question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>That's how it's framed in my Physics school-book.</p>
<p>The question (or rather, the explanation) is that of the thrust of rockets and how the impulse is equal (with opposite signs) on the thrust-gases and the rocket itself.</p>
<p>$( m \frac { \Delta v}{ \Delta t} ) = -(v \frac {\Delta m}{ \Delta t} ) = F_i$ </p>
<p>I suppose it's a problem with how I see the transfer of impulse and exactly which part of the equation relates to which part of the physical world (gases, rocket). So we can start from there.</p>
<p><em><strong>Title equation:</em></strong></p>
<p>$F = \frac{ \Delta (mv)}{ \Delta t} = \left ( m \frac { \Delta v}{ \Delta t} \right) + \left ( v \frac { \Delta m}{ \Delta t} \right)$</p>
<p><em>Grade:</em> The equivalent of G-10 in the US.</p> | g12028 | [
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<p>Consider two identical heat pumps, for example, split-system air conditioners. There're two ways to make them work - in parallel or sequential. Parallel means that "hot" radiators of the machines are put outside the room, while the "cold" radiators are put inside the room. Sequential means that the cold radiator of the first machine is inside the room, while the hot radiator is put inside, say, a large isolated box, where it is cooled by the cold radiator of the second machine, and the hot radiator of the second machine is outside the room.</p>
<p>In which case - parallel or sequential - the efficiency of the cooling would be better?</p> | g12029 | [
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<p>I had a special relativity course at university. Now I'm trying to extract what new insight <a href="http://en.wikipedia.org/wiki/Mass-energy_equivalence" rel="nofollow">$E=mc^2$</a> did give us. I mean that moving mass has/is energy (kinetic) not new. The energy merely changed from classical kinetic energy to some relativistic form. And the offset with rest mass doesn't matter for energy.</p>
<p>I'm hoping for some in-depth answer.
Given a few hours I could probably recall physics myself, but I suppose someone will have a nicer, more fundamental answer :)</p> | g12030 | [
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<p>Suppose you have dynamics of a coherent state. The state presents a normal distribution of finding the particle. Does anyone know of any attempts to connect modern advances in the probability theory to quantum dynamics of a coherent state.</p> | g12031 | [
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<p>There are many free fermion systems that possess topological edge/boundary states. Examples include quantum Hall insulators and topological insulators. No matter chiral or non-chiral, 2D or 3D, symmetry protected or not, their microscopic origins are similar. Explicitly speaking, when placing such a system on a geometry with open boundary in one spacial dimension (say the $x$-axis), and closed boundary in other spacial dimensions, the bulk model Hamiltonian is always reduced to one or several copies of the following 1D Hamiltonian along the open-boundary $x$-axis direction (see <a href="http://prl.aps.org/abstract/PRL/v101/i24/e246807">B. Zhou et al.,PRL 101, 246807</a>)
$$H_\text{1D}=-i\partial_x\sigma_1+k_\perp\sigma_2+(m-\partial_x^2+k_\perp^2)\sigma_3,$$
where $\sigma_{1,2,3}$ are the three Pauli matrices, and $k_\perp$ denotes the momentum perpendicular to $x$-axis (and could be extended to a matrix in higher dimensions). The existence of the topological edge state is equivalent to the existence of edge modes of $H_\text{1D}$ on an open chain.</p>
<p>It was claimed that the edge modes exist when $m<0$. After discretize and diagonalize $H_\text{1D}$, I was able to check the above statement. But my question is that whether there is a simple mathematical argument that allows one to judge the existence of the edge mode by looking at the differential operator $H_\text{1D}$ without really solving it? I believe there should be a reason if the edge mode is robust.</p>
<p>PS: I am aware of but not satisfied with the topological argument that the bulk band has non-trivial topology, which can not be altered without closing the bulk gap, thus there must be edge states on the boundary. Is it possible to argue from the property of $H_\text{1D}$ without directly referring to the bulk topology?</p> | g12032 | [
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0.03198116272687912,
... |
<p>Is double well potential related to Maxican hat potential?
I have found on Quantum Field Theory in a Nutshell
by A. Zee</p>
<p>He wrote the double well potential as : $V (φ) = (λ/4)(φ^ 2 − v^2)^2$.
Can anyone give me an argument for writing the equation like that.</p> | g12033 | [
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<p>Let's temporarily ignore spin. If 3 denotes the standard representation of SU(3), 1 the trivial rep, 8 the adjoint rep and 10 the symmetric cube then it's well-known that</p>
<p>3 x 3 x 3 = 1 + 8 + 8 + 10</p>
<p>Interpreting the 3's as the space of up/down/strange flavour states for a quark, the tensor cube is interpreted as the space of baryon states that can be obtained by combining three light quarks. Obviously spin matters, but at least this should give a classification of baryons modulo spin into SU(3)-multiplets.</p>
<p><strong>There are two octets here, but in the literature I have only seen one of them described. What is the second octet?</strong></p>
<p>I appreciate that the answer may be "it's more complicated than that".</p> | g12034 | [
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<p>E.g. in exploding nuclear bomb or some other big explosions.</p>
<p>I mean if the speed of electrons as waves/particles is a constant or changes according to other "forces" involved?</p> | g12035 | [
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<p>I found this on <a href="https://en.wikipedia.org/wiki/Black_body" rel="nofollow">Wikipedia article on black bodies</a>:</p>
<blockquote>
<p>A black body in thermal equilibrium (that is, at a constant
temperature) emits electromagnetic radiation called black-body
radiation. The radiation is emitted according to Planck's law, meaning
that it has a spectrum that is determined by the temperature alone
(see figure at right), not by the body's shape or composition.</p>
</blockquote>
<p>Now I'm a bit confused. Isn't the black body radiation given by $\frac{P}{A}=\sigma T^4$</p>
<p>So it doesn't depend on body color, composition or anything else than its size.
Shouldn't the radiation be the same for all bodies, but we use the black body because its a convenient model because all of its radiation comes from emission and not reflection or anything else?</p> | g12036 | [
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<p>I've done basic or introductory mechanics at the level of Resnick and Halliday. I'm currently studying calculus of variations and the Lagrangian formulation of mechanics on my own. I read somewhere that an understanding of classical mechanics is necessary for appreciating quantum mechanics. Can someone please give me the big picture, where I can see the connections between classical and quantum mechanics? (I am fairly new to quantum mechanics).</p>
<p>Is it the case that the Lagrangian and Hamiltonian formulations are what one uses, primarily, in quantum mechanics?</p> | g12037 | [
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<p>By definition scalar fields are independent of coordinate system, thus I would expect a scalar field $\psi [x]$ would not change under the transformation $x^\mu \to x^\mu + \epsilon^\mu $. Correct?</p>
<p>Now when I look in the book "Introduction to QFT" by Peskin and Schroeder they state (in an example) that the scalar field $\psi[x]$ under an infinitesimal coordinate transformation $x^\mu \to x^\mu -a^\mu$ transforms as $\psi[x] \to \psi[x+a] = \psi[x] +a^\mu\partial_\mu\psi[x]$.</p>
<p>One possible solution I thought was that a scalar field $f:M\to\mathcal{R}$ from a variety (in this case spacetime) is invariant under coordinate transformations, but that the coordinate representation $\psi[x]$ does change under coordinate transformations (obviously).</p>
<p>Is this anywhere near correct?</p> | g12038 | [
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<p>I'm trying to calculate the Integrated Water Vapor (IWV) using GPS data.</p>
<p>I'm following the equations in the following publication: </p>
<blockquote>
<p>GPS Meteorology: Remote Sensing of Atmospheric Water Vapor Using
the Global Positioning System, MICHAEL BEVIS et al. 1992. <a href="http://nldr.library.ucar.edu/repository/assets/osgc/OSGC-000-000-001-090.pdf" rel="nofollow">link</a></p>
</blockquote>
<p>which are the same equations of <a href="http://www.csr.utexas.edu/texas_pwv/midterm/gabor/gpsground.html" rel="nofollow">this website</a>.</p>
<p>The problem that I'm having is that I'm obtaing a IWV of an order of magnitude different than I should.</p>
<p>Where's the gps data that I'm using:</p>
<pre><code>latitude=-3.09589*pi/180; % degrees to radians
height=85.8/1000; % converting to km
temperature=28.7 + 273.15; % celsius to Kelvin
ztd=2583.3; % mm
pressure=995.9; % mbar
</code></pre>
<p>The constants that I'm using:</p>
<p>$Rv=461.5$</p>
<p>$k_2'=17$</p>
<p>$k_3=3.776 \mbox{ x } 10^5$</p>
<p>And the calculations that I'm doing:</p>
<p>$zhd=(2.2768pressure) / (1-0.00265cos(2latitude)-0.000285height)$</p>
<p>$zwd=ztd-zhd$</p>
<p>$tm=0.72temperature + 70.2$</p>
<p>$\pi=1/(10^{-6}(k_3/tm+k_2')Rv)$</p>
<p>$iwv=\pi .zwd$</p>
<p>I'm obtaing as result a $iwv$ of <strong>504.5616</strong> $kg/m^{2}$ when accordingly with (BEVIS,92) results (looking at fig. 1) I should obtain something like <strong>50.45616</strong> $kg/m^{2}$.</p>
<p>Can you help me to find where this problem of magnitude comes from?</p>
<p>P.S. If you need more information feel free to ask me.</p> | g12039 | [
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<p>This question is because something made me confused. I always thought that the idea behind electrodynamics was to postulate some things, like <a href="http://en.wikipedia.org/wiki/Coulomb%27s_law" rel="nofollow">Coulomb's law</a> in electrostatics and so on, and then manipulate those things to derive <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations" rel="nofollow">Maxwell's Equations</a>. After that we could then use Maxwell's Equations at will.</p>
<p>Now, I'm confused because I've seen people assuming the equations. Namely saying that the electromagnetic field is a pair of vector fields $(E,B)$ such that $E$ and $B$ satisfies Maxwell's equations. Then with this the consequences are derived. But this seems strange to me: if you start by Maxwell's Equations, is because you already know them, but to know them, you needed to start by assuming other things, instead of the equations themselves!</p>
<p>My thought was: historically we start really with Coulomb's law and so on, and then we find out that there's a system of $4$ differential equations that completely specify the magnetic and electric field. Then since we found this out, practically speaking, we simply forget about the rest and restart from these equations. Now, why do we do this? Why do we start from the equations rather than deriving them?</p> | g12040 | [
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<p>I'm trying to figure out the density (g/cm^3) of La2CuO4. I know that the mass is 405.355 g/mol; what do I have to do to calculate the volume? Thanks!</p> | g12041 | [
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<p>Lets imagine an electromagnetic wave is vertically polarized. If you ignore the magnetic component, the electric field lines would point upwards from the ground or downwards in a cyclical way and of course vary in field strength.</p>
<p>Now lets say you attach a battery to two metal plates and you produce an electric field having an horizontal polarization/direction.</p>
<p>Does the presence of an electromagnetic wave "modulate" the horizontally orientated electric field, in terms of it's strength and direction?</p> | g12042 | [
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<p>I have often read that the generators for $\mathrm{SU(N)}$ gauge theories must be $N \times N$ matrices; see for instance these notes at the top of page 3: <a href="http://www.staff.science.uu.nl/~wit00103/ftip/Ch12.pdf" rel="nofollow">http://www.staff.science.uu.nl/~wit00103/ftip/Ch12.pdf</a>. Why is this?</p>
<p>I don't think this is necessary from a mathematical point of view. For instance, for $\mathrm{SU(2)}$ we can consider the $2 \times 2$ generators:
\begin{equation}
\begin{array}{ccc}
\displaystyle J_{1/2}^1=\frac{1}{2}\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix} \; ,&
\displaystyle J_{1/2}^2=\frac{1}{2}\begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix} \; ,&
\displaystyle J_{1/2}^3=\frac{1}{2}\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}
\end{array}
\end{equation}
However, also the following $3 \times 3$ generators satisfy the Lie algebra:
\begin{equation}
\begin{array}{ccc}
\displaystyle J_{1}^1=\frac{1}{\sqrt{2}}\begin{pmatrix} 0 & 1 & 0\\ 1 & 0 & 1 \\ 0 & 1 & 0 \end{pmatrix} \; ,&
\displaystyle J_{1}^2=\frac{1}{\sqrt{2}}\begin{pmatrix} 0 & -i & 0 \\ i & 0 & -i \\ 0 & i & 0 \end{pmatrix} \; ,&
\displaystyle J_{1}^3=\begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & -1 \end{pmatrix}
\end{array}
\end{equation}</p> | g12043 | [
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<p>What's a good book (or other resource) for an advanced undergraduate/early graduate student to learn about <a href="http://en.wikipedia.org/wiki/Symmetry_%28physics%29" rel="nofollow">symmetry</a>, <a href="http://en.wikipedia.org/wiki/Conservation_law" rel="nofollow">conservation laws</a> and <a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether's theorems</a>?</p>
<p><a href="http://rads.stackoverflow.com/amzn/click/0801896940" rel="nofollow">Neuenschwander's book</a> has a <a href="http://www.amazon.com/review/R2MR5IQSI0VUNA/ref=cm_cr_dp_title?ie=UTF8&ASIN=0801896940&nodeID=283155&store=books" rel="nofollow">scary review</a> that makes me wary of it, but something like it would be great.</p> | g12044 | [
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<p>Take for example a slide of 3m tall. </p>
<p>Would an object (starting from rest) sliding down a gentle slope have a lower speed than a steep slope? (Note: Height of slide is the same,disregard friction.)</p>
<p>Why is this so?</p>
<p>What if the slide was a spiral one?</p> | g12045 | [
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<p>I want to ask about the workings of the <a href="http://en.wikipedia.org/wiki/Hall_effect" rel="nofollow">Hall effect</a>. Why do the electrons come to rest on the edge of the wire? The magnetic field pushes them up, and the electric field pushes them forward. Shouldn't they reach the top of of the conductor and then stop moving up but continue moving forward?</p>
<p>Why does the magnetic field stop them from continuing to flow? The magnetic force is up so why would it effect their velocity forwards?</p> | g12046 | [
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<p>I was reading about second-harmonic generation (SHG) crystals (or frequency-doubling crystals) used to produce green laser light from IR. </p>
<p>What low-level process in the crystal is actually driving the combination of two photons into one? I'm thinking of a process at the QED level (or at least motivating what happens at that level). The wikipedia entry on SHG doesn't really address this (it just mentions it's a non-linear phenomena..).</p>
<p>Or put another way - what's the simplest system possible (theoretically) that can show the phenomena even if at a very low efficiency?</p>
<p>Edit: A supplement to the question, is what entropy-related constraints are there on the incoming photons in these processes, in order to avoid for example turning heat into nicer higher-energy photons? </p> | g12047 | [
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<p><a href="http://physics.stackexchange.com/q/110692/">Here</a> there is the old problem.
