret described "circular insanity" (, ); the lecture was summarized in 1851 in the ("Hospital Gazette"). Three years later, in 1854, Jules-Gabriel-François Baillarger (1809–1890) described to the French Imperial Académie Nationale de Médecine a biphasic mental illness causing recurrent oscillations between mania and melancholia, which he termed (, "madness in double form"). Baillarger's original paper, "", appeared in the medical journal Annales médico-psychologiques (Medico-psychological annals) in 1854.
These concepts were developed by the German psychiatrist Emil Kraepelin (1856–1926), who, using Kahlbaum's concept of cyclothymia, categorized and studied the natural course of untreated bipolar patients. He coined the term manic depressive psychosis, after noting that periods of acute illness, manic or depressive, were generally punctuated by relatively symptom-free intervals where the patient was able to function normally. | Bipolar disorder | Wikipedia | 465 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
The term "manic–depressive reaction" appeared in the first version of the DSM in 1952, influenced by the legacy of Adolf Meyer. Subtyping into "unipolar" depressive disorders and bipolar disorders has its origin in Karl Kleist's concept – since 1911 – of unipolar and bipolar affective disorders, which was used by Karl Leonhard in 1957 to differentiate between unipolar and bipolar disorder in depression. These subtypes have been regarded as separate conditions since publication of the DSM-III. The subtypes bipolar II and rapid cycling have been included since the DSM-IV, based on work from the 1970s by David Dunner, Elliot Gershon, Frederick Goodwin, Ronald Fieve, and Joseph Fleiss.
Society and culture
Cost
The United States spent approximately $202.1 billion on people diagnosed with bipolar I disorder (excluding other subtypes of bipolar disorder and undiagnosed people) in 2015. One analysis estimated that the United Kingdom spent approximately £5.2 billion on the disorder in 2007. In addition to the economic costs, bipolar disorder is a leading cause of disability and lost productivity worldwide. People with bipolar disorder are generally more disabled, have a lower level of functioning, longer duration of illness, and increased rates of work absenteeism and decreased productivity when compared to people experiencing other mental health disorders. The decrease in the productivity seen in those who care for people with bipolar disorder also significantly contributes to these costs. | Bipolar disorder | Wikipedia | 301 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Advocacy
There are widespread issues with social stigma, stereotypes, and prejudice against individuals with a diagnosis of bipolar disorder. In 2000, actress Carrie Fisher went public with her bipolar disorder diagnosis. She became one of the most well-recognized advocates for people with bipolar disorder in the public eye and fiercely advocated to eliminate the stigma surrounding mental illnesses, including bipolar disorder. Stephen Fried, who has written extensively on the topic, noted that Fisher helped to draw attention to the disorder's chronicity, relapsing nature, and that bipolar disorder relapses do not indicate a lack of discipline or moral shortcomings. Since being diagnosed at age 37, actor Stephen Fry has pushed to raise awareness of the condition, with his 2006 documentary Stephen Fry: The Secret Life of the Manic Depressive. In an effort to ease the social stigma associated with bipolar disorder, the orchestra conductor Ronald Braunstein cofounded the ME/2 Orchestra with his wife Caroline Whiddon in 2011. Braunstein was diagnosed with bipolar disorder in 1985 and his concerts with the ME/2 Orchestra were conceived in order to create a welcoming performance environment for his musical colleagues, while also raising public awareness about mental illness.
Notable cases
Numerous authors have written about bipolar disorder and many successful people have openly discussed their experience with it. Kay Redfield Jamison, a clinical psychologist and professor of psychiatry at the Johns Hopkins University School of Medicine, profiled her own bipolar disorder in her memoir An Unquiet Mind (1995). It is likely that Grigory Potemkin, Russian statesman and alleged husband of Catherine the Great, suffered from some kind of bipolar disorder. Several celebrities have also publicly shared that they have bipolar disorder; in addition to Carrie Fisher and Stephen Fry these include Catherine Zeta-Jones, Mariah Carey, Kanye West, Jane Pauley, Demi Lovato, Selena Gomez, and Russell Brand.
Media portrayals
Several dramatic works have portrayed characters with traits suggestive of the diagnosis which have been the subject of discussion by psychiatrists and film experts alike. | Bipolar disorder | Wikipedia | 408 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
In Mr. Jones (1993), (Richard Gere) swings from a manic episode into a depressive phase and back again, spending time in a psychiatric hospital and displaying many of the features of the syndrome. In The Mosquito Coast (1986), Allie Fox (Harrison Ford) displays some features including recklessness, grandiosity, increased goal-directed activity and mood lability, as well as some paranoia. Psychiatrists have suggested that Willy Loman, the main character in Arthur Miller's classic play Death of a Salesman, has bipolar disorder.
The 2009 drama 90210 featured a character, Silver, who was diagnosed with bipolar disorder. Stacey Slater, a character from the BBC soap EastEnders, has been diagnosed with the disorder. The storyline was developed as part of the BBC's Headroom campaign. The Channel 4 soap Brookside had earlier featured a story about bipolar disorder when the character Jimmy Corkhill was diagnosed with the condition. 2011 Showtime's political thriller drama Homeland protagonist Carrie Mathison has bipolar disorder, which she has kept secret since her school days. The 2014 ABC medical drama, Black Box, featured a world-renowned neuroscientist with bipolar disorder.
In the TV series Dave, the eponymous main character, played by Lil Dicky as a fictionalized version of himself, is an aspiring rapper. Lil Dicky's real-life hype man GaTa also plays himself. In one episode, after being off his medication and having an episode, GaTa tearfully confesses to having bipolar disorder. GaTa has bipolar disorder in real life but, like his character in the show, he is able to manage it with medication.
Creativity
A link between mental illness and professional success or creativity has been suggested, including in accounts by Socrates, Seneca the Younger, and Cesare Lombroso. Despite prominence in popular culture, the link between creativity and bipolar has not been rigorously studied. This area of study also is likely affected by confirmation bias. Some evidence suggests that some heritable component of bipolar disorder overlaps with heritable components of creativity. Probands of people with bipolar disorder are more likely to be professionally successful, as well as to demonstrate temperamental traits similar to bipolar disorder. Furthermore, while studies of the frequency of bipolar disorder in creative population samples have been conflicting, full-blown bipolar disorder in creative samples is rare. | Bipolar disorder | Wikipedia | 479 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Research
Research directions for bipolar disorder in children include optimizing treatments, increasing the knowledge of the genetic and neurobiological basis of the pediatric disorder and improving diagnostic criteria. Some treatment research suggests that psychosocial interventions that involve the family, psychoeducation, and skills building (through therapies such as CBT, DBT, and IPSRT) can benefit in addition to pharmacotherapy. | Bipolar disorder | Wikipedia | 85 | 4531 | https://en.wikipedia.org/wiki/Bipolar%20disorder | Biology and health sciences | Mental disorder | null |
Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically designed to ease the types of calculations that frequently come up in quantum mechanics. Its use in quantum mechanics is quite widespread.
Bra–ket notation was created by Paul Dirac in his 1939 publication A New Notation for Quantum Mechanics. The notation was introduced as an easier way to write quantum mechanical expressions. The name comes from the English word "bracket".
Quantum mechanics
In quantum mechanics, bra–ket notation is used ubiquitously to denote quantum states. The notation uses angle brackets, and , and a vertical bar , to construct "bras" and "kets".
A ket is of the form . Mathematically it denotes a vector, , in an abstract (complex) vector space , and physically it represents a state of some quantum system.
A bra is of the form . Mathematically it denotes a linear form , i.e. a linear map that maps each vector in to a number in the complex plane . Letting the linear functional act on a vector is written as .
Assume that on there exists an inner product with antilinear first argument, which makes an inner product space. Then with this inner product each vector can be identified with a corresponding linear form, by placing the vector in the anti-linear first slot of the inner product: . The correspondence between these notations is then . The linear form is a covector to , and the set of all covectors forms a subspace of the dual vector space , to the initial vector space . The purpose of this linear form can now be understood in terms of making projections onto the state to find how linearly dependent two states are, etc.
For the vector space , kets can be identified with column vectors, and bras with row vectors. Combinations of bras, kets, and linear operators are interpreted using matrix multiplication. If has the standard Hermitian inner product , under this identification, the identification of kets and bras and vice versa provided by the inner product is taking the Hermitian conjugate (denoted ). | Bra–ket notation | Wikipedia | 449 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
It is common to suppress the vector or linear form from the bra–ket notation and only use a label inside the typography for the bra or ket. For example, the spin operator on a two-dimensional space of spinors has eigenvalues with eigenspinors . In bra–ket notation, this is typically denoted as , and . As above, kets and bras with the same label are interpreted as kets and bras corresponding to each other using the inner product. In particular, when also identified with row and column vectors, kets and bras with the same label are identified with Hermitian conjugate column and row vectors.
Bra–ket notation was effectively established in 1939 by Paul Dirac; it is thus also known as Dirac notation, despite the notation having a precursor in Hermann Grassmann's use of for inner products nearly 100 years earlier.
Vector spaces
Vectors vs kets
In mathematics, the term "vector" is used for an element of any vector space. In physics, however, the term "vector" tends to refer almost exclusively to quantities like displacement or velocity, which have components that relate directly to the three dimensions of space, or relativistically, to the four of spacetime. Such vectors are typically denoted with over arrows (), boldface () or indices ().
In quantum mechanics, a quantum state is typically represented as an element of a complex Hilbert space, for example, the infinite-dimensional vector space of all possible wavefunctions (square integrable functions mapping each point of 3D space to a complex number) or some more abstract Hilbert space constructed more algebraically. To distinguish this type of vector from those described above, it is common and useful in physics to denote an element of an abstract complex vector space as a ket , to refer to it as a "ket" rather than as a vector, and to pronounce it "ket-" or "ket-A" for . | Bra–ket notation | Wikipedia | 410 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
Symbols, letters, numbers, or even words—whatever serves as a convenient label—can be used as the label inside a ket, with the making clear that the label indicates a vector in vector space. In other words, the symbol "" has a recognizable mathematical meaning as to the kind of variable being represented, while just the "" by itself does not. For example, is not necessarily equal to . Nevertheless, for convenience, there is usually some logical scheme behind the labels inside kets, such as the common practice of labeling energy eigenkets in quantum mechanics through a listing of their quantum numbers. At its simplest, the label inside the ket is the eigenvalue of a physical operator, such as , , , etc.
Notation
Since kets are just vectors in a Hermitian vector space, they can be manipulated using the usual rules of linear algebra. For example:
Note how the last line above involves infinitely many different kets, one for each real number .
Since the ket is an element of a vector space, a bra is an element of its dual space, i.e. a bra is a linear functional which is a linear map from the vector space to the complex numbers. Thus, it is useful to think of kets and bras as being elements of different vector spaces (see below however) with both being different useful concepts.
A bra and a ket (i.e. a functional and a vector), can be combined to an operator of rank one with outer product
Inner product and bra–ket identification on Hilbert space
The bra–ket notation is particularly useful in Hilbert spaces which have an inner product that allows Hermitian conjugation and identifying a vector with a continuous linear functional, i.e. a ket with a bra, and vice versa (see Riesz representation theorem). The inner product on Hilbert space (with the first argument anti linear as preferred by physicists) is fully equivalent to an (anti-linear) identification between the space of kets and that of bras in the bra ket notation: for a vector ket define a functional (i.e. bra) by
Bras and kets as row and column vectors | Bra–ket notation | Wikipedia | 450 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
In the simple case where we consider the vector space , a ket can be identified with a column vector, and a bra as a row vector. If, moreover, we use the standard Hermitian inner product on , the bra corresponding to a ket, in particular a bra and a ket with the same label are conjugate transpose. Moreover, conventions are set up in such a way that writing bras, kets, and linear operators next to each other simply imply matrix multiplication. In particular the outer product of a column and a row vector ket and bra can be identified with matrix multiplication (column vector times row vector equals matrix).
