Questions tagged [non-linear-systems]

The term non-linear or nonlinear has several definitions but is generally used to describe a system that cannot be approximated by a superposition principle or perturbative approach.

Filter by
Sorted by
Tagged with
1
vote
1answer
186 views

Nonlinear dynamics and chaos theory in electrical systems and circuits [closed]

Is there a possible application of the field of chaos theory and nonlinear dynamics to electrical systems such as circuits and power? If so, are they based on conventional nonlinear dynamics or are ...
0
votes
1answer
61 views

Book on Non-Linear dynamics [duplicate]

I am currently planning on self studying Non-linear dynamics, with an intention of developing a decent idea about it and see how its applied. I don't want to be too rigorous in my dealing with the ...
1
vote
1answer
85 views

Question about Strange Attractors

I'm reading the book Chaos by James Gleick and came upon a certain excerpt in the chapter 'Strange Attractors'. I'm having a hard time understanding it (the merging of two surfaces part, in particular)...
0
votes
1answer
79 views

Understanding Boyle's Law and Charles's Law

Boyle's Law is defined as follows: $PV=k$ This implies that $P_{1}V_{1}=P_{2}V_{2}$ is true while temperature and mass of confined gas is constant. This would mean that $P_{2}=P_{1}V_{1}/V_{2}$ ...
3
votes
1answer
159 views

Free energy in Allen-Cahn PDE

I am a mathematician and I am taking a mathematical physics course. In the part of reaction-diffusion equations, there is something that I do not understand. I have been defined the Allen-Cahn ...
2
votes
1answer
108 views

Why some dynamic systems can undergo sudden changes?

Everybody has observed that the weather may change from beautiful sunshine to extremely bad weather (heavy rain, stormy winds, ...) within less than half hour. What is the fundamental reason for this? ...
-1
votes
1answer
320 views

Is an 'angle of slope' really the same on Earth and Moon? [closed]

I know (and it's easy to proof the formula), that the maximum angle at which an object will stay static on a slope being at an $\alpha$ angle to the ground is $$\tan \alpha = \mu$$ where $\mu$ is the ...
1
vote
0answers
48 views

Nonlinearities arising from linear equations

I have sources that tell me that the Bloch Equations, which describe the magnetization vector in nuclear magnetic resonance, are nonlinear. In vector form, without relaxation, they are: $$ \partial_t \...
3
votes
1answer
294 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. ...
0
votes
1answer
26 views

When can raw data can be used to look for phase synchronization between time series?

I'm studying a system formed by multiple rotors non-linearly coupled to each other. If I want to look for phase synchronization, I could just look at the angle for predefined points around the ...
1
vote
3answers
343 views

Non-linear dynamics problem: A mechanical analog of dx/dt=sinx [closed]

I have been stuck at this particular problem for a while.This is a problem from Nonlinear Dynamics And Chaos by Strogatz. The thing I am having hard time finding a mechanical system following dx/dt=...
2
votes
1answer
322 views

Are bifurcations in dynamical systems related to phase transitions? [closed]

Bifurcation is a qualitative measure for a dynamical system changing the system parameter. Does the statistical behavior in the system shows phase transition-like characteristics?
0
votes
1answer
86 views

Are there some necessary and sufficient conditions that a system can be modeled using Monte Carlo Methods?

Is there a certain set of conditions a system need to follow such that it can be effectively modeled using any "general" Monte Carlo method, maybe to find some average value of a thermodynamic ...
1
vote
1answer
99 views

How do nonlinear phenomena arise from linear theories

How is it possible that linear theories, for example maxwells equations or the schroedinger equation, produce nonlinear physics?
1
vote
2answers
169 views

Part1 — Beginner level confusion regarding terminologies — symbolic dynamics, trajectory, phase space

I came across the topic of symbolic dynamics when studying about time series analysis. Since I have not formally taken any course on chaotic dynamics, I have some difficulties in understanding some ...
0
votes
1answer
42 views

Books for memory mechanism of nonlinear systems?

The description of complex-systems aka dynamical-systems says: In such systems, nonlinear interactions can lead to memory and feedback mechanisms, self-organized criticality, and chaotic behavior. ...
7
votes
2answers
595 views

Is closed phase trajectory a necessary feature of any one-dimensional periodic motion?

The phase trajectory of a one-dimensional simple harmonic oscillator is a closed one (In particular, it's an ellipse). Is closed phase trajectory a generic feature of any periodic motion at least in ...
0
votes
1answer
49 views

Can damped motion in a time-varying potential escape to infinity?

