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Let $H_1,H_2\in\mathcal{C}^1(\mathbb{R}^3;\mathbb{R})$ be two scalar fields. Consider a trajectory $\vec{x}(t)\in\mathbb{R}^3$ such that, for all observable $f\in\mathcal{C}^1(\mathbb{R}^3;\mathbb{R})$,
$$\frac{\mathrm{d}}{\mathrm{d}t}f(x)=\det\big(\nabla f,\nabla H_1, \nabla H_2\big)=\frac{\partial(f,H_1,H_2)}{\partia... |
In an isolated system of two colliding protons [ say, proton1(p1) and proton2(p2)];
initially p2 is at rest, and p1 is moving with uniform horizontal velocity $\vec{u_1}=a \hat{i}$ m/s.
First way of analysing the collision:
I have considered the Columbian Force as an internal force.
For an elastic collision of two obje... |
I want to understand the physics that occur during the attempt at tipping over a bottle / rocking a bottle back and forth.
I am expecting that:
when the finger pushes the bottle for a tiny moment, it applies a force (F1). It makes sense that the bottle will tip in that direction. I'll call this vector V1.
after a peri... |
I wonder if there is any difference between these two terms. Is transverse conductivity always equal to Hall's conductivity?
I am asking in the context of the thermal and electrical conductivities of a material.
|
This question is about an application of crystallography to topological string theory.
Plane partitions are discrete models of the Planck scale geometry of Calabi-Yau manifolds in the A-model topological string (quantum foam and topological strings). The following are four different examples of plane partitions:
Fo... |
Apparently the absorption of any neutron, even without attached kinetic energy, is enough to overcome the binding energy of U235, and fast neutrons scatter more vs thermal neutrons, so thermal neutrons are better for U235.
What about the structure of U238 is different vs U235 to not also scatter fast neutrons but to ab... |
When I purchase a quartz table/wall clock, most of the time it has a sticker saying not to use alkaline battery and from this quora question. There is also mixed thought about this but in theory (I think) both alkaline and zinc-carbon battery should not have any differences because both of them have $1.5\,\text{V}$ so ... |
In J.J. Sakurai's Modern Quantum Mechanics, he introduces the concept of 'Unitary Equivalent Observables'.
If $|a^{'}\rangle$ and $|b^{'}\rangle$ are the orthonormal bases eigenkets of two non-commuting hermitian operators connected by the unitary operator $\hat{U}$ ($|b^{'}\rangle = \hat{U}|a^{'}\rangle$), we can cons... |
Could not find answer via web search. To avoid motion blur we use high speed cameras. For seeing with high speed more light is needed lighting-for-high-speed.
If alien spaceship would not emit billions times per square space more intense light then our sun Visualizing video at the speed of light — one trillion frames p... |
So I am trying to find equations of motion for the Lagrangian associated with a non-Abelian Gauge theory for $SU(N)$, and while I was doing the math, I was a bit confused the indices.
So I have $\mathcal{L} = -\frac{1}{4}F^i_{\mu\nu}F^{i\mu\nu}$
Where $F^i_{\mu\nu} = \partial_\mu A^i_\nu -\partial_\nu A^i_\mu +gf^{ijk}... |
I came across this word Center of Percussion while reading SHM from Resnick Halliday Krane Vol. 1 and couldn't figure out why it is called so. Please help me in doing so.
|
In my textbook, there is an equation expressing a nonperiodic wave function as an infinite sum of waves over a continuum of wave numbers
$$
\psi(x) = \int_{-\infty}^\infty A(k)e^{ikx}dk
$$
I know that
$$
\mathrm{probability \ density} = |\psi|^2 \\
k=\frac{2\pi}{\lambda}
$$
I determine the unit of $\psi(x)$ to be $m^... |
I have read often that charge, like mass, is an intrinsic property of an electron. But even the mass is due to its interaction with the Higgs Field. So is there something which explains where the electron, or any fundamental particle for that matter, get its charge from?
|
I understand that polar unit vectors are given by
$e_r= \cos(θ)i + \sin(θ)j$
$e_θ=−\sin(θ)i + \cos(θ)j$
How do I now express cartesian unit vectors in terms of polar unit vectors to show that they are independent of the $r$ and $θ$?
|
There is an important theorem in vector calculus that says $\boldsymbol{\nabla}\boldsymbol{\cdot}\mathbf{G}\boldsymbol{=}0$
(where $\mathbf{G}$ is some differentiable vector function) implies and is implied by $\mathbf{G}\boldsymbol{=}\boldsymbol{\nabla}\boldsymbol{\times}\mathbf{H}$ (where $\mathbf{H}$ is another dif... |
I'm trying to learn how to draw a momentum diagram but I didn't find any specific method to do so. I following the The Geometry of space-time by Tevian Dray.