For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector:
Based on this, the bras and kets can be defined as:
and then it is understood that a bra next to a ket implies matrix multiplication.
The conjugate transpose (also called Hermitian conjugate) of a bra is the corresponding ket and vice versa:
because if one starts with the bra
then performs a complex conjugation, and then a matrix transpose, one ends up with the ket
Writing elements of a finite dimensional (or mutatis mutandis, countably infinite) vector space as a column vector of numbers requires picking a basis. Picking a basis is not always helpful because quantum mechanics calculations involve frequently switching between different bases (e.g. position basis, momentum basis, energy eigenbasis), and one can write something like "" without committing to any particular basis. In situations involving two different important basis vectors, the basis vectors can be taken in the notation explicitly and here will be referred simply as "" and "".
Non-normalizable states and non-Hilbert spaces
Bra–ket notation can be used even if the vector space is not a Hilbert space. | Bra–ket notation | Wikipedia | 402 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
In quantum mechanics, it is common practice to write down kets which have infinite norm, i.e. non-normalizable wavefunctions. Examples include states whose wavefunctions are Dirac delta functions or infinite plane waves. These do not, technically, belong to the Hilbert space itself. However, the definition of "Hilbert space" can be broadened to accommodate these states (see the Gelfand–Naimark–Segal construction or rigged Hilbert spaces). The bra–ket notation continues to work in an analogous way in this broader context.
Banach spaces are a different generalization of Hilbert spaces. In a Banach space , the vectors may be notated by kets and the continuous linear functionals by bras. Over any vector space without topology, we may also notate the vectors by kets and the linear functionals by bras. In these more general contexts, the bracket does not have the meaning of an inner product, because the Riesz representation theorem does not apply.
Usage in quantum mechanics
The mathematical structure of quantum mechanics is based in large part on linear algebra:
Wave functions and other quantum states can be represented as vectors in a complex Hilbert space. (The exact structure of this Hilbert space depends on the situation.) In bra–ket notation, for example, an electron might be in the "state" . (Technically, the quantum states are rays of vectors in the Hilbert space, as corresponds to the same state for any nonzero complex number .)
Quantum superpositions can be described as vector sums of the constituent states. For example, an electron in the state is in a quantum superposition of the states and .
Measurements are associated with linear operators (called observables) on the Hilbert space of quantum states.
Dynamics are also described by linear operators on the Hilbert space. For example, in the Schrödinger picture, there is a linear time evolution operator with the property that if an electron is in state right now, at a later time it will be in the state , the same for every possible .
Wave function normalization is scaling a wave function so that its norm is 1.
Since virtually every calculation in quantum mechanics involves vectors and linear operators, it can involve, and often does involve, bra–ket notation. A few examples follow:
Spinless position–space wave function | Bra–ket notation | Wikipedia | 481 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
The Hilbert space of a spin-0 point particle is spanned by a "position basis" , where the label extends over the set of all points in position space. This label is the eigenvalue of the position operator acting on such a basis state, . Since there are an uncountably infinite number of vector components in the basis, this is an uncountably infinite-dimensional Hilbert space. The dimensions of the Hilbert space (usually infinite) and position space (usually 1, 2 or 3) are not to be conflated.
Starting from any ket in this Hilbert space, one may define a complex scalar function of , known as a wavefunction,
On the left-hand side, is a function mapping any point in space to a complex number; on the right-hand side,
is a ket consisting of a superposition of kets with relative coefficients specified by that function.
It is then customary to define linear operators acting on wavefunctions in terms of linear operators acting on kets, by
For instance, the momentum operator has the following coordinate representation,
One occasionally even encounters an expression such as , though this is something of an abuse of notation. The differential operator must be understood to be an abstract operator, acting on kets, that has the effect of differentiating wavefunctions once the expression is projected onto the position basis,
even though, in the momentum basis, this operator amounts to a mere multiplication operator (by ). That is, to say,
or
Overlap of states
In quantum mechanics the expression is typically interpreted as the probability amplitude for the state to collapse into the state . Mathematically, this means the coefficient for the projection of onto . It is also described as the projection of state onto state .
Changing basis for a spin-1/2 particle
A stationary spin- particle has a two-dimensional Hilbert space. One orthonormal basis is:
where is the state with a definite value of the spin operator equal to + and is the state with a definite value of the spin operator equal to −.
Since these are a basis, any quantum state of the particle can be expressed as a linear combination (i.e., quantum superposition) of these two states:
where and are complex numbers.
A different basis for the same Hilbert space is:
defined in terms of rather than .
Again, any state of the particle can be expressed as a linear combination of these two:
In vector form, you might write | Bra–ket notation | Wikipedia | 501 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
depending on which basis you are using. In other words, the "coordinates" of a vector depend on the basis used.
There is a mathematical relationship between , , and ; see change of basis.
Pitfalls and ambiguous uses
There are some conventions and uses of notation that may be confusing or ambiguous for the non-initiated or early student.
Separation of inner product and vectors
A cause for confusion is that the notation does not separate the inner-product operation from the notation for a (bra) vector. If a (dual space) bra-vector is constructed as a linear combination of other bra-vectors (for instance when expressing it in some basis) the notation creates some ambiguity and hides mathematical details. We can compare bra–ket notation to using bold for vectors, such as , and for the inner product. Consider the following dual space bra-vector in the basis :
It has to be determined by convention if the complex numbers are inside or outside of the inner product, and each convention gives different results.
Reuse of symbols
It is common to use the same symbol for labels and constants. For example, , where the symbol is used simultaneously as the name of the operator , its eigenvector and the associated eigenvalue . Sometimes the hat is also dropped for operators, and one can see notation such as .
Hermitian conjugate of kets
It is common to see the usage , where the dagger () corresponds to the Hermitian conjugate. This is however not correct in a technical sense, since the ket, , represents a vector in a complex Hilbert-space , and the bra, , is a linear functional on vectors in . In other words, is just a vector, while is the combination of a vector and an inner product.
Operations inside bras and kets
This is done for a fast notation of scaling vectors. For instance, if the vector is scaled by , it may be denoted . This can be ambiguous since is simply a label for a state, and not a mathematical object on which operations can be performed. This usage is more common when denoting vectors as tensor products, where part of the labels are moved outside the designed slot, e.g. .
Linear operators
Linear operators acting on kets | Bra–ket notation | Wikipedia | 453 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
A linear operator is a map that inputs a ket and outputs a ket. (In order to be called "linear", it is required to have certain properties.) In other words, if is a linear operator and is a ket-vector, then is another ket-vector.
In an -dimensional Hilbert space, we can impose a basis on the space and represent in terms of its coordinates as a column vector. Using the same basis for , it is represented by an complex matrix. The ket-vector can now be computed by matrix multiplication.
Linear operators are ubiquitous in the theory of quantum mechanics. For example, observable physical quantities are represented by self-adjoint operators, such as energy or momentum, whereas transformative processes are represented by unitary linear operators such as rotation or the progression of time.
Linear operators acting on bras
Operators can also be viewed as acting on bras from the right hand side. Specifically, if is a linear operator and is a bra, then is another bra defined by the rule
(in other words, a function composition). This expression is commonly written as (cf. energy inner product)
In an -dimensional Hilbert space, can be written as a row vector, and (as in the previous section) is an matrix. Then the bra can be computed by normal matrix multiplication.
If the same state vector appears on both bra and ket side,
then this expression gives the expectation value, or mean or average value, of the observable represented by operator for the physical system in the state .
Outer products
A convenient way to define linear operators on a Hilbert space is given by the outer product: if is a bra and is a ket, the outer product
denotes the rank-one operator with the rule
For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:
The outer product is an matrix, as expected for a linear operator.
One of the uses of the outer product is to construct projection operators. Given a ket of norm 1, the orthogonal projection onto the subspace spanned by is
This is an idempotent in the algebra of observables that acts on the Hilbert space.
Hermitian conjugate operator
Just as kets and bras can be transformed into each other (making into ), the element from the dual space corresponding to is , where denotes the Hermitian conjugate (or adjoint) of the operator . In other words, | Bra–ket notation | Wikipedia | 501 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
If is expressed as an matrix, then is its conjugate transpose.
Properties
Bra–ket notation was designed to facilitate the formal manipulation of linear-algebraic expressions. Some of the properties that allow this manipulation are listed herein. In what follows, and denote arbitrary complex numbers, denotes the complex conjugate of , and denote arbitrary linear operators, and these properties are to hold for any choice of bras and kets.
Linearity
Since bras are linear functionals,
By the definition of addition and scalar multiplication of linear functionals in the dual space,
Associativity
Given any expression involving complex numbers, bras, kets, inner products, outer products, and/or linear operators (but not addition), written in bra–ket notation, the parenthetical groupings do not matter (i.e., the associative property holds). For example:
and so forth. The expressions on the right (with no parentheses whatsoever) are allowed to be written unambiguously because of the equalities on the left. Note that the associative property does not hold for expressions that include nonlinear operators, such as the antilinear time reversal operator in physics.
Hermitian conjugation
Bra–ket notation makes it particularly easy to compute the Hermitian conjugate (also called dagger, and denoted ) of expressions. The formal rules are:
The Hermitian conjugate of a bra is the corresponding ket, and vice versa.
The Hermitian conjugate of a complex number is its complex conjugate.
The Hermitian conjugate of the Hermitian conjugate of anything (linear operators, bras, kets, numbers) is itself—i.e.,
Given any combination of complex numbers, bras, kets, inner products, outer products, and/or linear operators, written in bra–ket notation, its Hermitian conjugate can be computed by reversing the order of the components, and taking the Hermitian conjugate of each.
These rules are sufficient to formally write the Hermitian conjugate of any such expression; some examples are as follows:
Kets:
Inner products: Note that is a scalar, so the Hermitian conjugate is just the complex conjugate, i.e.,
Matrix elements:
Outer products: | Bra–ket notation | Wikipedia | 484 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
Composite bras and kets
Two Hilbert spaces and may form a third space by a tensor product. In quantum mechanics, this is used for describing composite systems. If a system is composed of two subsystems described in and respectively, then the Hilbert space of the entire system is the tensor product of the two spaces. (The exception to this is if the subsystems are actually identical particles. In that case, the situation is a little more complicated.)
If is a ket in and is a ket in , the tensor product of the two kets is a ket in . This is written in various notations:
See quantum entanglement and the EPR paradox for applications of this product.
The unit operator
Consider a complete orthonormal system (basis),
for a Hilbert space , with respect to the norm from an inner product .
From basic functional analysis, it is known that any ket can also be written as
with the inner product on the Hilbert space.
From the commutativity of kets with (complex) scalars, it follows that
must be the identity operator, which sends each vector to itself.
This, then, can be inserted in any expression without affecting its value; for example
where, in the last line, the Einstein summation convention has been used to avoid clutter.
In quantum mechanics, it often occurs that little or no information about the inner product of two arbitrary (state) kets is present, while it is still possible to say something about the expansion coefficients and of those vectors with respect to a specific (orthonormalized) basis. In this case, it is particularly useful to insert the unit operator into the bracket one time or more.