I know from the old problem that the work $W_v$ that I need to make a rocket fast enough to reach the escape velocity is
$$W_v= G \frac{mM}{r}$$
therefore because $$W_v=F\cdot S = G \frac{mM}{r} \rightarrow F_v=\frac{W}{S}=G \frac{mM}{rS} $$
that is the force I need to make a rocket fast enough to reach the escape velocity <strong>BUT</strong><br>
<em>Do I also have to count the weight of the rocket?</em></p>
<p>If yes then the equation will be like this:
$$F_f=F_g - F_v= G \frac{mM}{r^2}-G \frac{mM}{rS}=G \frac{mM}{r}\biggl(\frac{1}{r} \cdot \frac{1}{S}\biggr) = G \frac{mM}{r}(rS)^{-1} $$</p> | g12048 | [
-0.008795511908829212,
0.04094401001930237,
-0.010043064132332802,
0.015825582668185234,
-0.014635997824370861,
-0.016287898644804955,
0.012400980107486248,
-0.034202683717012405,
-0.08922058343887329,
0.009051858447492123,
-0.05032768473029137,
0.03926056995987892,
0.013245864771306515,
0... |
<p>Like all my questions, I fear this will be very naive, because my physics background is very limited. Please bear with me. </p>
<p>I think of the electromagnetic field as a section of a vector bundle over spacetime, but I think nothing will be lost if we just treat it as a function $f:{\mathbb R}^4\rightarrow{\mathbb R}^6$. </p>
<p>Now suppose I want to send you a wireless message (by radio, cellphone, TV, whatever). I encode my message by jigglinig some electrons around so as to change the electromagnetic field from $f$ to a new function $f+g$. You are able to observe some values of this function $f+g$, or at least to infer something about some values of that function from the way the electrons in your receiver are jiggling around. </p>
<p>So at the very most, you are able to observe the function $f+g$. How on earth, then, can you infer anything about the function $g$?</p>
<p>I understand that you can decompose the field $f+g$ into Fourier components, but given that the ambient field $f$ can be anything at all, I don't see how that helps. The ambient field $f$ is affected by all sorts of things, from other people's communications to cosmic rays, to the fact that I happen to have just carried a 9-volt battery across my living room, much of which you have no knowledge of. Now I add a function $g$ to this completely unknown function $f$, and you're supposed to recover $g$ by observing the sum.</p>
<p>Clearly, this can't work. Clearly it goes ahead and works anyway. What am I missing?</p> | g12049 | [
0.002380264224484563,
-0.030942145735025406,
-0.007621769327670336,
-0.04315745085477829,
0.032260362058877945,
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0.013522930443286896,
0.030260659754276276,
-0.0334283821284771,
-0.056789468973875046,
-0.04179718345403671,
0.005877745803445578,
0.04457987844944,
0.006... |
<p>I came across some problems related to finding the center of pressure. Please guide me how to go about them. Posting them all so that I can find out the intricacies involved when there are so many different geometrical shapes involved.</p>
<ol>
<li><p>A quadrant of the ellipse $$x^2+4y^2 = 4$$ is just immersed vertically in a homogeneous liquid with the major axis in the surface. Find the center of pressure.</p></li>
<li><p>Find the depth of the center of pressure of a triangular lamina with vertex in the surface of the liquid and the other two vertices at depths $b$ and $c$ from the surface.</p></li>
<li><p>A circular area of radius $a$ is immersed with its plane vertical and its center at a depth $c$. Find the position of its center of pressure.</p></li>
</ol>
<p>Thanks in advance!!</p> | g12050 | [
0.06626743078231812,
0.023431867361068726,
0.003553301328793168,
-0.06158978492021561,
0.04449992626905441,
-0.008278321474790573,
0.025295354425907135,
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0.00728946877643466,
0.05127669870853424,
-0.006998394150286913,
0.0029655976686626673,
0.022505462169647217,
-0.0... |
<p>Could someone tell me about Frobenius-Schur indicator and the associated cups and caps notation in context of anyon model. One possible reference could be Parsa Bonderson thesis which is freely accessible here: <a href="http://thesis.library.caltech.edu/2447/2/thesis.pdf" rel="nofollow">http://thesis.library.caltech.edu/2447/2/thesis.pdf</a></p> | g12051 | [
-0.017115116119384766,
-0.04063631594181061,
0.010555818676948547,
-0.04675520211458206,
0.04717106372117996,
0.0007047401159070432,
0.022174490615725517,
0.030832594260573387,
0.017926383763551712,
0.044609203934669495,
0.0004063801607117057,
0.04568514600396156,
0.07792101800441742,
0.03... |
<p>To calculate the pressure at the outlet of a pump we use pump performance characteristics i.e. charts giving pump head as a function of volumetric flow. When the fluid flows through a pump, it's temperature slightly rises.</p>
<blockquote>
<p>Is there a formula or other method to calculate the temperature rise in a pump?</p>
</blockquote> | g12052 | [
0.01240678783506155,
0.01148453913629055,
-0.0057193017564713955,
-0.015773918479681015,
0.008781303651630878,
-0.04243730753660202,
0.02697271853685379,
0.058716680854558945,
-0.039949409663677216,
0.04346247762441635,
0.00832650437951088,
0.03992348909378052,
0.05155492201447487,
-0.0273... |
<p>I firstly apologise if this question is off the topic.</p>
<p>I am a first year undergraduate student and the required textbook for the course Advanced Physics is Fundemental of physics by Halliday. This textbook is huge and to be honest I was scared when I saw the size of the textbook. There are too much text to read and there are many exercises at the end of each chapter and I do not think that I would have time to do every single problem at the end of each chapter.</p>
<p>So with this information, what is the effective way of studying physics? what to read and what not to read? what exercises should I do? should I try to do all exercises? any other advice that I should do to be successful in physics is also appreciated.</p>
<p>If you need also some information about my background: I am a first year combined bachelor of electrical engineering and bachelor of mathematics and I have good knowledge of math but did not do any physics in highschool.</p> | g115 | [
-0.009499062784016132,
0.05043434351682663,
0.02413109503686428,
-0.008029409684240818,
0.01782703399658203,
0.04247884079813957,
0.0031413587275892496,
0.03584493696689606,
0.01888299733400345,
0.0007164909620769322,
0.10689319670200348,
-0.07194793969392776,
0.00681712431833148,
-0.00936... |
<p>Lets assume that we can produce a quark-gluon plasma and then we try to cool it down, what will happen to it ?</p> | g12053 | [
0.09913456439971924,
0.056493282318115234,
0.017004387453198433,
-0.02620968595147133,
0.023571355268359184,
0.0036297196056693792,
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-0.06535987555980682,
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0.08080241829156876,
-0.023289624601602554,
... |
<p>I am reading Steven Weinberg's <em>Gravitation and Cosmology</em>. On page 10 he says:</p>
<blockquote>
<p>In $D$ dimensions there will be $D(D+1)/2$ independent metric
functions $g_{ij}$, and our freedom to choose the $D$ coordinates at
will allows us to impose $D$ arbitrary functional relations on the
$g_{ij}$...</p>
</blockquote>
<p>Can anyone tell me why the choice of coordinates will impose functional relations on the metric?</p> | g12054 | [
-0.004141657613217831,
0.07345002889633179,
-0.011174872517585754,
-0.021026169881224632,
0.0034733794163912535,
0.018838239833712578,
0.04040402173995972,
-0.028162840753793716,
-0.05119225010275841,
-0.048753783106803894,
0.030207442119717598,
-0.02771398425102234,
0.05457263067364693,
-... |
<p>I've been wondering lately about a problem that comes from, among other places, an old video game "Lunar Lander". In the game there is a spaceship that has a small tank of fuel, and you're supposed to pilot the ship from an initial height down to the surface of the moon. You win if the landing is sufficiently soft. Your only control (at least in a one-dimensional version of the game) is a dial to control the fuel for thrust during the descent.</p>
<p>Finding the optimal strategy is seemingly a problem in the calculus of variations---out of all possible ways to spend the thrust during the descent, you want the one that minimizes the speed when the lander reaches the surface. Besides the game, given that we've landed real ships on the moon or Mars, I'm guessing this optimization problem is well known. Could someone point me to results in textbooks or the literature?</p> | g12055 | [
0.025400040671229362,
0.0700625628232956,
-0.00693215848878026,
0.05083134025335312,
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-0.061835747212171555,
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-0.016020605340600014,
0.05215216428041458,
-0.021919090300798416,
0.03940974920988083,
0.0... |
<p>I know that the work capacity of the heart is</p>
<pre><code>Work capacity of the heart = pumping capacity x aortic impedance.