What I know is that The geometry of 2-Momentum looks like :
But I'm not able to use this in different problems for different observers. If there are any specific... |
I was wondering how can one describe the tension force in a continuous way along a rope. We can look at a rope segment of length $dx$ and say the net tension force is $$T\sin\theta_{x+dx} - T\sin\theta_{x}$$ but that of course describes the tension force on a segment. I sometimes see that in texts they refer to the ten... |
When developing Quantum Field Theory, we usually refer to the Minkowski coordinates which cover the whole space in the case it is flat. I don't know how to set distribution theory and Hilbert space theory in this scenario.
I suppose the Hilbert space to be based on the whole Manifold, although in each hypersurface we a... |
The Flamm's paraboloid is a slice of the Schwarzschild metric by two spatial dimensions. This shows the space dilation, but without the time component doesn't really give much insight into the geodesics. Is it possible to somehow plot a slice by the time and one spatial dimension instead?
|
Perhaps this is not the best place to ask this but I'll ask anyway.
In less than a year, I'll be getting my bachelor's in general physics from Afghanistan, however I feel like my knowledge is like a house of cards, it seems pretty from afar but slight wind might blow it all away.
What I mean is that while we have worke... |
According to Fourier's theorem, we know that a sawtooth wave can be represented as a sum of sine waves. These sine waves we know as harmonics (in the context of sound). My understanding is that it is the same for electrical current.
Let us take a band-limited sawtooth wave in an electrical circuit. Say its frequency is... |
The scalar product in special relativity is given by
\begin{equation}
V \cdot W = V^{\mu} g_{ \mu \nu} W^{\nu}
\end{equation}
and the components of the vectors $V^{\mu}$ and $W^{\nu}$. With the metric
\begin{equation}
\eta_{ \mu \nu} = \mathrm{diag} (-1,1,1,1)
\end{equation}
if we using Cartesian coordinates.... |
I was solving an exam when I came across this question:
A compressed spring projects a ball horizontally in a vacuum chamber. On the Earth, the ball reaches the chamber floor 4.0 m in front of the spring.An identical experiment is done on the Moon. The gravitational field strength is lower on the
Moon than on the Eart... |
I think that heating up a gas increases the temperature of the gas. A higher temperature increases the speed of the particles in the gas.
However, there is a step missing from my answer to get full marks.
The step is that we note that a higher temperature means a higher kinetic energy. This then means a greater average... |
I am following Nima's course on "Quantum mechanics and spacetime, total positivity and motives", and I wonder if there's a direct way to understand the ordering ambiguity when we are summing over different channels. In other words, how do we know if we should use $\langle12\rangle$ or $\langle21\rangle$.
I know it does... |
In the case of bosonic condensation such as BEC all the boson particles condensate into ground state. But fermion follow pauli exclusion principle so what is meant by fermionic condensation in superconductivity?
|
I'm a high school student.
We were taking Magnetic flux in school and the formula is $\Phi=BA\cosθ$.
Please Bear with me. My issue lies in the cosθ. I'm assuming here we treated the area as a vector but how can we treat the area as a vector? and how can the area decrease due to change in orientation?
I really want to u... |
I'm trying to find the solution to the 2D stationary diffusion equation
$$-D\nabla^2P(\vec{\rho_2})=\delta(\vec{\rho_1}-\vec{\rho_2})$$
where $\vec{\rho}=(x,y)$ and $D$ is the diffusion coefficient.
Help would be very much appreciated. Also, I'd be happy to get some references as well.
Thanks in advance.
|
I was recently studying Blackbody Radiation and the principle behind it (as far as used in the Plancks original paper) is to find the energy distribution which maximizes the number of ways in which energy quanta can be distributed.
