Questions tagged [differential-equations]
DO NOT USE THIS TAG just because the question contains a differential equation!
929 questions
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Why we can have fields without sources?
As the title suggests, one thing that when studying college physics shocked me was that fields can exist without sources. I'm not talking, for example, of EM waves. That kind of "fields without ...
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Intuitive analysis of d'Alembert's solution to the 1+1D wave equation
Why is the general equation for a 1+1D wave a superposition of two wave travelling in opposite directions $$u(x,t)=g(x+ct)+h(x-ct),$$ suggests d'Alembert's solution of $$\frac {\partial^2u}{\partial t^...
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Is it possible to construct classical differentiable single-valued solutions of the Aharonov-Bohm TDSE?
Note: I used the term "classical-solution" in the title to mean the standard notion of "solution" of a PDE: a single-valued, globally defined function that is sufficiently smooth (...
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How can eigenvalues be used to determine attitude stability in rocket flight? [closed]
I am aware of the linearization of ODE's and their link with eigenvalues where you are able to solve coupled differential equation problems utilising eigenvalues and vectors. Additionally, I ...
0
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1
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Mass lifting off a harmonic oscillator
Consider this setup:
A classic, harmonic oscillator made of a spring with spring constant $k$ and a mass $m_1$ that oscillates vertically. $m_1$ is formed like a horizontal plate, and on the plate ...
4
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WKB at second order
I have a similar question to this forum that was asked 6 years ago... Transmission coefficient of second-order WKB approximation
I am working on solving a differential equation using the WKB method up ...
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1
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Partial Differential Equations (PDEs) in 2+1 Spacetime with Gradient of the Time Derivative
I have a set of 2 variables $f_1,f_2$, on the Domain of 1+1 spacetime $\{t,x\}$ and a set of PDEs with multiple terms of mixed 2nd-order partial-differentials.
$$\partial_t{f_1} = F_1(f_1,f_2, \...
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EM Fields inside a wire
Imagine that we have a (copper) wire with radius $a$ and length $L$ oriented along the $z$ axis.
Maxwell's equations inside the wire are:
$$
\nabla \cdot \mathbf{E} = \rho/\varepsilon \\ \; \\
\nabla \...
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3
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1
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The continuum limit of antiferromagnetic magnons
There is a lot of setup needed to ask this question, and numerous steps of which I'm not 100% sure, but my main question is contained in the last paragraph.
Consider an antiferromagnetic quantum spin ...
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0
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Equation of motion, 4th order
I have the following term in my Lagrangian:
$$
L=V(r)((\Delta \phi )^2-5(\partial_i\partial_j \phi)^2).
$$
I am kind of confused about computing the equation of motion, I would say (is there a ...
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Is it possible to construct Smooth solutions for the unsimplified version of the viscid and incompressible Navier-Stokes eqs.? Smooth is essential
There are many exact solutions to the simplified Navier-Stokes equations. However smooth and 3d solutions do still remain elusive.
Is there a way to construct an exact 3d smooth solution generator of ...
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Loaded string problem
A primer on Green's functions contains a simple example of a "loaded string" problem. The forcing function in the text was not specified, and it reminded me of a related question.
The ...
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1
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Ensuring the stability and validity of a numerical solution for the Fokker-Planck equation
I am developing a finite-difference numerical scheme for solving the Fokker–Planck equation. The scheme is validated by comparing its solutions with histograms constructed from trajectories of the ...
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Physical Means to State-Dependent Solutions to Schrödinger Equations? [closed]
Disclaimer: I am a mathematician/computer scientist interested in quantum computers.
Recently, I started reading about quantum computing, and I read that one uses unitary matrices since they ...
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1
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Well-posedness of initial value problem in chaotic systems?
Quoting Wald from his seminal textbook on general relativity (Chapter 10):
First, in an appropriate sense, "small changes" in initial data should produce only correspondingly "small ...
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