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0
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1answer
22 views

What does the term 'hyperbolic model' mean?

I am reading this non-linear discrete dynamical system paper. The authors mention the term hyperbolic model. What does that mean?
11
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2answers
509 views

Why is the computer useful if a chaotic system is sensitive to numeric error?

In every textbook on chaos, there are a lot of numerical simulations. A typical example is the Poincare section. But why is numerical simulation still meaningful if the system is very sensitive to ...
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3answers
103 views

Solving the simplest coupled nonlinear ODES for chemical kinetics [closed]

I am just trying to get the integrated form for the kinetics of the reaction $A + B \rightarrow C + D$ characterized by: $$ -\dfrac{d[A]}{dt} = -\dfrac{d[B]}{dt} = k[A][B] \; . $$ As you note, ...
0
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1answer
63 views

Steady state average of physical quantities

Consider the following Hamiltonian: $$ H = \sum_n \left[\dfrac{p_n^2}{2m_n} + U(x_l) + V(x_{l+1} - x_l) \right], $$ that corresponds to a 1-D system of particles with nearest-neighbor interactions ...
1
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0answers
25 views

A voltage-controlled oscillator? [closed]

I already apologize for my medium english... I'm a french guy, not really gifted to recognize electronic circuits : In fact, I need to identify a circuit from is function. So, here is the block ...
2
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2answers
158 views

Liouville's theorem and conservation of phase space volume

It can be proved that the size of an initial volume element in phase space remain constant in time even for time-dependent Hamiltonians. So I was wondering whether it is still true even when the ...
1
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0answers
118 views

Trying to solve 2D Toda Lattice Equation with Lax Pair Approach

I am working on this Hamiltonian: $$ H = \frac{p_1^2 + p_2^2}{2m} + e^{q_2-q_1} + e^{q_2} + e^{-q_1} -3 $$ Thank you for the hint that it is a modification of the Toda Lattice Equation. Let me sketch ...
0
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1answer
38 views

What is the difference between a linear and non-linear solution in the bending of beams?

I have been working on a simulator for bending of beams and came now to a tricky doubt: What should be the difference between a linear and non linear solution in this case (graphic at bottom)? The ...
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3answers
336 views

Non-linear dynamics vs Chaos

I am confusing between non linear dynamics and chaos. Chaos is also a non-linear dynamics right? then what is the difference between chaos and non-linear dynamics? What I understood about chaos is ...
1
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1answer
143 views

Does Lyapunov exponent equate to exponential inflation?

Physics can be modeled by dynamical systems $f^t(x)$ as well as by PDEs. The most common dynamical system has hyperbolic fixed point and can be an attractor or a repellor. The dynamics at repellors ...
1
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1answer
42 views

Meaning of Smooth Dynamical System?

What does smooth dynamical system mean? It is the title of a paper I am supposed to read in non linear systems.
0
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0answers
42 views

What is a non-linear capacitor?

I'm new here. I have a (maybe dumb) question: What are non-linear capacitors? I'm given a circuit including a capacitor and the question says The given capacitor is non-linear with the ...
1
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0answers
44 views

KdV equation and classical linear wave equation

Like we know, the standard form of KdV equation is $$u_{t}-6uu_{x}+u_{xxx}=0,\tag{1}$$ where this equation describes a solitary wave propagation and $u=u(x,t)$. On the other hand, we know the ...
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0answers
32 views

Solution to the “cubic” Helmholtz equation

What is known about the solutions of the differential equation in three-dimensions $$ \nabla^2 \phi = -\kappa^2 (\phi + (1/3!)\phi^3) $$ Without the cubic term, this gives a linear operator ...
4
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1answer
235 views

Calculating Lyapunov exponents from a multi-dimensional experimental time series

Wolf's paper Determining Lyapunov Exponents from a Time Series states that: Experimental data typically consist of discrete measurements of a single observable. The well-known technique of phase ...
3
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0answers
43 views

Reference for the Landau-Lifshitz system

I'm interested in understanding the dynamics of the discrete Landau-Lifshitz system. It's solutions to equations like $$\frac{\partial X_n}{\partial t} = X_n\times (X_{n-1}+X_{n+1})$$ where the $X_n$ ...
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0answers
36 views

Experimentally determining photon lifetime of a laser from transient response

At our lab, we have a DBR laser set up to some measuring equipment (oscilloscope, spectrum analyzer and random number generator). I have been tasked to experimentally obtain the photon lifetime of the ...
2
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3answers
72 views

Simple Experimental Laser Characterization Parameters Ideas?