Since the radiation formula is derived due to quantization + maximum entropy reasons, ca... |
As I understand it, the scalar curvature is a function that assigns a real number between $]-\infty,\infty[$ to each point $(x,y,z,t)$ of a manifold:
$$
R:\mathbb{R}^4\to \mathbb{R}
$$
I am having difficulty picturing the scalar curvature and why it is treated as an independent quantity. Specifically, according to Wiki... |
I understand that the Earth (or someone standing on our planet) will undergo time dilation due to a number of reasons compared with someone hovering in interstellar space. I would like to focus on two of those causes. One the time dilation due to the motion around the sun, the other the time dilation caused by the grav... |
In quantum mechanics, the kinetic energy of a particle described by the wave function $\psi$, is related to the curvature of the $\psi$. This is easily seen, but I have confused my self with the negative sign. That is: $\hat{T} = -\frac{\hbar^2}{2m}\nabla^2$, is the kinetic energy operator. So what I gather is, that th... |
Unfortunately, for chemists, are curriculum is (usually) not as rigorous in the mathematics and physics as I would’ve liked. This (in my humble opinion) is a disservice to those looking to explore more physical areas of chemistry.
As an aspiring nuclear chemist, I need some recommendations for a good place to start to ... |
The problem statement is as follows:
Two balls of masses $M$ and $2M$ are thrown horizontally with the same initial velocity $u$ from the top of a tall tower and experience a viscous drag of $-kv$ ($k>0$) where $v$ is the instantaneous velocity. Compare the ranges of the two projectiles.
Now, I separately considered ... |
When doing 2d CFTs we typically complexify coordinates and formally consider $\mathbb C^2$, with the understanding that, in the end, we are to restrict to the real slice $\bar z=z^*$. If we do not impose this, but regard $z,\bar z$ as truly independent, does the resulting object define a healthy four-dimensional QFT? I... |
For a set of two double pulleys, the force acting on each should be equal to the tension in the rope times the number of ropes connected to the individual pulley if I understand correctly. In this pulley system on mcmaster, it looks as though the force acting on the upper pulley should be 5T (with T being tension) and... |
suppose we have a potential that's independent of time $V(x,t) = V(x)$
so in Schrödinger equation we get:
$$i\hbar \frac{\partial \Psi (x,t)}{\partial t}=-\frac{\hbar^2}{2m}\frac{\partial^2 \Psi (x,t)}{\partial x^2}+V(x)\Psi(x,t)$$
since the LHS involves a variation of $\Psi$ with $x$ and the LHS involves a variation o... |
In quantum mechanics one can "always" write the way an operator acts on a wave function as a coordinate transformation. As an example we can look at unitary representation of the momentum operator
\begin{equation}
U=e^{\frac{i}{\hbar}p} \psi= \psi(x)+a\psi '(x)+\frac{a^2}{2}\psi '' (x)+...=\psi(x+a)
\end{equation}
with... |
I have almost finished reading the basics of Bosonic String Theory from Becker, Becker and Schwartz as well as Tong's notes.
What is the best book to start reading about Superstring theory (something which is slightly easier than Polchinski). I am confused among these options:
String Theory in a nutshell by E. Kiritsi... |
First of all please do not flag this question as duplicate(I have read all the others like this one, this one and this one is just talking about observable universe. none of them talked in this context) read it completely.
There is not any proof that energy remains constant for universe just evidence for a observable s... |
Given:
$$m_1 = 2*m_2$$
$$m_{disc} = 3*m_1 = 6*m_2$$
$$h = 3R$$ (R is the radius of the cylinder at the top)
Find $v^2$ in terms of $g$ and $r$, where $v$ is the velocity of the blocks when $m_1$ is just about to hit the floor. Assume that the string does not slip over the cylinder at the top, and that the cylinder doe... |
Lets say we have a well full of water (For now lets say it is cylindrical) .Lets say its height is $h$$well$. The water is filled upto a height $h$$water$. The radius of the well (cylindrical) is $r$ .Here , $h$$water$ $\lt$ $h$$well$ . A Pump has to bring all of that water from the well upto the height $h$$target$. Th... |
The electron is known to have an intrinsic magnetic moment, where a magnetic moment is generally defined as "the magnetic strength and orientation of a magnet or other object that produces a magnetic field."
