All Questions
Tagged with non-linear-dynamics or non-linear-systems
473 questions
2
votes
0
answers
29
views
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\...
- 97
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
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 ...
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.
- 3,295
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 ...
- 101
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
$$G_{\mu\...
- 2,042
1
vote
2
answers
161
views
Understanding linearity of Maxwell's equation compared to non-linarity of GR
In this post, it is mentioned that a linear equation means that the solutions 'do not interact with each other' or 'do not know' about each other. But we know that Maxwell's equations are linear ...
- 849
-6
votes
2
answers
79
views
Non-linear time and concurrent perceptions of reality [closed]
I am asking about what the fact that a photograph and a physical space can exist, in what we perceive to be different moments in linear time (with the photo being made from what we regard as our ...
6
votes
1
answer
206
views
Can spring constant change by twisting or unwinding spring?
I am trying to study analytically the behaviour twisting springs and I noticed that if I consider mass and shape of spring the winding and unwinding of spring affects it's mass distribution and was ...
- 61
8
votes
1
answer
341
views
How are far from equilibrium systems studied analytically?
I've read about stuff having to do with complex systems where some pretty wacky stuff happens, mostly involving "phase changes", which as I understand don't really have much to do with ...
- 93
0
votes
0
answers
45
views
How would you interpret the quantum limit cycle represented by the Wigner function?
This paper by Arosh et. al. discusses the emergence of limit cycles in the quantum phase space (the Wigner function) for nonlinear oscillators.
(The quantum limit cycle of the quantum RvdP oscillator ...
- 786
0
votes
1
answer
97
views
Nonlinear physics [closed]
Hey I wanna start studying nonlinear physics, and to be honest I don't know from where to start, I need books for beginners that explains things in general about the nonlinear science branches, so ...
1
vote
0
answers
78
views
Symmetry and integrability in classical Hamiltonian
I am trying to understand the behaviour of an Hamiltonian system I'm simulating. I will give a quick context setting. The system is defined as
$$
\mathcal{H}(\mathbf{z};\mathbf{z}^*) = \sum_{i=1}^{M}...
- 61
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,
...
2
votes
3
answers
204
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) ...
- 21
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 ...
- 19
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 ...
- 3,347
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-...
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/...
- 3
1
vote
0
answers
23
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 ...
2
votes
2
answers
596
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\...
- 173
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),...
- 173
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 ...
- 3,898
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
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 ...
- 355
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 ...
- 11
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 ...
- 355
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
245
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 ...
- 352
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 ...
- 355
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 ...
- 168
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} \...
- 109
-1
votes
1
answer
95
views
Applications of Schrodinger's to dark solitons [closed]
The Schrodinger equation (SE) admits dark solitons as particular solutions. The SE and the The Korteweg-de Vries (KdV) equations can be used to model them.
Questions:
What are the applications of ...
- 99
0
votes
0
answers
74
views
How to find the stability of time dependent Lyapunov equation?
After linearization of the nonlinear equations, I want to find the covariance matrix $v$ through the numerical solution of time dependent Lyapunov equation, $$dv/dt=a*v + v*a'+ d,$$ where $a$ is my ...
- 31
0
votes
1
answer
30
views
$\rm InP$ Mach-Zender modulator
I know how a Mach-Zender electro-optical modulator (MZM) works when based on non-linear crystals like LN. On-chip realization of MZMs is often done with $\rm InP$ that is a semiconductor. What is the ...
- 131
0
votes
1
answer
51
views
Non-linear optics, non-linear polarization reference system?
in the Boyd's book about non-linear optics he defines the non-linear polarization for sum frequency generation, under particular symmetries, as
$$
\left[\begin{array}{c}
P_{x}(2 \omega) \\
P_{y}(2 \...
- 454
0
votes
0
answers
62
views
Oscillator with non-linear damping - question re a specific approach
The following paper
https://core.ac.uk/reader/82037870
Oscillators with nonlinear elastic and damping forces
L.Cveticanin
studies the general problem
$$ \ddot{x} + 2 b_k \, \dot{x} \, |\dot{x}|^k + \...
- 947
4
votes
2
answers
168
views
Resistivity: related to $V/I$ or $dV/dI$?
The resistivity of tungsten is given by $\rho(T) \propto T^{1.209}$ (from Paul Gluck's Physics Project Lab] 1).
Let's assume that we can ignore the changes in the geometry of the wire due to ...
- 2,200
1
vote
0
answers
133
views
Oscillator with non-linear damping / drag equation
For linear damping
$$ \ddot{y} + 2\beta_0 \, \dot{y} + \omega_0^2 y = 0 $$
the solution with initial conditions $y(0) = y_0, \; \dot{y}(0) = 0$ reads
$$ y(t) = y_0 \, \sec\delta \, e^{-\beta_0 t} \, \...
- 947
0
votes
1
answer
142
views
How do I calculate the electrical resistance for a sodium chloride solution? [closed]
Im doing a paper on how the concentration of sodium chloride in water affects the electrical resistivity of the solution. My teacher told me that I may not be able to use $R = V/I$ for this as sodium ...
0
votes
1
answer
40
views
Combing two non-linear forces
Imagine a permanent magnet suspended in the air with an iron disc below it. Inbetween these a thick aluminium barrier. Attached to the disc at an angle is an air spring (or air shock). The magnet ...
2
votes
1
answer
158
views
Is there a rigorous proof regarding the non-linear stability of the $L_4$ and $L_5$ Lagrange points?
I have found that many proofs regarding the stability of the $L_4$ and $L_5$ Lagrange points are based on linear approximations of the equations of motion near these points. However, from a dynamical ...
- 51
2
votes
2
answers
54
views
Is there any effect of gravity in a vertical nonlinear spring? [closed]
I know that for a linear vertical spring, the governing equation of motion written in the presence of gravity is the same as the one written in the absence of gravity. We can either undergo a ...
- 23
3
votes
4
answers
649
views
Reformulate Einstein equations to make them linear
Is it possible to reformulate the Einstein equation in terms of a new variable, say $k_{\mu\nu}$ in terms of the metric $g_{\mu\nu}$, in order to make the Einstein equations linear in $k_{\mu\nu}$?
- 758
7
votes
1
answer
342
views
What evidence do we have for GR in the nonlinear regime?
The classical equations for Einstein's GR (modulo the cosmological constant) read
$$R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = \kappa T_{\mu\nu}.$$ These equations have a complicated linearization that ...
- 820
0
votes
1
answer
33
views
Interactions in nonlinear chiral theories
When discussing nonlinear realizations of $SU(3)_L \times S(3)_R$ in Chiral theories, it is usual to introduce the interactions between the baryon octet ($B$) and some meson matrix $M$ as
\begin{...
- 778
0
votes
1
answer
35
views
Is nonlinearity a denser encoding of information?
At the microscopic level, an $n$-particle system in 3D can be described by the Liouville equation, which governs the evolution of the distribution function in a $6n$-dimensional phase space.
Going ...
- 63
1
vote
0
answers
160
views
How does convex splitting method work?
I'm an undergraduate physics student and I'm simulating some partial differential equations using finite element method. For non-linear equations I found a method called linear convex splitting ...
- 11
0
votes
1
answer
53
views
Why for motion planning of quadrators the goal is to minimize the jerk/snap?
In motion planning for quadrators the optimization goal is sometimes to minimize the (norm squared of the) jerk and more often the (norm squared of the) snap. Can someone provide an intuitive and ...
- 41