Let $x_t \in \mathbb{R}^n$ satisfy the differential equation $$m \ddot{x} + c \dot{x} = -\nabla_x f_t(x),$$ where each $f_t$ is a nonnegative function that blows up as $||x|| \rightarrow \infty$. Here ...
0
votes
2answers
325 views

Why is it difficult to understand the phenomena of chaos in Newtonian mechanics?

This is a very simple-minded question. Why is it difficult to understand the phenomena of chaos in Newtonian mechanics and one has to turn to Hamiltonian formulation? I haven't read much about chaos ...
1
vote
0answers
172 views

Nonlinear acoustic processes in air - how to quantitatively estimate power in four-wave mixing?

I'd like to understand if non-linear mixing of human speech with a high-power ultrasonic "carrier" in air could produce sidebands with more power than the original speech. 30 kHz to 300 kHz has a ...
3
votes
0answers
66 views

Books for studying non-linear dynamics [closed]

I've recently developed interest into non-linear dynamics and chaos theory after having read a large part of the book by Steven Strogatz. Is it possible for me to delve into a research area dealing ...
0
votes
0answers
52 views

Computing index of a closed curve (non linear dynamics)

My question is specific to the method for computing the index of a closed curve C with respect to a vector field in phase space as described in the book by Steven Strogatz (page 176). Briefly, the ...
4
votes
1answer
182 views

Stochastic process vs high dimensional chaos in models

I'm trying to figure out what are the theoretical and practical, implications and limitations, when a high-dimensional chaotic process is modeled as a random process. I understand how low-dimensional ...
0
votes
1answer
148 views

Why is an ellipse not a self-intersecting curve?

For a Hamiltonian which is time-independent, the phase trajectories don't intersect. But the Hamiltonian of a one-dimensional harmonic oscillator with constant energy, for example, has an elliptical ...
1
vote
1answer
167 views

Can we let the lowest of n by equal (lenght and k) springs connected masses in equilibrium move in a siusoid way after giving the lowest a pull?

Imagine we hang n masses, connected by equal springs of equal length and with equal k (suspended on a very high ceiling or whatever what, as long as it doesn't exchange energy with the system). So ...
4
votes
1answer
519 views

Nonlinear waves equations derivation from Navier-Stokes

In my professor's lecture notes, I came across the next approach of studying non-linear waves in fluids. So we have compressible Navier-Stokes and continuity equation in 1D and we assume adiabatic ...
5
votes
1answer
194 views

Hamiltonian system with velocity singularity

I am studying a classical mechanical system for which Hamilton's equations are the following: $$ \psi' = \frac{p}{\sqrt{1-p^2}},~~~~~p' = -\phi \sin \psi, $$ where $\phi$ is a parameter. If $\phi>...
0
votes
1answer
80 views

Is linearity of quantum theory important for existence of quantum gravity?

Kiefer (2014) claims that, "It is, in fact, the superposition principle that points towards the need for quantizing gravity." Moreover, Kiefer (2009) stresses that, "The only assumptions are ...
0
votes
1answer
91 views

Finding the stability from the eigenvalues of two second-order DEs

I'm analysing the stability of a double physical pendulum, and have determined the dimensionless system of equations to be \begin{align} \label{eq:dimensionless} \begin{aligned} & \ddot{\...
2
votes
0answers
142 views

Differential equation with nonlinear nonlocal interaction

I am studying literature on the nonlinear Schroedinger equation. More generally, I am wondering how to tackle an equation of motion such as $\bigl(i\partial_t-\Delta\bigr)\psi(\vec{x},t)+V(\vec{x},t)=...
3
votes
1answer
215 views

Nonlinear PT-symmetric model and integrability

I am coming from a maths background and these concepts are a bit new to me. I am studying an exercise paper and I am encountering the following problem. With $u_i(t)=u_i$ and of course $u_i u_i^*=|u|^...
2
votes
0answers
247 views

Propagation of error through the solution for system of non-linear equations [closed]

I am currently working with a physical system governed by $n$ number of parameters. Thus the functional form of the behaviour of this system over a length-scale $z$ can be represented by a non-linear ...
2
votes
0answers
324 views

Trial function in variational principle - why do we choose this ansatz?

I am reading this paper right now and I cannot understand the intuition behind their choice of ansatz in the variational principle. Specifically this passage on the second page of the paper puzzles ...
3
votes
3answers
748 views

What is a nonlinear manifold?