In various sources (e.g. The Feynman Lectures, Wikipedia, popular science videos), it is commonly stated that "a... |
I am struggling with understand the whole situation that is described in the following question:
Two balls attached to a string that connects with the same volume of 15 ${cm}^3$. They float on the water(fresh water) when only one half of the top ball is in the water and the other one is floating above water level. The ... |
I'm reading the book $[1]$ (which is not a scientific communication book, rather a student-friendly introduction to Quantum Mechanics).
Jakob $[1]$ then writes:
Many people unfamiliar with quantum mechanics may wonder how an electron could be a partile and a wave at the same time. Please ignore this kind of idle specu... |
Suppose a classical Hamiltonian of the form
$$\mathcal{H}=\frac{1}{2m}(p^2_x+p^2_y)+a(x^2+y^2)^{1/2}$$
We know that this change to following quantum operator
$$\hat{H}\rightarrow -\frac{\hbar^2}{2m}\left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial x^2}\right)+a(x^2+y^2)^{1/2}$$
in coordinate basis. But d... |
In canonical formalism we know that a symmetry for the dynamical system can be expressed by $\{H,f\}=0$, where $H$ is the hamiltonian of the system and $f$ is the smooth function associated to the infinitesimal generator of a transformation (because you can think about the infinitesimal generator of a transformation as... |
I have had this doubt for a while now.
Let there be a circular banked road of some inclination with the ground.
For the sake of this question let's assume it is frictionless.
If an object with a constant velocity is travelling on it, it is in turn having a centripetal force acting on it towards the centre of its path.
... |
I encountered the following integral in dimensional regularization
$$
I=\int d^d k \,e^{i\vec{k}\cdot \vec{x}}\frac{1}{\vec{k}^2}\frac{1}{(\vec{q}-\vec{k})^2},
$$
say that we already Wick rotated the integral.
This looks like something which would be possible to evaluate but I'm not managing to do so. I tried Schwinger... |
I saw this animation (in which a man is running in place) and thought to repeat it and guess what ... I was able to do this.
My legs were pushing the earth back (I know this since my legs were sliding on the rough surface) but I was not being displaced. I would like to know how is this even possible. There is just a s... |
Consider the force due to a point charged particle at the origin and the particle which we move to also be charged with the same charge.
When we move a particle from point $\mathbf{x}$(position vector) from origin to infinity(radially), if there is some force $\mathbf{f}$ at $\mathbf{x}$ (position vector) then some wor... |
I have started learning about the wave nature of matter. But unlike classical physics, I am having trouble imagining the wave nature. I am unable to imagine that a particle with mass, can also have a frequency. I asked this question to my teacher and he said that I do not have the necessary skills to imagine the situat... |
When I tried to derive General relativity I realized that in different non-inertial frames we just can't compare anything, including time intervals, because gravity spoils everything thus making everything uncomparable. So we just can't construct an ideal clock.
We can't measure anything, because in a non-inertial fram... |
Neutral wire has a V same as ground i.e almost 0. Also it carries some current. So if we touch the wire don't we to become a part of the circuit? Even if we are on the ground and current should flow through us, but I read we don't get a shock as there is no potential difference between ground and neutral wire, but the ... |
Suppose there's an upright cylinder in the water. The pressure at the bottom's more then the pressure at the top, so shouldn't there be a net force upwards? Does this matter much?
|
No-hair theorem asserts that black holes can be defined by only their mass, angular momentum and electric charge.
Do black holes treat strong force differently, ie can black hole have color charge? While not very likely to happen in practice, is there any theoretical blockers for this to happen?
|
In particular, we know that $P$ symmetry (parity transformation, which is basically a reflection), is not the symmetry of the universe, a whole combination of $C$, $P$, and $T$ is. Because of this, it's not clear to me why Minkowski space preserves reflections (universe doesn't). Is this property really necessary to mo... |
We say that a complex periodic wave has an energy at certain frequencies.
Or we can also say that such waveform has a certain “frequency component”.
I understand that mathematically it means we can extract this frequency component from our initial complex waveform using Fourier transform.
