Questions tagged [non-linear-systems]
The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or perturbative approach.
488 questions
0 votes
1 answer
70 views
From phase portrait to equation
Given a certain phase portrait/phase space, what is the right approach in order to find an equation $\dot{x}=f(x)$ (or a set of equations $\dot{x_n}$) with a flow consistent with that portrait? More ...
- 17
3 votes
1 answer
150 views
Why are solitons reluctant to disperse their energy?
Can somebody explain in words alone why solitons survive in water so long? Are they moving with low friction through the surrounding water imparting little energy to it?
user547468
7 votes
3 answers
1k views
Is the collapse of the wavefunction really part of the quantum theory?
The collapse of the wavefunction by comparing it with the Schrodinger equations has some differences: it is higly non-linear while the Schrodinger equation is linear, it is non-local as proven by Bell'...
- 257
7 votes
1 answer
514 views
Well-posedness of initial value problem in chaotic systems?
Quoting Wald from his seminal textbook on general relativity (Chapter 10): First, in an appropriate sense, "small changes" in initial data should produce only correspondingly "small ...
- 463
2 votes
1 answer
311 views
Can physical waves develop an infinitesimally narrow singularity?
consider a wave described by some field. the mod square of this field often corresponds to energy density or particles density. Mathematically, the total energy or particle number could be finite even ...
- 254
3 votes
1 answer
243 views
Charge in non-linear Electrodynamics and GR
How do we define charge in a theory of curvature with non-linear electrodynamics? For example, suppose we have an action \begin{equation} S = \int d^D x \sqrt{-g}\Big( R - k\Lambda + (cF)^n\Big) \end{...
- 712
0 votes
1 answer
316 views
A brick sliding in an horizontal plane after an initial push (under Coulomb's dry friction) - part 2
A brick sliding in an horizontal plane after an initial push (under Coulomb's dry friction) - part 2 Intro This is a follow up of a previous question. Main Body From these Wikipedia sites: Contact ...
- 133
2 votes
1 answer
152 views
Applications of systems exhibiting strange attractors
I have always thought of strange attractors as mathematically interesting and aesthetically pleasing phenomena. In investigating a system for my PhD research, I have surprisingly stumbled across the ...
- 518
0 votes
1 answer
175 views
Normal coordinates in context of gravity
When doing coupled oscillator problems. Normal coordinates are those such that couplings (the off-diagonal terms in the matrix) appear vanish. This is diagonalization of the eigenvalue problem. In ...
- 17
0 votes
2 answers
86 views
Term similar to potential energy but for oscillation cycles instead
I'm not sure if this question makes sense, but similar to how one can assign a potential energy based on the instantaneous spatial configuration of a system, which gives us insight into what state the ...
- 94
2 votes
1 answer
196 views
Attractor in Poincaré section
I have a dynamical system which is shown by 2 second order differential equation which are coupled: $$\ddot{x} + \gamma\dot{x} + \frac{1}{m} \frac{\partial H}{\partial x} = 0$$ $$\ddot{y}+ \gamma\dot{...
- 21
1 vote
2 answers
274 views
Demonstrate hysteresis of Duffing equation in numerical solution
Objective I would like to model the following Duffing equation using Runge-Kutta 4 algorithm : $$ \ddot{x} + 2\mu\dot{x} + \gamma\dot{x}^3 + \omega_0^2x + \alpha x^3 = k\cos{\omega t} $$ I am using an ...
- 41
0 votes
0 answers
84 views
Nonlinear dynamics: analytical solutions to a sinusoidally forced
I asked this question on math stack exchange but I wanted to repeat it here, since I was studying a physical system when I came across the following differential equation: $$ \ddot{\theta}+\alpha \dot{...
- 83
0 votes
0 answers
95 views
Derivation of the Fokker-Planck equation
A nonlinear dynamical system is considered $$ dx/dt = f(x) + z(x)p(t), $$ where $p(t)$ Gaussian noise with zero mean and exponential correlation function. How I can derivation of the Fokker-Plank ...
0 votes
0 answers
92 views
How can I estimate the velocity of a conveyor belt relative to a laser line profiler?
I have a laser line profiler scanning a conveyor belt: At every time, step i: $t_i = i \Delta t$ the line profiler measures n points on the line: $$ (Y_j,Z_j,I_j) $$ Where $Y_j$ is the position along ...
- 367