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4
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2answers
200 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 ...
1
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1answer
19 views

To describe crystallity structures of this ferromagnetic material

MOKE microscope picture of the ferromagnetic Material $Co_{40} Fe_{40} B_{20}$ of 20 nm thin film All other pictures look the same, also from different angles: [0,360] by 15 degree separation. I ...
1
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1answer
23 views

Tangent and Normal accelerations position estimation

How can I derive a particle position given it's last known positions (x,y), velocities in it's components (vx, vy), tangential and centripetal (normal) accelerations? (this is the only available data) ...
1
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1answer
32 views

Numerical construction of phase space for a dynamical system

Suppose I have a standard, deterministic dynamical system. For concreteness I'll assume it's a two variable system of the form, $$ \dot x_1 = f(x_1,x_2; \theta_1)\\ \dot x_2 = g(x_1,x_2; \theta_2) $$ ...
1
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1answer
183 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 ...
0
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1answer
55 views

How to simulate pendulum movement with high amplitude

I need to make a C# simulator for a simple pendulum. I have been searching the web for 3 days and I am stuck. The problem is I have found many equations that would give the angle position as a ...
0
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1answer
35 views

Definition of “nonlinear” in the context of perturbation of gravity

What exactly is the definition of a nonlinear perturbation when applied to a background spacetime metric? I have seen so called "linear perturbations" which look like $$ds^2 = -(1+2\Phi)dt^2 ...
0
votes
1answer
47 views

Time it takes for a mass in a linked pendulum to flip?

I have created Mathematica code that simulates a double pendulum. So I've numerically solved for $\theta_{1}(t)$ and $\theta_{2}(t)$. I have also found the momentum from the Lagrangian as well. My ...
0
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1answer
43 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?
4
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0answers
87 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
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0answers
43 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
0answers
66 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
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0answers
52 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
0answers
29 views

Categorization of electromagnetic solitons?

I've seen over the years several mentions of electromagnetic solitons that appear in the high-intensity regime (where vacuum polarization becomes important). Some of these are coupled with plasmas, ...
2
votes
0answers
52 views

Why can any pair of master coordinates be used to calculate a nonlinear mode of a nonlinear dynamical system?

This is a question I have been asking myself for some time since the following technique is often used in the nonlinear dynamics community, but never managed to get an answer why it could be applied. ...
2
votes
0answers
165 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 ...
2
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0answers
99 views

value of $\omega$ in nonlinear equation

In this article the authors wrote 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, ...
2
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0answers
418 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 ...
2
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0answers
93 views

Macroscopic chromodynamics

Lately I've been reading about gamma ray lasing phenomena, and I've been wondering about the applications of this. More concretely, the above fantastic question led me to wonder if we could somehow ...
1
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0answers
29 views

Origin of chaos in Chua's circuit

I am doing a project on Chua's circuit, but I can't seem to find anything that explains where the chaotic nature of the system comes from. Does anyone know of articles that explain it well on an ...
1
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0answers
13 views

Change of variables to apply Melnikov method

Supposing there is a system of non-autonomous non-linear differential equations with small damping and small forcing. The unperturbed system (zero damping and forcing) is Hamiltonian but neither has a ...
1
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0answers
65 views

Hysteresis in the Lorenz Equations

I was going through Strogatz's wonderful book on nonlinear dynamics and while reading through one problem he posed at the end of the chapter, I did not really understand what was going on. So I hope ...
1
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0answers
27 views

Data Collection of oscillatory motion

I'd like to study nonlinear oscillatory motion this semester. I plan to build several different mechanical systems (pendula, masses on springs, etc with and without driving forces, large/ small drag, ...
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0answers
101 views

What are the equations of motion that model near light speed orbits of a massive body about incredibly massive bodies?

In Kip Thorne's recently published book, The Science of Interstellar, he describes, by means of an illustration, the complex nature of a spacecraft orbiting a massive black hole with velocities ~ ...
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0answers
37 views

Restoring force surface method for nonlinear system identification

I am working on nonlinear system parameters identification using the restoring force surface method (or the force-state mapping method). I found some references in which the method is explained but I ...
1
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0answers
57 views

Showing the Hamiltonian of the $\alpha$ FPU is real

I am studying the $\alpha$ FPU chain which is a model of coupled oscillators with small non-linearity. For these systems, I derived the following Hamiltonian $H$ which is given by $$ H=\sum_{j=1}^{N} ...
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0answers
69 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
262 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? ...
1
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0answers
141 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 ...
1
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0answers
82 views

Toolbox for Complex Networks and Graphs

Is there a toolbox which helps in visual simulation and modeling of a network (say a mesh or ring) consisting of coupled synchronized system of nonlinear equations(ODE) which represent a system of ...
0
votes
0answers
27 views

Generalized long wave and KdV equation

I have read many papers about benjamin-bona-mahony (BBM) equation or Regularized Long Wave (RLW) equation and found that BBM equation can be derived from KdV equation. from other papers i got others ...
0
votes
0answers
26 views

Non-linearity of energy conversion efficiency

I have a very general question to all of you. I am wondering if there is any basic physics principle that would state that energy conversion efficiency will be always non-linear (for the practical ...
0
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0answers
33 views

Nonlinear constitutive state equation

Between the Tait equation, and the B/A type of equation, which one is better suited to approximate the isentropic equation of state? Why B/A type is mostly used in nonlinear acoustics?
0
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0answers
16 views

When longitudinal waves and transversal waves enter air from a soild, what will happen? How do waves transform?

When ultrasonic waves meet the interface (surface) between two media they will reflect and refract. What is the effect of the acoustic impedance on reflection? Is there any list about acoustical ...