For more information, see Resolution of the identity,
where
Since , plane waves follow,
In his book (1958), Ch. III.20, Dirac defines the standard ket which, up to a normalization, is the translationally invariant momentum eigenstate in the momentum representation, i.e., . Consequently, the corresponding wavefunction is a constant, , and
as well as
Typically, when all matrix elements of an operator such as are available, this resolution serves to reconstitute the full operator,
Notation used by mathematicians
The object physicists are considering when using bra–ket notation is a Hilbert space (a complete inner product space).
Let be a Hilbert space and a vector in . What physicists would denote by is the vector itself. That is, | Bra–ket notation | Wikipedia | 507 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
Let be the dual space of . This is the space of linear functionals on . The embedding is defined by , where for every the linear functional satisfies for every the functional equation .
Notational confusion arises when identifying and with and respectively. This is because of literal symbolic substitutions. Let and let . This gives
One ignores the parentheses and removes the double bars.
Moreover, mathematicians usually write the dual entity not at the first place, as the physicists do, but at the second one, and they usually use not an asterisk but an overline (which the physicists reserve for averages and the Dirac spinor adjoint) to denote complex conjugate numbers; i.e., for scalar products mathematicians usually write
whereas physicists would write for the same quantity | Bra–ket notation | Wikipedia | 162 | 4542 | https://en.wikipedia.org/wiki/Bra%E2%80%93ket%20notation | Physical sciences | Quantum mechanics | Physics |
Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The term blue generally describes colours perceived by humans observing light with a dominant wavelength that's between approximately 450 and 495 nanometres. Most blues contain a slight mixture of other colours; azure contains some green, while ultramarine contains some violet. The clear daytime sky and the deep sea appear blue because of an optical effect known as Rayleigh scattering. An optical effect called the Tyndall effect explains blue eyes. Distant objects appear more blue because of another optical effect called aerial perspective.
Blue has been an important colour in art and decoration since ancient times. The semi-precious stone lapis lazuli was used in ancient Egypt for jewellery and ornament and later, in the Renaissance, to make the pigment ultramarine, the most expensive of all pigments. In the eighth century Chinese artists used cobalt blue to colour fine blue and white porcelain. In the Middle Ages, European artists used it in the windows of cathedrals. Europeans wore clothing coloured with the vegetable dye woad until it was replaced by the finer indigo from America. In the 19th century, synthetic blue dyes and pigments gradually replaced organic dyes and mineral pigments. Dark blue became a common colour for military uniforms and later, in the late 20th century, for business suits. Because blue has commonly been associated with harmony, it was chosen as the colour of the flags of the United Nations and the European Union.
In the United States and Europe, blue is the colour that both men and women are most likely to choose as their favourite, with at least one recent survey showing the same across several other countries, including China, Malaysia, and Indonesia. Past surveys in the US and Europe have found that blue is the colour most commonly associated with harmony, confidence, masculinity, knowledge, intelligence, calmness, distance, infinity, the imagination, cold, and sadness.
Etymology and linguistics
The modern English word blue comes from Middle English or , from the Old French , a word of Germanic origin, related to the Old High German word (meaning 'shimmering, lustrous'). In heraldry, the word azure is used for blue. | Blue | Wikipedia | 473 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
In Russian, Spanish, Mongolian, Irish, and some other languages, there is no single word for blue, but rather different words for light blue (, ; ) and dark blue (, ; ) (see Colour term).
Several languages, including Japanese and Lakota Sioux, use the same word to describe blue and green. For example, in Vietnamese, the colour of both tree leaves and the sky is . In Japanese, the word for blue (, ) is often used for colours that English speakers would refer to as green, such as the colour of a traffic signal meaning "go". In Lakota, the word is used for both blue and green, the two colours not being distinguished in older Lakota (for more on this subject, see Blue–green distinction in language).
Linguistic research indicates that languages do not begin by having a word for the colour blue. Colour names often developed individually in natural languages, typically beginning with black and white (or dark and light), and then adding red, and only much later – usually as the last main category of colour accepted in a language – adding the colour blue, probably when blue pigments could be manufactured reliably in the culture using that language.
Optics and colour theory
The term blue generally describes colours perceived by humans observing light with a dominant wavelength between approximately 450 and 495 nanometres. Blues with a higher frequency and thus a shorter wavelength gradually look more violet, while those with a lower frequency and a longer wavelength gradually appear more green. Purer blues are in the middle of this range, e.g., around 470 nanometres.
Isaac Newton included blue as one of the seven colours in his first description of the visible spectrum. He chose seven colours because that was the number of notes in the musical scale, which he believed was related to the optical spectrum. He included indigo, the hue between blue and violet, as one of the separate colours, though today it is usually considered a hue of blue.
In painting and traditional colour theory, blue is one of the three primary colours of pigments (red, yellow, blue), which can be mixed to form a wide gamut of colours. Red and blue mixed together form violet, blue and yellow together form green. Mixing all three primary colours together produces a dark brown. From the Renaissance onward, painters used this system to create their colours (see RYB colour model). | Blue | Wikipedia | 485 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
The RYB model was used for colour printing by Jacob Christoph Le Blon as early as 1725. Later, printers discovered that more accurate colours could be created by using combinations of cyan, magenta, yellow, and black ink, put onto separate inked plates and then overlaid one at a time onto paper. This method could produce almost all the colours in the spectrum with reasonable accuracy.
On the HSV colour wheel, the complement of blue is yellow; that is, a colour corresponding to an equal mixture of red and green light. On a colour wheel based on traditional colour theory (RYB) where blue was considered a primary colour, its complementary colour is considered to be orange (based on the Munsell colour wheel).
LED
In 1993, high-brightness blue LEDs were demonstrated by Shuji Nakamura of Nichia Corporation. In parallel, Isamu Akasaki and Hiroshi Amano of Nagoya University were working on a new development which revolutionized LED lighting.
Nakamura was awarded the 2006 Millennium Technology Prize for his invention.
Nakamura, Hiroshi Amano and Isamu Akasaki were awarded the Nobel Prize in Physics in 2014 for the invention of an efficient blue LED.
Lasers
Lasers emitting in the blue region of the spectrum became widely available to the public in 2010 with the release of inexpensive high-powered 445–447 nm laser diode technology. Previously the blue wavelengths were accessible only through DPSS which are comparatively expensive and inefficient, but still widely used by scientists for applications including optogenetics, Raman spectroscopy, and particle image velocimetry, due to their superior beam quality. Blue gas lasers are also still commonly used for holography, DNA sequencing, optical pumping, among other scientific and medical applications.
Shades and variations
Blue is the colour of light between violet and cyan on the visible spectrum. Hues of blue include indigo and ultramarine, closer to violet; pure blue, without any mixture of other colours; Azure, which is a lighter shade of blue, similar to the colour of the sky; Cyan, which is midway in the spectrum between blue and green, and the other blue-greens such as turquoise, teal, and aquamarine. | Blue | Wikipedia | 449 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Blue also varies in shade or tint; darker shades of blue contain black or grey, while lighter tints contain white. Darker shades of blue include ultramarine, cobalt blue, navy blue, and Prussian blue; while lighter tints include sky blue, azure, and Egyptian blue (for a more complete list see the List of colours).
As a structural colour
In nature, many blue phenomena arise from structural colouration, the result of interference between reflections from two or more surfaces of thin films, combined with refraction as light enters and exits such films. The geometry then determines that at certain angles, the light reflected from both surfaces interferes constructively, while at other angles, the light interferes destructively. Diverse colours therefore appear despite the absence of colourants.
Colourants
Artificial blues
Egyptian blue, the first artificial pigment, was produced in the third millennium BC in Ancient Egypt. It is produced by heating pulverized sand, copper, and natron. It was used in tomb paintings and funereal objects to protect the dead in their afterlife. Prior to the 1700s, blue colourants for artwork were mainly based on lapis lazuli and the related mineral ultramarine. A breakthrough occurred in 1709 when German druggist and pigment maker Johann Jacob Diesbach discovered Prussian blue. The new blue arose from experiments involving heating dried blood with iron sulphides and was initially called Berliner Blau. By 1710 it was being used by the French painter Antoine Watteau, and later his successor Nicolas Lancret. It became immensely popular for the manufacture of wallpaper, and in the 19th century was widely used by French impressionist painters. Beginning in the 1820s, Prussian blue was imported into Japan through the port of Nagasaki. It was called bero-ai, or Berlin blue, and it became popular because it did not fade like traditional Japanese blue pigment, ai-gami, made from the dayflower. Prussian blue was used by both Hokusai, in his wave paintings, and Hiroshige.
In 1799 a French chemist, Louis Jacques Thénard, made a synthetic cobalt blue pigment which became immensely popular with painters. | Blue | Wikipedia | 430 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
In 1824 the Societé pour l'Encouragement d'Industrie in France offered a prize for the invention of an artificial ultramarine which could rival the natural colour made from lapis lazuli. The prize was won in 1826 by a chemist named Jean Baptiste Guimet, but he refused to reveal the formula of his colour. In 1828, another scientist, Christian Gmelin then a professor of chemistry in Tübingen, found the process and published his formula. This was the beginning of new industry to manufacture artificial ultramarine, which eventually almost completely replaced the natural product.
In 1878 German chemists synthesized indigo. This product rapidly replaced natural indigo, wiping out vast farms growing indigo. It is now the blue of blue jeans. As the pace of organic chemistry accelerated, a succession of synthetic blue dyes were discovered including Indanthrone blue, which had even greater resistance to fading during washing or in the sun, and copper phthalocyanine.
Dyes for textiles and food
Woad and true indigo were once used but since the early 1900s, all indigo is synthetic. Produced on an industrial scale, indigo is the blue of blue jeans. Blue dyes are organic compounds, both synthetic and natural.
For food, the triarylmethane dye Brilliant blue FCF is used for candies. The search continues for stable, natural blue dyes suitable for the food industry.
Various raspberry-flavoured foods are dyed blue. This was done to distinguish strawberry, watermelon and raspberry-flavoured foods. The company ICEE used Blue No. 1 for their blue raspberry ICEEs.
Pigments for painting and glass
Blue pigments were once produced from minerals, especially lapis lazuli and its close relative ultramarine. These minerals were crushed, ground into powder, and then mixed with a quick-drying binding agent, such as egg yolk (tempera painting); or with a slow-drying oil, such as linseed oil, for oil painting. Two inorganic but synthetic blue pigments are cerulean blue (primarily cobalt(II) stanate: ) and Prussian blue (milori blue: primarily ). The chromophore in blue glass and glazes is cobalt(II). Diverse cobalt(II) salts such as cobalt carbonate or cobalt(II) aluminate are mixed with the silica prior to firing. The cobalt occupies sites otherwise filled with silicon. | Blue | Wikipedia | 493 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Inks
Methyl blue is the dominant blue pigment in inks used in pens. Blueprinting involves the production of Prussian blue in situ.
Inorganic compounds
Certain metal ions characteristically form blue solutions or blue salts. Of some practical importance, cobalt is used to make the deep blue glazes and glasses. It substitutes for silicon or aluminum ions in these materials. Cobalt is the blue chromophore in stained glass windows, such as those in Gothic cathedrals and in Chinese porcelain beginning in the Tang dynasty. Copper(II) (Cu2+) also produces many blue compounds, including the commercial algicide copper(II) sulfate (CuSO4.5H2O). Similarly, vanadyl salts and solutions are often blue, e.g. vanadyl sulfate.
In nature
Sky and sea
When sunlight passes through the atmosphere, the blue wavelengths are scattered more widely by the oxygen and nitrogen molecules, and more blue comes to our eyes. This effect is called Rayleigh scattering, after Lord Rayleigh and confirmed by Albert Einstein in 1911.
