All Questions
Tagged with non-linear-dynamics or non-linear-systems
473 questions
2
votes
0
answers
29
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Find closed orbit problem (Strogatz 8.3.2) [closed]
I'm having trouble solving this excercise from Strogatz
Consider the following system for a chemical oscilator:
$$
\dot x= a -x+x^2y
$$
$$
\dot y=b -x^2y
$$
Where $a,b>0$ are parameters and $x,y\...
- 213k
1
vote
0
answers
25
views
About barium titanate
Is barium titanate (BaTiO3) thin film martensite? Recently, Everhardt et al., in PRL (123, 087603 (2019)), show that as temperature increases, the domain evolution shows period-doubling bifurcation ...
- 61
2
votes
3
answers
205
views
The "small amplitude" assumption in the derivation of the wave equation for the string
I am reading about the wave equation for transverse waves in a string from the book Mathematics of wave propagation (2000) by J. Davis. On page 10, just before the derivation of the (one-dimensional) ...
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1
vote
0
answers
36
views
Non-linear crystals' interaction with light
This is really just a general question because we've been seeing non-linear crystals in a crystallography class, very briefly.
I was wondering how can we possibly understand the unique way non-linear ...
- 213k
3
votes
6
answers
2k
views
Why do people say the dynamics of quantum mechanics is always linear?
This statement seems false. An example of a non-linear equation governing the dynamics of a quantum system is the Gross-Pitaevskii equation.
- 23.3k
6
votes
1
answer
1k
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Is *every* autonomous first-order planar/2D system integrable?
Consider a general autonomous first-order planar/2D system:
$$\begin{cases}
\frac{dx}{dt} = A(x,y)\\
\\
\frac{dy}{dt} = B(x,y),
\end{cases}$$
where $A,B$ are two functions. Reading Classical Mechanics ...
- 213k
0
votes
1
answer
49
views
How to understand the non-linear calculation model of demagnetization curve correctly?
in the doc of MotorCAD, I found that the demagnetization curve can be calculated by like this non linear model:
In above formula, the Br at specific temperature can be calculated like this:
And the ...
- 12.9k
2
votes
1
answer
394
views
Wave vector relation in nonlinear material
A light wave ($k_1,\omega_1$) travels in a medium of refractive index $n_1$ and then encounters a nonlinear medium ($n_2$) under the angle $\theta_1$.
Snell's law tells us the wave's direction in the ...
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14
votes
4
answers
2k
views
How do gravitational fields combine together in GR?
When we have 2 massive bodies coming close together say 2 black holes or 2 massive stars, how do their respective metrics/spacetime curvature combine in the space in between them?
Do we write
$$G_{\mu\...
- 213k
1
vote
2
answers
161
views
Understanding linearity of Maxwell's equation compared to non-linarity of GR
In this post, it is mentioned that a linear equation means that the solutions 'do not interact with each other' or 'do not know' about each other. But we know that Maxwell's equations are linear ...
- 213k
2
votes
2
answers
390
views
Four-wave mixing and modulation transfer spectroscopy: why do sidebands appear on the probe?
I'm trying to understand modulation transfer spectroscopy in simple terms.
For those unfamiliar with it, this article gives a very good summary. To sum it up, two counterpropagating beams, a pump and ...
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- 1
-6
votes
2
answers
79
views
Non-linear time and concurrent perceptions of reality [closed]
I am asking about what the fact that a photograph and a physical space can exist, in what we perceive to be different moments in linear time (with the photo being made from what we regard as our ...
- 28.4k
6
votes
1
answer
206
views
Can spring constant change by twisting or unwinding spring?
I am trying to study analytically the behaviour twisting springs and I noticed that if I consider mass and shape of spring the winding and unwinding of spring affects it's mass distribution and was ...
- 16.2k
3
votes
1
answer
313
views
Do these Lagrange equations of 1st kind exhibit numerical instabilities?
I followed the lead of "Theoretische Physik", 1e, 2015 by Bartelmann et al. (pp. 171 - 174) to form the set of constituting Lagrange equations of the 1st kind for the double pendulum: eight ...
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8
votes
1
answer
342
views
How are far from equilibrium systems studied analytically?
I've read about stuff having to do with complex systems where some pretty wacky stuff happens, mostly involving "phase changes", which as I understand don't really have much to do with ...
- 1,723
0
votes
1
answer
98
views
Nonlinear physics [closed]
Hey I wanna start studying nonlinear physics, and to be honest I don't know from where to start, I need books for beginners that explains things in general about the nonlinear science branches, so ...
