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Mean-squared displacements of rough particles in polydisperse granular gases
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2026. Vol. 113. No. 4. Article 045403.
Anna S. Bodrova
We investigate the diffusion coefficients and mean-squared displacements in a polydisperse granular gas in
a homogeneous cooling state by considering the roughness of the particles. We study their dependence on the
normal and tangential restitution coefficients. We show that the motility of particles is strongly affected by their
mechanical properties and surface characteristics.
Gordin V. A., Efremenko D., Boundary-Layer Meteorology 2026 Vol. 192 No. 51
An inverse problem of reconstructing the turbulent exchange tensor from large archives of observed wind profiles within the Åkerblom–Ekman (A-E) model framework is investigated using high-vertical-resolution radiosonde observations. The reconstructed tensor provides improved agreement between modeled and observed wind profiles compared to classical formulations based on real turbulent exchange coefficient. Instead of the classical A-E ...
Added: October 16, 2026
Kuznetsov A. P., Sedova Y. V., Stankevich N., Chaos, Solitons and Fractals 2026 Vol. 213 No. 12 Article 119309
We analyze the interaction of a quasi-periodic subsystem, in which two-, three-, and four- frequency quasi-periodic oscillations are possible, with a chaotic subsystem. A discrete version is obtained via the Euler scheme from the corresponding flow model. The dynamics of individual subsystems are discussed, including quasi-periodic bifurcations of invariant tori and the occur rence of ...
Added: October 16, 2026
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Dmitriev A., Kornilov V., Batienkov R., Lecture Notes in Civil Engineering 2026 Vol. 886 P. 249–255
Numerous studies have provided compelling evidence that the probability distribution of avalanche sizes follows a power law, and that 1/f noise is present in the stochastic dynamics of landslides. We present a theoretical explanation of these phenomena within the framework of self-organized criticality theory, proposing a discrete-time model in the form of a sandpile cellular ...
Added: October 13, 2026
Dmitriev A., Shulman I., Lebedev A., Studies in Computational Intelligence 2026 Vol. 1265 P. 266–273
A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu ...
Added: October 13, 2026
Arutyunov K., Kharitonov I. A., Petrosyants K. O., JETP Letters 2026 Vol. 124 No. 6 P. 1–16
Superconducting properties of metallic micro- and nanowires can be entirely different from those of bulk superconductors. Of particular interest is the nonequilibrium current-induced state of a quasi-one-dimensional superconducting channel. The most interesting phenomenon here is the stepped I–V characteristic, explained by a process known as phase slip center activation. If the origin of such step-like ...
Added: October 13, 2026
Makarov D. M., Kalikin N., Fashchevsky K. A. et al., Electrochimica Acta 2026 Vol. 579 Article 150159
Machine learning (ML) has become a powerful tool for accelerating the development of carbon-based supercapacitors;
however, most published models assume that a single predictive framework can describe both conventional
porous carbons and hybrid carbon electrodes. Here, we test this assumption using a comprehensive
benchmark dataset and an extended literature-curated dataset enriched with synthesis- and electrolyte-related
descriptors. Three ML algorithms ...
Added: October 13, 2026
Butko Ya. A., Bender C., Fractional Calculus and Applied Analysis 2022 Vol. 25 P. 488–519
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between the parameters of the equation and the distribution of the underlying stochastic processes, as well as discuss different classes of processes providing ...
Added: September 3, 2026
Anna S. Bodrova, Osinsky A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2025 Vol. 111 No. 3 Article 035402
We investigate both ensemble and time-averaged mean-squared displacements of particles in a polydisperse granular system in a homogeneous cooling state and derive rigorous analytical expressions valid both at short and long time scales. The discrepancies in ensemble and time-averaged mean-squared displacements indicate ergodicity breaking in granular systems consisting of an arbitrary number of species of ...
Added: March 5, 2025
Anna S. Bodrova, Chechkin A., Dubey A. K., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2025 Vol. 111 No. 1 Article 015405
We investigate the granular temperatures in force-free granular gases under exponential resetting. When a resetting event occurs, the granular temperature attains its initial value, whereas it decreases because of the inelastic collisions between the resetting events. We develop a theory and perform computer simulations for granular gas cooling in the presence of Poissonian resetting events. ...
Added: January 3, 2025
Anna S. Bodrova, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 109 No. 2 Article 024903
We investigate diffusion in polydisperse granular media. We derive the mean-squared displacement of granular particles in a polydisperse granular gas in a homogeneous cooling state, containing an arbitrary amount of species of different sizes and masses. We investigate both models of constant and time-dependent restitution coefficients and obtain a universal law for the size dependence ...