The sea is seen as blue for largely the same reason: the water absorbs the longer wavelengths of red and reflects and scatters the blue, which comes to the eye of the viewer. The deeper the observer goes, the darker the blue becomes. In the open sea, only about 1% of light penetrates to a depth of 200 metres (see underwater and euphotic depth).
The colour of the sea is also affected by the colour of the sky, reflected by particles in the water; and by algae and plant life in the water, which can make it look green; or by sediment, which can make it look brown.
The farther away an object is, the more blue it often appears to the eye. For example, mountains in the distance often appear blue. This is the effect of atmospheric perspective; the farther an object is away from the viewer, the less contrast there is between the object and its background colour, which is usually blue. In a painting where different parts of the composition are blue, green and red, the blue will appear to be more distant, and the red closer to the viewer. The cooler a colour is, the more distant it seems. Blue light is scattered more than other wavelengths by the gases in the atmosphere, hence our "blue planet".
Minerals | Blue | Wikipedia | 476 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Some of the most desirable gems are blue, including sapphire and tanzanite. Compounds of copper(II) are characteristically blue and so are many copper-containing minerals.
Azurite (, with a deep blue colour, was once employed in medieval years, but it is unstable pigment, losing its colour especially under dry conditions. Lapis lazuli, mined in Afghanistan for more than three thousand years, was used for jewelry and ornaments, and later was crushed and powdered and used as a pigment. The more it was ground, the lighter the blue colour became. Natural ultramarine, made by grinding lapis lazuli into a fine powder, was the finest available blue pigment in the Middle Ages and the Renaissance. It was extremely expensive, and in Italian Renaissance art, it was often reserved for the robes of the Virgin Mary.
Plants and fungi
Intense efforts have focused on blue flowers and the possibility that natural blue colourants could be used as food dyes. Commonly, blue colours in plants are anthocyanins: "the largest group of water-soluble pigments found widespread in the plant kingdom". In the few plants that exploit structural colouration, brilliant colours are produced by structures within cells. The most brilliant blue colouration known in any living tissue is found in the marble berries of Pollia condensata, where a spiral structure of cellulose fibrils scattering blue light. The fruit of quandong (Santalum acuminatum) can appear blue owing to the same effect.
Animals | Blue | Wikipedia | 308 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Blue-pigmented animals are relatively rare. Examples of which include butterflies of the genus Nessaea, where blue is created by pterobilin. Other blue pigments of animal origin include phorcabilin, used by other butterflies in Graphium and Papilio (specifically P. phorcas and P. weiskei), and sarpedobilin, which is used by Graphium sarpedon. Blue-pigmented organelles, known as "cyanosomes", exist in the chromatophores of at least two fish species, the mandarin fish and the picturesque dragonet. More commonly, blueness in animals is a structural colouration; an optical interference effect induced by organized nanometre-sized scales or fibres. Examples include the plumage of several birds like the blue jay and indigo bunting, the scales of butterflies like the morpho butterfly, collagen fibres in the skin of some species of monkey and opossum, and the iridophore cells in some fish and frogs.
Eyes
Blue eyes do not actually contain any blue pigment. Eye colour is determined by two factors: the pigmentation of the eye's iris and the scattering of light by the turbid medium in the stroma of the iris. In humans, the pigmentation of the iris varies from light brown to black. The appearance of blue, green, and hazel eyes results from the Tyndall scattering of light in the stroma, an optical effect similar to what accounts for the blueness of the sky. The irises of the eyes of people with blue eyes contain less dark melanin than those of people with brown eyes, which means that they absorb less short-wavelength blue light, which is instead reflected out to the viewer. Eye colour also varies depending on the lighting conditions, especially for lighter-coloured eyes.
Blue eyes are most common in Ireland, the Baltic Sea area and Northern Europe, and are also found in Eastern, Central, and Southern Europe. Blue eyes are also found in parts of Western Asia, most notably in Afghanistan, Syria, Iraq, and Iran. In Estonia, 99% of people have blue eyes. In Denmark in 1978, only 8% of the population had brown eyes, though through immigration, today that number is about 11%. In Germany, about 75% have blue eyes. | Blue | Wikipedia | 482 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
In the United States, as of 2006, 1 out of every 6 people, or 16.6% of the total population, and 22.3% of the white population, have blue eyes, compared with about half of Americans born in 1900, and a third of Americans born in 1950. Blue eyes are becoming less common among American children. In the US, males are 3–5% more likely to have blue eyes than females.
History
In the ancient world
As early as the 7th millennium BC, lapis lazuli was mined in the Sar-i Sang mines, in Shortugai, and in other mines in Badakhshan province in northeast Afghanistan.
Lapis lazuli artifacts, dated to 7570 BC, have been found at Bhirrana, which is the oldest site of Indus Valley civilisation. Lapis was highly valued by the Indus Valley Civilisation (7570–1900 BC). Lapis beads have been found at Neolithic burials in Mehrgarh, the Caucasus, and as far away as Mauritania. It was used in the funeral mask of Tutankhamun (1341–1323 BC).
A term for Blue was relatively rare in many forms of ancient art and decoration, and even in ancient literature. The Ancient Greek poets described the sea as green, brown or "the colour of wine". The colour is mentioned several times in the Hebrew Bible as 'tekhelet'. Reds, blacks, browns, and ochres are found in cave paintings from the Upper Paleolithic period, but not blue. Blue was also not used for dyeing fabric until long after red, ochre, pink, and purple. This is probably due to the perennial difficulty of making blue dyes and pigments. On the other hand, the rarity of blue pigment made it even more valuable. | Blue | Wikipedia | 373 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
The earliest known blue dyes were made from plants – woad in Europe, indigo in Asia and Africa, while blue pigments were made from minerals, usually either lapis lazuli or azurite, and required more. Blue glazes posed still another challenge since the early blue dyes and pigments were not thermally robust. In , the blue glaze Egyptian blue was introduced for ceramics, as well as many other objects. The Greeks imported indigo dye from India, calling it indikon, and they painted with Egyptian blue. Blue was not one of the four primary colours for Greek painting described by Pliny the Elder (red, yellow, black, and white). For the Romans, blue was the colour of mourning, as well as the colour of barbarians. The Celts and Germans reportedly dyed their faces blue to frighten their enemies, and tinted their hair blue when they grew old. The Romans made extensive use of indigo and Egyptian blue pigment, as evidenced, in part, by frescos in Pompeii.
The Romans had many words for varieties of blue, including , , , , , , , and , but two words, both of foreign origin, became the most enduring; , from the Germanic word blau, which eventually became bleu or blue; and , from the Arabic word , which became azure.
Blue was widely used in the decoration of churches in the Byzantine Empire. By contrast, in the Islamic world, blue was of secondary to green, believed to be the favourite colour of the Prophet Mohammed. At certain times in Moorish Spain and other parts of the Islamic world, blue was the colour worn by Christians and Jews, because only Muslims were allowed to wear white and green.
In the Middle Ages
In the art and life of Europe during the early Middle Ages, blue played a minor role. This changed dramatically between 1130 and 1140 in Paris, when the Abbe Suger rebuilt the Saint Denis Basilica. Suger considered that light was the visible manifestation of the Holy Spirit. He installed stained glass windows coloured with cobalt, which, combined with the light from the red glass, filled the church with a bluish violet light. The church became the marvel of the Christian world, and the colour became known as the . In the years that followed even more elegant blue stained glass windows were installed in other churches, including at Chartres Cathedral and Sainte-Chapelle in Paris. | Blue | Wikipedia | 490 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
In the 12th century the Roman Catholic Church dictated that painters in Italy (and the rest of Europe consequently) to paint the Virgin Mary with blue, which became associated with holiness, humility and virtue. In medieval paintings, blue was used to attract the attention of the viewer to the Virgin Mary. Paintings of the mythical King Arthur began to show him dressed in blue. The coat of arms of the kings of France became an azure or light blue shield, sprinkled with golden fleur-de-lis or lilies. Blue had come from obscurity to become the royal colour.
Renaissance through 18th century
Blue came into wider use beginning in the Renaissance, when artists began to paint the world with perspective, depth, shadows, and light from a single source. In Renaissance paintings, artists tried to create harmonies between blue and red, lightening the blue with lead white paint and adding shadows and highlights. Raphael was a master of this technique, carefully balancing the reds and the blues so no one colour dominated the picture.
Ultramarine was the most prestigious blue of the Renaissance, being more expensive than gold. Wealthy art patrons commissioned works with the most expensive blues possible. In 1616 Richard Sackville commissioned a portrait of himself by Isaac Oliver with three different blues, including ultramarine pigment for his stockings.
An industry for the manufacture of fine blue and white pottery began in the 14th century in Jingdezhen, China, using white Chinese porcelain decorated with patterns of cobalt blue, imported from Persia. It was first made for the family of the Emperor of China, then was exported around the world, with designs for export adapted to European subjects and tastes. The Chinese blue style was also adapted by Dutch craftsmen in Delft and English craftsmen in Staffordshire in the 17th-18th centuries. in the 18th century, blue and white porcelains were produced by Josiah Wedgwood and other British craftsmen.
19th-20th century
The early 19th century saw the ancestor of the modern blue business suit, created by Beau Brummel (1776–1840), who set fashion at the London Court. It also saw the invention of blue jeans, a highly popular form of workers's costume, invented in 1853 by Jacob W. Davis who used metal rivets to strengthen blue denim work clothing in the California gold fields. The invention was funded by San Francisco entrepreneur Levi Strauss, and spread around the world. | Blue | Wikipedia | 477 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Recognizing the emotional power of blue, many artists made it the central element of paintings in the 19th and 20th centuries. They included Pablo Picasso, Pavel Kuznetsov and the Blue Rose art group, and Kandinsky and Der Blaue Reiter (The Blue Rider) school. Henri Matisse expressed deep emotions with blue, "A certain blue penetrates your soul." In the second half of the 20th century, painters of the abstract expressionist movement use blues to inspire ideas and emotions. Painter Mark Rothko observed that colour was "only an instrument;" his interest was "in expressing human emotions tragedy, ecstasy, doom, and so on".
In society and culture
Uniforms
In the 17th century. The Prince-Elector of Brandenburg, Frederick William I of Prussia, chose Prussian blue as the new colour of Prussian military uniforms, because it was made with Woad, a local crop, rather than Indigo, which was produced by the colonies of Brandenburg's rival, England. It was worn by the German army until World War I, with the exception of the soldiers of Bavaria, who wore sky-blue.
In 1748, the Royal Navy adopted a dark shade of blue for the uniform of officers. It was first known as marine blue, now known as navy blue. The militia organized by George Washington selected blue and buff, the colours of the British Whig Party. Blue continued to be the colour of the field uniform of the US Army until 1902, and is still the colour of the dress uniform.
In the 19th century, police in the United Kingdom, including the Metropolitan Police and the City of London Police also adopted a navy blue uniform. Similar traditions were embraced in France and Austria. It was also adopted at about the same time for the uniforms of the officers of the New York City Police Department.
Gender
Blue is used to represent males. Beginning as a trend the mid-19th century and applying primarily to clothing, gendered associations with blue became more widespread from the 1950s. The colour became associated with males after the second world war.
Religion | Blue | Wikipedia | 412 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Blue in Judaism: In the Torah, the Israelites were commanded to put fringes, tzitzit, on the corners of their garments, and to weave within these fringes a "twisted thread of blue (tekhelet)". In ancient days, this blue thread was made from a dye extracted from a Mediterranean snail called the hilazon. Maimonides claimed that this blue was the colour of "the clear noonday sky"; Rashi, the colour of the evening sky. According to several rabbinic sages, blue is the colour of God's Glory. Staring at this colour aids in mediation, bringing us a glimpse of the "pavement of sapphire, like the very sky for purity", which is a likeness of the Throne of God. (The Hebrew word for glory) Many items in the Mishkan, the portable sanctuary in the wilderness, such as the menorah, many of the vessels, and the Ark of the Covenant, were covered with blue cloth when transported from place to place.