The Wikipedia article defines a non-linear sigma model as model for a scalar field $\Sigma$ which takes on values in a nonlinear manifold called the target manifold $T$. What is the definition of a ...
0
votes
2answers
421 views

How to explain the Schwinger Limit?

I have read that the Schwinger limit is the limit after which the electromagnetic field is expected to become nonlinear. Is there more to what this limit is? What does this practically means? What ...
0
votes
1answer
50 views

How to determine the linearity of a numerically simulated mass-spring system?

I did some numerical simulation of a mass-spring system, which is a 2D 1-degree-of-freedom spring-mounted cylinder vibrating due to moving fluid surrounding it. The cylinder's motion may be described ...
5
votes
1answer
100 views

What are some experimental verification of the non-linearity of gravitation?

According to my (limited) knowledge, all experiments to date probe only situations which can be understood using the linearized version of general relativity. For example, measuring gravitational ...
0
votes
0answers
237 views

Physical example for a non-linear mass-spring system?

Let's say there is a mass-spring system: ${\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+2\zeta \omega _{0}{\frac {\mathrm {d} x}{\mathrm {d} t}}+\omega _{0}^{\,2}x=F$ I would like to ask for a real-...
1
vote
1answer
178 views

Is it a linear mass-spring system?

Please look at this equation representing a mass-spring system: ${\frac {\mathrm {d} ^{2}x}{\mathrm {d} t^{2}}}+2\zeta \omega _{0}{\frac {\mathrm {d} x}{\mathrm {d} t}}+\omega _{0}^{\,2}x=F$ where ...
1
vote
2answers
80 views

Why is stress linearly dependent on strain in elastic materials?

The displacement vector $\mathbf{u}(\mathbf{x}, t) = \mathbf{r}(\mathbf{x}) - \mathbf{x}$ is used to keep track of the motion of the material points in a material. Firstly, we take the gradient of the ...
1
vote
2answers
415 views

a Non-linear Mass-spring system with different force and vibration frequency?

I got a classic mass-spring system with zero damp ratio, having weird behaviour. The input frequency of external force is twice that of the output displacement results. While linear systems' input &...
1
vote
0answers
103 views

Why do the Manley-Rowe relations use this Hamiltonian and how can I derive it?

The derivation of the Manley-Rowe relations begin with the following Hamiltonian for 3 classical, coupled harmonic oscillators: $H=(p_1^2+p_2^2+p_3^2)/2m+1/2(k_1q_1^2+k_2q_2^2+k_3q_3^2)+\lambda ...
1
vote
3answers
190 views

Are all the quantum based equations linear?

I dont know much about the subject, but the wave equations (classical and modern) as well as classical equations of motion all seem to be inherently linear differential equations. Presumably this also ...
0
votes
1answer
222 views

Third eigenvalue of Lorentz equations

I was reading and working on the Strogatz's book on nonlinear dynamics and chaos on my own. I was trying to solve problem 9.2.1. The thing is that, I do not understand how can I solve part c) of that ...
8
votes
0answers
184 views

Nonlinear stability question

I am looking for a simple example where a system is linearly unstable, but nonlinearly unstable or stable, depending on the sign of the initial perturbation. For instance, assume the linear normal ...
20
votes
3answers
3k views

Is the universe non-linear?

First of all, I've read this other question Is the universe linear? If so, why? and I'm aiming at a different kind of answer. Theories like General Relativity or QFT, which are believed to be quite ...
20
votes
3answers
3k views

Highly nonlinear equations

I understand the concept of non-linear equations. I was recently having a conversation with a colleague and he used the term "highly non-linear" equation. This got me thinking, how do we classify ...
3
votes
1answer
175 views

Can a molecular dynamics simulation enter attractors like stable limit cycle?

In my rough understanding Molecular Dynamics using Classical Newtonian mechanics is a 6N dimensional non linear system. 6N dimension because we have 3 position vectors and 3 momentum vectors for each ...
7
votes
1answer
464 views

Is LIGO able to detect the memory effect of gravitational waves?

Recently some articles in popular media1, 2 informed that LIGO will be able to measure the memory effect of gravitational waves described by Demetrios Christodoulou in 1991.3 The measurement method ...
2
votes
3answers
750 views

Example of non-linear time evolution in quantum mechanics

Preamble: I am a mathematician and not a physicist. From what little I know about quantum mechanics, Schrödinger's equation is a linear PDE that describes the time-evolution of a system. In general ...