Nonlinear Definition and 558 Threads

Hello, I would be interrested to learn if there are some (new) open source and/or possibly free librairies available for nonlinear optimisation and equations solving. I would be mostly interrested in modern languages like java or C# . "Clean" fortran could also be interresting as long as...

Hello, I would be interrested to learn if there are some (new) open source and/or possibly free librairies available for nonlinear optimisation and equations solving. I would be mostly interrested in modern languages like java or C# . "Clean" fortran could also be interresting as long as...

Homework Statement A particle moves in a medium under the influence of a retarding force equal to mk(v^3 + a^2 v), where k and a are constants. Show that for any value of the initial speed the particle will never move a distance greater than pi/2ka and that the particle comes to rest only for...

I'm interested in focusing on nonlinear dynamics or mathematical physics for my PhD and was wondering if anyone could tell me what US universities have strong departments in these topics. I've heard that Cornell is good for dynamics and chaos but haven't heard much about other colleges. Thanks.

Why are diodes nonlinear?

I don't know much about nonlinear optics, but does doing a PhD in this field give you a chance in landing a job in the industry afterwards? i.e what does the job market look like? I always kinda thought that nonlinear optics was a very mature field and hence the opportunity to do exciting...

Hi, Ok, I have notice that for several finite groups the following situation occurs... I will use the non-abelian group of order 27 to illustrate the point I'm making: The group has 11 charachers, 9 of which are linear. The group has derived subgroup G' (= Z(G) the centre of the...

Hello: I am solving for the fixed point of this nonlinear system: x^2 - x + 2y^2 + yz - 10 = 0 5x - 6y + z = 0 -x^2 - y^2 + z = 0 Somehow, I got stuck with my function for g, g(x) = x. I ran this in a program applying the Newton's method and I got its...

Homework Statement The following set of nonlinear Ordinary Differential equations is known as the Lotka-Volterra modek:dx/dt = (a - bx - cy)x dy/dt = (-d+ex)y where a,b,c,d,e are positive constants. These equations model a simple eco system of preator and pray. the x is hares and y is foxes...

Solved the problem.

Ive been working on a bunch of non linear systems problems for homework and can't figure this one out: y=xcubed x-y=0 I get to the substitution stage and get x-xcubed=0, but you can't factor that so I am wondering what you do next to get the answers for x, and y. Thanks in advance for...

Hi, I'm looking for an analytical solution to this set of coupled equations: U^{'}_{i}(x)=c (f_i(x)-(\vec{U}\cdot\vec{f})U_i(x)) Where the vectors are 3 dimentional, c is constant and f is a vector of given functions: f_i(x) , i\in 1..3 There probably isn't one but I thought I'd...

I'm just curious as to what the actual distinction means. I understand that the requirement for a linear ODE, is for all the coefficients to be functions of x (independent variable), and that all derivatives or y's (dependent variable) must be of degree one, but that doesn't tell me much...

Einsteins field equations are nonlinear but I guess that nobody has already found solutions to the full nonlinear equations (because of course it is very hard to do so). Nevertheless, such solutions could (I think) hold a number of surprises. Instead of linear gravitational waves, one could...

Can someone give me an example of a nonlinear operator? My textbooks always proves that some operator is a linear operator, but I don't think I really know what a nonlinear operator looks like. One of my books defines an operator like \hat{B} \psi = \psi^2. I see that this is a nonlinear...

Hello! I tried to prove, that ideal rope (see picture in attachment) has a shape of the function ch[x]. I finished with this equation [h'(x)]^2-h(x)\cdot h''(x)+1=0 Yes, when you try function h[x]=ch[x], you get 0 on the left side, but I have no clue how to solve this equation (find...

I have a naive question about nonlinear ODEs, supose I have one of such equations, and that it is homogeneous NL(y(x))=0, (1) and I know the solution. Then I want to solve the "associated" non-homogeneous equation NL(y(x))=f(x) (2) There is a method to attack this kind of...

third-order hyperpolarizability "γ" in nonlinear optics In nonlinear optics third-order hyperpolarizability of molecules "γ" is often measured by THG(third-harmonic generation) experiments. So third-order nonlinear susceptibility "X(3)" could be calculated from formula using the value of...