Added: February 15, 2024
Lubashevsky I., Friedrich R., Heuer A., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 79 Article 011110
Based on multivariate Langevin processes we present a realization of Lévy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity-dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Lévy flights. Our procedure is similar to ...
Added: November 6, 2021
Smirnov G., Physical Review B: Condensed Matter and Materials Physics 2020 Vol. 102 P. 184110-1–184110-8
Anomalous diffusion in some bcc metals is the long-standing topic in material science. In this work, I obtain the temperature dependence of the self-diffusion coefficient in bcc titanium directly from molecular dynamics (MD) calculation. MD simulations indicate that both vacancies and self-interstitials contribute to diffusivity in bcc Ti. The resultant self-diffusion coefficient is non-Arrhenius, but ...
Added: October 30, 2020
Bodrova A., Соколов И. М., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 102 P. 032129
We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the mean-squared displacement (MSD) in this process. We study two different resetting protocols: exponentially distributed time intervals ...
Added: September 20, 2020
Bodrova A., Sokolov I. M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2020 Vol. 101 No. 5 P. 052130
We consider a random two-phase process which we call a reset-return one. The particle starts
its motion at the origin. The rst, displacement, phase corresponds to a stochastic motion of a
particle and is nished at a resetting event. The second, return, phase corresponds to the particle's
motion towards the origin from the position it attained at the ...
Added: September 10, 2020
Palamarchuk E. S., Theory of Probability and Its Applications 2019 Vol. 64 No. 2 P. 209–228
We obtain upper functions that serve as almost sure asymptotic upper bounds for a displacement process given by an integrated time-varying Ornstein--Uhlenbeck process. The form of upper functions depends on the characteristics (the stability rate and the diffusion coefficient) of a stochastic linear differential equation. We introduce the notion of anomalous diffusion related to behavior ...
Added: September 25, 2019
Bodrova A., Chechkin A., Sokolov I., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 100 No. 1 P. 012120-1–012120-13
We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion
coefficient D(t ) ∼ t α−1 with α > 0 (scaled Brownian motion) is stochastically reset to its initial position, and
starts anew. In the present work we discuss the situation in which the memory on the value of the diffusion
coefficient at a ...
Added: August 15, 2019
Bodrova A., Чечкин А. В., Соколов И. М., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 100 P. 1–10
We investigate an intermittent stochastic process in which diffusive motion with a time-dependent diffusion
coefficient, D(t ) ∼ t α−1, α > 0 (scaled Brownian motion), is stochastically reset to its initial position and starts
anew. The resetting follows a renewal process with either an exponential or a power-law distribution of the
waiting times between successive renewals. The ...
Added: August 15, 2019
Palamarchuk E. S., Automation and Remote Control 2018 Vol. 79 No. 2 P. 289–299
We consider the problem of modeling anomalous diffusions with the Ornstein–Uhlenbeck process with time-varying coefficients. An anomalous diffusion is defined as a process whose mean-squared displacement non-linearly grows in time which is nonlinearly growing in time. We classify diffusions into types (subdiffusion, normal diffusion, or superdiffusion) depending on the parameters of the underlying process. We ...
Added: June 1, 2018
Tamm M., Polovnikov K., Cosentino Lagomarsino M. et al., Physical Review Letters 2018 Vol. 120 No. 088101 P. 088101-1–088101-6
Chromosomes are key players of cell physiology, their dynamics provides valuable information about its physical organization. In both prokaryotes and eukaryotes, the short-time motion of chromosomal loci has been described with a Rouse model in a simple or viscoelastic medium. However, little emphasis has been put on the influence of the folded organization of chromosomes ...
Added: February 24, 2018
Gherardi M., Calabrese L., Tamm M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 96 No. 042402 P. 042402-1–042402-8
The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we ...
Added: December 22, 2017
Kondratyuk N., Norman G., Stegailov V., Polymer Science - Series A 2016 Vol. 58 No. 5 P. 825–836
With the use of n -triacontane models as examples, abnormal characteristics of diffusion that manifest themselves during the application of the Einstein–Smoluchowski relationship and the asymptotic behavior of velocity autocorrelation function of the molecule-mass centers that is used to calculate the diffusion coefficient via the Green–Kubo formula are investigated. On the basis of the data of complementary approaches, the ...
Added: April 10, 2017