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25
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3answers
3k views

Why can't the Navier Stokes equations be derived from first principle physics?

At the 109th UCLA Faculty Research lecture, Seth Putterman gave a talk on Sonoluminescence. During the lecture he emphasized that "The Navier Stokes equations cannot be derived from first principles ...
14
votes
3answers
630 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 ...
13
votes
2answers
847 views

A good, concrete example of using “chaos theory” to solve an easily understood engineering problem?

Can anyone suggest a good, concrete example of using "chaos theory" to solve an easily understood engineering problem? I'm wondering if there is a an answer of the following sort: "We have a high ...
11
votes
4answers
633 views

Non-linear systems in classical mechanics

In general, what is meant by non-linear system in classical mechanics? Does it always concern the differential equations one ends up with (any examples would be greatly appreciated)? If so, is it ...
8
votes
1answer
478 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 ...
8
votes
1answer
142 views

Deviation from power law distribution of earthquakes

One of the most accepted frameworks for the relationship between the magnitude and frequency of an earthquake is that of the critical phenomena. In this framework, the magnitude of events must be ...
8
votes
3answers
925 views

Current scope of Chaos theory and non-linear dynamics? [closed]

I am a physics undergrad interested in stuff like dynamical systems, chaos theory etc. Is there ongoing research in these fields? I am talking about pure research and not applications to things like ...
8
votes
1answer
655 views

warp drive with gravitational waves in the nonlinear regime

gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, ...
7
votes
6answers
908 views

Could the Schrödinger equation be nonlinear?

Is there any specific reasons why so few consider the possibility that there might be something underlying the Schrödinger equation which is nonlinear? For instance, can't quantum gravity (QG) be ...
7
votes
2answers
242 views

Chaos is predictable?

I'm reading a book of computational physics [1] where the driven nonlinear pendulum is studied in deep. This is the equation used in the book: $$ \frac{d^2\theta}{dt^2} = -\frac{g}{l}\sin\theta - ...
7
votes
2answers
1k 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?
6
votes
1answer
1k views

Poincaré maps and interpretation

What are Poincaré maps and how to understand them? Wikipedia says: In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is ...
6
votes
2answers
340 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 ...
6
votes
2answers
327 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 ...
6
votes
4answers
89 views

Energy conservation without action principle?

The normal tagline for energy conservation is that it's a conserved quantity associated to time-translation invariance. I understand how this works for theories coming from a Lagrangian, and that this ...
5
votes
2answers
706 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 ...
5
votes
2answers
327 views

Modeling stochastic process with frequency-dependent power spectrum

I'm trying to model of Johnson-Nyquist noise propagation in a nonlinear circuit. An ideal (linear) resistor can be modeled very nicely by the Fokker-Planck equation (equivalently, the drift-diffusion ...
5
votes
2answers
334 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 ...
5
votes
1answer
82 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 ...
4
votes
3answers
294 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? ...
4
votes
2answers
448 views

How and why can random matrices answer physical problems?

Random matrix theory pops up regularly in the context of dynamical systems. I was, however, so far not able to grasp the basic idea of this formalism. Could someone please provide an instructive ...
4
votes
2answers
326 views

Why are non-linear optics called non-linear?

Looking at the wikipedia article on nonlinear optics you can see a huge list of frequency mixing (or multi-photon) processes. What makes these different from single-photon interactions? More ...
4
votes
1answer
198 views

Viscous Burgers equation physical meaning

The viscous Burgers' equation: $$ q_{t}+q\:q_{x}~=~\nu\:q_{xx}, \mbox{ where } \:\:\nu >0, $$ combines the nonlinear propagation of $q(x,t)$ and the diffusion. What is this equation for? (in ...
4
votes
1answer
659 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 ...
4
votes
1answer
598 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 ...
4
votes
1answer
140 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 ...
4
votes
1answer
148 views

Why is the critical state in the Mean Field Bak-Sneppen Model a global attractor?

Simulations of the Bak-Sneppen Model of Species Evolution (introduced in http://link.aps.org/doi/10.1103/PhysRevLett.71.4083) show that it exhibits Self-Organized Criticality where after a transient ...
4
votes
2answers
208 views

Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes on page 8 (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and ...
4
votes
0answers
96 views

What is the source of water and waves on the water planet in the movie Interstellar?

We will ignore some of the more obvious issues with the movie and assume all other things are consistent to have fun with some of these questions. Simple [hopefully] Pre-questions: 1) If the water ...
4
votes
0answers
44 views

Solutions of nonlinear systems invariant wrt. perturbations (looking for applications)

I want to ask if the following purely mathematical problem (that I'm working on) might have some applications to physics. The problem in a nutshell: describe properties of solution sets of real ...
3
votes
3answers
802 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 ...
3
votes
2answers
416 views

What are the solution spaces of Nonlinear Schrödinger equations?

As we know, the solution space of Schrödinger equation is a Hilbert space, however, what about it of Nonlinear Schrödinger equations such as $$i\partial_t\psi=-{1\over ...
3
votes
1answer
135 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?
3
votes
3answers
100 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 ...
3
votes
1answer
367 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 ...
3
votes
0answers
71 views

Non-linear Wave Equation - Numerical Methods

Motivation: I'm working with a highly non-linear spherical wave-like equation (second order PDE). The equation can be written on the form $$\ddot{u} = f(t, \dot{u},\dot{u}',u',u'')$$ where ...
3
votes
0answers
53 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 $X_n$ ...
2
votes
3answers
666 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 ...
2
votes
4answers
448 views

Nonlinear waves superposition

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

Non linear QM and wave function collapse

I heard that there have been some propositions about describing the collapse of the wave-function by adding non-linear terms, but I couldn't anything in any any textbooks or even articles (probably ...
2
votes
3answers
153 views

How to do linear stability analysis on this system of ODEs?

I was trying to do linear stability analysis of spring pendulum. I arrived at the differential equations which describe the system. But I am unable to proceed to linear stability analysis. Is it ...
2
votes
1answer
67 views

Non-linearity and self-coupling of gravity

I have heard that non-linearity of Einstein's field equations has to do with the fact that gravity self-couples. What does non-linearity have to do with self-coupling?
2
votes
1answer
820 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
votes
4answers
181 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 ...
2
votes
2answers
299 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 ...
2
votes
1answer
230 views

Equivalent system in Centre manifold theory

I was studying the centre manifold theory. It says (see Kuznetsov page 155, theorem 5.2) that the system on the left side of the picture is topologically equivalent to the one on the right. $ ...
2
votes
3answers
560 views

What is a nonlinear field?

I have read two possible definitions. A nonlinear field is A field taking values on a manifold. A field whose equation is nonlinear. What do you understand by a nonlinear field or a nonlinear ...
2
votes
1answer
31 views

Solitons and its infinite extension

A soliton, for example the KdV equation solution, has the profile proportional to a hyperbolic secant squared ${\text{sech}}^{2}(x-ct)$. And since it is hyperbolic it has an exponential dependence, so ...
2
votes
1answer
137 views

The universality of the Stuart-Landau equation to describe nonlinear oscillators

I have read numerous papers which boldly suggest that the Stuart-Landau equation can be successfully used to model any weakly nonlinear oscillating system near a Hopf bifurcation. Even thought it has ...
2
votes
1answer
167 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 ...