Hi, Can somebody guide me in getting solution for the following non-linear differential equation? u''=K/((a-u)^2) ...K is a constant Where u is a function of x and the boundary conditions are u(0)=0 u(L)=0 I need solution in form of 'u' as a function of 'x' with two...

Hello. I am taking a self study diff e course, and I have run into a problem with no one to ask for help. Here is the problem: y\prime=1+x+y^2+xy^2 The question asks to find the general solution. I simply don't understand how to solve this problem. Here is the direction I am going in...

I have a quick question. For a project that I'm doing, I need to numerically solve systems of nonlinear differential equations. Can anyone suggest a numerical method which I could code as a short C program? Thanks.

I numerically integrate the following nonlinear oscillator: x''(t) + e (x'(t)^3) + x(t) = 0 , where e<<1 and what I get is a limit cycle. The energy derivative appears to be negative , which means that x(t) approaches zero while t approaches infinity. I also used the analytical...

Hi all! I am coming back here after a long time. Last time I got the answer I was looking for, here. I hope that I will find it again. I need the possible numerical methods for solving the following PDE: Its a nonlinear parabolic boundary value problem. I want a very stable algorithm as...

I have some fairly basic (hopefully) questions about tensor equations. Hopefully someone here can help out. Let us say I have a tensor equation, (I will use this as the example for discussion: A^{u} = b C^{uv}D_{v}). If this is true in one coordinate system, it will be true in all of...

I'm stuck in a classical mechanics problem. I have to solve this equation (actually I need only \ddot{x}) to conclude it: x \frac{d^2x}{dt^2} + (\frac{dx}{dt})^2 -gx = 0 The book offers a solution At^n and it turns out that it's satisfied for n=2 and A=g/6 . Well, how am I supposed to guess...

Are there any analytical solutions to: ay''+bx^2y+cxy+dy=0 where a,b,c,d are constants and y(x) If so how would you go about it? Is there a website that teaches you how to solve these?

Hi, As far as I know this is a first order, nonlinear diff eqn with both dependant and independant variables...so it is not solvable?? y'+ay^2 = bx If anybody knows if there is a method to solving it, please let me know. Thanks, danmag :confused:

http://www.imagebucket.net/images/bigslowy/physicsproblem.jpg What is the strength of the electrostatic force on the top charge? Answer in units of N. I tried breaking it down into components of Fabx + Fbcx ect. but I still don't get a correct answer. Is there a different approach I...

Hi Everybody, I have just finished the control systems components of the engineering degree and found it very enjoyable. I'm now undertaking a holiday project to create a quad rotor aircraft. There is a surprising amount of information on these aircraft on the internet and while most of it is...

At this link: http://www.geocities.com/ptep_online/PP-04-07.PDF is a recent paper by Carlos Castro on a new nonlinear Schrodinger equation--for those that work in this area.

could somebody please explain lorenzos non lineare effect ? how does it happen is it percussive ,displacement , other/ it troubles me that i don't under stand some thing so simple :

Hi all, I am more into physics than maths and I need you guys to please help me out. Also I am new to programming in MATLAB. I have done some but still I consider myself a novice. I need to solve the problem in MATLAB. So here is the problem.Its a 2 point BVP(boundary value problem) along...

Could somebody who knows well the method of numerical solutions of system of nonlinear algebraic equations nonlinear algebraic equations recommand a global convergence methods? thank you very much!

What's the best study plan to get into nonlinear equations/dynamics, etc. Let's say we start with Calculus... how far should I go? Differential Equations afterwards? What's a typical course tracking into such math?

Hello, I have a system of trigonometric equations from which I should find theta1,..., theta5. Is it possible you can give me a hint on how to proceed. Thanks. theta, phi, psi, Px, Py, Pz, l1, l2, l3, l4, l5, d1, d2, d3, d4, d5 are all constants. Cos[t1+t2] Cos[t3+t4] Cos[t5]+Sin[t1+t2]...

