Nonlinear Definition and 558 Threads

As is known, when calculating localized states in a crystal it is roughly considered that the point charge is “immersed” on medium with static dielectric constant ε. However, a simple estimate, for example, shows that an impurity atom with charge modulo equal to the electron charge creates at...

(a'[t]/a[t])^2 == K*(A + B*a[t]^-6)^1/2} is the equation to be solved for getting the solution of a(t) in terms of time(t). Any ideas on how to solve this problem? Use of Matlab or Mathematica is accepted.

Hi good day. I am trying to find the general Inverted Pendulum on a cart nonlinear state space equations with two degrees of freedom with x, x_dot, theta, theta_dot which represents displacement, velocity, pendulum angle from vertical, angular velocity. However from research, I am seeing...

Homework Statement Let $$\frac{1}{2}\dot{r}^2=e+\frac{m}{r}-\frac{L^2}{2r^2}$$ where L is angular moment, and e is energy (so I guess I'll take as constants for now...) Homework Equations Not sure for now. The Attempt at a Solution So, if I let $$u=\frac{1}{r}$$ then my equation becomes...

Dear All short explanation: I am trying to leverage my limited understanding of representation theory to explain (to myself) how many non-vanshing components of, for example, nonlinear optical susceptibility tensor ##\chi^{(2)}_{\alpha\beta\gamma}## can one have in a crystal with known point...

Hi PF, Suppose I numerically solve a nonlinear system of differential equations. How can I know if my solution is correct (if there is no known analytic solution)? What are the standard practices people do? I have a couple of ideas, but I want to know what people are already doing. Danke!

Hi. I've just learned about enumerating the second-order susceptibility (rather blindly) by 3^3 * (3*2*1) * 2 = 324. (tensor size * 3 frequency permutation * negative frequency) I'm guessing that for the third-order susceptibility would similarly yeild 3^4 * (4*3*2*1) * 2 = 3888? I couldn't...

Hi all, I have this (nondimensionalised) system of ODEs that I am trying to analyse: \[ \begin{align} \frac{dr}{dt}= &\ - \left(\alpha+\frac{\epsilon}{2}\right)r + \left(1-\frac{\epsilon}{2}\right)\alpha p - \alpha^2\beta r p + \frac{\epsilon}{2} \\ \frac{dp}{dt}= &\...

Hello guys I struggle since yesterday with the following problem I am reading the book "Elements of applied bifurcation theory" by Kuznetsov . At one point he has the following Taylor expansion of a nonlinear system with respect to x=0 where ##x\in \mathbb(R)^n## $$\dot{x} = f(x) = \Lambda x +...

Greetings, is anyone here familiar with nonlinear optics? I want to know wether the Pockels effect only occurs in optically anisotropic media or not. Of course, we need a medium with inversion symmetry ("non-centrosymmetric medium"), but I am not sure about the optical isotropy. In an...

A geometry problem I'm working on has boiled down to finding a function ##f(t)## such that $$f'' + \frac{2}{t}f' + \frac{f'^2}{\left( 1 - \frac{f}{t} \right) t } + \frac{f'f}{\left(1- \frac{f}{t} \right) t^2} = 0$$ It has two fairly simple solutions, namely ##f(t) = a## and ##f(t) =...

I would like to solve this system, which is a sets of non linear quadratic equations, the system needed to be solved can be expressed in general as follow: ϒϒ'C – ϒα = B Where ϒ=(ϒ1,ϒ2,...ϒn)’ is a column vector and ϒ’ its transpose C=(c1,c2,…,cn)’ and B=(b1,b2,…bn)’ are a columns vector And...

Mentor note: Thread moved from the Technical Math section, so there is no template. @yamata1, , in the future, please post homework problems or exercises in the Homework & Coursework sections, not in the Technical Math sections. I have moved your post. Hello, I would like some help with an...

I have the following system of PDEs: \hat{\rho}\hat{c}_{th}\frac{\partial\hat{T}}{\partial\hat{x}}-\alpha_{1}\frac{\partial}{\partial\hat{x}}\left(\hat{k}(\hat{x})\frac{\partial\hat{T}}{\partial\hat{x}}\right)=\alpha_{1}\hat{\sigma}(\hat{x})\hat{E}...

Hi Physics Forums, I am stuck on the following nonlinear recurrence relation $$a_{n+1}a_n^2 = a_0,$$ for ##n\geq0##. Any ideas on how to defeat this innocent looking monster? I have re-edited the recurrence relation

For Schwarzschild geomery $$ds^2=-(1-\frac{2GM}{r})dt^2+(1-\frac{2GM}{r})^{-1}dr^2+r^2d\Omega^2$$ For a Schwarzschild observer , the proper time and coordinate time are related by $$d\tau=(1-\frac{2GM}{r})^{1/2}dt$$ There is a often used relation between proper time and coordinate time $$d\tau...

