Questions tagged [physics]
Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.
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Can a 4D spacecraft, with just a single rigid thruster, achieve any rotational velocity?
It seems preposterous at first glance. I just want to be sure. Even in 3D the behaviour of rotating objects can be surprising (see the Dzhanibekov effect); in 4D it could be more surprising.
A 2D or ...
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Questions on color theory, expressed in linear algebra
I'm reading into color theory and there were a few questions which I asked myself along the way, maybe you can put me forward to some source where I can find answers or give them directly.
The ...
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How to solve a time-dependent Schrodinger equation in periodic Dirac delta potential
I'm trying to solve a 1D time-dependent Schrodinger equation:
$$
i\,\frac{\partial \psi(x,t)}{\partial t}=\left[-\frac{1}{2} \frac{\partial^2}{\partial x^2}+V(x)+F(t)\,x\right]\!\psi(x,t)
$$
where $...
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Intuition for the Yang-Baxter Equation (was: Giving relations via formal power series)
I'm reading a book (Yangians and Classical Lie Algebras by Molev) which regularly uses (what appear to me to be) clever tricks with formal power series to encapsulate lots of relations. For instance, ...
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Is there a simple maximally general generalization of Noether's theorem to arbitrary dynamical systems?
Noether's theorem informally states something like "symmetries in the dynamical law imply conserved quantities". However, the theorem is generally stated in terms of physics-specific classes ...
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Gauss-Bonnet theorem proof considering membrane Force and hydrostatic fluid Pressure equilibrium
Is it possible to prove Gauss-Bonnet Theorem by using physics (Mechanics of materials) models?
For example in mechanics could one consider static equilibrium by action of hydrostatic pressure ...
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Why are Wigner matrices the appropriate representation for rotations in physics?
Question. Why are the Wigner-D-matrices the appropriate representation for rotation of operators with respect to space-coordinates in physics?
Background. A physics paper brought up this question in ...
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Is this physical model exactly solvable?
There exists a popular model in the Physics of heavy quark bound systems, called the Cornell potential model, in which the inter-quark potential is modeled to vary with radial distance $r$ as
$$V(r) ...
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Integrating $\int_{0}^{\infty} \frac{p^6 dp }{1 + a p^4 + b p^6 } \int_{0}^{\pi}\frac{\sin^5 \theta \,d\theta}{1 + a |p-k|^4 + b |p-k|^6 }$
This is my first question here, so I hope I'm not giving too little/too much information. I need some help calculating (or even approximating) an integral which I've been wrestling with for a while.
...
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Movement time of object with constant jerk, limited acceleration and velocity
A product is initially at rest on a conveyor belt:
The initial conditions of the product can be described as follows:$$x_i=0$$ $$v_i=0$$ $$a_i=0$$$$j_i = j⋆ $$.
The product will be moved forward ...
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What does it mean that the three-body problem has been proved to be "unsolvable" and how was it done?
Wikipedia says:
In 1887, mathematicians Heinrich Bruns and Henri Poincaré showed that there is no general analytical solution for the three-body problem given by algebraic expressions and integrals....
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Stokes' Theorem and Vector Fields with Jump Discontinuities
What are the continuity requirements on a vector field $\boldsymbol{A}$ such that Stokes' theorem,
$$
\iint_S\nabla\times\left[(\boldsymbol{\hat{x}}\cdot\nabla\phi)\boldsymbol{A}\right]\cdot d\...
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Developing solution for electrodynamics problem
Although it is a question related to physics, since the point it really matters is its mathematical aspect, I post this question on MSE.
There's an additional exercise from Introduction to ...
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Shape of very long wire between two very tall posts (many km tall) which are attached to the earth
Consider for a moment a length of uniform wire or chain which goes between two posts of equal height. If we assume the earth to be flat then we can predict the shape of the curve using
$$y = a \cosh \...
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What are the equations that describe a Gömböc?
By 'Gömböc', I am referring to the family of shapes pictured on the Wikipedia page S.V. 'Gömböc',
https://en.wikipedia.org/wiki/Gömböc
In their paper "Static equilibria of rigid bodies: dice, ...
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Tautochrone and Brachistochrone problems are equivalent
It is a well known fact that the brachistochrone (the problem of finding the curve of quickest descent in a uniform gravitational field) and the tautochrone (the problem of finding a curve from which ...
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Implementation of a simulation of an incompressible Newtonian fluid with uniform density
Let $d\in\left\{2,3\right\}$ and $\Omega\subseteq\mathbb R^d$ be a bounded domain. I want to simulate an incompressible Newtonian fluid with uniform density $\rho$ and viscosity $\nu$.
