Towards a continuum theory of clustering in a freely cooling inelastic gas

We performed molecular dynamics simulations to investigate the clustering instability of a freely cooling dilute gas of inelastically colliding disks in a quasi-one-dimensional setting. We observe that, as the gas cools, the shear stress becomes negligibly small, and the gas flows by inertia only. Finite-time singularities, intrinsic in such a flow, are arrested only when close-packed clusters are formed. We observe that the late-time dynamics of this system are describable by the Burgers equation with vanishing viscosity, and predict the long-time coarsening behavior.Comment: 7 pages, 5 eps figures, to appear in Europhys. Let

Symmetry-breaking instability in a prototypical driven granular gas

Symmetry-breaking instability of a laterally uniform granular cluster (strip state) in a prototypical driven granular gas is investigated. The system consists of smooth hard disks in a two-dimensional box, colliding inelastically with each other and driven, at zero gravity, by a "thermal" wall. The limit of nearly elastic particle collisions is considered, and granular hydrodynamics with the Jenkins-Richman constitutive relations is employed. The hydrodynamic problem is completely described by two scaled parameters and the aspect ratio of the box. Marginal stability analysis predicts a spontaneous symmetry breaking instability of the strip state, similar to that predicted recently for a different set of constitutive relations. If the system is big enough, the marginal stability curve becomes independent of the details of the boundary condition at the driving wall. In this regime, the density perturbation is exponentially localized at the elastic wall opposite to the thermal wall. The short- and long-wavelength asymptotics of the marginal stability curves are obtained analytically in the dilute limit. The physics of the symmetry-breaking instability is discussed.Comment: 11 pages, 14 figure

Formation and evolution of density singularities in hydrodynamics of inelastic gases

We use ideal hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a new type of finite-time density blowup, where the gas pressure remains finite. The density blowups signal formation of close-packed clusters. The blowup dynamics are universal and describable by exact analytic solutions continuable beyond the blowup time. These solutions show that dilute hydrodynamic equations yield a powerful effective description of a granular gas flow with close-packed clusters, described as finite-mass point-like singularities of the density. This description is similar in spirit to the description of shocks in ordinary ideal gas dynamics.Comment: 4 pages, 3 figures, final versio

Psychological Safety and Communication Difficulties of Teachers and Students During Long-term Online Training

Due to the growing concerns related to the psychological well-being of students and teachers during a long and intensive online training, it becomes necessary for teachers, psychologists, practitioners to take measures to prevent threats to online communication and identify personal resources of psychological security in the online environment.The purpose of the study was to identify the communicative difficulties of long-term online learning during the COVID-19 pandemic, and the personal resources of students and teachers that contribute to ensuring their psychological safety.The study was conducted in February-March 2022. The study sample included 132 students and 40 teachers of the Faculty of Psychology of the Russian State Social University (Moscow). The following techniques were used: “The test of hardiness” (S. Muddy, in the Russian-language adaptation of E.N. Osin, E.I. Rasskazova), “The scale of subjective well-being” (A. Perrudet-Badoux, G.A. Mendelssohn, J. Chiche, in the Russian-language adaptation of M.V. Sokolova), “Methodology for assessing the level of sociability” (V.F. Ryakhovsky), questionnaires “Difficulties of online communication” for students and teachers. The empirical data obtained were interpreted and processed using qualitative and quantitative methods of analysis, including: descriptive statistics, frequency analysis, Spearman correlation analysis. The study showed that during the long-term distance learning, students and teachers experienced significant difficulties in online educational communication, had low levels of subjective well-being, resilience and sociability. These personal qualities are systemic in nature, interrelated and can act as resources to ensure the psychological safety of subjects of education, prevention or coping with difficulties of online communication and hybrid forms of learning.The data obtained make it necessary for teachers to create psychodidactic conditions for a safe online educational environment in which students will be involved as subjects of education, will be able to freely share their opinions and not be afraid to make a mistake, will feel belonging to a group and protected from verbal aggression

Anomalous Dynamic Scaling in Locally-Conserved Coarsening of Fractal Clusters

We report two-dimensional phase-field simulations of locally-conserved coarsening dynamics of random fractal clusters with fractal dimension D=1.7 and 1.5. The correlation function, cluster perimeter and solute mass are measured as functions of time. Analyzing the correlation function dynamics, we identify two different time-dependent length scales that exhibit power laws in time. The exponents of these power laws are independent of D, one of them is apparently the classic exponent 1/3. The solute mass versus time exhibits dynamic scaling with a D-dependent exponent, in agreement with a simple scaling theory.Comment: 5 pages, 4 figure

Normal scaling in globally conserved interface-controlled coarsening of fractal clusters

Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The sharp-interface limit of this equation is volume preserving motion by mean curvature. The scaled form of the correlation function has a power-law tail accommodating the fractal initial condition. The coarsening length exhibits normal scaling with time. Finally, shrinking of the fractal clusters with time is observed. The difference between global and local conservation is discussed.Comment: 4 pages, 3 eps figure

Hydrodynamics of thermal granular convection

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.Comment: 4 pages, 4 EPS figures, some details adde

Weak selection and stability of localized distributions in Ostwald ripening

We support and generalize a weak selection rule predicted recently for the self-similar asymptotics of the distribution function (DF) in the zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation theory is developed that, when combined with an exact invariance property of the system, yields the selection rule, predicts a power-law convergence towards the selected self-similar DF and agrees well with our numerical simulations for the interface- and diffusion-controlled OR.Comment: 4 pages, 2 figures, submitted to PR

Scaling anomalies in the coarsening dynamics of fractal viscous fingering patterns

We analyze a recent experiment of Sharon \textit{et al.} (2003) on the coarsening, due to surface tension, of fractal viscous fingering patterns (FVFPs) grown in a radial Hele-Shaw cell. We argue that an unforced Hele-Shaw model, a natural model for that experiment, belongs to the same universality class as model B of phase ordering. Two series of numerical simulations with model B are performed, with the FVFPs grown in the experiment, and with Diffusion Limited Aggregates, as the initial conditions. We observed Lifshitz-Slyozov scaling $t^{1/3}$ at intermediate distances and very slow convergence to this scaling at small distances. Dynamic scale invariance breaks down at large distances.Comment: 4 pages, 4 eps figures; to appear in Phys. Rev.

Breakdown of Scale Invariance in the Phase Ordering of Fractal Clusters

Our numerical simulations with the Cahn-Hilliard equation show that coarsening of fractal clusters (FCs) is not a scale-invariant process. On the other hand, a typical coarsening length scale and interfacial area of the FC exhibit power laws in time, while the mass fractal dimension remains invariant. The initial value of the lower cutoff is a relevant length scale. A sharp-interface model is formulated that can follow the whole dynamics of a diffusion controlled growth, coarsening, fragmentation and approach to equilibrium in a system with conserved order parameter.Comment: 4 pages, 4 figures, RevTex, submitted to PR