Influence of Harmonic Perturbation on Speed of Billiard Particle as Combination of Deterministic Acceleration and White Noise

Abstract

Chaotic system under influence of harmonic force is considered. Namely, the motion of Fermi-accelerated billiard particles interacting with scatterers with harmonically oscillating boundaries is investigated. The domain of main parameters in which the acceleration of particles does not depend on the period of scatterers oscillations is found. In this domain, the effect of such oscillations can be considered as an impact of white Gaussian noise whose intensity depends only on the amplitude of velocity of scatterer oscillations and the mean free path of particles. The results of numerical simulations are in good agreement with the results of analytical considerations.

The correlation parameter of renewal processes and structures with positive and negative periodicity

“…The mean and variance are T = µ, σ 2 = α 2 1/3 − 2/π 2 . The spectral density is in perfect agreement with the theory (see figure 6(a)) The spectral density for normal distribution (19), which is not represented here, looks identical to this one in figure 6(a) for all parameters values. This similarity supports the possibility of using raised cosine distribution instead of the normal one in numerical calculation, when restriction ϑ ∈ [µ − α, µ + α] is convenient.…”

“…The renewal process describes the registration of the interacting particles by a detector [14][15][16][17], collisions of billiard particles with the boundary [18][19][20], steps and moments of resetting in the search process [21][22][23][24][25], the nucleation events in a supersaturated nanophase [26], switching between two states of diffusivity [27], signals in a neuron network [28], the entry of particles into a living cell [29,30], animal population dynamics [31][32][33][34], networks of queues [35], and even special events in music [36]. The renewal theory has experienced a wave of new theoretical development, as well as some experimental progress in connection with the model of resetting a stochastic process (see [37] and references there).…”

Unsolved Problems of Noise Preface to the UPoN-2018 Special Issue of Fluctuation and Noise Letters

“…Application of stochastic descriptions to complex deterministic systems are presented in the papers of Goldobin [6] and Dubkov et al [7]. In the former case, cumulant analysis À À À one of the basic tools in the description of noise À À À is applied to characterize phase dynamics.…”