- 213k
0
votes
0
answers
45
views
How would you interpret the quantum limit cycle represented by the Wigner function?
This paper by Arosh et. al. discusses the emergence of limit cycles in the quantum phase space (the Wigner function) for nonlinear oscillators.
(The quantum limit cycle of the quantum RvdP oscillator ...
- 786
3
votes
2
answers
153
views
Do meaningful bifurcation diagrams exist for systems described by vector fields on circles?
I've been reading about the vector field on a circle, and how it's used to describe stable points for periodic motion. I have also read about how bifurcation diagrams describe changes in positions of ...
- 12.9k
1
vote
0
answers
78
views
Symmetry and integrability in classical Hamiltonian
I am trying to understand the behaviour of an Hamiltonian system I'm simulating. I will give a quick context setting. The system is defined as
$$
\mathcal{H}(\mathbf{z};\mathbf{z}^*) = \sum_{i=1}^{M}...
- 350
0
votes
2
answers
395
views
RG flow diagram plotting
I want to be able to plot a flow diagram with a given recursion relation.
For example, I have the follow recursion relation:
\begin{align*}
\frac{dT}{d\ell} &= 2T{y_0}^2 a^2
\\
\frac{d ...
CommunityBot
- 1
13
votes
1
answer
752
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 ...
CommunityBot
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2
votes
1
answer
454
views
Vacuum birefringence
Many of the papers (e.g., this) dealing with nonlinear electrodynamics treat a theory's prediction of vacuum birefringence as undesirable, but don't explain why it would be undesirable. For example:
...
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- 1
5
votes
4
answers
676
views
Non-linear QM and wave function collapse [closed]
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 ...
- 213k
3
votes
4
answers
649
views
Reformulate Einstein equations to make them linear
Is it possible to reformulate the Einstein equation in terms of a new variable, say $k_{\mu\nu}$ in terms of the metric $g_{\mu\nu}$, in order to make the Einstein equations linear in $k_{\mu\nu}$?
- 31
6
votes
3
answers
492
views
How to linearise on Lagrangian level?
Consider a Lagrangian density
$$\mathcal{L}(\phi, \nabla \phi) = \frac{1}{2} \, g^{\mu \nu} \, \partial_{\mu} \phi \; \partial_{\nu} \phi + V(\phi) \tag{1}$$
The equation of motion (EOM), i.e. the ...
- 685
1
vote
0
answers
28
views
What are some good resources to learn fluid mechanics? [duplicate]
I know that there are a lot of resources out there to be explored and I have gone through several of them. What I want is some resource where fluid mechanics is treated,
from a geometric viewpoint,
...
- 213k
0
votes
0
answers
34
views
Burger equation and shock waves
Given the burger equation, $$m_{\tau} + mm_x = 0,$$ one expects to have discontinuities and thus shock waves in the case the initial conditions are smooth. For example, one may take $$m_0(x) = \sin(x),...
- 213k
1
vote
2
answers
223
views
Sum harmonic and sum frequency generation
Can two collinear beams of two different wavelengths generate the sum frequency or they need to pass each other at a certain angle. For a monochromatic light how does the sum harmonic gets generated ...
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- 1
1
vote
1
answer
66
views
Are there Dirac equations for different energy-momentum dispersion relations?
When I was introduced to the Dirac equation they wrote a PDE such that plane waves satisfy $E^2 = P^2 + m^2$. They went on to show that other options (ie Klein–Gordon) don't have spin.
Are there Dirac ...
- 707
1
vote
2
answers
375
views
How to determine if gravity is roughly linear?
The Einstein field equations are famously nonlinear, which is one of the properties that makes them difficult to solve. I know (or at least I believe) that a linear system's behavior is roughly ...
- 13.4k
18
votes
3
answers
3k
views
Is there a second-order non-linear addition to Maxwell's equations?
Maxwell's equations are famously linear and are the classical limit of QED. The thing is QED even without charged particles is pretty non-linear with photon-photon interaction terms. Can these photon-...
- 213k
0
votes
1
answer
62
views
Do all nonlinear systems store energy?
I would like to clarify, this question comes from my own curiosity while solving for nonlinear differential equations. I have noticed that I lack the fundamental understanding of linearity/...
- 51.7k
1
vote
0
answers
24
views
Resources on Phase Ordering Dynamics and Non-Linear System
I am doing a course on Non-Equilibrium Physics. Prof. was initially following Strogatz but has now started teaching Phase ordering dynamics, Cahn-Hillard equation and all?
I can't seem to find a good ...
