We investigate the granular temperatures in force-free gases under exponential resetting. When a resetting event occurs, temperature attains its initial value, whereas it decreases because of inelastic collisions between events. develop theory and perform computer simulations for gas cooling presence Poissonian also probability density function to quantify distribution temperatures. Our may help us understand behavior nonperiodically driven systems.

Saturn's rings consist of a huge number water ice particles, with tiny addition rocky material. They form flat disk, as the result an interplay angular momentum conservation and steady loss energy in dissipative inter-particle collisions. For particles size range from few centimeters to meters, power-law distribution radii, $\sim r^{-q}$ $q \approx 3$, has been inferred; for larger sizes, steep cutoff. It suggested that this may arise balance between aggregation fragmentation ring yet...

We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t)\ensuremath{\sim}{t}^{\ensuremath{\alpha}\ensuremath{-}1}$ $\ensuremath{\alpha}>0$ (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. In present work we discuss situation memory on value of at a resetting time erased, so that whole fully renewal one. The when coordinate does not affect coefficient's dependence considered other...

We consider a random two-phase process which we call reset-return one. The particle starts its motion at the origin. first, displacement, phase corresponds to stochastic of and is finished resetting event. second, return, particle's toward origin from position it attained end displacement phase. This takes place according given equation motion. whole renewal provide general expressions for stationary probability density function mean hitting time in one dimension. perform explicit analysis...

Abstract It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of dynamics classical Brownian particle in long time limit. We establish and investigate paradigm anomalous diffusion process governed by an underdamped with explicit dependence system temperature thus damping coefficients. show for this scaled motion (UDSBM) limit fails to describe behaviour may practically even not exist at all certain range parameter values. Thus persistent...

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 renewal either exponential or power-law distribution of the waiting times between successive renewals. events, however, do not affect time dependence so that whole appears be nonrenewal one. discuss mean squared displacement particle...

Recent Molecular Dynamics simulations of glass-forming liquids revealed superdiffusive fluctuations associated with the position a tracer particle (TP) driven by an external force. Such anomalous response, whose mechanism remains elusive, has been observed up to now only in systems close their glass transition, suggesting that this could be one its hallmarks. Here, we show presence superdiffusion is actual fact much more general, provided system crowded and geometrically confined. We present...

We define and study in detail utraslow scaled Brownian motion (USBM) characterized by a time dependent diffusion coefficient of the form . For unconfined mean squared displacement (MSD) USBM exhibits an ultraslow, logarithmic growth as function time, contrast to conventional motion. In harmonic potential MSD does not saturate but asymptotically decays inverse-proportionally reflecting highly non-stationary character process. show that process is weakly non-ergodic sense averaged converge...

We study analytically and by event-driven molecular dynamics simulations the nonergodic aging properties of force-free cooling granular gases with both constant velocity-dependent (viscoelastic) restitution coefficient $\varepsilon$ for particle pair collisions. compare gas an effective single stochastic model based on underdamped Langevin equation time dependent diffusivity. find that models share same behavior ensemble mean squared displacement (MSD) velocity correlations in small...

We investigate both analytically and by computer simulations the ensemble- time-averaged, nonergodic, aging properties of massive particles diffusing in a medium with time dependent diffusivity. call this stochastic diffusion process (aging) underdamped scaled Brownian motion (UDSBM). demonstrate how mean squared displacement (MSD) time-averaged MSD UDSBM are affected inertial term Langevin equation, at short, intermediate, even long times. In particular, we quantify ballistic regime for as...

We investigate diffusion in polydisperse granular media. derive the mean-squared displacement of particles a gas homogeneous cooling state, containing an arbitrary amount species different sizes and masses. both models constant time-dependent restitution coefficients obtain universal law for size dependence steep distributions.

