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17 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, ...
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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 ...
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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 ...
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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 $$ ...
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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 ...
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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, ...
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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 ...
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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, ...
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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 ($E_x,E_y,E_z,B_x,B_y,B_z$). ...
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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: ...
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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. ...
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14 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 ...
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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 ...
3
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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 ...
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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: $u(x,y,z,t)$. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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) ...
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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
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1answer
68 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 ...
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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 ...
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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 ...
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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 ...
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0answers
63 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 ...
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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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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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) = ...
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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} ...
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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 ...
2
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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 ...
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34 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( ...
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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 ...
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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 ...
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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, ...
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1answer
16 views

Solving a first order non linear differential equation in the specific case of the orbit of a particle moving under a central conservative force

Hello it's my first time posting in here and I hope someone in here can help me as my teachers quite dislike questions that aren't specifically in the curriculum. I'm reading About classical mechanics ...
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1answer
63 views

Differential equation for velocity regarded as a function of distance [closed]

Given a differential equation for velocity, $dv/dt + v = 1$, as well as its solution, is it possible to derive a differential equation for velocity with respect to distance? I found a solution to the ...
2
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1answer
230 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 ...
3
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0answers
67 views

Linear KDV eq. asymptotics

The question arises from the book Solitons by P. G. Drazin about the linearized KDV eq. $$ u_t+u_{xxx}=0 $$ My first step was to take a Fourier transform of the equation, find that the dispersion ...
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36 views

Steady-state solution of Fokker-Planck DE

I have this differential equation: $$\frac{\partial f}{\partial t} = \frac{1}{\tau_s v^2} \frac{\partial}{\partial v}(v^3+v_c^3)f + S$$ It is a Fokker-Planck equation that describes collisional ...
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93 views

Lang-Kobayashi rate equation derivation

The Lang-Kobayashi rate equations of a semiconductor laser experiencing feedback are as follows: \begin{align*} \frac{d}{dt}\left(E(t)e^{i\omega t}\right) &= \left[\omega_N(n) + \frac{1}{2}(G(n) ...
2
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1answer
71 views

Massless limit to massive scalar in AdS space

I was trying to solve massive scalar wave equation in AdS spacetime (or rather in BTZ). I noticed few funny things : The $m\to 0$ limit to the solution is subtle. One of the two independent ...
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0answers
41 views

How can I get the boundary and initial conditions of the convection–diffusion equation consistant?

I want to solve the 1D convection–diffusion equation. The boundary conditions are a flux in from the bottom and a flux out on the top. Furthermore I want no concentration inside at the beginning. I ...
0
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2answers
162 views

Diffusion of gas into vaccum

I'm interested in solving the diffusion equation for gas in vacuum. I have a general question and a more specific questions. What I know: The Diffusion Equation: For density function ...