But what is the physical meani... |
I am a beginner in mechanics, and when I was introduced to moments there was a theorem that says "if a set of forces acting on a rigid body has a resultant, then the algebraic sum of these forces about a certain point is equal to the moment of the resultant about this point" so what I understood is if the resultant of ... |
I have been working the Rydberg equation with large $n$ to see how quantum systems when they become very large are functionally identical to classical systems. The problem I'm facing is trying to approximate the energy between two states when $n \gg 1$.
I've gotten up to the point of
$$\frac{1}{n^2(1+1/n)^2} - \frac{1}... |
Consider a complex scalar field $\psi(x)$ with Lagrangian density
$$
\mathcal{L} = \partial_\mu\psi^* \partial^\mu\psi - M^2\psi^*\psi.
$$
From the Lagranigan density we obtain the momentum $\pi = \dot\psi^*$. How do you obtain this? I expanded $\partial_\mu\psi = \partial _{0}\psi -\nabla\psi$ and then took the conjug... |
There are well-known definitions of complete geodesic and geodesically complete spacetime:
A geodesic is complete if an affine parameter for the geodesic extends to ±∞.
A spacetime is geodesically complete if all inextendible causal geodesics are complete.
For example, Minkowski spacetime is geodesically complete, ... |
In the book Critical Dynamics by Tauber the following scaling hypotheses are made for the static correlation function and for the characteristic frequency in Fourier space
$$
C(\tau, q) = |q|^{-2+\eta} \hat{C}_{\pm}(q \xi)
$$
$$
\omega_{c}(\tau, q) = |q|^z \hat{C}_{\pm}(q \xi)
$$
Here $\tau$ is the reduced temperature ... |
If I am given the energy bond of a specific bond in a molecule, is that the energy of one photon? and if I have, for example 2 bonds like this, there will be needed 2 photons, etc...? (In other words- does each photon required to break one bond)?
Thank you very much
|
If I have some action that depends on a set of variables like so:
$S(\{\phi_{i} \}) = \phi_{i}A^{-1}_{ij}\phi_{j} + g(\phi_{i})$
(where einstein summation notation is being used for the term $\phi_{i}A^{-1}_{ij}\phi_{j}$ and $g$ is just some function)
How could I taylor expand the action around a specific value of $\ph... |
In QFT, when we take the scattering matrix $S$ and work it out to compute amplitudes, it is usually said that $S$ is written in the interaction (Dirac) image such that the fields $\phi_I$ that $S$ depend on evolve in time in following way:
$$
\phi_I(\vec{x}, t) = U_0^\dagger (t, t_0)\phi(\vec{x}, t_0) U_0(t, t_0) \tag1... |
If one considera a dipole system, is it possible to model the system using complex variables and if ao, how can we use complex analysis to model it? I have the idea that we can model dipole moment as a complex variable and then use a line integral to determine the potential energy at any point in the system. However,I ... |
Luttinger in his publication about the theory of thermal transport coefficients write phenomenological equations in the form
$$
j_\alpha(r) = L_{\alpha\gamma}^{(1)}\bigg[E_\gamma-\frac{1}{e}T\nabla_\gamma(\frac{\mu}{T})\bigg]+L_{\alpha\gamma}^{(2)}T\nabla_\gamma(\frac{1}{T}) + \tilde{L}_{\alpha\gamma}^{(2)}(-\nabla_\ga... |
I was reviewing a little of quantum mechanics in a rigorous way, so i realized there is a lot of concepts similar in words but different in its meanings, i would appreciate any help to understand it:
Kets -> It is the "physics entity" you are measuring: Momentum, energy, etc...
Operators -> What you actually use to get... |
Consider the following scenario: https://youtu.be/8H98BgRzpOM?t=27.
How would I calculate the total angular momentum of this system? The spinning wheel is rather easy, and it's $L_{\rm wheel}=I\omega$. However, I am not sure how to account for the angular momentum due to precession. Is it simply $L_{\rm press} = I\Omeg... |
I'm making a spaceship piloting game, and I'm trying to make the movement follow the laws of physics. The ship is able to control it's angular acceleration in pitch, yaw, and roll. The way I've implemented it, the ship rotates around it's local x, y, and z axis, however, I'm having a hard time wrapping my head around r... |
Example 16.17, on page 380 of the dynamics part of the 14th edition of R.C. Hibbeler's Engineering Mechanics: Statics & Dynamics, states:
The crankshaft $AB$ turns with a clockwise angular acceleration of $20\;\text{rad/s}^2$. Determine the acceleration of the piston at the instant $AB$ is in the position shown. At thi... |
I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention:
At page 195 the authors say that universes with different symmetries could be modeled and they would have dramatic results like having different conservation laws.