The oblique impacts of nanoclusters is studied by means Molecular Dynamics and theoretically. In simulations we explore two models -- Lennard-Jones clusters particles with covalently bonded atoms. contrast to the case macroscopic bodies, standard definition normal restitution coefficient yields for this negative values collisions nanoclusters. We explain effect propose a proper which always positive. develop theory an impact based on continuum model particles. A surprisingly good agreement...

We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to origin, a power-law between events. Two situations are considered. Under complete resetting, CTRW after event starts anew, new time, independent prehistory. incomplete coordinate does not influence until next jump. focus on behavior mean squared displacement (MSD) from its initial position, conditions probability density functions walker's show universal...

We investigate both ensemble and time-averaged mean-squared displacements of particles in a polydisperse granular system homogeneous cooling state derive rigorous analytical expressions valid at short long time scales. The discrepancies indicate ergodicity breaking systems consisting an arbitrary number species different sizes masses. compare the results our study with Monte Carlo simulations terms powerful low-rank algorithm find nice agreement.

Brownian motion in a granular gas homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principles model for impact-velocity dependent restitution coefficient, as it follows viscoelastic spheres. reveal that wide range initial conditions ratio temperatures bath particles demonstrates complicated nonmonotonic behavior, which results transition between different regimes dynamics: It starts from ballistic motion, switches later to...

A simple model of ballistic aggregation and fragmentation is proposed. The characterized by two energy thresholds, Eagg Efrag, which demarcate different types impacts: If the kinetic relative motion a colliding pair smaller than or larger particles respectively merge break; otherwise they rebound. We assume that are formed from monomers cannot split any further in collision-induced particle splits into fragments. start Boltzmann equation for mass-velocity distribution function derive...

We consider Brownian motion under resetting in higher dimensions for the case when return of particle to origin occurs at a constant speed. investigate behavior probability density function (PDF) and mean-squared displacement (MSD) this process. study two different protocols: exponentially distributed time intervals between events (Poissonian resetting) fixed (deterministic resetting). moreover discuss general problem invariance PDF with respect speed, as observed one-dimensional system...

We perform large-scale event-driven molecular dynamics (MD) simulations for granular gases of particles interacting with the impact-velocity-dependent restitution coefficient ε(v(imp)). use ε(v(imp)) as it follows from simplest first-principles collision model viscoelastic spheres. Both cases force-free and uniformly heated are studied. formulate a simplified an effective constant ε(eff), which depends on current temperature, we compute ε(eff) using kinetic theory. develop theory velocity...

Distribution of granular temperatures in gas mixtures is investigated analytically and numerically. We analyze space uniform systems a homogeneous cooling state (HCS) under heating with mass-dependent rate $\Gamma_k\sim m_k^{\gamma}$. demonstrate that for steep size distributions particles the obey universal power-law distribution, $T_k \sim m_k^{\alpha}$, where exponent $\alpha$ does not depend on particular form number species inelasticity grains. Moreover, constant HCS depends piecewise...

In this paper, we propose an efficient and fast numerical method of finding a stationary solution large systems aggregation–fragmentation equations Smoluchowski type for concentrations reacting particles. This is applicable when the steeply decrease with increasing aggregate size, which fulfilled most important cases. We show that under rather mild restrictions, imposed on kernel equation, following procedure may be used: First, complete relatively small number (a “seed system”) generated...

Abstract We study analytically and numerically the distribution of granular temperatures in mixtures for different dissipation mechanisms inelastic inter-particle collisions. Both driven force-free systems are analyzed. demonstrate that simplified model a constant restitution coefficient fails to predict even qualitatively temperature homogeneous cooling state. At same time we reveal stunning result – is universal. That is, it does not depend on particular mechanism inter-particles...

We develop a theory of microphase separation in melt flexible AB block copolymers with liquid crystalline side groups (C) attached to the B using strong segregation approximation. Within this theory, we analyze case when all components system are strongly incompatible each other. predict thermodynamic stability two kinds cylindrical structures having amorphous and cores, four lamellar structures. One includes A layers perpendicular orientations (so-called ⊥ lamellae). Three other have...