The evolution ...
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Modelling a Water Rocket. Requires Some Validation and Help. ( WARNING : Extremely Long but Interesting Post )
Good day people of math.stackexchange.com
UPDATE: Version 2 can be found here: https://physics.stackexchange.com/questions/275284/modelling-a-water-bottle-rocket-version-2-long-post-warning.
This is ...
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Integral of a gaussian function of trigonometric functions
I need help with the analytical solution of this integral:
$$\int_{0}^{2\pi}\frac{1}{\sqrt{a^2-b^2\cos^{2}2\phi}}\exp{\left(-\frac{(x-c\cos\phi)^2}{a+b\cos2\phi}-\frac{(y-d\sin\phi)^2}{a-b\cos2\phi}\...
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3blue1brown Playing Pool with Pi Variation.
I often like doing variations of math puzzles and riddles. For this one though, it's extremely hard for me to find a simulation runner to solve this variation, and this variation also is a lot tougher....
user818490
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Is exterior calculus efficient for simple vector calculus problems?
Exterior calculus and invariant formulations are important and lead to many breakthroughs and great insights in physics and mathematics.
But for daily vector calculus tasks, I still struggle to apply ...
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The Virasoro-Bott group and the KdV equations
The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group. For the famous $KdV$ equations these equations are given on the Virasoro-Bott ...
- 1,852
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Calculate the resistance between 2 adjacent nodes on a shape using graph theory
In shapes like regular octahedron or dodecahedron, how can Graph Theory be used to calculate the resistance between two adjacent vertices? All edges are assumed to have unit resistance. Is there ...
- 3,528
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Approximating a discrete measure with a continuous one
In physics it is common to approximate distributions of point masses or charges with continuous distributions. To do this, one typically defines a density function by moving throughout the space a ...
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On the Visual Manifestation of Curves in Nature
A wide variety of curves are useful in modelling and describing phenomena we observe. Trig functions, logarithms, exponentials, polynomials, hyperbolas, circles, and so forth are all very useful in ...
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A light beam enters a closed room. What is the maximal number of reflections?
I have the following problem: a light beam enters a mirror room with integer coordinates in the plane (consider it as a polygon). One of the walls of the room is removed and the light beam enters the ...
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Solving numerically the equation of motion of D7 brane perturbation
I want to solve this equation
$$
\partial_{\rho}^{2}\phi+\frac{3}{\rho}\partial_{\rho}\phi+\left(\frac{M^{2}}{(1+\rho^{2})^{2}}-\frac{l(l+2)}{\rho^{2}}\right)\phi=0
$$
numerically.
I know that ...
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Deconvolution of distribution of diffraction reflexes
I'm a chemist stuck in a mathematical problem. Please bear with me as I'm trying to express myself in Math language.
Let me explain in short terms the experimental method I'm using: X-ray diffraction....
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Decomposing products of spinor representations into anti-symmetric tensors
There is always a natural $2^{[\frac{d}{2}]}$ dimensional spinorial representation of $SO(d-1,1)$ (..induced from a representation of the related Clifford algebra..) and if $[m]$ denote the space of ...
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Analytic caustics for 3D objects
Is it possible to efficiently calculate caustics for a given 3D object, like a torus, or a cube?
To be more precise: let's assume that we have a 3d torus, resting on a 2d plane and a single light ...
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Is Leibniz rule fundamental?
Disclaimer, I am a physicist and mess up with math and really think that derivatives are just fractions (roughly).
I am starting to study maths itself as the discipline it is and not as a tool for my ...
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How to derive the Sommerfeld radiation condition from the resolvent?
Suppose the resolvent $R_0(\zeta)$ for an operator $P_0(\zeta)$ is known to satisfy a limiting absorption principle at $\lambda \in \Bbb R$. For some perturbation $P(\zeta)$ of $P_0(\zeta)$ with $V (\...
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Relation between the homotopy classes of map $S^n \to S^2$ and $T^n \to S^2$ for $n=2,3$
I wonder if there is any relation between the homotopy classes of map $S^n \to S^2$, and the homotopy classes of map $T^n \to S^2$, where $n=2,3$.
In particular, I want to understand the below quotes ...
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What are the solutions for $y(t)\cdot\left(y'(t) + a\right)=-b\sin(t)$?
What are the solutions for $y(t)\cdot\left(y'(t) + a\right)=-b\sin(t)$?
