Non-linear Definition and 318 Threads

If a vector field ##\vec{v}## is non-divergent, so the identity is satisfied: ##\vec{\nabla}\cdot\vec{v}=0##; if is non-rotational: ##\vec{\nabla}\times\vec{v}=\vec{0}##; but if is "non-linear" Which differential equation the vector ##\vec{v}## satisfies? EDIT: this isn't an arbritrary...

Dear Experts! I am currently try to measure the drag of an buoyant object. I did 10 replicates, in general terms 10 tests all with the same set-up and same release mechanisms. To start off with I will explain my project: Drag reduction in swim cap First of all I got one accelerometer...

Homework Statement Ok, so I'm trying to fit a set of data (21000 points to be exact) to a sine function. Homework Equations Y = A*sin(ωt) The Attempt at a Solution I used NumPy to get the parameters A and ω with the least squares method. So far, so good. However, i appear to...

Ohm's law only applies to linear circuits. If most loads in life are non-linear, what use is ohm's law?

Homework Statement Hello, I was given an extension problem in a Dynamics lecture today and am struggling to solve it. It is a simple scenario: a particle of mass m is accelerating due to Galilean gravity, but is subject to a resistive force that is non-linear in the velocity of the particle...

Kindly solve it and i need help to understand NON LINEAR Questions

EDIT: my problem is solved, thank you to those who helped Homework Statement Solve: x y^{\prime \prime} = y^{\prime} \log (\frac{y^{\prime}}{x}) Note: This is the first part of an undergraduate applications course in differential equations. We were taught to solve second order...

Homework Statement i'm trying to find a solution for these two equations, p & q are variables and c is known constant (it's given randomly) : $$ \begin{align}...

Hello, I'm not really sure where does this question fit and what title should it bear, but here is my problem: \psi(x) \exp (a\psi(x)^2) = C f(x) given a positive definite f(x), find ψ(x) and the constant C, subject to the condition \int \psi(x)\, dx = 1 I want to solve this numerically...

What does one mean by normal mode of an object? Why is it 3n-5 for linear particles, 3n-6 for non linear particle where n is the number of particle.

Hello people, I couldn't solve the given D.E by using exact d.e & substitution method :( Thanks in advance. (x*y*sqrt(x^2-y^2) + x)*y' = (y - x^2*(sqrt(x^2-y^2) ) gif file of d.e can be found in the attachments part.

Hello, I am having difficulty inputting a non linear algebraic equation into polymath to solve for reference the equation is x*(100-.5*x)^0.5/(15-x)/(20-.5 * x)^0.5 - 87.824 == 0 and I want to solve for x, but haven't gotten anything. Also I don't know how to program it into matlab...

Hi. This is not actually not part of the homework; but it's something I'd like to do. I have to solve the following system using Newton-Raphson's method: $$\begin{matrix} \frac{X}{\mu }+Y=1 \\ X=\left( \lambda -\left( K-1 \right)X \right)Y \\ \end{matrix}$$ Surfing the...

I wanted to know if there is any way of classifying the set of all non-linear multivariable functions. I wish to analyse something over all possible non linear functions with 4 variables. In fact these variables are binary variables. for example f(x,y,u,v)= x.y - u\oplusv

Homework Statement x'= E - sin x + K sin (y-x) y'= E + sin y + K sin (x-y) E and K >0 Find fixed points for this system of equations Homework Equations This system is the form of coupled oscillators described in Strogatz. θ1'= ω1 + K sin (θ2-θ1) θ2'= ω2 + K sin (θ1-θ2)...

Hi, I think some background is necessary: I'm a Psychology undergraduate student. I also really love math. I've incorporated some pure math into my studies - next semester I'll have room for a course on "Foundational Mathematics" (I'm not sure if that's exactly what they call it outside my...

Hi, I derived the equation: 1+(y')^2-y y''-2y\left(1+(y')^2\right)^{3/2}=0 Letting y'=p and y''=p\frac{dp}{dy}, I obtain: \frac{dp}{dy}=\frac{1+p^2-2y(1+p^2)^{3/2}}{yp} I believe it's tractable in p because Mathematica gives a relatively simple answer: p=\begin{cases}\frac{i...

