Canonical-dissipative limit cycle oscillators with a short-range interaction in phase space

Mongkolsakulvong,

doi:10.5488/cmp.13.13001

Cited by 13 publications

(9 citation statements)

References 23 publications

(42 reference statements)

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“…Furthermore, studies in accelerator physics, [26][27][28][29][30] plasma physics, 31 and astrophysics 32,33 can be found that make extensive use of nonlinear Fokker-Planck equations. Nonlinear Markov processes described by nonlinear Fokker-Planck equations, [34][35][36][37][38][39][40][41][42][43] generalized master equations [44][45][46][47] and Boltzmann equations [48][49][50][51] have been studied to address issues of non-extensive thermostatistics [52][53][54] and classical quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Collective Behavior of Biophysical Systems With Thermodynamic Feedback Loops: A Case Study for a Nonlinear Markov Model — The Takatsuji System

Frank

2011

Mod. Phys. Lett. B

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We study order-disorder transitions and the emergence of collective behavior using a particular mean field model: the dynamic Takatsuji system. This model satisfies linear non-equilibrium thermodynamics and can be described in terms of a nonlinear Markov process defined by a nonlinear Fokker-Planck equation, that is, an evolution equation that is nonlinear with respect to its probability density. We discuss quantitatively the impact of a feedback loop that involves a macroscopic, thermodynamic variable. We demonstrate by means of semi-analytical methods and numerical simulations that the feedback loop increases the magnitude of order, increases the gap between the free energy of the ordered and disordered states, and increases the maximal rate of entropy production that can be observed during the order-disorder transition.

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Section: Introductionmentioning

confidence: 99%

Collective Behavior of Biophysical Systems With Thermodynamic Feedback Loops: A Case Study for a Nonlinear Markov Model — The Takatsuji System

Frank

2011

Mod. Phys. Lett. B

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“…This form is motivated by the exact form for an ordinary constant-mass Brownian particle in a potential. In our case this ansatz turns out to work for the joint probability density of x and p, but in contrast to the constantmass case [28], it can then not work for the probability density of x andẋ. Inserting the ansatz into (9), we obtain:…”

Section: Analytical Solutionsmentioning

confidence: 69%

Statistics of a noise-driven elastic inverted pendulum

Halvorsen

Litak

2015

Eur. Phys. J. Appl. Phys.

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Abstract.Recently an elastic inverted pendulum structure was proposed as a means to make nonlinear energy harvesters. An effective dynamical model of this bi-stable system has an effective lumped mass that is dependent on the displacement, hence preventing direct application of previous analyses for nonlinear harvesters driven by random vibrations. We have set up a stationary Fokker-Planck equation for the inverted pendulum and solved it to obtain explicit expressions for the stationary probability densities of the system. We found that the marginal distribution of velocity is non-Gaussian, but numerically it differs little from a Gaussian when parameters for a recently published device are used. The conditional probability of position given velocity, has two peaks for low velocities. These merge into one upon increase of velocity.

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“…In order to arrive at a more precise interpretation of the stationary distributions, we may discuss the stationary distribution in appropriately-defined one-dimensional spaces related to the invariants H 1 and H 2 , rather than in the original state space [57][58][59]. That is, we define the distributions:…”

Section: Active Spinning Top Featuring Non-extensive Statistics: An Amentioning

confidence: 99%

Active and Purely Dissipative Nambu Systems in General Thermostatistical Settings Described by Nonlinear Partial Differential Equations Involving Generalized Entropy Measures

Frank

2016

Entropy

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Abstract:In physics, several attempts have been made to apply the concepts and tools of physics to the life sciences. In this context, a thermostatistic framework for active Nambu systems is proposed. The so-called free energy Fokker-Planck equation approach is used to describe stochastic aspects of active Nambu systems. Different thermostatistic settings are considered that are characterized by appropriately-defined entropy measures, such as the Boltzmann-Gibbs-Shannon entropy and the Tsallis entropy. In general, the free energy Fokker-Planck equations associated with these generalized entropy measures correspond to nonlinear partial differential equations. Irrespective of the entropy-related nonlinearities occurring in these nonlinear partial differential equations, it is shown that semi-analytical solutions for the stationary probability densities of the active Nambu systems can be obtained provided that the pumping mechanisms of the active systems assume the so-called canonical-dissipative form and depend explicitly only on Nambu invariants. Applications are presented both for purely-dissipative and for active systems illustrating that the proposed framework includes as a special case stochastic equilibrium systems.

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Canonical-dissipative limit cycle oscillators with a short-range interaction in phase space

Cited by 13 publications

References 23 publications

Collective Behavior of Biophysical Systems With Thermodynamic Feedback Loops: A Case Study for a Nonlinear Markov Model — The Takatsuji System

Collective Behavior of Biophysical Systems With Thermodynamic Feedback Loops: A Case Study for a Nonlinear Markov Model — The Takatsuji System

Statistics of a noise-driven elastic inverted pendulum

Active and Purely Dissipative Nambu Systems in General Thermostatistical Settings Described by Nonlinear Partial Differential Equations Involving Generalized Entropy Measures

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