DO NOT USE THIS TAG just because the question contains a differential equation!

learn more… | top users | synonyms

0
votes
0answers
18 views

Solving traveling wave using the shooting method

The spatially-dependent Hodgkin-Huxley equation for a cylindrical dendrite or unmyelinated axon: where $\frac{a}{2\rho}\frac{\partial^2V}{\partial x^2}$ is a diffusion term $a$ is the fiber radius, ...
0
votes
0answers
20 views

how did Enrico Fermi solve his partial differential equation in his 1918 essay “characteristics of sound”? [on hold]

https://tutordoctorofwny.files.wordpress.com/2011/08/enrico-fermi.pdf In 1918 Enrico Fermi (age 17) wrote his college admissions essay called "characteristics of sound". In that essay he did ...
1
vote
1answer
15 views

Equations involved in freezer burn

Assuming a sphere with a given percentage of moist uniformly distributed through the sphere. It's surrounded by air with no humidity. How could I model the sublimation of the sphere's moist into the ...
1
vote
0answers
31 views

Derivative with respect to a difference of independent variables

I am dealing with an equation from nonlinear acoustics (Khokhlova-Zabolotskaya-Kuznetsov equation) where a strange term (for me as a mathematician) is used. The equation looks like this $$ ...
0
votes
0answers
8 views

Modeling stilts with equations

I'm trying to make a set of stilts 20 ft in the air that someone could wear to run/jog with, but I was advised that I should first start by modeling the system (user + environment + stilts) in the ...
0
votes
0answers
26 views

Linear DEs without separation of variables in physics?

I'm looking for examples of real world physics problems that require solving linear (or linearisable) differential equations (DEs) that aren't separable in the variables. Most (admittedly) simple, ...
2
votes
2answers
143 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C ...
0
votes
0answers
50 views

Is this differential equation solved properly? [migrated]

I have following differential equation for the speed of a particle: $g=\dfrac{3\alpha}{\alpha t + R_0}v + \overset{.}{v}$ Is my approach right? $\int (g-\dfrac{3\alpha}{\alpha t + R_0}v)dt = \int ...
5
votes
1answer
177 views

Physical interpretation related to a non-linear partial differential equation

I am doctoral student in pure mathematics working on a particular problem. My question is if this problem has applications to real world phenomena. I will try to explain the direct problem starting ...
1
vote
3answers
173 views

Maxwell's equations - underdetermined - uniqueness

Maxwell's equations can be seen as two dynamical equations (the two curl equations), and two constraint equations (the two divergence equations). So we have 6 unknowns ($E_x,E_y,E_z,B_x,B_y,B_z$). ...
1
vote
1answer
40 views

Hamiltonian from a differential equation

In my differential equations course an example is given from the Lotka-Volterra system of equations: $$ x'=x-xy$$ $$y'=-\gamma y+xy.\tag{1}$$ This is then transformed by the substitution: $q=\ln x, ...
45
votes
7answers
4k views

Do Maxwell's Equations overdetermine the electric and magnetic fields?

Maxwell's equations specify two vector and two scalar (differential) equations. That implies 8 components in the equations. But between vector fields $\vec{E}=(E_x,E_y,E_z)$ and ...
0
votes
0answers
13 views

Modeling: State variables and algebraic variables

I am new to modeling of differential-algebraic systems. I dont understand the coherence between: state-variables, differential variables and algebraic variables. Standard form of the system: ...
0
votes
0answers
21 views

Which formulas would tell me the gradient of an electromagnetic field at an arbitrary distance from a pole? [duplicate]

I'm a newbie to physics and was wondering where I can read about electromagnetic gradients. From what I understand (and my intuition) electromagnetic fields create force gradients around its poles. ...
0
votes
0answers
15 views

Linear viscoelastic differential operators

I am starting with differential operators: $P = \sum_{i=0}^{N}p_i \cfrac{d^i}{dt^i}$ $Q = \sum_{i=0}^{N}q_i \cfrac{d^i}{dt^i}$ $p_i$ and $q_i$ are functions of time only. $K$ is a constant that ...
-2
votes
0answers
21 views

Legendary problem [migrated]

Show that for the Legendre polynomial Integral $\int_{-1}^{+1} P_n (x) dx$ =0 When n is not zero I put this polynomial in the Legendre equation then got stuck from there on Can you tell me what to ...
6
votes
1answer
197 views

Integrating Factor Solution for Plasma Wave Equation

As part of a derivation in Bernstein '58 [1] a linear first-order (eqn. (9) in the image) appears: But the general solution I would usually take (as appears in Gradshteyn and Ryzhik and checked in ...
0
votes
1answer
89 views

Can $Ae^{-bt^2}\sin(kx-\omega t)$ be considered a wave?