Blue in Christianity: Blue is particularly associated with the Virgin Mary. This was the result of a decree of Pope Gregory I (540–601) who ordered that all religious paintings should tell a story which was clearly comprehensible to all viewers, and that figures should be easily recognizable, especially that of the figure of Mary. If she was alone in the image, her costume was usually painted with the finest blue, ultramarine. If she was with Christ, her costume was usually painted with a less expensive pigment, to avoid outshining him.
Blue in Hinduism: Many of the gods are depicted as having blue-coloured skin, particularly those associated with Vishnu, who is said to be the preserver of the world, and thus intimately connected to water. Krishna and Rama, Vishnu's avatars, are usually depicted with blue skin. Shiva, the destroyer deity, is also depicted in a light-blue hue, and is called Nīlakaṇṭha, or blue-throated, for having swallowed poison to save the universe during the Samudra Manthana, the churning of the ocean of milk. Blue is used to symbolically represent the fifth, and the throat, chakra (Vishuddha). | Blue | Wikipedia | 460 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Blue in Sikhism: The Akali Nihangs warriors wear all-blue attire. Guru Gobind Singh also has a blue roan horse. The Sikh Rehat Maryada states that the Nishan Sahib hoisted outside every Gurudwara should be xanthic (Basanti in Punjabi) or greyish blue (modern day navy blue) (Surmaaee in Punjabi) colour.
Blue in Paganism: Blue is associated with peace, truth, wisdom, protection, and patience. It helps with healing, psychic ability, harmony, and understanding. | Blue | Wikipedia | 113 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
Sports
In sports, blue is widely represented in uniforms in part because the majority of national teams wear the colours of their national flag. For example, the national men's football team of France are known as Les Bleus (the Blues). Similarly, Argentina, Italy, and Uruguay wear blue shirts. The Asian Football Confederation and the Oceania Football Confederation use blue text on their logos. Blue is well represented in baseball (Blue Jays), basketball, and American football, and Ice hockey. The Indian national cricket team wears blue uniform during One day international matches, as such the team is also referred to as "Men in Blue".
Politics
Unlike red or green, blue was not strongly associated with any particular country, religion or political movement. As the colour of harmony, it was chosen as the colour for the flags of the United Nations, the European Union, and NATO. In politics, blue is often used as the colour of conservative parties, contrasting with the red associated with left-wing parties. Some conservative parties that use the colour blue include the Conservative Party (UK), Conservative Party of Canada, Liberal Party of Australia, Liberal Party of Brazil, and Likud of Israel. However, in some countries, blue is not associated main conservative party. In the United States, the liberal Democratic Party is associated with blue, while the conservative Republican Party with red. US states which have been won by the Democratic Party in four consecutive presidential elections are termed "blue states", while those that have been won by the Republican Party are termed "red states". South Korea also uses this colour model, with the Democratic Party on the left using blue and the People Power Party on the right using red. | Blue | Wikipedia | 342 | 4543 | https://en.wikipedia.org/wiki/Blue | Physical sciences | Color terms | null |
A blizzard is a severe snowstorm characterized by strong sustained winds and low visibility, lasting for a prolonged period of time—typically at least three or four hours. A ground blizzard is a weather condition where snow that has already fallen is being blown by wind. Blizzards can have an immense size and usually stretch to hundreds or thousands of kilometres.
Definition and etymology
In the United States, the National Weather Service defines a blizzard as a severe snow storm characterized by strong winds causing blowing snow that results in low visibilities. The difference between a blizzard and a snowstorm is the strength of the wind, not the amount of snow. To be a blizzard, a snow storm must have sustained winds or frequent gusts that are greater than or equal to with blowing or drifting snow which reduces visibility to or less and must last for a prolonged period of time—typically three hours or more.
Environment Canada defines a blizzard as a storm with wind speeds exceeding accompanied by visibility of or less, resulting from snowfall, blowing snow, or a combination of the two. These conditions must persist for a period of at least four hours for the storm to be classified as a blizzard, except north of the arctic tree line, where that threshold is raised to six hours.
The Australia Bureau of Meteorology describes a blizzard as, "Violent and very cold wind which is laden with snow, some part, at least, of which has been raised from snow covered ground."
While severe cold and large amounts of drifting snow may accompany blizzards, they are not required. Blizzards can bring whiteout conditions, and can paralyze regions for days at a time, particularly where snowfall is unusual or rare.
A severe blizzard has winds over , near zero visibility, and temperatures of or lower. In Antarctica, blizzards are associated with winds spilling over the edge of the ice plateau at an average velocity of .
Ground blizzard refers to a weather condition where loose snow or ice on the ground is lifted and blown by strong winds. The primary difference between a ground blizzard as opposed to a regular blizzard is that in a ground blizzard no precipitation is produced at the time, but rather all the precipitation is already present in the form of snow or ice at the surface. | Blizzard | Wikipedia | 444 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
The Oxford English Dictionary concludes the term blizzard is likely onomatopoeic, derived from the same sense as blow, blast, blister, and bluster; the first recorded use of it for weather dates to 1829, when it was defined as a "violent blow". It achieved its modern definition by 1859, when it was in use in the western United States. The term became common in the press during the harsh winter of 1880–81.
United States storm systems
In the United States, storm systems powerful enough to cause blizzards usually form when the jet stream dips far to the south, allowing cold, dry polar air from the north to clash with warm, humid air moving up from the south.
When cold, moist air from the Pacific Ocean moves eastward to the Rocky Mountains and the Great Plains, and warmer, moist air moves north from the Gulf of Mexico, all that is needed is a movement of cold polar air moving south to form potential blizzard conditions that may extend from the Texas Panhandle to the Great Lakes and Midwest. A blizzard also may be formed when a cold front and warm front mix together and a blizzard forms at the border line.
Another storm system occurs when a cold core low over the Hudson Bay area in Canada is displaced southward over southeastern Canada, the Great Lakes, and New England. When the rapidly moving cold front collides with warmer air coming north from the Gulf of Mexico, strong surface winds, significant cold air advection, and extensive wintry precipitation occur.
Low pressure systems moving out of the Rocky Mountains onto the Great Plains, a broad expanse of flat land, much of it covered in prairie, steppe and grassland, can cause thunderstorms and rain to the south and heavy snows and strong winds to the north. With few trees or other obstructions to reduce wind and blowing, this part of the country is particularly vulnerable to blizzards with very low temperatures and whiteout conditions. In a true whiteout, there is no visible horizon. People can become lost in their own front yards, when the door is only away, and they would have to feel their way back. Motorists have to stop their cars where they are, as the road is impossible to see.
Nor'easter blizzards | Blizzard | Wikipedia | 453 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
A nor'easter is a macro-scale storm that occurs off the New England and Atlantic Canada coastlines. It gets its name from the direction the wind is coming from. The usage of the term in North America comes from the wind associated with many different types of storms, some of which can form in the North Atlantic Ocean and some of which form as far south as the Gulf of Mexico. The term is most often used in the coastal areas of New England and Atlantic Canada. This type of storm has characteristics similar to a hurricane. More specifically, it describes a low-pressure area whose center of rotation is just off the coast and whose leading winds in the left-forward quadrant rotate onto land from the northeast. High storm waves may sink ships at sea and cause coastal flooding and beach erosion. Notable nor'easters include The Great Blizzard of 1888, one of the worst blizzards in U.S. history. It dropped of snow and had sustained winds of more than that produced snowdrifts in excess of . Railroads were shut down and people were confined to their houses for up to a week. It killed 400 people, mostly in New York.
Historic events
1972 Iran blizzard
The 1972 Iran blizzard, which caused 4,000 reported deaths, was the deadliest blizzard in recorded history. Dropping as much as of snow, it completely covered 200 villages. After a snowfall lasting nearly a week, an area the size of Wisconsin was entirely buried in snow.
2008 Afghanistan blizzard
The 2008 Afghanistan blizzard, was a fierce blizzard that struck Afghanistan on 10 January 2008. Temperatures fell to a low of , with up to of snow in the more mountainous regions, killing at least 926 people. It was the third deadliest blizzard in history. The weather also claimed more than 100,000 sheep and goats, and nearly 315,000 cattle died.
The Snow Winter of 1880–1881
The winter of 1880–1881 is widely considered the most severe winter ever known in many parts of the United States. | Blizzard | Wikipedia | 398 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
The initial blizzard in October 1880 brought snowfalls so deep that two-story homes experienced accumulations, as opposed to drifts, up to their second-floor windows. No one was prepared for deep snow so early in the winter. Farmers from North Dakota to Virginia were caught flat with fields unharvested, what grain that had been harvested unmilled, and their suddenly all-important winter stocks of wood fuel only partially collected. By January train service was almost entirely suspended from the region. Railroads hired scores of men to dig out the tracks but as soon as they had finished shoveling a stretch of line a new storm arrived, burying it again.
There were no winter thaws and on February 2, 1881, a second massive blizzard struck that lasted for nine days. In towns the streets were filled with solid drifts to the tops of the buildings and tunneling was necessary to move about. Homes and barns were completely covered, compelling farmers to construct fragile tunnels in order to feed their stock.
When the snow finally melted in late spring of 1881, huge sections of the plains experienced flooding. Massive ice jams clogged the Missouri River, and when they broke the downstream areas were inundated. Most of the town of Yankton, in what is now South Dakota, was washed away when the river overflowed its banks after the thaw.
Novelization
Many children—and their parents—learned of "The Snow Winter" through the children's book The Long Winter by Laura Ingalls Wilder, in which the author tells of her family's efforts to survive. The snow arrived in October 1880 and blizzard followed blizzard throughout the winter and into March 1881, leaving many areas snowbound throughout the winter. Accurate details in Wilder's novel include the blizzards' frequency and the deep cold, the Chicago and North Western Railway stopping trains until the spring thaw because the snow made the tracks impassable, the near-starvation of the townspeople, and the courage of her future husband Almanzo and another man, Cap Garland, who ventured out on the open prairie in search of a cache of wheat that no one was even sure existed.
The Storm of the Century | Blizzard | Wikipedia | 439 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
The Storm of the Century, also known as the Great Blizzard of 1993, was a large cyclonic storm that formed over the Gulf of Mexico on March 12, 1993, and dissipated in the North Atlantic Ocean on March 15. It is unique for its intensity, massive size and wide-reaching effect. At its height, the storm stretched from Canada towards Central America, but its main impact was on the United States and Cuba. The cyclone moved through the Gulf of Mexico, and then through the Eastern United States before moving into Canada. Areas as far south as northern Alabama and Georgia received a dusting of snow and areas such as Birmingham, Alabama, received up to with hurricane-force wind gusts and record low barometric pressures. Between Louisiana and Cuba, hurricane-force winds produced high storm surges across northwestern Florida, which along with scattered tornadoes killed dozens of people. In the United States, the storm was responsible for the loss of electric power to over 10 million customers. It is purported to have been directly experienced by nearly 40 percent of the country's population at that time. A total of 310 people, including 10 from Cuba, perished during this storm. The storm cost $6 to $10 billion in damages.