It could be proben that there exists some solutions?
Are these solutions unique?
and obviously, which are these solutions? (...
- 1,390
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Explicit classical solution to this Stokes problem.
Consider the following Stokes equation (to be understood in the classic form) , where $B$ is a ball of center $0$ and radius $a$ :
\begin{aligned}
- \mu \Delta u + \nabla p= 0 \text{ in } \mathbb{R}^3 ...
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Not following this formula for coincidence rate among 'simultaneous' Gaussian distributions?
I'm reading this paper, which describes (among other things) the "triggering" system for a peice instrumentation used in the detection of subatomic particles in an astroparticle physics ...
- 1,371
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How to define Chirality and Polarity on a graph?
Is there a concept of Chirality or Polarity defined on graphs?
For example, consider a system with spin-$1/2$ (up/down polarity) particles which have also chirality (right/left).
I thought to take a ...
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Proving an equality for Schrödinger equation
Let $\phi\in \mathcal S(\mathbb R)$ and consider the uni-dimensional global Cauchy problem for the Schrödinger equation of a free particle, that is
$$(*)\qquad iu_t+u_{xx}=0\quad \text{and}\quad u(x, ...
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Abelian instantons for generic metric
Let $(X,g)$ be a Riemannian 4-manifold and let $G \to X$ be a principal $G$ bundle. The ASD equations $F^+=-F$ are satisfied for $F=dA$ the curvature two-form of the $G$-equivariant connection $A$.
...
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Relationship between squaring a complex number and acceleration
I know that the formula relating initial velocity, final velocity, acceleration, and distance is $v^2-u^2=2as$ and that squaring a complex number $v+u\mathrm{i}$ leads to $(v^2-u^2)+(2uv)\mathrm{i}$, ...
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Vector Laplace equation with constraint
I want to solve Laplace equation for a vector $\boldsymbol v=(v_x,v_y)$: $$\nabla^2 \boldsymbol{v}=0$$ but under the constraint that $$(1+v_x)^2+v_y^2=1$$
which becomes $v_y = -(2v_x+v_x^2)^{1/2}$.
...
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Fourier transform of $\frac{1}{r}$ (Coulomb potential)
When calculating the Fourier transform of a function of the form $f(\vec{r}) = \frac{1}{4 \pi \left|\vec{r}\right|}$, one encounters the problem that the resulting integral does not converge, i.e.
$$\...
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C. Neumann passage in Latin from *Annali di Matematica Pura ed Applicata*
Neumann, Carl. “Theoria nova phaenomenis electricis applicanda.” Annali di Matematica Pura ed Applicata 2, no. 1 (August 1868): 120–128. doi:10.1007/BF02419606. p. 121:
Nova introducitur suppositio,...
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Quantum and Paraconsistent Logics
Is there any relation between these two logics? I know both are completely different "from construction", but recently I've read that paraconsistent logics tries to explain some things in quantum ...
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Designing a mathematical physics class
Surprisingly, the university (a major tech school) I attended does not offer a mathematical physics class. Consequently, I often get asked by my physics friends what are some good math classes to take ...
user13255
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answer
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Charge distribution on an arbitrarily shaped conductor
From physics we know that given a charged conductor put in vacuum ( no external electric fields) , the charge distribution on its surface is approximately proportional to the curvature of the surface ...
- 1,355
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Harmonic oscillator differential equation question
Consider a harmonic oscillator subject to a frictional force proportional to velocity: $$\ddot{x}+2\gamma\dot{x}+\omega^2x=0.$$
Here $\dot{x}$ and $\ddot{x}$ are $\frac{dx}{dt}$ and $\frac{d^2x}{dt^2}....
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What are the family of geodesics/curves between point weights/balls on an elastic sheet?
ASSUMPTIONS:
no deformation is separate, all deformations touch with at least another points deformation, i.e., no deformation is by itself.
point force preferred, but small dense balls okay too.
The ...
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Number of light bulbs to light a cubical room to a certain number of lumens
Consider a cubical room of edge $l$ with light bulbs which can be placed on any of the faces (imagine they are point size). For a given light bulb, the lumens produced decreases with inverse square of ...
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2D Random Walk or just simple math?
I'm looking into a physical problem that involves the following sum:
$$r(t)=\sum_{\substack{z_l=0,1\\1\leq l \leq N}}|b_{z_1z_2\dots z_N}|^2e^{-2i\epsilon_{z_1z_2\cdots z_N}t}$$
where $\epsilon_{...
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