</code></pre>
<p>I would mark work by W and impedance by Z.
However, I am not sure how to mark the pumping capacity.</p>
<p>I think the units of W are joules and of impedance Ns / m.
So pumping capacity m / s^2.
I think something wrong, since does not feel right. </p>
<p>I think the units of pumping capacity should be m^3.
So aortic impedance is N/m^2, which is the same as Pressure.
Aortic impedance should not be the same as pressure.</p>
<p>My problem is to understand the word capacity.
Normally, I relate energy per temperature unit with it but here I cannot.</p>
<p><strong>How can you write this sentence with correct units?</strong></p> | g12056 | [
-0.004977472126483917,
0.034824397414922714,
-0.014857866801321507,
-0.011875485070049763,
0.029396655037999153,
0.0060796113684773445,
0.02288118191063404,
0.05399463698267937,
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0.0115544768050313,
0.009108573198318481,
0.031098835170269012,
0.00495868967846036,
-0.0... |
<p>what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I do hope the + or - sign definitely talks about direction of spin! (kindly elaborate!)</p> | g383 | [
-0.04657502472400665,
-0.003542200895026326,
-0.023372836410999298,
-0.007474472280591726,
0.052397776395082474,
0.008689644746482372,
0.07395914942026138,
0.0631006732583046,
0.035227805376052856,
-0.028125638142228127,
-0.02757337875664234,
0.04377340152859688,
0.05407989025115967,
-0.00... |
<p>Since the mutual repulsion term between electrons orbiting the same nucleus does not commute with either electron's angular momentum operator (but only with their sum), I'd assume that the electrons don't really have a well-defined angular momentum (i.e., they do not occupy a pure $\left|lm\right>$ state). I would assume that the actual wavefunction is dominated by one such state compared to others, so it is approximately pure, but is there really a points in enumerating electrons according to their momenta, like the s, p, d, f and so on sub-shells?</p> | g12057 | [
-0.001389780780300498,
-0.0023825473617762327,
0.00721682608127594,
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0.08146683126688004,
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0.004622305743396282,
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0.027123400941491127,
-0.022034015506505966,
-0.04177987575531006,
0.007656175177544355,
0.022668566554784775,
... |
<p>The solution of Poisson equation is given by
$$
\mathbf E = \int \frac{\rho (\mathbf r )(\mathbf r_{0} - \mathbf r )}{|\mathbf r_{0} - \mathbf r|^{3}}d^{3}\mathbf r.
$$
I tried to use this term for a field of uniformly charged ball and got incorrect result: for the field inside the ball integration gives
$$
\int \frac{\rho (\mathbf r )(\mathbf r_{0} - \mathbf r )}{|\mathbf r_{0} - \mathbf r|^{3}}d^{3}\mathbf r = \rho \int \frac{\mathbf r_{0}}{|\mathbf r_{0} - \mathbf r|^{3}}d^{3}\mathbf r - \rho \int \frac{\mathbf r}{|\mathbf r_{0} - \mathbf r|^{3}}d^{3}\mathbf r =
$$</p>
<p>$$
= |\mathbf r_{0} = r_{0}\mathbf e_{z}| = \rho r_{0}\mathbf e_{z} \int \limits_{0}^{R} \int \limits_{0}^{\pi} \int \limits_{0}^{2 \pi} \frac{r^{2}dr sin(\theta )d\theta d \varphi}{(r^{2} + r_{0}^2)^{\frac{3}{2}}} + 0 = 4 \pi \rho r_{0}\mathbf e_{z} \left( \frac{1}{\sqrt{2}} - ln(\sqrt{2} + 1)\right),
$$
which isn't correct. Where did I make the mistake?</p> | g12058 | [
0.056319840252399445,
-0.01710781268775463,
-0.018135087564587593,
-0.05294858664274216,
0.07791599631309509,
0.02558348886668682,
0.056733131408691406,
-0.028423374518752098,
-0.014512698166072369,
-0.004727955441921949,
-0.0870029553771019,
0.05320018529891968,
-0.040872447192668915,
-0.... |
<p>I have a question about the Michelson Interferometer with spherical waves: I know that the pattern produced by this kind of waves is a pattern of concentric circles. But what I'm not sure is how the pattern changes when I move one mirror. I believe that If I move the mirror away from the beam spliter, the circles in the pattern will move from the center of the screen to the sides of the screen, i.e. the radius will increase. Am I right? </p> | g12059 | [
0.0033997339196503162,
0.014079968445003033,
0.01577375829219818,
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0.0373496413230896,
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0.05215045437216759,
0.02963048592209816,
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-0.031436894088983536,
-0.07643318176269531,
0.002783931326121092,
0.041944555938243866,
0.0156... |
<p>I am hosting a dinner tonight for which I'll be serving white wine (Riesling to be more specific). Generally white wine is best served chilled (not COLD!) at around <code>50 F</code> or <code>10 C</code>. </p>
<p>Just for kicks, I thought I'd treat this as a problem of transient conduction. I assume that (forced)convection is negligible since I will leave my wine bottle in my kitchen which has <em>still air</em>.</p>
<p><strong>The following assumptions are made:</strong></p>
<ul>
<li>The wine bottle is assumed to be cylindrical with an outside to inside radii, $r_o/r_i$ ratio of <code>1.10</code></li>
<li>The only mode of heat transfer for this bottle is conduction (perhaps a poor assumption?). The kitchen air is considered to be still and at <code>25 C</code></li>
<li>The un-open bottle of wine is a <strong>closed thermodynamic system</strong>. The glass material has a conductivity $k$ of <code>1.0 W/m-K</code> and the wine itself has a specific heat at constant volume, $C_v$ of <code>2.75 kJ/kg-k</code> <a href="http://www.refrigeration-engineer.com/forums/showthread.php?33429-Specific-heat-capacity-of-Wine" rel="nofollow">as per this</a></li>
<li>The volume of the bottle of wine is <code>750 mL</code> or $750 \times 10^{-6} m^3$</li>
<li>The wine is at a temperature of <code>5 C</code> and hence needs to be warmed for a while. The entire wine is assumed to have a <strong>lumped capacitance</strong> (all the wine is at the same temperature with little variation with radius).</li>
<li>The temperature difference between the wine and the bottle wall is assumed to be $\sim 10 C$ and so is the temperature difference between the bottle wall and the room (just a rough order of magnitude).</li>
</ul>
<p>The first law of thermodynamics (transient) is applied to this closed system bottle of wine:</p>
<p>$$\frac{\mathrm{d}{E}}{\mathrm{d}t} = \delta\dot{Q} - \delta\dot{W}$$</p>
<p>The $\delta\dot{W}$ term is zero for this closed system as only heat is exchanged with the kitchen atmosphere.</p>
<p>$$\frac{m C_v \Delta T_\text{wine-bottle}}{\Delta t} = \frac{2 \pi k \Delta T_\text{bottle-kitchen}}{ln(r_o/r_i)}$$</p>
<p>This gives me the time the bottle of wine needs to be placed in my kitchen <strong>outside</strong> the fridge as:</p>
<p>$$\Delta t \approx 0.025 \frac{\Delta T_\text{bottle-air}}{\Delta T_\text{wine-bottle}} C_v \approx 68 \text{ seconds}$$</p>
<p>This seems to be a rather small amount of time!!! Are my assumptions wrong? Should I improve this with convective heat transfer between the bottle and the kitchen air? Will my guests be disappointed? <code>:P</code></p>
<p><strong>EDIT::Including convective heat transport:</strong></p>
<p>$$\underbrace{\frac{m C_v \Delta T_\text{wine-bottle}}{\Delta t}}_\text{Change in total/internal energy w.r.t time} = \underbrace{\frac{2 \pi k \Delta T_\text{bottle-kitchen}}{ln(r_o/r_i)}}_\text{conduction} + \underbrace{h A \Delta T_\text{bottle-kitchen}}_\text{convection}$$.</p>
<p>Here $h$ is the heat transfer coefficient $\sim 1 W/m-K$, $A$ is the surface area of the cylinder. Based on the volume of the cylinder being $70 mL = \pi r_i^2 h$. The height of the bottle is about $1 foot$ or $0.3048 m$ and the generally close assumption that $r_o \approx 1.1 r_i$, I have (all $\Delta T$'s are close and cancel out):</p>
<p>$$\Delta t = \frac{m C_v ln(r_o/r_i)}{\left[ 2 \pi k + 2\pi r_o(r_o + h) ln(r_o/r_i)\right]} \\
\Delta t \approx 260.76 \text{ seconds} \approx 4 \text{ minutes}
$$</p>
<p>This seems more plausible..... But I start doubting myself again.</p> | g12060 | [
0.022941958159208298,
-0.010725289583206177,
-0.004175680223852396,
0.031909529119729996,
0.015765104442834854,
-0.02574927918612957,
0.04604795575141907,
0.04095105081796646,
-0.08018472790718079,
0.03992556035518646,
-0.0176729504019022,
0.0730045959353447,
-0.04055310785770416,
0.018139... |
<p>I am working through some notes of Gould and Tabochnik <a href="http://www.compadre.org/STP/document/ServeFile.cfm?ID=7271&DocID=445" rel="nofollow">here</a> and I am confused by their argument showing that entropy does not change in a quasi-static adiabatic process. First, entropy is defined to be an additive function of the state which is not allowed to decrease in an isolated system. Then a bit later there is the following paragraph</p>
<blockquote>
<p>For pure heating or cooling the increase in the entropy is given by
$$dS = \left(\frac{\partial S}{\partial E}\right) dE.\qquad (2.68)$$
In this case $dE = dQ$ because no work is done. If we express the partial derivative in (1.68) in
terms of $T$, we can rewrite (1.68) as
$$dS =
dQ/T
\qquad \text{(pure heating)}. (2.69)$$
We emphasize that the relation (1.69) holds only for quasistatic changes. Note that (1.69) implies
that the entropy does not change in a quasistatic, adiabatic process.</p>
</blockquote>
<p>But (2.69) (mis-labelled as 1.69) only applies when no work is done. But certainly work might be done in a quasi-static adiabatic process, so how can (2.69) possibly apply?</p>
<p>Instead, is the following argument valid? A quasi-static process is one which passes through a sequence of equilibrium states. In each equilibrium state, the entropy has to be at its maximum value. Thus, the entropy cannot increase in passing from one equilibrium state to another. So overall the entropy can't change in a quasi-static process either.</p>
<p>But I don't think this argument can be right either, because then the same argument would apply to any quasi-static process, so why do we need "adiabatic" as well?</p> | g12061 | [
-0.018852999433875084,
0.014478226192295551,
0.011872385628521442,
-0.025980787351727486,
0.03396110236644745,
-0.012687782756984234,
0.051964495331048965,
0.0009075988782569766,
-0.0369967482984066,
0.002069047885015607,
-0.06379121541976929,
0.0435883030295372,
0.04834599420428276,
0.004... |
<p>Exercise 12.2.2 in <a href="http://www.amazon.co.uk/Principles-Quantum-Mechanics-R-Shankar/dp/0306447908" rel="nofollow">Shankar's Principles of Quantum Mechanics</a> asks to derive the expression for the angular momentum operator $L_z$
\begin{equation}
L_z = XP_y-YP_x
\end{equation}
using its commutation relations with the coordinate and momentum operators
\begin{align}
[X,L_{z}]&=-i\hbar Y\\
[Y,L_{z}]&=i\hbar X \\
[P_{x},L_{z}]&=-i\hbar P_{y}\\
[P_{y},L_{z}]&=i\hbar P_{x}
\end{align}
I have seen a <a href="http://dl.dropboxusercontent.com/u/23776383/hmwk11_solutions.pdf#page=2" rel="nofollow">solution</a> which uses the coordinate representations of the momenta.</p>
<p><strong>However, I would like to find one that relies purely on the abstract relations.</strong></p>
<p>All I have been able to prove so far is that $L_z$ and $XP_y-YP_x$ commute. Multiply the first relation on the right by $P_{y}$ and the third relation
\begin{align}
[X,L_{z}]P_{y}&=-i\hbar YP_{y}\\
Y[P_{x},L_{z}]&=-i\hbar YP_{y}
\end{align}
Equating the LHS's we obtain
\begin{align}
(XL_{z}-L_{z}X)P_{y}&=Y(P_{x}L_{z}-L_{z}P_{x})\\
XL_{z}P_{y}-L_{z}XP_{y}&=YP_{x}L_{z}-YL_{z}P_{x}
\end{align}
Now subtract $XP_{y}L_{z}$ from both sides
\begin{align}
XL_{z}P_{y}-XP_{y}L_{z}-L_{z}XP_{y}&=YP_{x}L_{z}-XP_{y}L_{z}-YL_{z}P_{x}\\
X[L_{z},P_{y}]-L_{z}XP_{y}&=(YP_{x}-XP_{y})L_{z}-YL_{z}P_{x}\\
\end{align}
Add $L_{z}YP_{x}$ to both sides
\begin{align}
X[L_{z},P_{y}]+L_{z}YP_{x}-L_{z}XP_{y}&=(YP_{x}-XP_{y})L_{z}+L_{z}YP_{x}-YL_{z}P_{x}\\
X[L_{z},P_{y}]+L_{z}(YP_{x}-XP_{y})&=(YP_{x}-XP_{y})L_{z}+[L_{z},Y]P_{x}\\
[L_{z},XP_{y}-YP_{x}]&=X[P_{y},L_{z}]-[Y,L_{z}]P_{x}
\end{align}
However, using the commutation relations we deduce that $X[P_{y},L_{z}]=[Y,L_{z}]P_{x}=i\hbar XP_{x}$, therefore
\begin{equation}
[L_{z},XP_{y}-YP_{x}]=0
\end{equation}</p>
<p>Any other manipulations left me spinning in logical circles. I would appreciate any help in completing the argument. </p> | g12062 | [
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0.07235535234212875,
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0.03854890540242195,
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0.04869212210178375,
0.05472756177186966,
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-0.049738869071006775,
-0.038928404450416565,
0... |
<p>How do I make a ripple effect in a bowl of water. I have tried throwing small pebble sin but it just splashes and sinks. I have read that I need to make the water a thicker liquid ie add glycerine, will this work and why? </p> | g12063 | [
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0.016155272722244263,
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0.02149355411529541,
0.006129249464720488,
0.010504664853215218,
-0.049691036343574524,
-0.00661952281370759,
0.014625315554440022,
0.035698872059583664,
0.0309... |
<p>How should I compute the amount of energy of an EM wave absorbed by a material?
