Dynamics of a driven harmonic oscillator coupled to pairwise interacting Ising spins in random fields

Zech, Paul; Otto, Andreas; Radons, Günter

doi:10.1103/physreve.104.054212

Cited by 4 publications

(3 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Besides being of considerable academic interest, the results obtained may prove productive in the study of complex networks whose structure has the property of self-similarity (fractals and multifractals). Note, that the fractal properties of systems whose mathematical models include the classical Preisach converter have been studied in [214][215][216].…”

Section: Technical Systemsmentioning

confidence: 99%

The Preisach model of hysteresis: fundamentals and applications

Semenov,

Borzunov,

Meleshenko

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

The Preisach model is a well-known model of hysteresis in the modern nonlinear science. This paper provides an overview of works that are focusing on the study of dynamical systems from various areas (physics, economics, biology), where the Preisach model plays a key role in the formalization of hysteresis dependencies. Here we describe the input-output relations of the classical Preisach operator, its basic properties, methods of constructing the output using the demagnetization function formalism, a generalization of the classical Preisach operator for the case of vector input-output relations. Various generalizations of the model are described here in relation to systems containing ferromagnetic and ferroelectric materials. The main attention we pay to experimental works, where the Preisach model has been used for analytic description of the experimentally observed results. Also, we describe a wide range of the technical applications of the Preisach model in such fields as energy storage devices, systems under piezoelectric effect, models of systems with long-term memory. The properties of the Preisach operator in terms of reaction to stochastic external impacts are described and a generalization of the model for the case of the stochastic threshold numbers of its elementary components is given.

show abstract

Section: Technical Systemsmentioning

confidence: 99%

The Preisach model of hysteresis: fundamentals and applications

Semenov,

Borzunov,

Meleshenko

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Periodically driven harmonic oscillator systems are of paramount importance in the classical [1][2][3][4][5][6][7][8] and quantum sciences [9][10][11][12][13][14] and thus can find plenteous applications across the whole scientific and technological disciplines. In particular, a model of damped harmonic oscillator [15] driven by a train of delta-kick forces [2,3,12] has been provided theoretical understandings of the temporal behaviors of the physical oscillators under the influence of periodic short pulses.…”

Section: Introductionmentioning

confidence: 99%

Underdamped harmonic oscillator driven by a train of short pulses: Analytical analysis

Lee¹,

Yoon²

2022

Preprint

View full text Add to dashboard Cite

A theoretical model of an underdamped harmonic oscillator (UHO) driven by periodic short pulses may find plenty of applications in classical, semiclassical, and quantum physics.We present here two different forms of analytical solutions: time-periodic solutions and harmonic solutions for one-dimensional classical UHO driven by three different trains of short pulses. They are a Dirac comb, a train of square pulses, and a train of Gaussian pulses with the same pulse-to-pulse time interval T and pulse width 2τ . Two solutions for square and Gaussian pulses approach to that of the Dirac comb when the pulse width 2τ → 0 as expected. In particular, the harmonic solutions for Dirac comb and Gaussian pulses could be expressed approximately with harmonic terms of the repetition frequency ω R = 2π/T up to the second order. The presented analytical solutions would provide a practical way to determine experimentally the system parameters such as the underdamped oscillation frequency ω = ω 2 0 − γ 2 , the natural frequency ω 0 , and the damping rate γ, by nonlinear curve fitting procedures for different driving force parameters of T and 2τ .

show abstract

“…Replacing the latter by a spatially random potential leads in the same limit to the systems studied in this paper. While spatial randomness is a fundamental concept in solid state physics [58][59][60], it is largely unexplored for dynamical systems although it is known that it can change the dynamics drastically (for instance, see [61][62][63][64][65]). Results for the special case of expanding circle maps and general expanding dynamical systems, which is not considered here, can be found in [66,67] and [68], respectively.…”

mentioning

confidence: 99%

Suppression of Quasiperiodicity in Circle Maps with Quenched Disorder

Müller-Bender,

Kastner,

Radons

2022

Preprint

Self Cite

View full text Add to dashboard Cite

We show that introducing quenched disorder into a circle map leads to the suppression of quasiperiodic behavior in the limit of large system sizes. Specifically, for most parameters the fraction of disorder realizations showing quasiperiodicity decreases with the system size and eventually vanishes in the limit of infinite size, where almost all realizations show mode-locking. Consequently, in this limit, and in strong contrast to standard circle maps, almost the whole parameter space corresponding to invertible dynamics consists of Arnold tongues.

show abstract

Dynamics of a driven harmonic oscillator coupled to pairwise interacting Ising spins in random fields

Cited by 4 publications

References 67 publications

The Preisach model of hysteresis: fundamentals and applications

The Preisach model of hysteresis: fundamentals and applications

Underdamped harmonic oscillator driven by a train of short pulses: Analytical analysis

Suppression of Quasiperiodicity in Circle Maps with Quenched Disorder

Contact Info

Product

Resources

About