I asked Mr. Lewis if he could give me more... |
I don't understand the principles at play that make a Shkadov Thruster produce thrust upon a star. As I understand the idea, you produce a mega structure on one side of a star, reflecting half of its light back in the direction of the other light produced from the star. Somehow this produces a thrust for the star in th... |
The action for the free Maxwell theory is given by $$S=\int d^dx\sqrt{-g}\bigg(-\frac{1}{4}F^{\mu\nu}F_{\mu\nu}\bigg)$$
The theory is invariant under conformal transformations $g_{\mu\nu}\to\Omega^2(x)g_{\mu\nu}$ only in $d=4$ as can be recognized by looking at the trace of the energy-momentum tensor of the theory, or ... |
I am trying to derive the Thin Plate Energy Functional. Given a Thin Plate $z = z(x,y)$, how does one derive the energy function:
$$\iint_{\mathbb{R}^2} \,\left[\left(\frac{\partial ^2z}{\partial x^2}\right)^2+2\left(\frac{\partial^2 z}{\partial x\partial y}\right)^2+\left(\frac{\partial^2 z}{\partial y^2}\right)^2\rig... |
Q. The gravitational field due to a mass distribution is given by $E=k/(x^3)$ in $x$-direction. Taking the
gravitational potential to be zero at infinity, find its value at a distance $x$.
for the answer let the 'integral where the lower limit is infinity and upper limit x' be denoted as I
The answer my textbook gives ... |
I read this paper on Lorentzian Quantum Cosmology. But I couldn't understand the term minisuperspace which is used to define the path integral $$\int\mathcal{D}N \mathcal{D}\pi\mathcal{D}a\mathcal{D}p\mathcal{D}c \mathcal{D}\bar{P} e^{\frac{i}{h}\int_0^1 dt(\dot{N}\pi+\dot{a}p+\dot{c}\bar{P}-NH)} $$ where $a,N$ are r... |
For example, assume you have two sintered neodymium magnets that are 10mm x 20mm x 30 mm.
Will these magnets both generate the same magnetic field? Ie, is the field a consequence of the geometry, or the manufacturing process?
If the field is simply a result of the geometry, how do you calculate the magnetic field from ... |
I have just been watching about EPR experiment on Leonard Susskind videos called entanglements and at
the end of the 7 lecture he said that for say two particles of opposite spin up/down and at long seperation
if you "measure the spin of one you instantly know the spin of other particle". He then said something
like "... |
I'm in a first course on statistical mechanics at the moment and I'm having trouble wrapping my head around an example problem involving the canonical partition function. The question setup has a three particle system with three different energy levels corresponding to $0$ J, $1000$ J, and $2000$ J. The microstates tha... |
I know that in special relativity, the invariant interval $ds^2$ for a light signal's worldline is $$ds^2=\eta_{\mu\nu}dx^\mu dx^\nu=0$$ where the flat metric $\eta_{\mu\nu}=\text{diag}(-1,1,1,1)$.
How does this result extend to
$$ds^2=g_{\mu\nu}dx^\mu dx^\nu=0$$
for the worldline of a light signal in general relativt... |
I've heard a lot of times that energy cannot be created or destroyed. I get this in a nonfundamental way, a car's energy is the form of gas is transferred into another type of energy which allows the car to move, etc. Anyways, if energy cannot be created or destroyed, how does our universe exist? Our universe is made o... |
Say you have some $\textbf{B}$ field from an alternating current, $\textbf B(t) = \textbf{B}_0\cos{\omega \,t}$. And using Faraday law, e.m.f. $\varepsilon$ = turns of a coil $\times$ the time derivative of the flux of the $\textbf{B}$ field going through the coil area. $$\varepsilon = -N \cdot \frac{d\phi_B}{dt}.$$
If... |
One should minimize the distance between two points x1=(x1,y1) and x2=(x2,y2). The holonomic constraint states that $f(x)=x^2-2x+5$ where x1 is an element of this graph and x2 is an element of the graph of a different function: $g(x)=2x-1$.