Can I just use the divergence of the Poynting vector?</p> | g12064 | [
0.0713663101196289,
0.014247193932533264,
0.00269373320043087,
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0.010784017853438854,
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0.0015107010258361697,
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-0.003222700208425522,
0.... |
<p>For a fixed current load, will the voltage drop be larger in a small cell or a big cell battery? Why?</p> | g12065 | [
0.04246433824300766,
0.029182864353060722,
0.005801759194582701,
0.027444083243608475,
0.02925427444279194,
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0.01... |
<p>I considered a Ring-like one dimensional geometry. In this, if we fix an origin (at some point on the circumference), we can think of <strong>set of all displacements along the circumference</strong> to form a <strong>vector space</strong>. Now one vector can be denoted by (for some reasons that will become clear),
$$ \left( \begin{array}{ccc}
x \\
1 \end{array} \right) $$
Further one can obtain any other vector in the space by translating the vector, say $ x_0 \rightarrow x_0+a $. We can use the linear transformation :
$$ T(a) =
\left( \begin{array}{cc}
0 & a \\
0 & 0\end{array} \right) $$
such that
$$ \left( \begin{array}{ccc}
x + a \\
1 \end{array} \right)
= \left( \begin{array}{ccc}
x \\
1 \end{array} \right)+
T(a)\left( \begin{array}{ccc}
x \\
1 \end{array} \right)
$$
Now the set of all such linear transformations will form a group. </p>
<p>Most important part of this transformation is that, if the circumference of the ring is some $L$, then the transformation $T(nL)$ where $ n \in \mathbb Z $ should not change the vector. Mathematically,
$$ T(nL) \left( \begin{array}{ccc}
x_0 \\
1 \end{array} \right)
=
\left( \begin{array}{ccc}
x_0 \\
1 \end{array} \right) $$</p>
<p>Now my question is, with these definitions is the <strong>group of Translations a Compact one</strong> ? And if it is the generator of the translations will have some properties like angular momenta (although this is a generator of translations) ?</p>
<p>PS : I hope I am not talking about rotations. I am just talking translations along the circumference of the circle.</p> | g12066 | [
-0.0024674769956618547,
0.013592148199677467,
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0.01407660637050867,
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-0.008253355510532856,
... |
<p>Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular formula cannot possibly be the correct expression for a particular quantity. The usual approach to teaching this is to go "well kids, you can't add apples and oranges!" and then assume that the student will just find it obvious that you can't add meters and seconds.</p>
<p>I'm sorry, but... I don't. I'm not convinced. $5$ meters plus $10$ seconds is $15$! Screw your rules! What are the units? I don't know, I actually don't understand what that question means.</p>
<p>I'm specifically not convinced when this sort of thing is used to prove that certain formulae can't possibly be right. Maybe the speed of a comet <em>is</em> given by its period multiplied by its mass. Why not? It's a perfectly meaningful operation - just measure the quantities, multiply them, and I claim that the number you get will always equal the current speed of the comet. I don't see how "but it doesn't make sense to say mass times time is equal to distance divided by time" can be a valid counterargument, particularly because I don't really know what "mass times time" is, but that's a different issue.</p>
<p>If it's relevant, I'm a math student and know extremely little about physics.</p> | g12067 | [
0.03290898725390434,
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-0.04049557447433472,
0.05560639500617981,
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0.01699232868850231,
0.02690... |
<p>Can anyone see a reason for $$\left(1+{U_\rho U^\rho\over c^2}\right)\left(U_\nu{d^2 U^\nu\over d\tau^2}\right)=0$$?</p>
<p>Here $U^\rho$ is the 4-velocity for a particle and $\tau$ the proper time. The context is for a particle moving in an electromagnetic field.</p>
<p>I believe it may be useful to introduce the antisymmetric tensor $F_{\mu\nu}$ -- the electromagnetic field tensor. </p> | g12068 | [
0.007362480740994215,
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0.04311823844909668,
-0.009488304145634174,
0.024... |
<p>Given: </p>
<ol>
<li>A <a href="http://en.wikipedia.org/wiki/Wave_plate" rel="nofollow">half wave plate</a> freely floating in space. </li>
<li>Circularly polarized light, falling perpendicularly to it.</li>
</ol>
<p>The plate changes polarisation of the beam to the opposite one. Therefore it receives angular momentum and starts to rotate. </p>
<p>Where does energy comes from?<br>
What would happen with a single photon passing through the plate? </p> | g12069 | [
0.059685274958610535,
0.02296401746571064,
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0.044148411601781845,
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-0.0070838299579918385,
-0.01848025619983673,
0.07337528467178345,
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-0... |
<p>I'm designing a new calendar and I want the first day of the year to be the first day after the longest night of year in the northern hemisphere. Under this plan, "natural" leap years, where the first day of two adajacent years are 366 days apart, will occur every four years, but sometimes with a five year gap instead.</p>
<p>If I want this calendar to be embraced by the software engineers of the world, the position of those leap years will need to be predictable with a mathematical function that operates only on the year number, making no reference to observed astronomy.</p>
<p>Given a year number <em>y</em>, how can I predict if that year is a leap year, as defined above?</p>
<p>For the puroses of this question, my year numbers are the same as standard years for the bulk of the year, with the exception of the period between the winter solstice and new years day where they will differ by one.</p>
<p>Also, for the purposes of this question, assume that the Earth's cycles will remain as they are now indefinitely.</p>
<hr>
<p>Update: I've rephrased the question a little after reading the comments.</p>
<p>Every year, there is day that's the first one after the longest night in the northern hemisphere. Most years, that day will be 365 days after the previous one.</p>
<p>Some years, that day will be 366 days later. I'll call them "natural leap years".</p>
<p>These "natural leap years" will mostly be four years apart, but will sometimes be five years apart instead.</p>
<p>How can I calculate, assuming the Earth's current cycles, when these "natural leap years" will occur?</p> | g12070 | [
0.024466373026371002,
0.03365494683384895,
0.0023861804511398077,
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-0.04493033513426781,
-0.03432382643222809,
0.006037430372089148,
0.0600372776389122,
-0.027990... |
<p>Which sky map application for mobile devices have the best "feature satisfaction"-to-investment ratio?</p>
<p>I would like to have a comparison between "sky map" applications for mobile devices and it should be a factual comparison made by astronomy professionals, enthusiasts, and hobbyists. The result would be a user guideline on valuable applications.</p>
<p>I am always looking for great tools for amateur and professional astronomy to use for outdoor night observations.</p>
<p>(Tagging suggestion: this question can be part of a "How to make observation easier", subpart "mobile application".)</p> | g12071 | [
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0.012146912515163422,
0.00905057042837143,
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0.042168810963630676,
-0.012106076814234257,
0.04274671524763107,
0.003357417182996869,
0.05643128603696823,
0.0... |
<p>I know of the <a href="http://en.wikipedia.org/wiki/Ariane_5#Variants" rel="nofollow">Ariane 5 ECA</a>, the <a href="http://en.wikipedia.org/wiki/Delta_IV" rel="nofollow">Delta IV</a> rocket and a few more, but which of the present day's rockets is the top heavy lifter, say, to <a href="http://en.wikipedia.org/wiki/Low_Earth_orbit" rel="nofollow">low Earth orbit</a> (LEO)?</p>
<p>Although it is not a certain fact, I would imagine that a very heavy lifter to LEO is also good for placing objects into <a href="http://en.wikipedia.org/wiki/Geostationary_transfer_orbit" rel="nofollow">geostationary transfer orbit</a> (GTO) and could be a good candidate for out of Earth orbit flight (for instance a trip to the Moon). </p> | g12072 | [
-0.004247899167239666,
0.04853525385260582,
-0.016316724941134453,
-0.022893428802490234,
-0.0041995118372142315,
0.010186883620917797,
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-0.022614343091845512,
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-0.040655914694070816,
0.020551148802042007,
0.008521596901118755,
0.05454108491539955,
... |
<p>Reading this wiki page about the <a href="http://en.wikipedia.org/wiki/Observable_universe" rel="nofollow">observable universe</a>, (and visible universe), implies that we humans, on this rock in the milkyway are seeing a static representation of the universe that is still effectively in the past. They're also saying that the observable universe is about 93 billion light years to observe it, because of Hubble's law, (I think), which implies that other objects far away in the universe are moving away from us faster than the speed of light (SoL). Now if we're moving slower than SoL then it would infer that we would never, from Earth be able to see the entire universe. In fact our sun is expected to consume us long before this would even be conceivably possible. </p>
<p>So, if we are seeing all of the observable universe when it was 13.75 billions years old and there is actually more "universe" to observe beyond this static reference, will we actually see more of it ? Or are we doomed to observe the universe at a specific place in time ?</p> | g12073 | [
-0.0008872291073203087,
0.06016174331307411,
0.015173044055700302,
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0.0490003302693367,
0.01175866462290287,
0.025015894323587418,
0.02984108030796051,
-0.04315119609236717,
0.056604545563459396,
-0.022822406142950058,
0.056614357978105545,
0.0185... |
<p>What would happen if instead of $F=m*d^2x/dt^2$, we had $F=m*d^3x/dt^3$ or higher? </p>
<p>Intuitively, I have always seen a justification for ~1/r^2 forces as the "forces beeing divided equally over the area of a sphere of radius r".</p>
<p>But why the 2 in $F=m*d^nx/dt^n$ ?</p> | g12074 | [
0.030876006931066513,
0.021473344415426254,
-0.011881258338689804,
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0.015948593616485596,
0.017008528113365173,
0.018004566431045532,
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-0.061333537101745605,
-0.028363384306430817,
-0.005479762330651283,
0.03785285726189613,... |
