Supercluster states and phase transitions in aggregation-fragmentation processes.

We study the evolution of aggregates triggered by collisions with monomers that either lead to the attachment of monomers or the break-up of aggregates into constituting monomers. Depending on parameters quantifying addition and break-up rates, the system falls into a jammed or a steady state. Supercluster states (SCSs) are very peculiar nonextensive jammed states that also arise in some models. Fluctuations underlie the formation of the SCSs. Conventional tools, such as the van Kampen expansion, apply to small fluctuations. We go beyond the van Kampen expansion and determine a set of critical exponents quantifying SCSs. We observe continuous and discontinuous phase transitions between the states. Our theoretical predictions are in good agreement with numerical results.

Collision of nanoparticles of covalently bound atoms: Impact of stress-dependent adhesion.

The impact of nanoparticles (NPs) composed of atoms with covalent bonding is investigated numerically and theoretically. We use recent models of covalent bonding of carbon atoms and elaborate a numerical model of amorphous carbon (a-C) NPs, which may be applied for modeling soot particles. We compute the elastic moduli of the a-C material which agree well with the available data. We reveal an interesting phenomenon-stress-dependent adhesion, which refers to stress-enhanced formation of covalent bonds between contacting surfaces. We observe that the effective adhesion coefficient linearly depends on the maximal stress between the surfaces and explain this dependence. We compute the normal restitution coefficient for colliding NPs and explore the dependence of the critical velocity, demarcating bouncing and aggregative collisions, on the NP radius. Using the obtained elastic and stress-dependent adhesive coefficients we develop a theory for the critical velocity. The predictions of the theory agree very well with the simulation results.

Why animals swirl and how they group.

We report a possible solution for the long-standing problem of the biological function of swirling motion, when a group of animals orbits a common center of the group. We exploit the hypothesis that learning processes in the nervous system of animals may be modelled by reinforcement learning (RL) and apply it to explain the phenomenon. In contrast to hardly justified models of physical interactions between animals, we propose a small set of rules to be learned by the agents, which results in swirling. The rules are extremely simple and thus applicable to animals with very limited level of information processing. We demonstrate that swirling may be understood in terms of the escort behavior, when an individual animal tries to reside within a certain distance from the swarm center. Moreover, we reveal the biological function of swirling motion: a trained for swirling swarm is by orders of magnitude more resistant to external perturbations, than an untrained one. Using our approach we analyze another class of a coordinated motion of animals-a group locomotion in viscous fluid. On a model example we demonstrate that RL provides an optimal disposition of coherently moving animals with a minimal dissipation of energy.

How risky is it to visit a supermarket during the pandemic?

We performed large-scale numerical simulations using a composite model to investigate the infection spread in a supermarket during a pandemic. The model is composed of the social force, purchasing strategy and infection transmission models. Specifically, we quantified the infection risk for customers while in a supermarket that depended on the number of customers, the purchase strategies and the physical layout of the supermarket. The ratio of new infections compared to sales efficiency (earned profit for customer purchases) was computed as a factor of customer density and social distance. Our results indicate that the social distance between customers is the primary factor influencing infection rate. Supermarket layout and purchasing strategy do not impact social distance and hence the spread of infection. Moreover, we found only a weak dependence of sales efficiency and customer density. We believe that our study will help to establish scientifically-based safety rules that will reduce the social price of supermarket business.

Nonextensive Supercluster States in Aggregation with Fragmentation.

Systems evolving through aggregation and fragmentation may possess an intriguing supercluster state (SCS). Clusters constituting this state are mostly very large, so the SCS resembles a gelling state, but the formation of the SCS is controlled by fluctuations and in this aspect, it is similar to a critical state. The SCS is nonextensive, that is, the number of clusters varies sublinearly with the system size. In the parameter space, the SCS separates equilibrium and jamming (extensive) states. The conventional methods, such as, e.g., the van Kampen expansion, fail to describe the SCS. To characterize the SCS we propose a scaling approach with a set of critical exponents. Our theoretical findings are in good agreement with numerical results.

Swirlonic state of active matter.