Homework Statement The problem is tough to type out correctly. Pasting problem statement image http://postimg.org/image/a0r92a0wl/ http://postimg.org/image/a0r92a0wl/ The Attempt at a Solution I just need to know how to proceed with the problem. Not the answer. This is the scan...

Hi friends, I have a system (with unknown properties) which takes an input vector of length 10 and outputs a vector with length 6. I select Inputs vector 'I' which is a 1000x10 matrix, : 1000 samples of 10 elements. And outputs vector 'O' is a 1000x6 matrix,: 1000 samples of 6...

I need help with the following so please help me -- Consider the following non-linear system X’ = x² - ay Y’ = y² - y(a) Find the fixed points of this system. (depending on a, there may be different fixed points!) (b) Study stability of each fixed point via linearization. In the case the...

Homework Statement Consider the nonlinnear diffusion problem u_t - (u_x)^2 + uu_{xx} = 0, x \in \mathbb{R} , t >0 with the constraint and boundary conditions \int_{\mathbb{R}} u(x,t)=1, u(\pm \inf, t)=0 Investigate the existence of scaling invariant solutions for the equation...

shooting method for non-linear equation(urgent) Homework Statement for shooting method , in non-linear equation, we're find $$t_{k}=t_{k-1}-\frac{[y(b,t_{k-1})-β](t_{k-1}-t_{k-2})}{y(b,t_{k-1})-y(b,t_{k-2})}$$ but how can we find the $$y(b,t_{k})$$ ? I am suppose to use Euler method for...

Hi! I'm having a lot of trouble solving the following ODE: dx/dt = A - B*sin(x) where A and B are constants. My ODE skills are a bit rusty, and I wasn't able to find anything on the Internet that could help me, so could someone please show me how to solve for x in terms of t? I've...

Assume we have a straight piece of wire with two end points A and B and with length L where x_{A}=0 and x_{B}=L. The wire has non-ohmic resistance and hence the current is not proportional to the potential difference, i.e. \left(V_{A}-V_{B}\right). In fact the current is a function of the...

Hi members of the forum, I am given to solve the following non-linear system: Solve $$(1+4^{2x-y})(5^{1-2x+y})=1+2^{2x-y+1}$$ and $$y^3+4x+\ln(y^2+2x)+1=0$$ I'm interested to know how you would approach this problem because I don't see a way to do so. Thanks!

My doubt is that whether we can apply non-linear smoothing to a almost linear data ( without one or 2 discontinuity) I have attached the pic in which the red data is the smoothed one. Blue is the original one. I multiplied each point with an increasing like 1, 1.1, 1.2, 1.3, 1.4...so on...

I received permission from my father to post this from his (unpublished) Calculus text. Note that this method will, I believe, work for proving existence of a limit for a nonlinear function at any point that is not a local extremum. My father thought it would be good to give you this proviso...

hello, guys Below is the equation I am concerned with: Is the above equation non-linear because of (delta P/delta x)^2 term assuming other variables are constant and don't change with pressure , P?

Is there a formal way to measure the error between some arbitrary points and a non-linear curve in order to minimize it?

Hi all, I have a nonlinear ODE in the following form: a x'' + b |x'|x' + c x' + d x = y where x and y are functions of time and a,b,c and d are constants. As far as I can tell the only way to solve this is numerically, something I've managed to do successfully using a Rung-Kutta scheme...

I model arterial baroreflex data that I have collected in humans using the Kent equation which is: y=p1/(1+exp((x-p3)*p2))+p4; where Y=heart rate, X= estimated carotid sinus pressure, p1=range of Y, p2=slope coeff, p3=centerpoint on X, p4 = minimum Y. I use Sigma Plot to do a best fit line...

I am investigating the mathematics behind driven damped oscillators, I will then simulate it in MATLAB and observe the unpredictable long term behavior of the system. In order to create non-linearity in a oscillating spring I can no longer use hookes law but a form of it by introducing a...

I am going to be simulating damped driven oscillators for my project and I was wondering if someone could give me a definitive answer on the matter. I know MATLAB is more of a 'tool' than a language so I'm thinking the maths behind damped driven oscillators might be easier to implement into...