<p>Could someone explain the correspondence between lines in twistor space and minkowski space-time points? a basic derivation would suffice</p> | g12075 | [
0.03327518701553345,
-0.012834395281970501,
-0.02933242730796337,
0.03162582218647003,
0.04303913563489914,
-0.01702858693897724,
0.05191947519779205,
0.015059085562825203,
-0.017791645601391792,
0.02558528631925583,
-0.035995904356241226,
-0.0027531851083040237,
0.02583342045545578,
0.023... |
<p>In Lorentzian AdS space there are both normalizable and non normalizable solutions and we also know (at least for scalar fields in bulk) what do they correspond to in the boundary. But I saw the calculation only for scalar fields. Can someone please give me a reference where people have calculated these modes for a gauge fields, say for a graviton field? McGreevy's lecture note says the relation $\Delta(\Delta-D)=m^2L^2$ gets modified to $(\Delta+j)(\Delta+j-D)=m^2L^2$ for form $j$ fields. Does this mean for other fields too the normalizable and non normalizable behavior remains the same: namely $Z_0^{\Delta_+}$ and $Z_0^{\Delta_-}$, as $z_0\rightarrow 0$ ($\Delta_{\pm}$ are two solutions of course)? How can that be?</p> | g12076 | [
-0.015702180564403534,
-0.007373284548521042,
-0.021652625873684883,
0.0028449948877096176,
0.06051429361104965,
0.06366243213415146,
0.06024155020713806,
-0.005211859941482544,
0.01690959371626377,
-0.03494613617658615,
-0.04118441417813301,
0.04586302116513252,
0.053419630974531174,
0.00... |
<p>As I learned, nuclear fission doesn't occur without the control of a human made nuclear reactor, by hitting a neutron to a fissile isotope. Thus, the fission reaction is considedred as a part of 'ARTIFICIAL REACTIONS' category.</p>
<p>But, I've just noticed in a wikipedia article (<a href="http://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor" rel="nofollow">Natural nuclear fission reactor</a>), that nuclear chain reactions had occurred on Earth about 2 billion years ago, what proves that fission existed naturally before.</p>
<p>Another additional question I was wondering is:
Is there any chance that a natural nuclear chain reaction can re-occur on Earth?</p> | g12077 | [
0.028755806386470795,
0.03336244076490402,
0.009814072400331497,
0.032179415225982666,
0.014934833161532879,
0.00003404794188099913,
0.009578581899404526,
0.04967569559812546,
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-0.06585393846035004,
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0.01172587089240551,
0.030055908486247063,
0.0135... |
<p>In eternal inflation, how can bubble universes collide if the space between them is exponentially stretching and moving them further and further away?</p> | g12078 | [
-0.001712697558104992,
0.0118712168186903,
0.02246953547000885,
0.006812809035181999,
-0.021414022892713547,
0.09220543503761292,
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-0.04308074712753296,
0.022303659468889236,
-0.007524239830672741,
0.007765568792819977,
-0.... |
<p>Chirality can be interpreted as a property of Lorentz group - Lorentz transformation of field through representation $(s, 0)$ or representation $(0, s)$. For the massless particles one says, that chirality and helicity are the same (helicity values are a chirality values multiplied by $ \hbar $). So it means, that chirality values are $\pm s$. </p>
<p>The questions: </p>
<p>1) How can I get these values for chirality? I.e., how right- and left-handed representation of the Lorentz group are connected with plus-minus signs of the chirality value?</p>
<p>2) Equivalence of helicity and chirality in the massless case is little not obvious for me. One uses idea that for the massless case helicity of given particle is Lorentz-invariant, the same as chirality. But it seems to me that this is not enough to identify these values. So how to identity them?</p>
<p>3) Also, in my previous question on the subject (<a href="http://physics.stackexchange.com/questions/73911/why-helicity-is-proportional-to-the-spin-of-particle-and-has-two-values">Why helicity is proportional to the spin of particle and has two values?</a>), there was a comment which give an idea of getting an answer on the question, using an equivalence of helicity and chirality. Can the helicity operator properties for massless case be given from the equivalence between helicity and chirality? Or at the beginning we get the properties of helicity operator, and only then we can identify them?</p> | g12079 | [
0.011356048285961151,
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-0.0046159978955984116,
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0.060390572994947433,
0.009213070385158062,
0.009141024202108383,
0.054609086364507675,
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0.015487589873373508,
-0.05081982910633087,
0.03840695321559906,
0.018722305074334145,
... |
<p>For the observation of solar or galactic gamma rays, one should ideally be above the atmosphere. Quoting the <a href="http://en.wikipedia.org/wiki/Gamma-ray_astronomy" rel="nofollow">Wikipedia article on Gamma-ray astronomy</a>:</p>
<blockquote>
<p>Most gamma rays coming from space are absorbed by the Earth's atmosphere, so gamma-ray astronomy could not develop until it was possible to get detectors above all or most of the atmosphere using balloons and spacecraft.</p>
</blockquote>
<p>However, satellites do observe <a href="http://en.wikipedia.org/wiki/Terrestrial_gamma-ray_flash" rel="nofollow">terrestrial gamma rays</a>, either from natural or <a href="http://en.wikipedia.org/wiki/Vela_%28satellite%29" rel="nofollow">anthropogenic sources</a>.</p>
<p>If the atmosphere absorbs gamma rays and solar or galactic gamma rays are best observed from space, how can <em>terrestrial</em> gamma rays be observed from <em>above</em> the Earth's atmosphere?</p>
<p>In other words, what does the atmospheric optical depth look like at very high frequencies? Is the following diagram inaccurate?</p>
<p><img src="http://i.stack.imgur.com/p8dDO.png" alt="Atmospheric opacity">
<br />Atmospheric opacity, from <a href="http://commons.wikimedia.org/wiki/File%3aAtmospheric_electromagnetic_opacity.svg" rel="nofollow">Wikimedia Commons</a>, originally from NASA.</p> | g12080 | [
0.0008761913049966097,
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0.05398615077137947,
0.018380872905254364,
0.015517671592533588,
-0.01817745715379715,
-0.005649886094033718,
0.09910737723112106,
0.0593891404569149,
0.05028139799833298,
-0.... |
<p><em>Is the following a possible scenario? If not, why not?</em></p>
<p>Assume there is a supermassive black hole $Z$ isolated in inter-galactic space.
Nearby and stationary relative to $Z$ is observer $A$.
A number of light years away spaceship $X$ is travelling at, say, $0.25c$ directly towards the black hole and (eventually) $X$ falls directly into $Z$.
$X$'s mass as observed by $A$ will increase as $X$'s velocity approaches $c$ as $X$ approaches $Z$'s event horizon. It seems that $X$'s velocity should be so close to $c$ as it encounters the event horizon of $Z$ that $X$'s apparent mass should cause it to have its own event horizon.</p>
<p>I am assuming that $A$ will observe that $X$ becomes a black hole just prior to its event horizon merging with $Z$'s.</p>
<p>Now assume that just prior to the merging of the event horizons a spaceship $Y$ is travelling a few light seconds behind $Z$ on the same path, but at about $0.5c$. Just prior to the merging of event horizons $Z$ radios $Y$ (to whom $Z$ will NOT appear to have an event horizon) and $Y$ relays this message to $A$. (Note: This could also happen in reverse, so a fast conversation may be possible.)</p>
<p><em>What is wrong with this, as it appears to anyone stationary with respect to $Z$, that $A$ and $Z$ are communicating, with information being exchanged from within a black hole?</em></p> | g12081 | [
0.03586208075284958,
0.00729311304166913,
0.01837833784520626,
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0.003944359254091978,
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-0.013654480688273907,
0.028205282986164093,
0.0132732093334198,
0.0065598501823842525,
0.01... |
<p>I remember studying that air pressure and temperature are inversely proportional. Now I saw in book that "Atmospheric pressure decreases as we go higher and higher." But in height the temperature is less, and so the air pressure is high. But it is given atmospheric pressure increases with altitude. I googled and understood that <a href="http://kids.earth.nasa.gov/archive/air_pressure/" rel="nofollow"><strong>air pressure</strong></a> and <a href="http://en.wikipedia.org/wiki/Atmospheric_pressure" rel="nofollow"><strong>atmospheric pressure</strong></a> are different. But I can't understand how each is different from the other in properties.`` </p> | g12082 | [
0.06362615525722504,
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0.03449803218245506,
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0.054181527346372604,
0.04793152958154678,
0.0029... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/28228/why-is-matter-drawn-into-a-black-hole-not-condensed-into-a-single-point-within-t">Why is matter drawn into a black hole not condensed into a single point within the singularity?</a> </p>
</blockquote>
<p>When we speak of black holes and their associated singularity, why is matter drawn into a black hole condensed into a single point within the singularity?</p> | g384 | [
0.011815407313406467,
-0.025493916124105453,
0.017748521640896797,
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0.049553144723176956,
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0.012359201908111572,
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0.044065169990062714,
-... |
<p>I need help to settle an argument about aeronautics. Particularly model aircraft. </p>
<p>It has been observed by some that when a model airplane flying with the wind turns back into the wind , some aircraft tend to pitch up and gain altitude indicating an increase in airspeed. Alternately, when flying into the wind, after turning around tend to lose altitude indicating a lower airspeed.</p>
<p>Most model pilots say that this is an “illusion” or “pilot error” and that given no change in throttle or thrust the airspeed remains constant. I disagree! It is my theory that in the first case forward momentum is carried through the turn causing a momentary increase in airspeed and when the model turns to fly with the wind it takes a while for the model, now with a slower ground speed to get up to optimum air speed. Thus airspeed is not constant but cyclical. </p>
<p>I realize that there are many factors involved and that some of my detractors base their belief on their training in full scale aircraft. Model aircraft tend to be smaller, have lower glide ratios and are often based on high performance aircraft designs as opposed to your typical civilian aircraft. Flying style is also quite different with faster scale speeds and sharper turns for the models. </p>
<p>Am I right? Wrong?