The damped wave PDE can have an exponential term, but the argument for the exponential term cannot be quadratic, AFAIK. $Ae^{-bt^2}\sin(kx-\omega t)$ So this isn't a solution for the damped wave ...
2
votes
1answer
47 views

Time responses (position and speed) of system

This is a basic question regarding state space representation and differential equations. I want to find the time response of states $x_{1} = x$ and $x_{2} = \dot{x}$ of the following system: $$ ...
3
votes
1answer
73 views

Existence and Uniqueness of Newton's Laws

I'm reading Arnold's book on classical mechanics. This is kind of a dumb question, but I'm having problems understanding his explanation for existence and uniqueness of Newton's laws. On page $8$ he ...
0
votes
0answers
23 views

Lets consider a cube with side $2$, which is cooling in an environment. Find its temperature at any point at any time: $u(x,y,z,t)$

Lets consider a cube with side $2$, which has an initial temperature of $1$°K and it is cooling in an environment of temperature $0$°K. Find its temperature at any point at any time: $u(x,y,z,t)$. ...
1
vote
1answer
58 views

Monodromy matrix and differential equations

What is the significance of monodromy matrix in the context of differential equations? I have seen some papers(1,2,3 etc) in CFT which use the monodromy method to compute conformal blocks at large ...
0
votes
1answer
29 views

How to extract heat transfer model parameters from empirical data?

I have made a simple model of heat transfer between ambient and a silicon chip (module) from which I can read its internal temperature $T_m$. I do not need fancy equations and an approximate model ...
0
votes
0answers
33 views

car dashboard problem

I stumbled upon this question while I was driving my car. On my dashboard I have fuel gauge and engine temperature gauge next to each other, look at the pic: http://i.stack.imgur.com/aDgKj.png Fuel ...
4
votes
1answer
158 views

Solution of QM tasks by using asymptotics

When we solve QM tasks by solving the Schrödinger equation, such as tasks about a particle in a Morse potential, a Poschl-Teller potential and many others, we usually find approximations (lets call ...
0
votes
0answers
34 views

Question about a solution of a partial differential equation by separation of variables

I'm trying to understand this text: http://www.ekayasolutions.com/UCDMath/HeatCondSphere.pdf But I'm having problem with this part: Whe have to solve: \begin{equation} \dfrac{\partial ...
0
votes
1answer
45 views

Differential derivation based upon time and space confusion

I have been doing a lot of derivations recently involving heat transfer. I was attempting to derive heat accumulation in a differential element based upon inflow and outflow as well as thermodynamic ...
3
votes
2answers
78 views

Interpretation of Eigenvalues and Eigenvectors of an hyperbolic conservation law $\partial_t W + A \partial_x W = 0$

I read in a article dealing with a hyperbolic partial differential equations this statement : For any system of hyperbolic partial differential equations (pde), expressed as (1) ...
1
vote
0answers
55 views

What type of differential equation is this? [closed]

Need to find the general solution and characteristics, but I can't define type of this differential equation $ u_{ttx}=u_{tx}^3 $
3
votes
1answer
69 views

A model for constant temperature of water in a container

I put some water in a container with initial temperature $T_0$ in a room, and the room's initial temperature is $T_a$. Now the container is filled to the maximum, so any more water coming in will ...
0
votes
0answers
17 views

Is there a “natural” way to interpolate between a set of bound state wave functions?

Consider for example the Coulomb potential, $-Z/r$, for which there exist a set of bound states with energy $\epsilon_n := {-Z^2 \over 2 n^2}$ (in Hartree). If I want the "wavefunctions" for some ...
1
vote
0answers
28 views

Cooling of a surface due to fluid passing over it

I am working on a project that requires me to measure the cooling effect of a liquid flowing through a surface. In order for me to effectively calculate the cooling effect, the solution of the below ...
3
votes
1answer
92 views

Numerically solving a simple Schrodinger equation with fast Fourier transforms

While trying to solve a stochastic Gross-Piaevskii equation I have found a problem that can be tracked down to something buggy occurring in the simplest Schrodinger equation possible: $$\partial_t ...
2
votes
0answers
64 views

Wronskian of complex second order linear differential equation

While studying certain analogue gravity models I came across a differential equation of the form: \begin{align} \frac{d^2y}{dz^2} + \omega^2 (z)~ y(z) = 0 \end{align} where $z$ is a complex variable ...
5
votes
0answers
140 views

on fundamental 2D conductivity equation boundary value problem

Consider the following homogeneous boundary value problem for a function/potential $u(x,y)$ on the infinite strip $[-\infty,\infty]\times[0,\pi/4]$ w/positive periodic coefficient/nductivity ...
0
votes
0answers
21 views