List of blizzards
North America | Blizzard | Wikipedia | 252 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
1700 to 1799
The Great Snow 1717 series of four snowstorms between February 27 and March 7, 1717. There were reports of about five feet of snow already on the ground when the first of the storms hit. By the end, there were about ten feet of snow and some drifts reaching , burying houses entirely. In the colonial era, this storm made travel impossible until the snow simply melted.
Blizzard of 1765. March 24, 1765. Affected area from Philadelphia to Massachusetts. High winds and over of snowfall recorded in some areas.
Blizzard of 1772. "The Washington and Jefferson Snowstorm of 1772". January 26–29, 1772. One of largest D.C. and Virginia area snowstorms ever recorded. Snow accumulations of recorded.
The "Hessian Storm of 1778". December 26, 1778. Severe blizzard with high winds, heavy snows and bitter cold extending from Pennsylvania to New England. Snow drifts reported to be high in Rhode Island. Storm named for stranded Hessian troops in deep snows stationed in Rhode Island during the Revolutionary War.
The Great Snow of 1786. December 4–10, 1786. Blizzard conditions and a succession of three harsh snowstorms produced snow depths of to from Pennsylvania to New England. Reportedly of similar magnitude of 1717 snowstorms.
The Long Storm of 1798. November 19–21, 1798. Heavy snowstorm produced snow from Maryland to Maine. | Blizzard | Wikipedia | 283 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
1800 to 1850
Blizzard of 1805. January 26–28, 1805. Cyclone brought heavy snowstorm to New York City and New England. Snow fell continuously for two days where over of snow accumulated.
New York City Blizzard of 1811. December 23–24, 1811. Severe blizzard conditions reported on Long Island, in New York City, and southern New England. Strong winds and tides caused damage to shipping in harbor.
Luminous Blizzard of 1817. January 17, 1817. In Massachusetts and Vermont, a severe snowstorm was accompanied by frequent lightning and heavy thunder. St. Elmo's fire reportedly lit up trees, fence posts, house roofs, and even people. John Farrar professor at Harvard, recorded the event in his memoir in 1821.
Great Snowstorm of 1821. January 5–7, 1821. Extensive snowstorm and blizzard spread from Virginia to New England.
Winter of Deep Snow in 1830. December 29, 1830. Blizzard storm dumped in Kansas City and in Illinois. Areas experienced repeated storms thru mid-February 1831.
"The Great Snowstorm of 1831" January 14–16, 1831. Produced snowfall over widest geographic area that was only rivaled, or exceeded by, the 1993 Blizzard. Blizzard raged from Georgia, to Ohio Valley, all the way to Maine.
"The Big Snow of 1836" January 8–10, 1836. Produced to of snowfall in interior New York, northern Pennsylvania, and western New England. Philadelphia got a reported and New York City of snow. | Blizzard | Wikipedia | 298 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
1851 to 1900
Plains Blizzard of 1856. December 3–5, 1856. Severe blizzard-like storm raged for three days in Kansas and Iowa. Early pioneers suffered.
"The Cold Storm of 1857" January 18–19, 1857. Produced severe blizzard conditions from North Carolina to Maine. Heavy snowfalls reported in east coast cities.
Midwest Blizzard of 1864. January 1, 1864. Gale-force winds, driving snow, and low temperatures all struck simultaneously around Chicago, Wisconsin and Minnesota.
Plains Blizzard of 1873. January 7, 1873. Severe blizzard struck the Great Plains. Many pioneers from the east were unprepared for the storm and perished in Minnesota and Iowa.
Great Plains Easter Blizzard of 1873. April 13, 1873
Seattle Blizzard of 1880. January 6, 1880. Seattle area's greatest snowstorm to date. An estimated fell around the town. Many barns collapsed and all transportation halted.
The Hard Winter of 1880-81. October 15, 1880. A blizzard in eastern South Dakota marked the beginning of this historically difficult season. Laura Ingalls Wilder's book The Long Winter details the effects of this season on early settlers.
In the three year winter period from December 1885 to March 1888, the Great Plains and Eastern United States suffered a series of the worst blizzards in this nation's history ending with the Schoolhouse Blizzard and the Great Blizzard of 1888. The massive explosion of the volcano Krakatoa in the South Pacific late in August 1883 is a suspected cause of these huge blizzards during these several years. The clouds of ash it emitted continued to circulate around the world for many years. Weather patterns continued to be chaotic for years, and temperatures did not return to normal until 1888. Record rainfall was experienced in Southern California during July 1883 to June 1884. The Krakatoa eruption injected an unusually large amount of sulfur dioxide (SO2) gas high into the stratosphere which reflects sunlight and helped cool the planet over the next few years until the suspended atmospheric sulfur fell to ground.
Plains Blizzard of late 1885. In Kansas, heavy snows of late 1885 had piled drifts high.
Kansas Blizzard of 1886. First week of January 1886. Reported that 80 percent of the cattle were frozen to death in that state alone from the cold and snow.
January 1886 Blizzard. January 9, 1886. Same system as Kansas 1886 Blizzard that traveled eastward.
Great Plains Blizzards of late 1886. On November 13, 1886, it reportedly began to snow and did not stop for a month in the Great Plains region. | Blizzard | Wikipedia | 509 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
Great Plains Blizzard of 1887. January 9–11, 1887. Reported 72-hour blizzard that covered parts of the Great Plains in more than of snow. Winds whipped and temperatures dropped to around . So many cows that were not killed by the cold soon died from starvation. When spring arrived, millions of the animals were dead, with around 90 percent of the open range's cattle rotting where they fell. Those present reported carcasses as far as the eye could see. Dead cattle clogged up rivers and spoiled drinking water. Many ranchers went bankrupt and others simply called it quits and moved back east. The "Great Die-Up" from the blizzard effectively concluded the romantic period of the great Plains cattle drives.
Schoolhouse Blizzard of 1888 North American Great Plains. January 12–13, 1888. What made the storm so deadly was the timing (during work and school hours), the suddenness, and the brief spell of warmer weather that preceded it. In addition, the very strong wind fields behind the cold front and the powdery nature of the snow reduced visibilities on the open plains to zero. People ventured from the safety of their homes to do chores, go to town, attend school, or simply enjoy the relative warmth of the day. As a result, thousands of people—including many schoolchildren—got caught in the blizzard.
Great Blizzard of March 1888 March 11–14, 1888. One of the most severe recorded blizzards in the history of the United States. On March 12, an unexpected northeaster hit New England and the mid-Atlantic, dropping up to of snow in the space of three days. New York City experienced its heaviest snowfall recorded to date at that time, all street railcars were stranded, and the storm led to the creation of the NYC subway system. Snowdrifts reached up to the second story of some buildings. Some 400 people died from this blizzard, including many sailors aboard vessels that were beset by gale-force winds and turbulent seas. | Blizzard | Wikipedia | 406 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
Great Blizzard of 1899 February 11–14, 1899. An extremely unusual blizzard in that it reached into the far southern states of the US. It hit in February, and the area around Washington, D.C., experienced 51 hours straight of snowfall. The port of New Orleans was totally iced over; revelers participating in the New Orleans Mardi Gras had to wait for the parade routes to be shoveled free of snow. Concurrent with this blizzard was the extremely cold arctic air. Many city and state record low temperatures date back to this event, including all-time records for locations in the Midwest and South. State record lows: Nebraska reached , Ohio experienced , Louisiana bottomed out at , and Florida dipped below zero to . | Blizzard | Wikipedia | 149 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
1901 to 1939
Great Lakes Storm of 1913 November 7–10, 1913. "The White Hurricane" of 1913 was the deadliest and most destructive natural disaster ever to hit the Great Lakes Basin in the Midwestern United States and the Canadian province of Ontario. It produced wind gusts, waves over high, and whiteout snowsqualls. It killed more than 250 people, destroyed 19 ships, and stranded 19 others.
Blizzard of 1918. January 11, 1918. Vast blizzard-like storm moved through Great Lakes and Ohio Valley.
1920 North Dakota blizzard March 15–18, 1920
Knickerbocker Storm January 27–28, 1922 | Blizzard | Wikipedia | 129 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
1940 to 1949
Armistice Day Blizzard of 1940 November 10–12, 1940. Took place in the Midwest region of the United States on Armistice Day. This "Panhandle hook" winter storm cut a through the middle of the country from Kansas to Michigan. The morning of the storm was unseasonably warm but by mid afternoon conditions quickly deteriorated into a raging blizzard that would last into the next day. A total of 145 deaths were blamed on the storm, almost a third of them duck hunters who had taken time off to take advantage of the ideal hunting conditions. Weather forecasters had not predicted the severity of the oncoming storm, and as a result the hunters were not dressed for cold weather. When the storm began many hunters took shelter on small islands in the Mississippi River, and the winds and waves overcame their encampments. Some became stranded on the islands and then froze to death in the single-digit temperatures that moved in over night. Others tried to make it to shore and drowned.
North American blizzard of 1947 December 25–26, 1947. Was a record-breaking snowfall that began on Christmas Day and brought the Northeast United States to a standstill. Central Park in New York City got of snowfall in 24 hours with deeper snows in suburbs. It was not accompanied by high winds, but the snow fell steadily with drifts reaching . Seventy-seven deaths were attributed to the blizzard. | Blizzard | Wikipedia | 281 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
The Blizzard of 1949 - The first blizzard started on Sunday, January 2, 1949; it lasted for three days. It was followed by two more months of blizzard after blizzard with high winds and bitter cold. Deep drifts isolated southeast Wyoming, northern Colorado, western South Dakota and western Nebraska, for weeks. Railroad tracks and roads were all drifted in with drifts of and more. Hundreds of people that had been traveling on trains were stranded. Motorists that had set out on January 2 found their way to private farm homes in rural areas and hotels and other buildings in towns; some dwellings were so crowded that there wasn't enough room for all to sleep at once. It would be weeks before they were plowed out. The Federal government quickly responded with aid, airlifting food and hay for livestock. The total rescue effort involved numerous volunteers and local agencies plus at least ten major state and federal agencies from the U.S. Army to the National Park Service. Private businesses, including railroad and oil companies, also lent manpower and heavy equipment to the work of plowing out. The official death toll was 76 people and one million livestock. Youtube video Storm of the Century - the Blizzard of '49 Storm of the Century - the Blizzard of '49 | Blizzard | Wikipedia | 250 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
1950 to 1959
Great Appalachian Storm of November 1950 November 24–30, 1950
March 1958 Nor'easter blizzard March 18–21, 1958.
The Mount Shasta California Snowstorm of 1959 – The storm dumped of snow on Mount Shasta. The bulk of the snow fell on unpopulated mountainous areas, barely disrupting the residents of the Mount Shasta area. The amount of snow recorded is the largest snowfall from a single storm in North America.
1960 to 1969
March 1960 Nor'easter blizzard March 2–5, 1960
December 1960 Nor'easter blizzard December 12–14, 1960. Wind gusts up to .
March 1962 Nor'easter Great March Storm of 1962 – Ash Wednesday. North Carolina and Virginia blizzards. Struck during Spring high tide season and remained mostly stationary for almost 5 days causing significant damage along eastern coast, Assateague island was under water, and dumped of snow in Virginia.
North American blizzard of 1966 January 27–31, 1966
Chicago Blizzard of 1967 January 26–27, 1967
February 1969 nor'easter February 8–10, 1969
March 1969 Nor'easter blizzard March 9, 1969
December 1969 Nor'easter blizzard December 25–28, 1969.
1970 to 1979
The Great Storm of 1975 known as the "Super Bowl Blizzard" or "Minnesota's Storm of the Century". January 9–12, 1975. Wind chills of to recorded, deep snowfalls.