How do Newton's laws of motion relate to this? </p> | g12083 | [
0.06345576792955399,
0.006475700996816158,
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0.04776777699589729,
0.06861624866724014,
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0.0073026809841394424,
0.052112169563770294,
-0.005527082830667496,
-0.003338757436722517,
0.0409... |
<p>I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly.</p>
<p><a href="http://en.wikipedia.org/wiki/Hilbert%27s_sixth_problem">Hilbert's sixth problem</a> consisted roughly about finding axioms for physics (and it was proposed in $1900$). I guess that at the time, such thing was impossible due to the nature of physics which is mainly based on observations and models. But it seems that after Gödel's work on $1931$, the axioms which were seen as self-evident truths started to be seen as unprovable statements and the job of a mathematician is grossly about deriving theorems from these axioms.</p>
<p>So if this shift of axiomatic conception really happened, couldn't we just accept anything (including the physical observations) as axioms and reason about their consequences? Thus somehow <em>solving</em> Hilbert's sixth problem?</p> | g203 | [
0.03413941338658333,
0.07513435184955597,
0.022116979584097862,
-0.06094704940915108,
0.024901745840907097,
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0.009948440827429295,
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-0.0120170209556818,
0.003221262479200959,
-0.018013043329119682,
0.03133928030729294,
-0.000982... |
<p>In Rivasseau's and Wang's <a href="http://arxiv.org/abs/1304.5913" rel="nofollow">How to Resum Feynman Graphs</a>, on page 11 they illustrate the intermediate field method for the $\phi^4$ interaction and represent Feynman graphs as ribbon graphs. I had to read up about ribbon graphs as I've never heard of them before and still don't fully understand their use for the intermediate field method. For the $\phi^4$ interaction, we have:</p>
<blockquote>
<p>In that case each vertex has exactly four half-lines. There are exactly three ways to pair these half-lines into two pairs. Hence each fully labeled (vacuum) graph of order $n$ (with labels on vertices and half-lines), which has $2n$ lines can be decomposed exactly into $3^n$ labeled graphs $G'$ with degree $3$ and two different types of lines</p>
<ul>
<li>the $2n$ old ordinary lines </li>
<li>$n$ new dotted lines which indicate the pairing chosen at each vertex (see Figure 5).</li>
</ul>
</blockquote>
<p>The extension illustrated in Figure 5 looks as follows:</p>
<p><img src="http://i.stack.imgur.com/EUhji.png" alt="enter image description here"></p>
<p>I'm not sure I correctly understand the way to create such "3-body extensions". I understand it in that way that we "split up" the given vertex into two vertices and add an edge between them. Then, each vertex has two additional half-edges and there are three ways to pair them together. Joining the upper half-edges together, we get the second term on the RHS and joining the two half-edges on one side together, we will get the first term on the RHS (the dashed line would be the new edge between the two vertices). The only case left is the one of joining the upper left and the lower right (and the upper right and lower left) half-edge together. However, when drawing that specific case, I don't see any way to stretch or rotate it such that the third term on the RHS results.</p>
<p>Am I misunderstanding the way 3-body extensions are intended to get or am I just missing a way to stretch the edges to get the third term on the RHS? Also, where exactly do we need the cyclic ordering characterising ribbon graphs? And why are there two dashed lines in the third term on the RHS?</p> | g12084 | [
0.051697853952646255,
0.020884577184915543,
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0.05065813288092613,
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0.037388451397418976,
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... |
<p>Just a thought experiment since bats are probably not swift enough to take evasive action in the scenario described.</p>
<p>If a cloud of bats were to encounter a B-2, or F-35, or F-117 or any of the other stealth aircraft in stealth-mode, would they detect the airframe in time, or fly smack into the aircraft?</p> | g12085 | [
-0.024646542966365814,
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0.05204933136701584,
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0.006542473565787077,
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0... |
<p>This is a question I got for my class.</p>
<p>We have the following situation.
We take two tuning forks, we hit them, then we take one of the tuning forks and walk away with it.
The sound changes as we walk away and it isn't consistent anymore. </p>
<p>Why?</p>
<p><strong>EDIT:</strong> I see I was a bit unclear, tho the question itself is unclear since i don't know anything except that. Silly teacher.</p>
<p>So, to clarify, two forks(my guess is that they have the same frequency).
We hit each fork at the same time, one student is holding the fork #1 next to the blackboard, other student is walking away with fork #2.</p> | g12086 | [
0.020189760252833366,
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0.05324649065732956,
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0.03593268245458603,
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0.05624997243285179,
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0... |
<p>I have two earthed metal plates, separated by a distance $d$ with a plane of charge density $\sigma$ placed a distance $a$ from the lower plate. I want to derive expressions for the strength of the electric field in the regions between the plane and the top plate and the plane and the bottom plate.</p>
<p>I'm not sure how to apply Gauss's Law to the given situation. I think the best Gaussian surface to use would be a cylinder(?), and then somehow integrate over the two regions. But this would suggest that the electric field between the charged plane and the bottom surface was independent of the total separation, $d$ of the two earthed plates, which I don't think is correct. I don't yet fully understand Gauss's Law, and need more practice with it.</p>
<p>Please can someone point me in the correct direction, and give me a hint as to what I should be looking to integrate?</p>
<p>With very many thanks,</p>
<p>Froskoy.</p> | g12087 | [
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0.017107246443629265,
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0.012721315026283264,
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0.018689515069127083,
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<p>The apparent size of an object decreases with increase in distance that's why we see rails get closer as they get farther. We don't see the rails parallel throughout their length but converging. But there is a contradiction:</p>
<p>Let,
the real size of the object be <strong>s</strong>, </p>
<p>the distance between the eye and the object be <strong>d</strong>, </p>
<p>the visual angle be <strong>Ɵ</strong>, </p>
<p>let the retinal image size be <strong>I</strong></p>
<p>the radius of eye ball is <strong>r</strong> = 8.5 mm</p>
<p><img src="http://i.stack.imgur.com/5Edd9.png" alt="enter image description here"></p>
<p>From the above figure, the visual angle is
<img src="http://i.stack.imgur.com/3XGjr.png" alt="enter image description here"></p>
<p>and the arc length I = 2Ɵ*r;
<img src="http://i.stack.imgur.com/dw0fj.png" alt="enter image description here"></p>
<p>Here r and s are constants. Thus we get a relation between retinal image size and distance (between the eye and the object).</p>
<p>A graph for I vs d (for s=1) is shown below,</p>
<p><img src="http://i.stack.imgur.com/QszuJ.gif" alt="enter image description here"></p>
<p>The retinal image size doesn’t varies directly with distance. The values of I for certain d’s are given below,</p>
<p>d=0.5 I= 0.05340708</p>
<p>d=1, I= 0.03152804</p>
<p>d=2, I= 0.03152804</p>
<p>d=3 , I= 0.06305608</p>
<p>d=4 , I= 0.00845614</p>
<p>d=5 , I= 0.006777468</p>
<p>d=10, I= 0.00339717</p>
<p>and here is an illustration of how things might work.</p>
<p><img src="http://i.stack.imgur.com/NMREt.png" alt="enter image description here"></p>
<p>Is the above explanation correct?</p> | g12088 | [
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0.027801766991615295,
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0.03479491174221039,
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<p>In his 1970 science fiction novel <a href="http://en.wikipedia.org/wiki/Ringworld" rel="nofollow">Ringworld</a>, author Larry Niven describes the eponymous Ringworld, a gigantic structure shaped as a ring with a radius of around 1 AU, rotating around a star in the center of the ring. This system is described as physically stable; however many readers have complained that it is actually unstable and the structure will drift away in time.</p>
<p>My first thought reading this is that the Ringworld's center of mass is identical to the star's center of mass, so the system should be stable. Why is it unstable?</p>
<p>Some additional details of the structure:</p>
<ul>
<li>Radius: ~1 AU</li>
<li>Mass: ~1 Solar Mass</li>
<li>Year duration: ~220 hours</li>
</ul>
<p>The Ringworld is also made of material strong enough to withstand the stresses affecting it in such a system.</p> | g12089 | [
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0.018047960475087166,
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... |
<p>What I'm really looking for is a formula for a <a href="http://en.wikipedia.org/wiki/Trebuchet" rel="nofollow">trebuchet</a> that I can input the desired initial velocity after launch and mass of the object, and from that figure out how long the long arm, short arm, sling and pivot need to be, and how much mass I need to have for a counterweight. Does this exist?</p> | g12090 | [
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0.05261808633804321,
0.0... |
<p>I need a book dealing in particular with the intermolecular forces and, if possible, the diffusive processes. Someone knows an appropriate one?</p> | g12091 | [
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<p>This question is in reference to question 13.2 in the QFT book by Peskin and Schroeder. </p>
<p>To put it in general - I would like to know how does one define "anomalous dimensions" if one is given the wave-function renormalization in the "epsilon" regularization scheme? (..without having to redo the whole calculation again!..) </p>
<p>The only way I know of defining the anomalous dimension is when one does the regularization in the MS-bar scheme. Is there a simple/obvious way to interchange between the two schemes? </p>
<ul>
<li>And in general is there a reference which does the anomalous dimensions calculation for O(N) vector model/linear sigma model and the non-linear sigma model? </li>
</ul> | g12092 | [
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<p>My <a href="http://books.google.com/books?id=ntZwxttZF-sC&lpg=PA28&ots=LU-xi3_Vw5&dq=lunar%20dichotomy%20method&pg=PA27#v=onepage&q=lunar%20dichotomy%20method&f=false" rel="nofollow">text</a> says that Aristarchus (310 BC – ~230 BC) measured the "angle subtended by the Earth-Moon distance at the Sun" ($\theta$ in the figure below) to establish the relative Earth-Moon and Earth-Sun distances. </p>
<p><img src="http://i.stack.imgur.com/YAlXy.png" alt="enter image description here"></p>
<p>I understand that he must, in fact have used the <a href="http://en.wikipedia.org/wiki/Aristarchus_On_the_Sizes_and_Distances#Half_Moon" rel="nofollow">Moon-Earth-Sun</a> angle, and then subtracted that from 90° to arrive at $\theta$; but how did he establish the Moon-Earth-Sun angle? The reference points for all three objects is their centers, yet what Aristarchus must have in fact measured was the angle between the Moon and the Sun at the <em>surface</em> of the Earth. </p>
<p>Did Aristarchus take this discrepancy into account in his calculations? If so, how?</p> | g12093 | [
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0.06639052927494049,
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0.009799850173294544,
-0.0005673721898347139,
0.040012702345848083,
0.08481671661138535,
-... |
<p>I can't figure out how to find the charge density for the following problem:</p>
<blockquote>
<p>A conductor is placed in an external electrostatic field. The external
field is uniform before the conductor is placed within it. The
conductor is completely isolated from any source of current or charge.</p>
<p>Assume that at some point just outside the surface of the conductor,
the electric field has magnitude E and is directed toward the surface
of the conductor. What is the charge density n on the surface of the
conductor at that point?</p>
</blockquote>
<p>I'm supposed to express my answer in terms of $E$ and $\epsilon_0$.</p>
<p>I know that Electric Flux = Normal Angle x Electric Field x cos(theta), but I don't know how to relate this to charge density?</p>
<p>What am I missing to solve this problem? This is very basic, I know, but I'm stumped. The hints on Mastering Physics also aren't really helping.</p> | g12094 | [
0.04825838655233383,
0.03570086881518364,
0.00010800538439070806,
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0.03079123981297016,
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0.020787935703992844,
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0.03612551465630531,
-0.04875762760639191,
0.014887155964970589,
0.030570486560463905,
-0.013... |
<p>First off, I know that a <a href="http://en.wikipedia.org/wiki/Black_hole" rel="nofollow">black hole</a> can theoretically exist at any size, and I know about the Schwarzschild radius, etc. Snowflakes could also exit at just about any size, and they of course vary considerably in different environments. But there's a characteristic area, say ~1mm$^2$, associated with snowflakes; nobody ever saw a 1 m$^2$ snowflake fall from the sky.</p>