Now the goal is to use the constraints in such a way, to eliminate two of the g... |
Consider the configuration pictured below: a cart with a u-shaped pipe on it, with a fan on one end blowing air into the pipe.
The fan rotates and makes wind towards the left. The wind will be curved in the bent part of the pipe and will come out with changed direction. The pipe is attached to the cart.
There are fact... |
A point mass $m$ is connected by a massless rod of length $l$ to a fixed point of support, now consider the mass moves on a circular path, rod has constant angle $θ$ with $e$ vertical, what's the angular velocity of motion around the circle.
If the $θ$ is constant, which is not change with time, should the angular velo... |
Let's say we have a particle of mass $M$ attached to a point $P_0$ by some massless rod of length $T$ and it is undergoing circular motion at a constant angular velocity.
There is more to this problem, but my confusion only lies here. We define torque as $\mathbf{\tau}=\mathbf{r}\times \mathbf{F}$ where $r$ is the posi... |
It is argued that the boundary conditions on a particle in a box (the box being a potential with value $0$ on the interval $[0,L]$ and infinite everywhere else) are $\psi(0) = \psi(L)=0$. Since the particle cannot with any probability be outside the box, the wave function there must be zero, so by continuity that bound... |
In other words, how much does gravity curve space at the earths surface?
Assuming the earth is “flat” over a distance of 1 meter, how far down is a horizontal beam of light deflected due to general relativity over a distance of 1 meter.
Does the beam just “fall” at 1G?
|
As for the title, by which way neutrinos can interact with matter such as, e.g., pseudocumene or other scintillators?
Is it a merely mechanical collision?
Do neutrinos collide with nuclei and how "to see" the collision? Normally collisions involve electromagnetic interactions.
I didn't find any hint on Wikipedia articl... |
If light rays do not intersect, there won't be any photons, but if we can see a virtual image there should be a source. Is there then a partial reflection connected to this?
|
For a particular cylindrical beam that is bent and twisted, its bending stiffness is found to increase with twist. I have a limited knowledge of continuum mechanics. Can the theory explain this, without introducing an ad hoc bending stiffness? For example, can twist-bending coupling explain it? If yes, how?
This is mot... |
The advection-diffusion equation is given by
$$\partial_{t}\rho=-\nabla\cdot\left(\rho\mathbf{v}_{drift}\right)+\nabla\cdot\left(D\nabla\rho\right)\equiv-\nabla\cdot\left(\rho\mathbf{v}_{current}\right).$$
Does this drift velocity $\mathbf{v}_{drift}$ satisfy a Newtonian equation of motion
$$m\frac{d}{dt}\mathbf{v}_{dr... |
Context: Trying to proof Lagrangian equations without an explicit usage of the concept of virtual displacement.
(disclaimer for happy close-vote triggers: I'm not related to any academic institution as student nor as teacher nor as dean)
Let a position vector in generalized coordinates $\mathbf{r}=\mathbf{r}(q_0,\dots,... |
I am wondering how can I bond a optical fiber to waveguide grating coupler. Should I use some type of glue? Or should I fix the fiber with a translation stage?
|
In D.K.Cheng's Field and wave electromagnetics he states the following:
The phasor electric field intensity for a uniform plane wave propagating in the +$z$-direction is $$\mathbf{E}(z)=E_0e^{-jkz} $$
where $E_0$ is a constant, $j$ is the imaginary unit and $k$ is the wavenumber.
My question is, why is this a wave? I... |
https://sites.rutgers.edu/barry-loewer/wp-content/uploads/sites/195/2019/06/Albert-Loewer-Interpreting-the-Many-Worlds-Interpretation.pdf
According to the paper above, it seems to suggest one single physical world.
Page 208: 3rd paragraph: Fourth, the MMV (unlike the SWV) entails that the choice of basis vectors in ter... |
If we hold one end of a slinky and leave other end free, the earth's gravity applies force on the slinky and it expands. If we do the same on the moon with the same slinky, will the acquired height of the slinky be different?
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Suppose I have a point charge sitting in the $z>0$ half-space in front of a (infinitely large) conducting plate lying in the $x,y$ plane. I know how to calculate the field in the upper half-space using mirror images.
But how does the field look like on the other side of the plate? Is it zero?
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