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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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 ...
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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 ...
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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 ...
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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 ...
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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
$\ddot{x}+2\lambda\dot{x}+\omega_0^2x = \frac{f}{m}\cos(\gamma t)-\alpha x^2-\beta x^3$ ...
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Finding critical value of bifurcation [migrated]
I have equations such as
$\frac{dx}{dt} = y \\
\frac{dy}{dt} = \mu y + x - x^{2} + xy$
This system is known to be homoclinic bifurcation at the origin. To find the critical value of $\mu_{c}$, one ...
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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 ...
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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 ...
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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 ...
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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,
$$\partial_t{d} + \frac{1}{r} \...
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Applications of Schrodinger's to dark solitons [closed]
The Schrodinger equation (SE) admits dark solitons as particular solutions. The SE and the The Korteweg-de Vries (KdV) equations can be used to model them.
Questions:
What are the applications of ...
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How to find the stability of time dependent Lyapunov equation?
After linearization of the nonlinear equations, I want to find the covariance matrix $v$ through the numerical solution of time dependent Lyapunov equation, $$dv/dt=a*v + v*a'+ d,$$ where $a$ is my ...
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$\rm InP$ Mach-Zender modulator
I know how a Mach-Zender electro-optical modulator (MZM) works when based on non-linear crystals like LN. On-chip realization of MZMs is often done with $\rm InP$ that is a semiconductor. What is the ...
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Non-linear optics, non-linear polarization reference system?
in the Boyd's book about non-linear optics he defines the non-linear polarization for sum frequency generation, under particular symmetries, as
$$
\left[\begin{array}{c}
P_{x}(2 \omega) \\
P_{y}(2 \...
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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
$$ \ddot{x} + 2 b_k \, \dot{x} \, |\dot{x}|^k + \...
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Resistivity: related to $V/I$ or $dV/dI$?
The resistivity of tungsten is given by $\rho(T) \propto T^{1.209}$ (from Paul Gluck's Physics Project Lab] 1).
Let's assume that we can ignore the changes in the geometry of the wire due to ...
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Oscillator with non-linear damping / drag equation
For linear damping
$$ \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} \, \...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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 ...
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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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References for harmonic oscillator with memory
I'm reading Neu's "Singular Perturbation in the Physical Sciences" and in problems 1.1 and 1.2 he defines systems that "have memory" as the the variant of the harmonic oscillator
$$...
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On the (non)linearity of electromagnetism
As a student you are typically told that Maxwell's equations (ME) in vacuum are linear. However, it seems that for extremely high electromagnetic fields the equations for electromagnetism turn out to ...
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Deriving Non-linear acoustic wave models, equilibrium state assumption
The standard derivation in obtaining a single wave equation involves making use of the heat equation with a Taylor expansion of the equation of state, then differentiating this equation and the ...
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Wave propagation speed in non-linear differential equations
Could it happen than a solitary travelling wave (soliton) had a different propagation speed when seen from the usual wave equations from that in a non-linear equation. I mean, suppose a solution $F=f(...
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Reference request for QFT $SO(3)$ non-linear sigma model
I was wondering if anyone has a reference that could help me understand quantum field theories that have a nonlinear configuration space. For example, from classical mechanics if we have a three-...
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Non-linear symmetry and symmetry at quantum level
Can anyone explain me what does the statement mean:
"the BRST symmetry is a non-linear symmetry, so the BRST is also a symmetry at the quantum level"?
What does "at the quantum level&...
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Could nonlinear quantum mechanics be found by future quantum computers?
How could working quantum computers test if nonlinear quantum mechanics or another nonlinear theory is at work at deeper levels or fundamental level?
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How to justify this small angle approximation $\dot{\theta}^2=0$?
Suppose the equation of motion for some oscillating system takes the following form:
$$\ddot{\theta}+\dot{\theta}^2\sin\theta+k^2\theta\cos\theta=0$$
Applying small angle approximation to $\theta$ ...
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Lagrangian for a non-linear wave equation
I have the following wave equation that I am trying to understand better:
$$\frac{\partial^2 \varphi}{\partial t^2}-\frac{\partial^2 \sin{\varphi}}{\partial x^2}=0.$$
This equation describes an LC ...
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A brick sliding in an horizontal plane after an initial push (under Coulomb's dry friction) - closed form solutions validation? [closed]
A brick sliding in an horizontal plane after an initial push (under Coulomb's dry friction) - closed form solutions validation?
Introduction_____________________
I am looking for simple mechanics ...
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Find the tensions in the supporting ropes of an inclined heavy beam supported by two diferent kinds of ropes [closed]
Recently I was making some late-revisit (for self reference) to undergraduate physics topics from the book Ohanian's Physics, 2E expanded-1989, which I loved to use during my freshman undergraduate ...
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