- 213k
2
votes
2
answers
597
views
Burgers' equations and shock waves
Given Burgers' equation, $m_{\tau} + mm_x = 0,$ one expects to have discontinuities and thus shock waves in the case the initial conditions are smooth. For example, one may take $m_0(x) = \sin(x), x\...
- 2,405
0
votes
1
answer
135
views
Parametric Resonance Analysis using Perturbative approach
I'm reading Parametric Resonance from Landau's Mechanics Text. A similar calculation is done here. Supposing a parametric oscillator given by
$$\ddot{x}(t)+\omega_0^2(1+h\cos(\gamma t))x(t)=0$$
It's ...
- 12.9k
14
votes
4
answers
1k
views
No-Cloning and Uncertainty: Connections or Misconception
In chapter 9 of Scott Aaronson's book "Quantum Computing Since Democritus", he make interesting but peculiar claims relating the no-cloning theorem and the Heisenberg Uncertainty Principle (HUP). Here ...
- 5,259
0
votes
2
answers
161
views
Why are the equations of motion for a free quantum field theory always linear?
So far all the Lagrangians I have come across in my studying of quantum field theory have had a free theory whose equations of motion are linear. A linear free theory is of course desirable from a ...
- 23.3k
4
votes
2
answers
306
views
Is every constraint involving only two coordinates integrable?
There is a footnote on Goldstein's Classical Mechanics (3rd ed., page 15) which says the following:
In principle, an integrating factor can always be found for a first-order differential equation ...
- 213k
2
votes
1
answer
664
views
Dimension analysis in Derrick theorem
The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe:
What I don't understand from the above statement:
why $e(\mu)$ has minimum for ...
- 213k
12
votes
5
answers
4k
views
Is non-linear quantum mechanics possible?
Say we have a state vector $|A\rangle$. Is it possible to have a theory where the evolution of $|A\rangle$ depends on the vector $|A\rangle$ itself? e.g.
$$ i\frac{\partial}{\partial t} \psi(t) = \...
- 5,093
5
votes
2
answers
3k
views
What is a diabolical point?
A lot of papers define a 'diabolical point' as a "double semi-simple eigenvalue." I know a semi-simple eigenvalue is one which has algebraic multiplicity and geometric multiplicity to be equal. ...
- 11
0
votes
0
answers
46
views
Why do shockwaves refract when they travel into the ground?
If a shockwave from something like an explosion travels into the ground, why will it refract? The speed of sound is far different in the ground, but what would make it refract? I can’t seem to find ...
- 355
1
vote
0
answers
81
views
Does every shockwave have an expansion wave behind it?
Do all shockwaves have an expansion fan or expansion wave behind them? Does the air always expand behind a shockwave?
I assume that the strength of the expansion wave depends on the strength of the ...
- 213k
2
votes
1
answer
85
views
How do shockwaves interact?
As seen here, there are two T-38's going supersonic. What happens when those shockwaves interact? They seem to dissipate in some places on this photo when they interact. Any source online says that ...
- 213k
1
vote
1
answer
45
views
How are shockwaves able to refract?
How are shockwaves able to refract? As said here,
When two shock waves collide, they interact with each other and produce complex patterns of compression, rarefaction, and reflection. The resulting ...
- 213k
1
vote
1
answer
79
views
Dispersion relation for non-harmonic waves
This question is related to my previous one.
The entire linear theory of waves is built on dispersion relations, which represent the algebraic dependence of frequency on wave number. That is we ...
- 31
1
vote
0
answers
70
views
Validity of approach to nonlinear, driven, damped oscillation amplitudes in L&L
In §29 of L&L mechanics, the authors discuss an approach to estimate the resonance amplitude of the equation
$\ddot{x}+2\lambda\dot{x}+\omega_0^2x = \frac{f}{m}\cos(\gamma t)-\alpha x^2-\beta x^3$ ...
- 173
2
votes
2
answers
246
views
Entropy in chaos dynamics
I'm curious about how entropy is defined within chaos theory. Are there analogous laws similar to the second law of thermodynamics? How do we define steady-state or equilibrium within the state space ...
- 408
0
votes
3
answers
65
views
Can protrusions on the smooth surface of a floating (or flying) body not slow it down, but accelerate it?
These protrusions are sure to create turbulent vortices. But what if these additional vortices can somehow lead to acceleration?
Additional clarification
It is clear that moving protrusions such as ...
- 45.6k
0
votes
0
answers
78
views
Self-similar solution of the second kind
I have a problem trying to understand the procedure for using self-similar solution of the second kind. More specifically, I was reading about an equation of this form,
$$\partial_t{d} + \frac{1}{r} \...
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