Does nature prefer second order differential equations? [duplicate]

We all know Newton's second law: $m \ddot{x} = F(x)$ or equivalently Euler-Lagrange or Hamilton's equations. In quantum mechanics the Schrödinger equation is also a second order differential equation. ...
1
vote
0answers
50 views

Contradictory argument to continous energy spectrum in quantum mechanics

The Schrodinger equation can be formulated as a regular Sturm-Liouville problem along with proper boundary conditions. Now the solution of regular Sturm Liouville problems with suitable boundary ...
0
votes
2answers
49 views

$Ae^{\mathrm{i}\omega t}$ assumption for oscillating systems (formal & intuitive)

When we obtain a system of ODE's for $n$ masses connected with springs (or otherwise obtained by small amplitudes approximation), the next steps are usually assuming a solution in form $Ae^{i\omega ...
1
vote
0answers
42 views

couple mode equation [closed]

Consider the nonlinear Schrodinger equation for the normalized wave envelope $\Psi(x,t)$, \begin{equation} i \frac{\partial \Psi}{\partial t}+\frac {1} {2}\frac{\partial^2\Psi}{\partial ...
2
votes
0answers
43 views

Transform QM radial equation to spherical Bessel equation

I'm currently learning about spherical potentials (ex. hydrogen and hydrogen-like systems) and am trying to work through the problem of a generic spherical potential well such as: $$V(r) = ...
1
vote
0answers
48 views

Existence of a solution for geodesic differential equations for a singular metric

In order to determine the geodesics, one must solve the following set of differential equations \begin{align} \frac{d^2 x^j}{ds^2} + {j\brace h\,\,k}\frac{dx^h}{ds}\frac{dx^k}{ds} = 0, \end{align} ...
1
vote
0answers
17 views

Attractors in Duffing equation

The Duffing equation in its full form is $$\ddot{x} + \delta \dot{x} -ax + \beta x^3 = \gamma \cos(\omega t)$$ Now for specific values of the parameters several attractors exist (or not). Let's ...
33
votes
6answers
889 views

Motion described by $m \frac{\mathrm{d}^2 x}{\mathrm{d}t^2}=-k\frac{\mathrm{d}^{\frac12 }x}{\mathrm{d}t^{\frac12}}$

What kind of motion would a (preferably dimensionless for simplicity) body do if the force acted on it was proportional to the semi-derivative of displacement, i.e. $$m \frac{\mathrm{d}^2 ...
2
votes
1answer
53 views

Difference between finite volume, characteristic method and plug flow models of a pipe

I have to model pipes (of a district heating network) with ODE's. My background is computer-science, so it is not that easy for me to understand different approaches. Finite volume approach. Method ...
5
votes
1answer
210 views

Why is the wave equation so pervasive?

The homogenous wave equation can be expressed in covariant form as $$ \Box^2 \varphi = 0 $$ where $\Box^2$ is the D'Alembert operator and $\varphi$ is some physical field. The acoustic wave ...
0
votes
0answers
35 views

How to solve numerically or analytically this Partial Differential Equation?

:D I'm modeling a problem of ecology with PDEs, So I gotta solve numerically this Reaction-Diffusion Partial Differential Equation $$ \frac{\partial u(t,x,y)}{\partial t}=D\Big( ...
0
votes
0answers
23 views

IBP Identities to solve differential equation

I am wondering if anyone has experience in using IBP( Integration by parts) identities in the evaluation of Feynman diagrams via differential equations? My question is that I can't seem to understand ...
0
votes
0answers
46 views

Physical background to the ODE $y'(x) + \frac{1}{x} = y(x)$

Most books on asymptotic methods start with a discussion on the ODE $y'(x) + \frac{1}{x} = y(x)$, which has solution $$y(x) = \int_0^{\infty} \frac{e^{-xt}}{1+t} \,dt. $$ A discussion on the ...
9
votes
0answers
86 views

Can one classify partial differential equations according to the causality properties of their solutions (and if yes, then how)?

Recently, I bumped into this interesting comment by Valter Moretti which made me wonder about the following, more general question (to which I suspect the answer is affirmative): Can we easily tell, ...
2
votes
1answer
232 views

Peskin Schroeder and the general solution to Callan-Symanzik Equation

I have a couple of questions regarding Peskin and Schroeder's derivation of the solution to the Callan-Symanzik equation. First of all, they claim that using ...