All Questions
Tagged with non-linear-dynamics or non-linear-systems
473 questions
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1
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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 ...
- 99
0
votes
0
answers
74
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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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83
votes
13
answers
8k
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Turbulent spacetime from Einstein equation?
It is well known that the fluid equations (Euler equation, Navier-Stokes, ...), being non-linear, may have highly turbulent solutions. Of course, these solutions are non-analytical. The laminar flow ...
- 10.1k
0
votes
1
answer
30
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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 ...
- 213k
0
votes
1
answer
51
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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
$$
\left[\begin{array}{c}
P_{x}(2 \omega) \\
P_{y}(2 \...
- 213k
10
votes
3
answers
1k
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Warp drive with gravitational waves in the nonlinear regime
gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, ...
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5
answers
1k
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Why is Newton's second law with potentials not a linear equations?
I was trying to learn Quantum physics by myself using MIT's 8.04 course. I came accross this equation:
I don't understand why the above is true. I understand the definition of linearity. But I don't ...
- 2,102
16
votes
1
answer
862
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Radiative corrections to Coulomb’s law and Euler-Heisenberg theory
Maxwell's electrodynamics is the classical limit of QED (quantum electrodynamics). Using Maxwell's equations, the electrostatic (Coulomb) potential of a point charge is obtained as $\Phi \propto \frac{...
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4
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2
answers
168
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Resistivity: related to $V/I$ or $dV/dI$?
The resistivity of tungsten is given by $\rho(T) \propto T^{1.209}$ (from Paul Gluck's Physics Project Lab] 1).
Let's assume that we can ignore the changes in the geometry of the wire due to ...
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0
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0
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62
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Oscillator with non-linear damping - question re a specific approach
The following paper
https://core.ac.uk/reader/82037870
Oscillators with nonlinear elastic and damping forces
L.Cveticanin
studies the general problem
$$ \ddot{x} + 2 b_k \, \dot{x} \, |\dot{x}|^k + \...
- 947
1
vote
0
answers
133
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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} \, \...
- 947
5
votes
3
answers
297
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Generating nonlinearities in renormalization group
In renormalization group (RG) calculations as performed in statistical physics (for example for Landau-Ginzburg theory - often a la Wilson), the first step is to coarse-grain the theory by integrating ...
4
votes
1
answer
243
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Spring non-linear behavior for small forces
While writing a report about a classical spring experiment I noticed that, if small forces were applied to our spring, this would stretch much less than expected.
Searching on the internet I've kinda ...
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0
votes
1
answer
142
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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 ...
- 13.2k
0
votes
1
answer
40
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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 ...
- 3,062
2
votes
1
answer
159
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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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1
vote
2
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1k
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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 ...
2
votes
2
answers
54
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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 ...
- 213k
30
votes
4
answers
7k
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What nonlinear deformations will a fast rotating planet exhibit?
It is common knowledge among the educated that the Earth is not exactly spherical, and some of this comes from tidal forces and inhomogeneities but some of it comes from the rotation of the planet ...
- 213k
7
votes
1
answer
342
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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}.$$ These equations have a complicated linearization that ...
- 3,912
0
votes
1
answer
33
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Interactions in nonlinear chiral theories
When discussing nonlinear realizations of $SU(3)_L \times S(3)_R$ in Chiral theories, it is usual to introduce the interactions between the baryon octet ($B$) and some meson matrix $M$ as
\begin{...
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0
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1
answer
35
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Is nonlinearity a denser encoding of information?
At the microscopic level, an $n$-particle system in 3D can be described by the Liouville equation, which governs the evolution of the distribution function in a $6n$-dimensional phase space.
Going ...
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1
vote
0
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160
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How does convex splitting method work?
I'm an undergraduate physics student and I'm simulating some partial differential equations using finite element method. For non-linear equations I found a method called linear convex splitting ...
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0
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1
answer
53
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Why for motion planning of quadrators the goal is to minimize the jerk/snap?
In motion planning for quadrators the optimization goal is sometimes to minimize the (norm squared of the) jerk and more often the (norm squared of the) snap. Can someone provide an intuitive and ...
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1
vote
0
answers
66
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Most general nonlinear Lorentz transformation law can be built from linear transformations?
Peskin and Schroeder give a Lorentz transformation law:
$$\Phi_a(x)\rightarrow M_{ab}(\Lambda)\Phi_b(\Lambda^{-1}x).\tag{3.8}$$
Then they say that
"the most general nonlinear [Lorentz] ...
- 213k
2
votes
1
answer
266
views
Finding dispersion relations
I was wondering if there is a general (theoretical, not experimental) method for finding the dispersion relation for waves in a medium, say given the equation governing purturbations in the medium? ...
CommunityBot
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0
votes
0
answers
42
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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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6
votes
3
answers
905
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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 ...
- 13.9k
1
vote
1
answer
113
views
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, ...
- 213k
2
votes
1
answer
91
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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 ...
- 213k
1
vote
1
answer
128
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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 ...
- 6,379
1
vote
1
answer
370
views
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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0
answers
101
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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 ...
- 213k
5
votes
0
answers
89
views
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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0
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1
answer
51
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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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2
votes
0
answers
94
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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 ...
- 213k
0
votes
1
answer
54
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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
$$...
- 213k
13
votes
2
answers
2k
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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 ...
- 65k
0
votes
1
answer
668
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 ...
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1
vote
1
answer
34
views
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 ...
- 2,040
1
vote
1
answer
40
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Possible Explanation for Behaviour Non-Linear Bead Knot Experiment
I have a very simple setup to study non-linear phenomena with plastic beads, as described here:
E. Ben-Naim, Z.A. Daya, P. Vorobieff, and R.E. Ecke, “Knots and Random Walks in Vibrated Granular ...
- 13.2k
1
vote
0
answers
47
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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(...
- 213k
1
vote
0
answers
118
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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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votes
0
answers
50
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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&...
- 213k
5
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4
answers
2k
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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?
CommunityBot
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3
votes
1
answer
185
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Turbulence, Euler equations and equipartition of energy
Recently the user CBBAM asked about the inviscid limit in turbulence and the relation between Navier-Stokes equations and Euler equations when $\nu \to 0$. There I pointed out that Onsager proposed ...
- 3,178
2
votes
3
answers
615
views
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 $\theta$ ...
rob♦
- 94.2k
3
votes
1
answer
110
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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 ...
- 213k
2
votes
0
answers
133
views
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 ...
- 213k
0
votes
1
answer
91
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Vector operations from nonlinear continnum mechanics with large deformation for curl of a vector $p_i$=$\epsilon_{ijk} s_{k,l}u_{l,j}$
I just found there is an expression from the curl operation of a vector component $p_i=\epsilon_{ijk}s_{k,l}u_{l,j}$, where $\mathbf {u}$ is deformation and $\mathbf {s}$ is another variable dependent ...
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