Groundhog Day gale of 1976 February 2, 1976
Buffalo Blizzard of 1977 January 28 – February 1, 1977. There were several feet of packed snow already on the ground, and the blizzard brought with it enough snow to reach Buffalo's record for the most snow in one season – .
Great Blizzard of 1978 also called the "Cleveland Superbomb". January 25–27, 1978. Was one of the worst snowstorms the Midwest has ever seen. Wind gusts approached , causing snowdrifts to reach heights of in some areas, making roadways impassable. Storm reached maximum intensity over southern Ontario Canada.
Northeastern United States Blizzard of 1978 – February 6–7, 1978. Just one week following the Cleveland Superbomb blizzard, New England was hit with its most severe blizzard in 90 years since 1888.
Chicago Blizzard of 1979 January 13–14, 1979
1980 to 1989
February 1987 Nor'easter blizzard February 22–24, 1987 | Blizzard | Wikipedia | 473 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
1990 to 1999
1991 Halloween blizzard Upper Mid-West US, October 31 – November 3, 1991
December 1992 Nor'easter blizzard December 10–12, 1992
1993 Storm of the Century March 12–15, 1993. While the southern and eastern U.S. and Cuba received the brunt of this massive blizzard, the Storm of the Century impacted a wider area than any in recorded history.
February 1995 Nor'easter blizzard February 3–6, 1995
Blizzard of 1996 January 6–10, 1996
April Fool's Day Blizzard March 31 – April 1, 1997. US East Coast
1997 Western Plains winter storms October 24–26, 1997
Mid West Blizzard of 1999 January 2–4, 1999
2000 to 2009
January 25, 2000 Southeastern United States winter storm January 25, 2000. North Carolina and Virginia
December 2000 Nor'easter blizzard December 27–31, 2000
North American blizzard of 2003 February 14–19, 2003 (Presidents' Day Storm II)
December 2003 Nor'easter blizzard December 6–7, 2003
North American blizzard of 2005 January 20–23, 2005
North American blizzard of 2006 February 11–13, 2006
Early winter 2006 North American storm complex Late November 2006
Colorado Holiday Blizzards (2006–07) December 20–29, 2006 Colorado
February 2007 North America blizzard February 12–20, 2007
January 2008 North American storm complex January, 2008 West Coast US
North American blizzard of 2008 March 6–10, 2008
2009 Midwest Blizzard 6–8 December 2009, a bomb cyclogenesis event that also affected parts of Canada
North American blizzard of 2009 December 16–20, 2009
2009 North American Christmas blizzard December 22–28, 2009 | Blizzard | Wikipedia | 327 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
2010 to 2019
February 5–6, 2010 North American blizzard February 5–6, 2010 Referred to at the time as Snowmageddon was a Category 3 ("major") nor'easter and severe weather event.
February 9–10, 2010 North American blizzard February 9–10, 2010
February 25–27, 2010 North American blizzard February 25–27, 2010
October 2010 North American storm complex October 23–28, 2010
December 2010 North American blizzard December 26–29, 2010
January 31 – February 2, 2011 North American blizzard January 31 – February 2, 2011. Groundhog Day Blizzard of 2011
2011 Halloween nor'easter October 28 – Nov 1, 2011
Hurricane Sandy October 29–31, 2012. West Virginia, western North Carolina, and southwest Pennsylvania received heavy snowfall and blizzard conditions from this hurricane
November 2012 nor'easter November 7–10, 2012
December 17–22, 2012 North American blizzard December 17–22, 2012
Late December 2012 North American storm complex December 25–28, 2012
February 2013 nor'easter February 7–20, 2013
February 2013 Great Plains blizzard February 19 – March 6, 2013
March 2013 nor'easter March 6, 2013
October 2013 North American storm complex October 3–5, 2013
Buffalo, NY blizzard of 2014. Buffalo got over of snow during November 18–20, 2014.
January 2015 North American blizzard January 26–27, 2015
Late December 2015 North American storm complex December 26–27, 2015 Was one of the most notorious blizzards in the state of New Mexico and West Texas ever reported. It had sustained winds of over and continuous snow precipitation that lasted over 30 hours. Dozens of vehicles were stranded in small county roads in the areas of Hobbs, Roswell, and Carlsbad New Mexico. Strong sustained winds destroyed various mobile homes.
January 2016 United States blizzard January 20–23, 2016
February 2016 North American storm complex February 1–8, 2016
February 2017 North American blizzard February 6–11, 2017
March 2017 North American blizzard March 9–16, 2017
Early January 2018 nor’easter January 3–6, 2018
March 2019 North American blizzard March 8–16, 2019
April 2019 North American blizzard April 10–14, 2019 | Blizzard | Wikipedia | 437 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
2020 to present
December 5–6, 2020 nor'easter December 5–6, 2020
January 31 – February 3, 2021 nor'easter January 31 – February 3, 2021
February 13–17, 2021 North American winter storm February 13–17, 2021
March 2021 North American blizzard March 11–14, 2021
January 2022 North American blizzard January 27–30, 2022
December 2022 North American winter storm December 21–26, 2022
March 2023 North American winter storm March 12–15, 2023
January 8–10, 2024 North American storm complex January 8–10, 2024
January 10–13, 2024 North American storm complex January 10–13, 2024
January 5–6, 2025 United States blizzard January 5–6, 2025
January 20–22, 2025 Gulf Coast blizzard January 20–22, 2025
Canada
The Eastern Canadian Blizzard of 1971 – Dumped a foot and a half (45.7 cm) of snow on Montreal and more than elsewhere in the region. The blizzard caused the cancellation of a Montreal Canadiens hockey game for the first time since 1918.
Saskatchewan blizzard of 2007 – January 10, 2007, Canada
United Kingdom
Great Frost of 1709
Blizzard of January 1881
Winter of 1894–95 in the United Kingdom
Winter of 1946–1947 in the United Kingdom
Winter of 1962–1963 in the United Kingdom
January 1987 Southeast England snowfall
Winter of 1990–91 in Western Europe
February 2009 Great Britain and Ireland snowfall
Winter of 2009–10 in Great Britain and Ireland
Winter of 2010–11 in Great Britain and Ireland
Early 2012 European cold wave
Other locations
1954 Romanian blizzard
1972 Iran blizzard
Winter of 1990–1991 in Western Europe
July 2007 Argentine winter storm
2008 Afghanistan blizzard
2008 Chinese winter storms
Winter storms of 2009–2010 in East Asia | Blizzard | Wikipedia | 353 | 4548 | https://en.wikipedia.org/wiki/Blizzard | Physical sciences | Storms | null |
A bison (: bison) is a large bovine in the genus Bison (Greek: "wild ox" (bison)) within the tribe Bovini. Two extant and numerous extinct species are recognised.
Of the two surviving species, the American bison, B. bison, found only in North America, is the more numerous. Although colloquially referred to as a buffalo in the United States and Canada, it is only distantly related to the true buffalo. The North American species is composed of two subspecies, the Plains bison, B. b. bison, and the wood bison, B. b. athabascae, which is the namesake of Wood Buffalo National Park in Canada. A third subspecies, the eastern bison (B. b. pennsylvanicus) is no longer considered a valid taxon, being a junior synonym of B. b. bison. | Bison | Wikipedia | 176 | 4583 | https://en.wikipedia.org/wiki/Bison | Biology and health sciences | Bovidae | Animals |
In particle physics, a baryon is a type of composite subatomic particle that contains an odd number of valence quarks, conventionally three. Protons and neutrons are examples of baryons; because baryons are composed of quarks, they belong to the hadron family of particles. Baryons are also classified as fermions because they have half-integer spin.
The name "baryon", introduced by Abraham Pais, comes from the Greek word for "heavy" (βαρύς, barýs), because, at the time of their naming, most known elementary particles had lower masses than the baryons. Each baryon has a corresponding antiparticle (antibaryon) where their corresponding antiquarks replace quarks. For example, a proton is made of two up quarks and one down quark; and its corresponding antiparticle, the antiproton, is made of two up antiquarks and one down antiquark.
Baryons participate in the residual strong force, which is mediated by particles known as mesons. The most familiar baryons are protons and neutrons, both of which contain three quarks, and for this reason they are sometimes called triquarks. These particles make up most of the mass of the visible matter in the universe and compose the nucleus of every atom (electrons, the other major component of the atom, are members of a different family of particles called leptons; leptons do not interact via the strong force). Exotic baryons containing five quarks, called pentaquarks, have also been discovered and studied.
A census of the Universe's baryons indicates that 10% of them could be found inside galaxies, 50 to 60% in the circumgalactic medium, and the remaining 30 to 40% could be located in the warm–hot intergalactic medium (WHIM).
Background
Baryons are strongly interacting fermions; that is, they are acted on by the strong nuclear force and are described by Fermi–Dirac statistics, which apply to all particles obeying the Pauli exclusion principle. This is in contrast to the bosons, which do not obey the exclusion principle. | Baryon | Wikipedia | 469 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
Baryons, alongside mesons, are hadrons, composite particles composed of quarks. Quarks have baryon numbers of B = and antiquarks have baryon numbers of B = −. The term "baryon" usually refers to triquarks—baryons made of three quarks (B = + + = 1).
Other exotic baryons have been proposed, such as pentaquarks—baryons made of four quarks and one antiquark (B = + + + − = 1), but their existence is not generally accepted. The particle physics community as a whole did not view their existence as likely in 2006, and in 2008, considered evidence to be overwhelmingly against the existence of the reported pentaquarks. However, in July 2015, the LHCb experiment observed two resonances consistent with pentaquark states in the Λ → J/ψKp decay, with a combined statistical significance of 15σ.
In theory, heptaquarks (5 quarks, 2 antiquarks), nonaquarks (6 quarks, 3 antiquarks), etc. could also exist.
Baryonic matter
Nearly all matter that may be encountered or experienced in everyday life is baryonic matter, which includes atoms of any sort, and provides them with the property of mass. Non-baryonic matter, as implied by the name, is any sort of matter that is not composed primarily of baryons. This might include neutrinos and free electrons, dark matter, supersymmetric particles, axions, and black holes.
The very existence of baryons is also a significant issue in cosmology because it is assumed that the Big Bang produced a state with equal amounts of baryons and antibaryons. The process by which baryons came to outnumber their antiparticles is called baryogenesis.
Baryogenesis | Baryon | Wikipedia | 402 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
Experiments are consistent with the number of quarks in the universe being conserved alongside the total baryon number, with antibaryons being counted as negative quantities. Within the prevailing Standard Model of particle physics, the number of baryons may change in multiples of three due to the action of sphalerons, although this is rare and has not been observed under experiment. Some grand unified theories of particle physics also predict that a single proton can decay, changing the baryon number by one; however, this has not yet been observed under experiment. The excess of baryons over antibaryons in the present universe is thought to be due to non-conservation of baryon number in the very early universe, though this is not well understood.
Properties
Isospin and charge
The concept of isospin was first proposed by Werner Heisenberg in 1932 to explain the similarities between protons and neutrons under the strong interaction. Although they had different electric charges, their masses were so similar that physicists believed they were the same particle. The different electric charges were explained as being the result of some unknown excitation similar to spin. This unknown excitation was later dubbed isospin by Eugene Wigner in 1937.