Hello all, you may already know that Q.M. is a linear theory however there is something called nonlinear Sch. eq. for example Gross-Pitaevskii equation. How can such a thing exist considering that Q.M. is a strictly linear theory. Cheers.

Hi, I am looking at the following system of ODEs: \begin{eqnarray*} \dot{\omega}_{3}+\alpha\omega_{3} & = & \frac{\beta_{1}+\beta_{3}}{\rho_{0}}J_{3} \\ \dot{J_{3}}+2(\alpha_{2}-\alpha_{1})\beta_{2} & = & 0 \\ \dot{\beta}_{1}+\omega_{3}\beta_{2} & = & 0 \\...

Hi, I tried to solve the following in Wolfram alpha: y''' + (1-x^2)y=0 y(0)=0 y'(0)=0 y''(0)=0 however, I got answer which cannot be reproduced (even at wolfram pages). I have tried ODE45 in MATLAB, but it only gives a plot. Is there any way to solve this analytically or numerically to give...

Hi, I have in a previous thread discussed the case where: \begin{equation} TT' = T'T \end{equation} and someone, said that this was a case of non-linear operators. Evidently, they commute, so their commutator is zero and therefore they can be measured at the same time. What makes them however...

Can someone please tell me how to go about optimizing this system of equations? It is weird because the residuals are computed with ##A = B*X_1+C*X_2## but X_1 and X_2 are computed in a separate function ##[X_1,X_2]=f(k1,k2,H0,G0)##, and what I am optimizing is a parameter in that second...

The question is posted in the following post in MSE, I'll copy it here: https://math.stackexchange.com/questions/1407780/a-question-on-matrixs-eigenvalue-problem-from-eberhard-zeidlers-first-volume-o I have a question from Eberhard Zeidler's book on Non-Linear Functional Analysis, question...

The term 'phase space' is often used in the study of nonlinear dynamics.What is it.

Homework Statement Find all solutions of: a + c = 5 b + d + ac = 5 ad+ bc = 5 bd = -6 Homework EquationsThe Attempt at a Solution I tried subsitution and end up with a cubic equations. I am pretty sure it can be done easier.

Hi. I wanted to learn more on this topic, but it seems all the available resources in the internet points to using R, SPSS, MINITAB or EXCEL. Is there an established numerical method for such cases? I am aware of the Levenberg-Marquardt, Gauss-Newton and such methods for nonlinear regression on...

1. Homework Statement Hello all. It is not a homework actually. I just didn't know at which forum I should post. I am working on a MATLAB code solving the finite wing properties iteratively by using the Anderson's Numerical Lifting Line Method. However, I got some wrong results. The...

For a given stationary cubic-quintic nonlinear Schrodinger equation, EU=-U_XX+G1|U|^2U+G2 |U|^4 U, where X=X(t,x). There are bright and dark solitons. In many references, it is found that there is typo or mistake in dark soliton by substituting their soliton solution to this above eqaution. The...

Is there a quick test to determine if a system of nonlinear equations is inconsistent. For example, suppose there is a system of equations such as: 3x cubed + 2y cubed = z cubed 2x cubed + 5y cubed = z cubed Since these two equations are clearly not dependent, could we say that since...

Homework Statement Would a switched reluctance motor be described as a non linear load? Since it is switched on and off rapidly to turn the rotor, does that make it non linear?

The Nonlinear Schrodinger Equation (NSE) is presented as: $$i\frac{∂A}{∂z} = \frac{1}{2}β_2\frac{∂^2A}{∂t^2}-\gamma|A^2|A$$ The steady state solution $$A(z)$$ Can be derived as an Ansatz given by: $$ A(z) = \rho(z)e^{i\phi(z)}$$ By substituting and solving the ODE, the steady state...

I am using the static structural module of ANSYS workbench to do a simulation. In my model, there is a gear and a spring which presses against the gear, moves along it and pushes it to turn counterclockwise. These two objects are in frictional contact. In my calculation, I always have the...

Classical physics is a nonlinear theory, but how is it that? Why is it nonlinear? Also quantum mechanics is a linear theory so that the sum of the solutions of the schrödinger equation is itself a solution. But I'm not sure I grasp this completely. Why is quantum mechanics linear while...

I wasn't sure into which category I should post this, so feel free to move it into a more appropriate place. As part of my work I'm solving a system of nonlinear equations, of a usual form: $$\vec{F}(\vec{X})=\begin{pmatrix}F_1(X_1, X_2, \cdots X_N) \\ F_2(\cdots) \\ \vdots \\...