I have 2 months to do a project on characterization of a laser parameter. We have typical optics lab equipment (DFB Lasers, oscilloscopes, random number generator, etc.). I was told to choose a laser ...
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2answers
314 views

How to find zero-point oscillations for this system?

Consider the following Hamiltonian which is absolutely relativistic literally: only sensitive to absolute pairwise relative phase space variables of objects for a system of $N$ objects moving in one ...
4
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1answer
132 views

How to find positions of $n$ masses in Newton mechanics?

I ran into a problem while doing research. The problem can be described as: consider the original $n$-body problem, and if we fix the position of them(unknowns), no interaction among them, they don't ...
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0answers
23 views

Pick marginal circles in phase plot of a non-linear dynamic system

Context: I'm studying non-linear dynamics with Mathematica. Part of the problem: Given the following system: $\ddot{x} = x - x^3 - 0.2 \dot{x} + g(\sin(t) + \cos(2t))$, find two values of $g$ that ...
1
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1answer
275 views

Classify equilibrium points and find bifurcation points of a non-linear dynamic system

Context: The question refers to computational physics of non linear systems with Mathematica. Excercise: Given the system $\{f_1: \dot{x} = a x + y + x^3, f_2: \dot{y} = x - y \}$: Find the ...
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0answers
12 views

Self-contained book about complex systems and nonlinear dynamics [duplicate]

I am a student at the 2nd year of a B.Sc. in Biotechnology. I started reading some papers about complex systems and nonlinear dynamics applied to economy, biology of course, climate model etc... I ...
8
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1answer
238 views

Anharmonic oscillators: why is $F=-k x-k' x^3$, with no quadratic terms?

The equation of motion of a general anharmonic oscillator includes a position-dependent force that can be expanded in a Taylor series as $$m\ddot{x}+2\mu\dot{x}+k_0+k_1x+k_2x^2+k_3x^3\ldots=F.$$ I ...
5
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1answer
69 views

Stability theory [closed]

I'm studying stability theory recently and met a lot of phrases like linear stability and nonlinear instability. After searching on Google, I became more confused. Thus I wonder if there is any ...
2
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1answer
132 views

Bose-Einstein condensate and nonlinear waves

Can Bose-Einstein condensate be written as non-linear wave equation (in terms of mean field approximation theory)? the equation is: source: http://xxx.tau.ac.il/abs/1308.2288 What I do ...
3
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1answer
183 views

Does the logistic map have an attractor for a particular value of the parameter?

Background: Currently I am studying a course on non-linear dynamics. We have been studying about attractors only intuitively, so I do not have a definition for an attractor. Let me give you a couple ...
1
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1answer
97 views

Why linear wave equation does not have solitonic solutions?

As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
1
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1answer
93 views

Doubts regarding dimension of a system:Definitions and algorithms

I need to do phase reconstruction from time series data. In doing so, I encountered Takens' embedding theorem and Cao's minimum embedding dimension $d$ by nearest neighbor method. In paper "Optimal ...
2
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0answers
81 views

value of $\omega$ in nonlinear equation

IN this article the author written a nonlinear equation as $$-\frac{\partial^2 \phi}{\partial t^2}+ \nabla \phi= \phi+ \sum_{k=2}^\infty g_k \phi^k$$ They have scaled the time as, ...
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0answers
46 views

Nonlinear waves and shock formation

In the cases of nonlinear acoustics, why is shock formation unlikely when the dispersion is strong when compared to the nonlinearity of the wave?
1
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1answer
100 views

Dimension analysis in Derrick theorem

The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe: What I don't understand from the above statement: why $e(\mu)$ has minimum ...
1
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0answers
27 views

Differences the nonlinerarties

I want to comparison between oscillons based on non-linearities. Can someone elaborate it with the reason behind it : When the sinusoidal vibrations are of the correct amplitude and frequency and ...
2
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1answer
446 views

What is the amplitude of the limit cycle of the van der Pol oscillator?

