# 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.

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### 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 ...
661 views

### Why didn't Einstein propose any metric solution to his equations? [migrated]

I've read about general relativity (GR) recently and something stroke me: Einstein came up with his equations in 1915, linking the metric of spacetime to the distribution of energy (more exactly, to ...
412 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 $k_{\mu\nu}$?
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### 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 ...
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### 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{...
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### 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 ...
1 vote
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### 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 ...
37 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 ...
1 vote
49 views

### Most general nonlinear Lorentz transformation law can be built from linear transformations?

Peskin and Schroeder give a Lorentz transformation law: $$\Phi_a(x)\rightarrow M_{ab}(\Lambda)\Phi_b(\Lambda^{-1}x).\tag{3.8}$$ Then they say that "the most general nonlinear [Lorentz] ...
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### Concerete examples of physical systems that can be (approximately) modelled using a 2D triharmonic equation?

I have some experimental measurements of input-driven standing-wave resonances in a nonlinear, 2D medium. I think it's fair to assume that the dynamics are homogeneous and isotropic, and we can think ...
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### Non-linear spring systems

I've recently been re-learning some physics, and a question came to me when looking over Hooke's law: In the following I am always assuming that the force required for permanent deformation is ...
1 vote
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### What does it mean for a material's elasticity to be non-linear?

Hooke's law only applies to materials with linear elasticity, usually for small displacements. Now, if you imagine having a material that does not deform permanently when crossing a specific limit, ...
66 views

### How causality and unitarity are ensured given a non-linear electromagnetic Lagrangian?

I am reading these notes on non-linear electrodynamics (NED). On page 8, below equation (5.1) the author states that the modified electromagnetism parameter $\gamma$ should be non-negative in order to ...
1 vote
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### Calculating the Lyapunov exponents spectrum from particle trajectories

I am simulating a forced, compressible 2D flow, that is turbulent and statistically steady, but not stationary. I want to calculate the Lyapunov exponents spectrum from the trajectories of Lagrangian ...
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### Efficient algorithm to calculate nonlinear conductivity spectra

I'm just thinking about the efficient algorithm to calculate the photovoltaic conductivity $$J(0) = \sigma^{(2)}(0, \omega, -\omega)E(\omega)E(-\omega)$$ in time domain calculation. In the case of ...
1 vote
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### What's the best open source alternatives of COMSOL? [closed]

Good time of day. I need to solve system of differential non-linear equations for 3D system. It requires parallel computing on a cluster. Our lab lacks the license on Comsol. It is necessary to ...
56 views

### Solubility of integrable systems and the classical XXZ model

I've been learning about integrability in the Hamiltonian sense, and trying to wrap my mind around the analytic power afforded by integrability, both in quantum and classical systems. My goal with ...
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### Is it physically relevant to restrict the solution of a nonlinear PDE to positive frequencies in the Fourier transfrom?

I would like to mention that I am a mathematician and not a physicist, so I apologize in advance if my question seems obvious. Considering any linear PDE, it is common to understand the behavior of ...
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### Problem identifying type of equation (linear/nonlinear)

I've looked at the answer to this Math.SE question, but I still can't know the answer to my question here. The following is the equation of equilibrium: divergence of stress tensor that is the sum of ...
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### Does Poisson Distribution means the system is chaotic?

The Berry-Tabor Conjecture says that for classically integrable systems, the corresponding quantum systems obey the Poisson distribution for their energy-level spacing. But generally, the integrable ...
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1 vote
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### Literature reference: example of stable and unstable manifolds in Henon-Heiles system

There is a quite classical description of chaotic systems based on the behaviour of stable and unstable manifolds around a stationary point of the Poincaré section. It is presented, for example, [here,...
66 views

### Prey-predator dynamical system

I'm working with a prey-predator differential equation system and I have a problem with the competitive exclusion principle. In its simplest form, this principle states that if there are 2 predators ...
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### Given a system, how to decide whether a closed orbit is homoclinic, not periodic, solely based on its phase portrait?

Background and definitions: A system is conservative if it has at least one conserved quantity. In a phase portrait of a nonlinear conservative system, trajectories that start and end at the same ...
19 views

### Dynamic equations for a gas discharge lamp

This question asks why a gas discharge lamp is blinking and making a noise when it is turned on. I think that the lamp (with potential on) is a bi-stable system where the current-carrying "bright&...
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1 vote
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### Fast solution for a nonlinear system of 3 equations of degree 3? [closed]

I have a nonlinear system of 3 equations with 27 constants and 3 unknowns x, y, z ...
1 vote