I need some help with the problem that follows. Any help is highly appreciated. Problem: "Consider the initial value problem y^{\prime}=y^{1/3}, \mbox{ }y(0)=0 from Example 3 in the text. (a) Is there a solution that passes through the point (1,1)? If so, find it. (b) Is there a solution...

I need to solve the following second order nonlinear differential equation: z''(b) * [6(1 - f)z(b) + (1+f)b z'(b)] = (15 - 9 f)[z'(b)]^2 + [2(1 - f) z(b) z'(b)] / b + [4 f z'(b)^(5/2)] / b^(1/2) where f is a constant between [0,1]. initial conditions are z(0)=0 and z'(0)=0 I...

The problem is on competing species. For the problem, I am supposed to find the critical points. For each critical point, I need to find the eigenvalues and eigenvectors and classify the type of critical point and its stability. dx/dt = x(1.5 - x - 0.5y) dy/dt = y(2 - y -0.75x) I got...

what is a non linear finite element finite element analysis. When does a structure behave non linearly and how do we calculate non linearity of an element by the nodal displacements.

I recently came across [FONT=Comic Sans MS]Nonlinear Dynamics and Chaos by Strogatz and I'm recommending it to all my Physics/Applied Math friends. This is a great introductory book on the subject and you don't need any more Math than is taught in a basic Diff. Eq. course. I love this book...

I'm posting this under analysis because of the method I'm thinking about using to solve it. Here is the equation: \varepsilon \left( x\right) =e^{\varepsilon \left( x-1\right) } and the initial condition is \varepsilon \left( 0\right) =1. My main goal is to consider x as a number in...

1. a line in my code is something like int(phi*x^2,0,2) where i want phi to be a function which the user has choosen. But how can i let the user choose a function? For numbers you can use input but how to do it with a function? 2. i want to solve a nonlinear system of equations...

Variable co-effiecients Linear Differential equation \frac{d^2 y}{dx^2} = c_1y(1-c_2x) any help? Is there a solution besides a series solution?

Relevant to the NLS is the differential equation, \left( -\sum^N_{i=1} \frac{\partial^2}{\partial x^2_i} +c \sum_{i\neq j} \delta(x_i-x_j)\right)f_N = E_Nf_N(2.87) How does one show that \left(\prod_{i<j}(\theta(x_i - x_j) +...

I have recently borrowed a new book from the local library: Calculus of Linear and Nonlinear Functions by Francis J. Flanigan and Jerry L. Kazdan. I have already finished first-year Calculus and I was wondering if this type of book would prepare me well for second-year Calculus in...

Is there anyone here studying chaos in graduate school? I have read a little on the subject and find it interesting. I cannot however, find many graduate schools offering studies in this field. (I know of only two, University of Maryland and Cornell) Also, what kind of real world applications...

Hello I study animation, and I wanted to make a script where I can automate pendulums in my scene with some kind of realistic physics, rather than animate them manually. So 'right' I think, 'I need to go study some physics and maths' - but it wasnt as easy as I hoped, I've hit a wall, and...

this is the problem: xy'' -x(y')^2 = y' my book says that i need to substitute u=y' and du/dx=y''... so i get: x(du/dx)-xu^2 = u so next the book says i need to separate the x's/dx' to one side and u's/du's to the other. however, i cannot do it am i using the correct technique...

hi! i want to know how to deal with the nonlinear coupled dfifferential equations? can anybody help me in that regard? if some one can paste MATLAB links/programs to solve the equations, it will be highly appreciated. regards, chap

problem: xy'' -x(y')^2 = y' what i have so far: u=y' and du/dx=y'' du/dx - u^2 = (1/x)u int[(1/u)-u]du = int[1/x]dx ln u - (1/2)u^2 = ln x +c ok, now is what I've done so far correct? what do i do next? ps: i'd like to say hi to everyon :) I am new here