This is actually not a homework problem, but a problem I'm encountering while working on a little project and I'm not sure if it's even solvable or if it makes sense what I'm doing 1. Homework Statement First, I have the equation $$p_{ij} = \frac{1}{2}\left( \tanh{(-\frac{\theta_i +...

Hi, The problem is to solve: dy/dx = −[2x + ln(y)]*(y/x) Attempt: I have tried to see if it is exact, I found it not to be, I can't easily find a function to multiply by to make it exact either (unless I am missing something obvious). It clearly isn't seperable, nor is it homogenous (I know...

From cosmology, the friedmann equations are given by, ##H^2 = (\frac{\dot a}{a})^2 = \frac{8\pi G}{3} \rho \, , \quad \frac{\ddot a}{a} = -\frac{4\pi G}{3}(\rho+3p) \, , \quad## where ##\rho = \frac{1}{2}(\dot \phi^2 + \phi^2)## and ##p = \frac{1}{2}(\dot \phi^2 - \phi^2)## To get ##\dot H##...

We're hearing things in the news these days about Squeezed Light, and how it can be used to improve everything from LIGO detectors, to positional sensors, to Quantum Computing. What is Squeezed Light, what useful applications is it being investigated for, and how does it provide this extra...

I am working on a problem, where I have arrived at the following nonlinear state space equation: dx1/dt = x2; dx2/dt = c11 x1 + c21x2 + c31x3 + c41x4 + c51x1x22; dx3/dt = x4; dx4/dt = c12 x1 + c22x2 + c32x3 + c42x4 + c52x1x22; c11, c21, c31, c41, c51, c12, c22, c32, c42, c52 are all a function...

I encountered several times the following problem: Say I have a variable y dependent in a nonlinear way on m parameters ##\{x_i\}##, with ##i \in \{1,m\}##. However there is a linear relation between n>m functions ##f_j\in{x_i}##, i.e., ##y=\sum_j z_j f_j##. So I can get a solution of my problem...

ρCp (∂T/∂t) + k (∂2T/∂x2) = exp(-σt2)exp(-λx2)φo i have this equation... i was thinking of taylor series expansion to solve it and make it easier... any ideas on how to solve?

Hi to everyone, I'm optimizing a nonlinear function but I'm struggling to achieve it. The function is the following: X and i are relationed so i doesn't go to infinite. Do you have any idea how to maximize this function? Thanks in advance, Eric

I am applying a 4th order Runge-Kutta code to solve the following: \begin{equation} \frac {\partial y_1}{\partial t} = y_2 y_3 - C_1 y_1 \end{equation} \begin{equation} \frac {\partial y_2}{\partial t} = y_3y_1 - C_2 y_2 \end{equation} \begin{equation} \frac {\partial y_3}{\partial z} = y_4...

Homework Statement 3y(t)+2=x(t) Homework Equations k1y1(t) + k2y2(t) + 2(k1+k2) = k1x1(t)+k2x2(t) The Attempt at a Solution I know the system is non linear but I cannot explain why. It has something to do with 2(k1+k2) but I am unsure.

Hi Could anybody guide me to a software that can be used to design a non linear spring from load deflection characteristics. need it for both extension and compression spring. thanks noor

Hello for an input signal with a noise we have and for obtain Power spectural density we use autocorrelation function where hkm is but I need to know what is autocorrelation function for different inputs with different frequencies? such as Any help will appericate

Hey everyone. I'm currently in a new research lab that focuses on optics. One thing I'm currently tasked with is handling the femtosecond laser we have. However, to do this, I need a stronger background in optics than I currently have (which is a few years of undergrad optics, some quantum...

I am currently an undergrad studying physics and am doing research on PPLN and nonlinear optics. I have a basic understanding of the math involved with my research, but would like to know more on nonlinear optics and why these materials behave the way they do. I am currently reading...

Is there an approach to the following 2nd order nonlinear ODE? xy'' + 2 y' = y^2 - k^2 I am interested in learning how to analyze for asymptotic behavior, proof of existence, etc.

Hi everyone! I have perhaps a basic question, but I can't dealt with it. I have a rectangular sample 50x150mm of let's say wood. The sample is compressed from the top over the width of 4mm. I know the shortening of the sample at 70 mm from the bottom (from experimental testing) and I know the...

Homework Statement Solve the following equation. Homework Equations ( 3x2y4 + 2xy ) dx + ( 2x3y3 - x2 ) dy = 0 The Attempt at a Solution M = ( 3xy4 + 2xy ) N = ( 2x3y3 - x2 ) ∂M/∂y = 12x2y3 + 2x ∂N/∂x = 6x2y3 - 2x Then this equation looks like that the integrating factor is (xM-yN). IF =...