In the second edition of Classical dynamics of particles and systems by Jerry B. Marion, it is said that the van der Pol equation $$\ddot{x}-\mu\left({x_0}^2-x^2\right)\dot{x}+{\omega_0}^2x=0$$ where ...
2
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4answers
201 views

Nonlinear waves superposition

Non-linear waves do not superimpose to each other, but why? What characteristics give this property?
2
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4answers
138 views

Suggestions of a non-linear example for a small research project on numerical solution of ODEs?

I'm a first year undergrad and I'm doing a small research extension on numerically solving ODEs. I have done the main ODE course at my university, as well as physics. The second part of the project ...
1
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1answer
132 views

Finding out Energy value

A Lagrangian is given by, $$L= \left(\frac{\pi}{2}\right)^2 R^d \left[\frac{1}{2}\dot A^2 - V(A_{max})\right]$$ $$E=\left(\frac{\pi}{2}\right)^2R^d V(A_{max}) $$ where V (A) now includes nonlinear ...
0
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1answer
257 views

Applications to the Van der Pol equation? [closed]

What are some applications to the Van der Pol equation? Are there any physical examples?
1
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2answers
123 views

Linear quantization in quantum electrodynamics?

This is a continuation of this question. What would be an example of linear quantization used on quantum electrodynamics? I ask this because QED is a nonlinear theory.
1
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0answers
165 views

Explain the Föppl–von Kármán equations

I am a newbe to elasticity. Could someone please explain to me briefly how the Föppl–von Kármán equations work? What are we trying to solve for? Is there some kind of intuition to the way they look? ...
6
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2answers
292 views

Change of basis in non-linear Schrodinger equation

At the mean-field level, the dynamics of a polariton condensate can be described by a type of nonlinear Schrodinger equation (Gross-Pitaevskii-type), for a classical (complex-number) wavefunction ...
2
votes
1answer
169 views

Deflection of a membrane

I am currently working on a project which is described as the deflection of a circular membrane. What I am trying to model is the deflection of a piece of plastic film (E=200MPa,v=0.5) when placed ...
1
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0answers
116 views

Implicit Differentiation, A doubt

$v=v_c(\tau, t)$ is a smooth function and suppose we have a relation $y_c(\tau,v_c;t)=0$ when $x_c$ is written in the form $x_c=c+ty_c(\tau,v_c;t)$, $c$ is real constant, $t$ is real number denotes ...
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2answers
506 views

What is a physical example of a Saddle-Node Bifurcation?

I am doing a presentation on bifurcations and would like physical examples to go along with each type of bifurcation but I am unable to find or think of any good example of a simple Saddle Node ...
4
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3answers
226 views

Non-SHM oscillatory motion

How to solve these kind of questions , where $|F| \propto x^2$? How to find time period and velocity type related things to the oscillatory motion? ...
7
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2answers
774 views

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics?

Does chaos theory occur in quantum mechanics? Or in any non-newtonian physics? Apart from perhaps thermodynamics?
2
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2answers
214 views

Phase volume contraction in dissipative systems

I am confused about phase-volume contraction in dissipative systems. Please help me catch the flaw in my understanding. From a macroscopic point of view I understand that a dynamic system tends to go ...
4
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1answer
476 views

Gross-Pitaevskii equation in Bose-Einstein condensates

I was hoping someone might be able to give a approachable explanation of the Gross-Pitaevskii equation. All the sources I've been able to find seem to concentrate on the derivation, and I don't have ...
2
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0answers
310 views

Nonlinear refraction index of vacuum above Schwinger limit

This question is more about trying to feel the waters in our current abilities to compute (or roughly estimate) the refraction index of vacuum, specifically when high numbers of electromagnetic quanta ...
0
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1answer
225 views

Inhomogenous schrodinger equation

Please help me out in solving this inhomogeneous Schrodinger equation in Cylindrical co-ordinates [You may suggest if I have to go for mathematics]: $$ \ddot R + \frac1r\dot ...