<p>So: is there a meaningful <em>average</em> or <em>characteristic</em> size for black holes that exist in nature? Or do we even have enough data to answer this question?</p>
<p>For example astronomers associate stars with the solar mass, although stars can of course be a couple orders of magnitude more/less massive. Galaxies also have a characteristic size, varying a few orders up or down from the size of our own.</p>
<p>My best guess (at least for a lower limit) is the size associated with the CMB temperature, as black holes smaller than this in nature should evaporate quickly, as they would Hawking-radiate more energy than gained through photon absorption. But I don't know if this is a meaningful consideration.</p> | g12095 | [
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<p>In position basis, we have,</p>
<p>$$\langle x \mid \hat p \mid \Psi(t) \rangle = -\imath \hbar \frac{\partial{\langle x \mid \Psi(t) \rangle}}{\partial{x}} $$</p>
<p>Now i know $\hat{p}$ is a hermitian operator which should be self adjoint. </p>
<p>The self adjoint operators are said to satisfy :</p>
<p>$$\langle A \psi \mid \phi \rangle = \langle \psi \mid A \phi \rangle$$ </p>
<p>But i'm failed to workout the following :</p>
<p>$$ \langle x \mid \hat{p\dagger} \mid \Psi(t) \rangle$$</p>
<p>For ladder operator $\hat{a}$ i found $\hat{a\dagger}$ by conjugating in position basis. And clearly $\hat{a}$ is not hermitian because
$$ \hat{a\dagger} \neq \hat{a}$$ in position basis. And thus $\hat{a}$ does not correspond to any observable.</p>
<p>But $\hat{p}$ is hermitian. but it seems, at position basis, complex conjugating $\hat{p}$ gives a different object.</p>
<p>Where i'm making a mistake here?</p>
<p><strong>EDIT:</strong></p>
<p>After posting the question i found some inconsistancies in my argument.</p>
<p>$$\hat a = \frac {\hat x}{\sqrt {\frac {2 \hbar}{m \omega}}} + \frac {i \hat p}{\sqrt {2 \hbar m \omega}}$$</p>
<p>is not a <strong>representation</strong> in any basis. Its just a operator relation with some scaling factor.</p>
<p>whereas $$-i \hbar \frac {\partial}{\partial x} $$ is a <strong>representation</strong> of $\hat p$ in postion $x$ basis.</p>
<p>So they should not be comparable.</p>
<p>But i still want to know whats $\hat{p \dagger}$ in position $x$ basis.</p>
<p>I just falsely took a wrong example.</p> | g12096 | [
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-0.029336854815483093,
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0.0117179024964571,
0.0167058277875185,
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/6384/why-does-dilation-invariance-often-imply-proper-conformal-invariance">Why does dilation invariance often imply proper conformal invariance?</a> </p>
</blockquote>
<p>What exactly is the difference between the two? Can someone give an example of a theory which is scale invariant but not conformally invariant?</p> | g385 | [
0.04264568164944649,
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0.05442285165190697,
0.00806826539337635,
0.020323731005191803,
-0.012036310508847237,
0.005853613372892141,
-0.004826867021620274,
-0.0037... |
<p>In my calc-physics class we were given the following question:</p>
<blockquote>
<p>A movie stuntwoman drops from a helicopter that is $30.0 m$ above the ground and moving with a constant velocity whose components are $10.0 \frac{m}{s}$ upward and $15.0 \frac{m}{s}$ horizontal and toward the south. You can ignore air resistance.</p>
<p>What is the horizontal distance(relative to the position of the helicopter when she drops) at which the stuntwoman should have placed the foam mats that break her fall?</p>
</blockquote>
<p>I figured I could simply calculate the magnitude of the components since that will give me the distance, but the answer I got was incorrect.</p>
<p>I'm not looking for an answer, but would appreciate any assistance you all could offer in helping me to solve this problem.</p> | g12097 | [
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0.007528088986873627,
0.001006605103611946,
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0.07944495975971222,
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0.03712855651974678,
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-0.01712075062096119,
-0.022840706631541252,
0.005551839247345924,
0.02435026690363884,
0.0294... |
<p>For the sake of clarity and brevity, here is the description from my textbook (Halliday & Resnick 9th):
<img src="http://i.stack.imgur.com/KMZZQ.jpg" alt="enter image description here"></p>
<p>This description states that the electric field is doubled. I am seriously confused. When the two plates are brought together, shouldn't the field quadruple? The surface density doubles on each inner surface, doubling their generated electric field. Additionally, these two fields should obey superposition rules of vectors, doubling the net-field, for a <strong>quadrupled</strong> total?</p> | g12098 | [
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-0.044... |
<p>In oil droplet experiment, x-ray makes the air molecules negatively charged. How does that work? X-ray carries high energy and ionizes air, doesn't that make air positively charged?</p> | g12099 | [
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0.007074075751006603,
-0.05297... |
<p>I would like to know if there is any analytical proof or relationship which can show that for a dynamical system in presence of chaos signal, if the phase space volume (PSV) minimization leads to the minimization of Kolmogorov Entropy (dynamical entropy). Say, I have a chaotic signal $c(t)$ from a
logistic map of dimension $dim_c$. </p>
<p>Let, $x(t) = s(t) + c(t)$ . Let dim_x denote minimal sufficient embedding dimension of a certain signal $x(t)$. In the absence of measurement noise (say additive white Gaussian noise) it is shown that
Consider, an inversely filtered signal : $u(t) = x(t) - s(t)$ and $u(t)$ is delay embedded using Takens embedding formula with embedding dimension d= 2 and delay = 1. $u$ has a finite phase space volume when the signal is chaotic. In the absence of noise it was shown in</p>
<pre><code>[H. Leung, X. Huang, Parameter Estimation in
Chaotic Noise, , IEEE Trans. on Signal Processing, vol.
44, No. 10, October 1996] and [http://www.eurasip.org/Proceedings/Eusipco/Eusipco2000/SESSIONS/THUAM/OR1/CR1473.PDF]
</code></pre>
<p>that if $d =dim_c$ which is less than $dim_s$, then the correct value of parameter
θ of $s(t)$ can be
estimated by PSV minimization of the
d
-dimensional time
delay reconstructed inversely filtered signal, $u(t)$. </p>
<p>Now, if the chaotic signal is corrupted with measurement noise, say additive white gaussian noise, then its phase space volume will be high or infinite. When, the additive noise gets reduced, the phase space volume also gets reduced. The phase space volume of $u(t)$ has a Kolmogorov entropy. Based on this I have the following difficulties</p>
<p>Q1: What is meant by the dimension of s(t) ? Assuming s(t) to be an AR model, as given in the paper I think the AR model is 1D. So, the dimension of s(t) is lesser than that of the embedding dimension $d$ of the chaotic signal. So, how come the relationship $dim_c < dim_s$ is satisfied ? </p>
<p>Q2: If the phase space volume is minimized, would it mean that Kolmogorov entropy is also minimized? How do I proof this?</p>
<p>Thank you</p> | g12100 | [
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-0.00521711353212595,... |
<p>Inspired by these two question on tex.SX</p>
<ul>
<li><a href="http://tex.stackexchange.com/questions/108818/asymmetric-uncertainties-with-siunitx-package">Asymmetrical tolerancing</a></li>
<li><a href="http://tex.stackexchange.com/questions/108818/asymmetric-uncertainties-with-siunitx-package">Asymmetric uncertainties with siunitx package</a></li>
</ul>
<p>I'd like to ask for a nice explanation for these kind of uncertainties, like $10_{-2}^{+6}$. I never saw them in real life. I'd like to give some question that may be stupid or redundant to each other but should show my problems that I currently have with them:</p>
<ul>
<li>What exactly do they mean? Example: $10_{-2}^{+6}$ means that the real value is much more likely to be bigger than $10$. So publishing $10_{-2}^{+6}$ as a value will much more likely be "more off" than someone publishing $11 \pm 3$ for the same quantity. What I mean: repeating the experiment often and always finding more possible "+" than possible "-" means in a statistical sense "value to low" <em>for sure</em>.</li>
<li>How to calculate them? They seem not to be based on some gaussian distribution or statistical assumptions.</li>
<li>Can they be "made" symmetric in some way?</li>
<li>Why and when is it useful to use them?</li>
</ul> | g12101 | [
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0.07568644732236862,
-0.003786948... |
<p>A few years ago there was a story about the Large Hadron Collider where a possible tachyon was supposedly observed. It was later shown it didn't occur yet the incident made me think. If a large experiment using extreme amounts of energy trying to duplicate some processes or events of the 'distant' past , would the intense amount of energy in this 'early' Universe experiment create a situation where the speed of light was different?? If a particle was observed emanating from this experiment and it seemed superluminal could this be due to a different speed of light measurement due to this phenomenon.</p> | g83 | [
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<p>Scientists succeeded in unifying EM with the weak force, then with the strong force to achieve the standard model. They then studied supersymmetry and GUTs that showed improved gauge coupling unification at high energies. The final dream was to unify all the known forces at very high energy, including gravity. In that picture there is a main single interaction we are after, from which all other interactions have emerged at lower energies. </p>
<p>On the other hand, theoretical breakthroughs with dualities have taken place in the last 10-20 years, such as gauge/gauge and gauge/gravity dualities. In that picture for example a QFT without gravity in some space is equivalent to gravitational theory in higher dimensional space. </p>
<p>So it seems to me that the old meaning of unification (namely to unify gravity with all the other 3 forces in one single force) has changed to saying that gravity and particle physics are the same thing, through duality.</p>
<p>So are researchers in string theory/particle physics thinking of unification in modern research in terms of dualities and have abandoned the old meaning of unification?</p> | g12102 | [
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<p>Approaching the following problem:</p>
<blockquote>
<p>A plane monochromatic electromagnetic wave with wavelength $\lambda = 2.0 cm$,
propagates through a vacuum. Its magnetic field is described by $
> \vec{B} = ( B_x \hat{i} + B_y \hat{j} ) \cos(kz + ωt) $,
where $B_x = 1.9 \times 10^{-6} T, B_y = 4.7 \times 10^{-6} T$, and $\hat i$ and $\hat j$ are
the unit vectors in the $+x$ and $+y$ directions, respectively.
What is $S_z$, the $z$-component of the Poynting vector at $(x = 0, y = 0, z = 0)$ at $t = 0$?</p>
</blockquote>
<h2>Question 1</h2>
<p>What is the Poynting vector in a general sense? i.e. Abstractly, what am I trying to compute?</p>
<p>I know it is described as the directional energy flux density of an electromagnetic field. But, it is not traveling through a symmetric surface or anything of this nature so what am I trying to compute here?</p>
<h2>Question 2</h2>
<p>How do I actually compute the value I am looking for?</p>
<p>I know $\vec S \equiv \frac{\vec E \times \vec B}{ \mu_0}$ where $\vec E$ is the electric field, $\vec B$ is the magnetic field, and $\mu_0 = 4 \pi \times 10^{-7}$. But, I was under the impression that the magnetic field and the electric field are always perpendicular, why <em>isn't</em> $S_z = \frac{ c}{ \mu_0}$ since we are in a vacuum and $E = cB$?</p> | g12103 | [
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0.03... |
<p>You know that for a potential function (conservative force/fields) that</p>
<p>$\nabla U = \pm \vec{F}$</p>
<p>In math, we don't have that minus sign, we have only the plus one. </p>
<p>What does it mean if you get rid of the plus sign? I remember the minus signs tells us that the force is always in the opposite direction of the increasing potential function. Does math tell me there exists a potential function such that it's force also increases as potential goes up?</p> | g12104 | [
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<p>I am planning to use an air compressor to inflate a rubber balloon. I need to size the compressor for inflating the balloon, but for sizing the compressor I need the pressure required to inflate the balloon. So, can anyone guide me to calculate the required pressure for inflating a rubber balloon?</p> | g12105 | [
0.019238801673054695,
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<p>I'm currently working on maxwell equations and in order to lower the fields dimension, we perform a Fourier decomposition (according to $\theta$) due to the system symmetry. For any vector field $\mathbf{U}(r, \theta, z)$, we have,
$$ \mathbf{U}(r,\theta,z) = \sum_\alpha \tilde{\mathbf{U}}^\alpha(t,z)e^{i\alpha \theta}.$$
Together with the usual Maxwell equations (in cylindrical coordinate system) we decide to work with metallic boundary conditions. Let $\Omega$ be our domain and $\Gamma$ its boundary, then, for the electric field,
$$ \mathbf{E} \times \mathbf{n} = 0 \quad \text{on $\Gamma$}$$
Where $\mathbf{n}$ is the normal vector oriented outside $\Gamma$.</p>
<p>Then, my question is how to get the boundary conditions verified by $\mathbf{\tilde{E}}$ instead of $\mathbf{E}$ ? Does it lead to $\mathbf{\tilde{E}} \times \mathbf{n} = 0$ ?