This belief lasted until Murray Gell-Mann proposed the quark model in 1964 (containing originally only the u, d, and s quarks). The success of the isospin model is now understood to be the result of the similar masses of u and d quarks. Since u and d quarks have similar masses, particles made of the same number then also have similar masses. The exact specific u and d quark composition determines the charge, as u quarks carry charge + while d quarks carry charge −. For example, the four Deltas all have different charges ( (uuu), (uud), (udd), (ddd)), but have similar masses (~1,232 MeV/c2) as they are each made of a combination of three u or d quarks. Under the isospin model, they were considered to be a single particle in different charged states. | Baryon | Wikipedia | 446 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
The mathematics of isospin was modeled after that of spin. Isospin projections varied in increments of 1 just like those of spin, and to each projection was associated a "charged state". Since the "Delta particle" had four "charged states", it was said to be of isospin I = . Its "charged states" , , , and , corresponded to the isospin projections I3 = +, I3 = +, I3 = −, and I3 = −, respectively. Another example is the "nucleon particle". As there were two nucleon "charged states", it was said to be of isospin . The positive nucleon (proton) was identified with I3 = + and the neutral nucleon (neutron) with I3 = −. It was later noted that the isospin projections were related to the up and down quark content of particles by the relation:
where the n'''s are the number of up and down quarks and antiquarks.
In the "isospin picture", the four Deltas and the two nucleons were thought to be the different states of two particles. However, in the quark model, Deltas are different states of nucleons (the N++ or N− are forbidden by Pauli's exclusion principle). Isospin, although conveying an inaccurate picture of things, is still used to classify baryons, leading to unnatural and often confusing nomenclature.
Flavour quantum numbers | Baryon | Wikipedia | 317 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
The strangeness flavour quantum number S (not to be confused with spin) was noticed to go up and down along with particle mass. The higher the mass, the lower the strangeness (the more s quarks). Particles could be described with isospin projections (related to charge) and strangeness (mass) (see the uds octet and decuplet figures on the right). As other quarks were discovered, new quantum numbers were made to have similar description of udc and udb octets and decuplets. Since only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers works well only for octet and decuplet made of one u, one d, and one other quark, and breaks down for the other octets and decuplets (for example, ucb octet and decuplet). If the quarks all had the same mass, their behaviour would be called symmetric, as they would all behave in the same way to the strong interaction. Since quarks do not have the same mass, they do not interact in the same way (exactly like an electron placed in an electric field will accelerate more than a proton placed in the same field because of its lighter mass), and the symmetry is said to be broken.
It was noted that charge (Q) was related to the isospin projection (I3), the baryon number (B) and flavour quantum numbers (S, C, B′, T) by the Gell-Mann–Nishijima formula:
where S, C, B′, and T represent the strangeness, charm, bottomness and topness flavour quantum numbers, respectively. They are related to the number of strange, charm, bottom, and top quarks and antiquark according to the relations:
meaning that the Gell-Mann–Nishijima formula is equivalent to the expression of charge in terms of quark content:
Spin, orbital angular momentum, and total angular momentum | Baryon | Wikipedia | 423 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
Spin (quantum number S) is a vector quantity that represents the "intrinsic" angular momentum of a particle. It comes in increments of ħ (pronounced "h-bar"). The ħ is often dropped because it is the "fundamental" unit of spin, and it is implied that "spin 1" means "spin 1 ħ". In some systems of natural units, ħ is chosen to be 1, and therefore does not appear anywhere.
Quarks are fermionic particles of spin (S = ). Because spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length , and has two spin projections (Sz = + and Sz = −). Two quarks can have their spins aligned, in which case the two spin vectors add to make a vector of length S = 1 and three spin projections (Sz = +1, Sz = 0, and Sz = −1). If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and has only one spin projection (Sz = 0), etc. Since baryons are made of three quarks, their spin vectors can add to make a vector of length S = , which has four spin projections (Sz = +, Sz = +, Sz = −, and Sz = −), or a vector of length S = with two spin projections (Sz = +, and Sz = −).
There is another quantity of angular momentum, called the orbital angular momentum (azimuthal quantum number L), that comes in increments of 1 ħ, which represent the angular moment due to quarks orbiting around each other. The total angular momentum (total angular momentum quantum number J) of a particle is therefore the combination of intrinsic angular momentum (spin) and orbital angular momentum. It can take any value from to , in increments of 1. | Baryon | Wikipedia | 415 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
Particle physicists are most interested in baryons with no orbital angular momentum (L = 0), as they correspond to ground states—states of minimal energy. Therefore, the two groups of baryons most studied are the S = ; L = 0 and S = ; L = 0, which corresponds to J = + and J = +, respectively, although they are not the only ones. It is also possible to obtain J = + particles from S = and L = 2, as well as S = and L = 2. This phenomenon of having multiple particles in the same total angular momentum configuration is called degeneracy. How to distinguish between these degenerate baryons is an active area of research in baryon spectroscopy.D.M. Manley (2005)
Parity
If the universe were reflected in a mirror, most of the laws of physics would be identical—things would behave the same way regardless of what we call "left" and what we call "right". This concept of mirror reflection is called "intrinsic parity" or simply "parity" (P). Gravity, the electromagnetic force, and the strong interaction all behave in the same way regardless of whether or not the universe is reflected in a mirror, and thus are said to conserve parity (P-symmetry). However, the weak interaction does distinguish "left" from "right", a phenomenon called parity violation (P-violation).
Based on this, if the wavefunction for each particle (in more precise terms, the quantum field for each particle type) were simultaneously mirror-reversed, then the new set of wavefunctions would perfectly satisfy the laws of physics (apart from the weak interaction). It turns out that this is not quite true: for the equations to be satisfied, the wavefunctions of certain types of particles have to be multiplied by −1, in addition to being mirror-reversed. Such particle types are said to have negative or odd parity (P = −1, or alternatively P = –), while the other particles are said to have positive or even parity (P = +1, or alternatively P = +).
For baryons, the parity is related to the orbital angular momentum by the relation:
As a consequence, baryons with no orbital angular momentum (L = 0) all have even parity (P = +). | Baryon | Wikipedia | 492 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
Nomenclature
Baryons are classified into groups according to their isospin (I) values and quark (q) content. There are six groups of baryons: nucleon (), Delta (), Lambda (), Sigma (), Xi (), and Omega (). The rules for classification are defined by the Particle Data Group. These rules consider the up (), down () and strange () quarks to be light and the charm (), bottom (), and top () quarks to be heavy. The rules cover all the particles that can be made from three of each of the six quarks, even though baryons made of top quarks are not expected to exist because of the top quark's short lifetime. The rules do not cover pentaquarks.
Baryons with (any combination of) three and/or quarks are s (I = ) or baryons (I = ).
Baryons containing two and/or quarks are baryons (I = 0) or baryons (I = 1). If the third quark is heavy, its identity is given by a subscript.
Baryons containing one or quark are baryons (I = ). One or two subscripts are used if one or both of the remaining quarks are heavy.
Baryons containing no or quarks are baryons (I = 0), and subscripts indicate any heavy quark content.
Baryons that decay strongly have their masses as part of their names. For example, Σ0 does not decay strongly, but Δ++(1232) does.
It is also a widespread (but not universal) practice to follow some additional rules when distinguishing between some states that would otherwise have the same symbol.
Baryons in total angular momentum J = configuration that have the same symbols as their J = counterparts are denoted by an asterisk ( * ).
Two baryons can be made of three different quarks in J = configuration. In this case, a prime ( ′ ) is used to distinguish between them.
Exception: When two of the three quarks are one up and one down quark, one baryon is dubbed Λ while the other is dubbed Σ. | Baryon | Wikipedia | 481 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
Quarks carry a charge, so knowing the charge of a particle indirectly gives the quark content. For example, the rules above say that a contains a c quark and some combination of two u and/or d quarks. The c quark has a charge of (Q = +), therefore the other two must be a u quark (Q = +), and a d quark (Q = −) to have the correct total charge (Q'' = +1). | Baryon | Wikipedia | 104 | 4584 | https://en.wikipedia.org/wiki/Baryon | Physical sciences | Fermions | null |
In cryptography, a block cipher is a deterministic algorithm that operates on fixed-length groups of bits, called blocks. Block ciphers are the elementary building blocks of many cryptographic protocols. They are ubiquitous in the storage and exchange of data, where such data is secured and authenticated via encryption.
A block cipher uses blocks as an unvarying transformation. Even a secure block cipher is suitable for the encryption of only a single block of data at a time, using a fixed key. A multitude of modes of operation have been designed to allow their repeated use in a secure way to achieve the security goals of confidentiality and authenticity. However, block ciphers may also feature as building blocks in other cryptographic protocols, such as universal hash functions and pseudorandom number generators.
Definition
A block cipher consists of two paired algorithms, one for encryption, , and the other for decryption, . Both algorithms accept two inputs: an input block of size bits and a key of size bits; and both yield an -bit output block. The decryption algorithm is defined to be the inverse function of encryption, i.e., . More formally, a block cipher is specified by an encryption function
which takes as input a key , of bit length (called the key size), and a bit string , of length (called the block size), and returns a string of bits. is called the plaintext, and is termed the ciphertext. For each , the function () is required to be an invertible mapping on . The inverse for is defined as a function
taking a key and a ciphertext to return a plaintext value , such that
For example, a block cipher encryption algorithm might take a 128-bit block of plaintext as input, and output a corresponding 128-bit block of ciphertext. The exact transformation is controlled using a second input – the secret key. Decryption is similar: the decryption algorithm takes, in this example, a 128-bit block of ciphertext together with the secret key, and yields the original 128-bit block of plain text.
For each key K, EK is a permutation (a bijective mapping) over the set of input blocks. Each key selects one permutation from the set of possible permutations. | Block cipher | Wikipedia | 467 | 4594 | https://en.wikipedia.org/wiki/Block%20cipher | Technology | Computer security | null |
History
The modern design of block ciphers is based on the concept of an iterated product cipher. In his seminal 1949 publication, Communication Theory of Secrecy Systems, Claude Shannon analyzed product ciphers and suggested them as a means of effectively improving security by combining simple operations such as substitutions and permutations. Iterated product ciphers carry out encryption in multiple rounds, each of which uses a different subkey derived from the original key. One widespread implementation of such ciphers named a Feistel network after Horst Feistel is notably implemented in the DES cipher. Many other realizations of block ciphers, such as the AES, are classified as substitution–permutation networks.
The root of all cryptographic block formats used within the Payment Card Industry Data Security Standard (PCI DSS) and American National Standards Institute (ANSI) standards lies with the Atalla Key Block (AKB), which was a key innovation of the Atalla Box, the first hardware security module (HSM). It was developed in 1972 by Mohamed M. Atalla, founder of Atalla Corporation (now Utimaco Atalla), and released in 1973. The AKB was a key block, which is required to securely interchange symmetric keys or PINs with other actors in the banking industry. This secure interchange is performed using the AKB format. The Atalla Box protected over 90% of all ATM networks in operation as of 1998, and Atalla products still secure the majority of the world's ATM transactions as of 2014.
The publication of the DES cipher by the United States National Bureau of Standards (subsequently the U.S. National Institute of Standards and Technology, NIST) in 1977 was fundamental in the public understanding of modern block cipher design. It also influenced the academic development of cryptanalytic attacks. Both differential and linear cryptanalysis arose out of studies on DES design. , there is a palette of attack techniques against which a block cipher must be secure, in addition to being robust against brute-force attacks.
Design
Iterated block ciphers
Most block cipher algorithms are classified as iterated block ciphers which means that they transform fixed-size blocks of plaintext into identically sized blocks of ciphertext, via the repeated application of an invertible transformation known as the round function, with each iteration referred to as a round.
Usually, the round function R takes different round keys Ki as a second input, which is derived from the original key: | Block cipher | Wikipedia | 496 | 4594 | https://en.wikipedia.org/wiki/Block%20cipher | Technology | Computer security | null |
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