4 equations, 4 unknowns: \[\frac{u(r^2 - u^2)}{r^2 + u^2}=156~~~~~~~~~~(1)\] \[\frac{v(r^2 - v^2)}{r^2 + v^2} = 96~~~~~~~~~(2)\] \[\frac{w(r^2 - w^2)}{r^2 + w^2} = 63~~~~~~~~~~(3)\] \[\frac{315uvw + 24336vw + 9216uw + 3969uv}{2r} = 943488~~~~~~~~~(4)\] Who can solve that mess?

Hi,I'd really appreciate any help on this as I've spent many many hours trying to get my head around it. I am simulating the vaporization of a droplet in hot air and I have two equations to use: m_lc_l\frac{dT_l}{dt} = \widetilde{h}A_0(T_\infty - T_l) + \dot{m}_l(h_v-h_l) \dot{m_l} = -\frac{\pi...

(d4x)/(dt4) + (1/(1+t))*(d2)/(dt2) = x(t) Is this differential equation linear or non-linear? I don't understand the difference.

I have an electrostatics problem (shown here: https://www.physicsforums.com/showthread.php?t=654877) which leads to the following system of differential equations: \frac{\partial E_z}{\partial z}=\frac{\rho}{\epsilon_0} (1) Z_i E_r \frac{\partial \rho}{\partial r}+(u_g+ Z_i E_z)...

Hi, I want to solve an overdetermined non-linear equation with the method of least squares. Assume it's f(x) = 1 + ax + a^2 + b, and I want to estimate a and b. This is non-linear, as I said, so the derivatives of the squared residuals involve a^3 terms and are difficult to solve. Now I thought...

I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.

How to transform non-linear frequency vibration to constant frequency of vibration of 2 Hz? Such as transform the different frequency of waves to constant frequency and then maintain it..

Hi, if we suppose x and y are two elements of some vector space V (say ℝn), and if we consider a linear function f:V→V', we know that the inner product of the transformed vectors is given by: \left\langle f\mathbf{x} , f\mathbf{y} \right\rangle = \left\langle \mathbf{x} ...

Hiya. I have to solve this bad boy under the assumptions that f, f' and f'' tend to 0 as |x| tends to infinity: 1/2(f')^2 = f^3 + (c/2)f^2 + af + b where a,b,c are constants. My thoughts are use Fourier Transforms to use the assumptions given, but not sure how to do them on these terms...

I want to understand the conductivity of ZnO. I know it is non-linear (that's why it is used in surge arrester to begin with), but can anyone enlighten me on why it is non-linear? Is it the function of electric field, current, or anything? I'd appreciate if you can provide the expression of...

Dear Friends, Would you please provide me with some hints to find the analytical solution of the non-linear PDE given below: U=U(z,t) Uzz-(A/U)*Uz=Ut BC's and IC's are: U(z,0)=B U(1,t)=B Uz(0,t)=A*H(t); "H" is the heaviside function and H(0)=0 where A, B, and C are constant...

Hello world, Is it possible to find all solutions to a system of non-linear equations, without solving them analytically? I have implemented a python solution of Newton's Method, is there a method of getting good guesses without scanning all numbers?

Have typed the question is latex format, here it is: http://i.stack.imgur.com/grxgI.png

Homework Statement 1. z^6=(64,0) 2. z^4=(3,4) Homework Equations These are expanded out into Real and Imaginary components (treat them seperate): 1. REAL (EQ 1) - x^6-15x^4y^2+15x^2y^4-y^6=64 IMAG (EQ 2) - 6x^5y-20x^3y^3+6xy^5=0 From here, you basically solve these for all six...

Hey gang, how would you specifically define what a non-linear DE is? I mean, what specifically qualifies a DE to be nonlinear, and what does that mean? I am currently working with a team that models brain function as an array of coupled oscillators with complex feedback profiles and I...

I am not sure I understand Linear and non-linear differential equations properly so I will ask some question which someone will hopefully answer. Is dx/dt = x + 2 a linear differential equation? If so does this mean that the rate of change of is constant? Is dx/dt = x^2 + 4x a non linear...

Hi, I several times heard that one way to describe the collapse of the wave-function is to add non linearities in the Schrodinger equation (I know that this approaches are not convincing but that's not my point), however, I don't see why a non linear SE would imply loss of unitarity? As long...