An additional question would be : what about a non homegenous conditions such as $\mathbf{E} \times \mathbf{n} = f$ ?</p>
<p>I know that's pretty dumb but I can't convice myself.
Thanks in advance.</p> | g12106 | [
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0.0... |
<p>The question is sometimes referred to as the "psychological arrow of time" (Hawking, 1985). Here the past is understood as a moment or time when the entropy of the universe was lower, and contrarily for the future. So it is generally thought that PAOT is a consequence of the thermodynamic arrow of time of our universe. If so (maybe not?), how do the two relate? </p>
<p>Some explanations in the literature:</p>
<ol>
<li>Practical memory systems work in a way that the formation of new memories entails an overall increase of total entropy of the system and the environment. For example, to create a memory, i.e. to cause our neurons to orient in a particular fashion, requires energy which results in our body heating up a little bit, increasing the total entropy (Hawking, 1985 and 1994); The initialization of memory to make it reusable is an irreversible process that increases total entropy (Landauer, 1961. Wolpert, 1992).</li>
<li>More recently, People have argued that even reversible and non-dissipative memory systems are subject to PAOT (Mlodinow and Brun, 2014). The conclusion is arrived by imposing some constraints on what a memory system should be like. Specifically, they argue that a memory should be somehow robust to small microscopic changes in states of the system it records (what they call "generality" requirement). But the smallest changes in the future state destroy the thermodynamic arrow of time between now and the future. So any memory of the future of the system "could remember only one possible configuration of that system". This fine-tuning disqualifies it as a bona fide memory.</li>
</ol>
<p>My problem with explanation (1) is that even if it's correct, it doesn't seem to be a complete answer in itself. Yes, increase of (new) memory happens only as total entropy of the universe increases. So what? It doesn't have anything to say on the nature of that memory. Why couldn't it occasionally be a memory of the future for that matter? Explanation (2) leaves no such ambiguity. But the generality requirement seems artificial: surely a memory that records the only future configuration of the system remembers the future in a deterministic world, there being no "what ifs" regarding that state? </p>
<p>Of course, my understanding of the problem is only preliminary. I'd like to know whether there is not some generally accepted explanation, or any other thoughts you have on it. </p> | g12107 | [
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0.01... |
<p>In electromagnetism we say that all the electromagnetic interactions are governed by the 4 golden rules of <a href="http://en.wikipedia.org/wiki/Maxwell%27s_equations" rel="nofollow">Maxwell</a>. But I want to know: is this(to assume that there is no requirement of any other rule)only an assumption, a practical observation, or is there a deeper theoretical point behind it? Could there be a deeper theory behind assuming that there is not requirement of rules other than Maxwell's equations?</p> | g12108 | [
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0.0... |
<p>I have a background in engineering so I have some familiarity with basic math and science. I've recently been reading about other topics such as Einstein's relativity and have become interested in learning more about this and other similar topics in science.</p>
<p>Are there any books you can recommend that explains this and similar topics (also stuff like astrophysics, spacetime, etc), but aimed at a more amateur audience?</p>
<p>Thanks!</p> | g98 | [
0.018125107511878014,
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0.0034231499303132296,
0.059290602803230286,
0.023052752017974854,
0.06186031177639961,
0... |
<p>If the universe is heading for a big crunch, when the universe starts to collapse will entropy decrease and the arrow of time consequently reverse or not? I'm interested in the explanations, not just the answer.</p> | g12109 | [
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0.07896015793085098,
-... |
<blockquote>
<p>Before answering, please see <a href="http://meta.physics.stackexchange.com/a/4698">our policy</a> on
resource recommendation questions. Please try to give substantial answers that detail the
style, content, and prerequisites of the book or paper (or other resource). Explain what the
resource is like as much as you can; that way the reader can decide which one is most suited
for them rather than relying on the suggestions of others. Answers which just suggest a book
or paper may be deleted. </p>
<p>Also note that all answers to this question are automatically <strong>community-owned</strong>, so they are often subject to major editing, often to make them comply with the book policy. </p>
</blockquote>
<p>I am now going through Isham's book <em>Modern differential geometry for physicists</em> and got stuck with the notions of <a href="http://ncatlab.org/nlab/show/etale+space" rel="nofollow"><em>etale bundle</em></a>, <a href="http://ncatlab.org/nlab/show/presheaf" rel="nofollow"><em>presheaf</em></a> and <a href="http://en.wikipedia.org/wiki/Sheaf_%28mathematics%29" rel="nofollow"><em>sheaf</em></a>. Could someone please suggest some other, more intuitive and more accessible references on etale bundles and sheaves, preferably the ones giving more motivation and sufficiently many explicit (and worked-out) examples and, preferably, accessible to theoretical physicists (i.e., not just mathematicians)? </p>
<p>P.S. To make things clear, a few math texts I have managed to find so far like Godement's and Bredon's <em>Sheaf Theory</em> (two books with the same title) seem way too tough for me. The part on sheaves in Arapura's <em>Algebraic Geometry over Complex Numbers</em> is somewhat better but still a bit too fast going and with too few examples and not too much motivation. Pretty much the same applies to the part on sheaves (which is too brief anyway) in the Clay Institute volume <em>Mirror Symmetry</em>. If there are no suitable books, are there perhaps some good lecture notes on the subject accessible to physicists rather than just mathematicians, from which one get a reasonable intuition on sheaves and stuff? </p> | g12110 | [
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0.07371603697538376,
0.0444268137216568,
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0.07179541885852814,
-0.0051121... |
<p>A half pipe of a skateboard park consists of a concrete trough with a semicircular section of radius 5m, I hold a frictionless skateboard on the side of the trough, pointing down toward the bottom and release it; how long will it take to come to back to the point of release?</p>
<p>Note: I am supposed to use Newton's laws and polar coordinates. The solution is already given in the book, I am just confused as to why $F_r$, the force in the radial direction, is equal to $mg\cos\theta$ minus the normal force (where $\theta$ is the angle from the origin of the half circle). Also, I am used to using the vector form of Newton's laws in polar coordinates and not using conservation of energy or free fall or anything else.</p> | g12111 | [
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0.01505452860146761,
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0.001220... |
<p>At the LHC, researchers smash particles into each other at speeds close to speed of light. Photons, on the other hand, already move at the speed of light. Do they ever smash into each other? Or do they just go through each other? Why?</p> | g386 | [
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<p>I know that $\frac{\lambda_2}{\lambda_1} = 1 + z$</p>
<p>Suppose a galaxy had redshfit $z=3$. Does this mean that the wavelength becomes $4\lambda$?</p>
<p>Then by wien's law where $\lambda \propto \frac{1}{T}$, does this mean that the temperature now observed is $\frac{1}{4} \times 2.73 K$?</p> | g12112 | [
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... |
<p>I wonder if I could use the technique for finding the tunneling rate given by $$ \Gamma=2 \Im[ F]$$ where $F$ is the free energy in case of time dependent potentials?
Relevant to the previous question, how can I find the perturbation to an instanton with a week time dependent potential?</p>
<p>I appreciate your help.</p> | g12113 | [
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<p>The explanation of shear rate in laminar flow is straightforward: We imagine small layers of fluid that glide on each other. Now, in turbulent flow, this does not work as there are no layers. I'm not even sure that shear rate is a meaningful concept in turbulent flow.</p>
<p>If I want to know the apparent viscosity of a shear thinning (or other non-Newtonian) liquid, I need to know the shear rate. How do I know the shear rate in turbulent flow?</p> | g830 | [
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0.026345496997237206,
0.057083... |
<p>I have always wondered why salt is white, water is clear and gold is, well, gold. What determines the color of a substance? Does it have something to do with the electrons? And is it possible to predict the color of a substance by looking at the formula?</p> | g12114 | [
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<p>I'd like to know (my knowledge at physics are realy poor) what would happen if I've got a generator connected to another generator and both of them generating electricity for a house or whatever.</p>
<p>Like this:</p>
<p>G1 is connected to G2 and the plug. So it gives electricity to both of them making G2 to "load electricity" and plug usable.</p>
<p>When G1's energy is finished, G2 starts using the "loaded electricity" making G1 to "load electricity" and still the plug usable.</p>
<p>Woudn't that make an infinite electricity system?</p>
<p>Thanks!</p>
<p>Diego</p> | g12115 | [
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<p>Comparing the simples form of the forces of both phenomena: the law of Newton for gravitation $V\propto \frac{1}{r}$, and the Coulomb law for electrostatics $V\propto \frac{1}{r}$, one might think that if one can be extended relativistically to a curvature in space-time, that the other one would lend itself to a similar description. Is this so?</p>
<p>Thanks for any useful thoughts and/or suggestions!</p> | g247 | [
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<p>In the recent <a href="http://cdsweb.cern.ch/record/1406042" rel="nofollow">Higgs seminar</a> at 73:38 <a href="http://cdsweb.cern.ch/record/1173837" rel="nofollow">Guido Tonelli</a> the spokesman for CMS, makes a mistake and refers to a Z-prime in a context that would imply that they see them frequently. He swiftly backpedals amid the general hilarity of the concept. However a few seconds later he remarks that "There is something behind this", implying that there is a reason why he might have Z-primes on his mind and he says "Fabio knows" referring to Fabiola Gianotti who leads the ATLAS team.</p>
<p>Can we expect some announcement regarding a Z-prime boson? Does anyone have more information? </p> | g12116 | [
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<p>I understand this is a homework problem. I don't expect anyone to do my homework for me, but help me understand what I am doing wrong.</p>
<blockquote>
<p>The problem goes: Two shuffleboard disks of equal mass, one orange and
the other green, are involved in a perfectly elastic glancing
collision. The green disk is initially at rest and is struck by the
orange disk moving initially to the right at oi = 5.30 m/s as in
Figure (a) shown below. After the collision, the orange disk moves in
a direction that makes an angle of θ = 35.0° with the horizontal axis
while the green disk makes an angle of = 55.0° with this axis as in
figure (b). Determine the speed of green disk if the final velocity of the orange disk is 4.34m/s</p>
</blockquote>
<p>First I draw the collision out. with the angles and everything. This helps me with visualizing what is happening.</p>
<p>Now i separate the Elastic Collision into x & ycomponents:</p>
<p><em>since the masses are all the same does that mean in the elastic collision equation the masses cancel out?</em></p>
<p>if so this is the equations</p>
<p><strong>My x equation</strong></p>
<p>5.30m/s + 0 = 4.34m/s*cos(35) + Vgf</p>
<p>Vgf(x) = -1.3513 m/s</p>
<p><strong>y equation</strong></p>
<p>0 + 0 = 5.30*sin(35)+Vgf</p>
<p>Vgf(y) = 2.6412</p>
<p>Then I do sqrt( (Vgf(x))^2 + (Vgf(y))^2) = 2.64 m/s (which is the incorrect velocity of the green disk.)</p>
<p>Though this is incorrect.</p>
<p>My only idea to why this is incorrect is probably because of the mass part of the Elastic Collision equation. I don't know how to use the collision equations without the masses given. What do I do? </p> | g12117 | [
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