We report a novel state of active matter-a swirlonic state. It is comprised of swirlons, formed by groups of active particles orbiting their common center of mass. These quasi-particles demonstrate a surprising behavior: In response to an external load they move with a constant velocity proportional to the applied force, just as objects in viscous media. The swirlons attract each other and coalesce forming a larger, joint swirlon. The coalescence is extremely slow, decelerating process, resulting in a rarified state of immobile quasi-particles. In addition to the swirlonic state, we observe gaseous, liquid and solid states, depending on the inter-particle and self-driving forces. Interestingly, in contrast to molecular systems, liquid and gaseous states of active matter do not coexist. We explain this unusual phenomenon by the lack of fast particles in active matter. We perform extensive numerical simulations and theoretical analysis. The predictions of the theory agree qualitatively and quantitatively with the simulation results.

Molecular fields and statistical field theory of fluids: Application to interface phenomena.

Using the integral transformation, the field-theoretical Hamiltonian of the statistical field theory of fluids is obtained along with the microscopic expressions for the coefficients of the Hamiltonian. Applying this approach to the liquid-vapor interface, we derive an explicit analytical expression for the surface tension in terms of temperature, density, and parameters of the intermolecular potential. We also demonstrate that a clear physical interpretation may be given to the formal statistical field arising in the integral transformation-it may be associated with the one-body local microscopic potential. The results of the theory, lacking any ad hoc or fitting parameters are in good agreement with available simulation data.

Size-polydisperse dust in molecular gas: Energy equipartition versus nonequipartition.

We investigate numerically and analytically size-polydisperse granular mixtures immersed into a molecular gas. We show that the equipartition of granular temperatures of particles of different sizes is established; however, the granular temperatures significantly differ from the temperature of the molecular gas. This result is surprising since, generally, the energy equipartition is strongly violated in driven granular mixtures. Qualitatively, the obtained results do not depend on the collision model, being valid for a constant restitution coefficient ɛ, as well as for the ɛ for viscoelastic particles. Our findings may be important for astrophysical applications, such as protoplanetary disks, interstellar dust clouds, and comets.

Temperature distribution in driven granular mixtures does not depend on mechanism of energy dissipation.

We study analytically and numerically the distribution of granular temperatures in granular mixtures for different dissipation mechanisms of inelastic inter-particle collisions. Both driven and force-free systems are analyzed. We demonstrate that the simplified model of a constant restitution coefficient fails to predict even qualitatively a granular temperature distribution in a homogeneous cooling state. At the same time we reveal for driven systems a stunning result - the distribution of temperatures in granular mixtures is universal. That is, it does not depend on a particular dissipation mechanism of inter-particles collisions, provided the size distributions of particles is steep enough. The results of the analytic theory are compared with simulation results obtained by the direct simulation Monte Carlo (DSMC). The agreement between the theory and simulations is perfect. The reported results may have important consequences for fundamental science as well as for numerous application, e.g. for the experimental modelling in a lab of natural processes.

Increasing temperature of cooling granular gases.

The kinetic energy of a force-free granular gas decays monotonously due to inelastic collisions of the particles. For a homogeneous granular gas of identical particles, the corresponding decay of granular temperature is quantified by Haff's law. Here, we report that for a granular gas of aggregating particles, the granular temperature does not necessarily decay but may even increase. Surprisingly, the increase of temperature is accompanied by the continuous loss of total gas energy. This stunning effect arises from a subtle interplay between decaying kinetic energy and gradual reduction of the number of degrees of freedom associated with the particles' dynamics. We derive a set of kinetic equations of Smoluchowski type for the concentrations of aggregates of different sizes and their energies. We find scaling solutions to these equations and a condition for the aggregation mechanism predicting growth of temperature. Numerical direct simulation Monte Carlo results confirm the theoretical predictions.

Regimes of electrostatic collapse of a highly charged polyelectrolyte in a poor solvent.

We perform extensive molecular dynamics simulations of a highly charged, collapsed, flexible polyelectrolyte chain in a poor solvent for the case when the electrostatic interactions, characterized by the reduced Bjerrum length lB, are strong. We find the existence of several sub-regimes in the dependence of the gyration radius of the chain Rg on lB characterized by Rg ∼ l. In contrast to a good solvent, the exponent γ for a poor solvent crucially depends on the size and valency of the counterions. To explain the different sub-regimes, we generalize the existing counterion fluctuation theory by including a more complete account of all possible volume interactions in the free energy of the polyelectrolyte chain. We also show that the presence of condensed counterions modifies the effective attraction among the chain monomers and modulates the sign of the second virial coefficient under poor solvent conditions.

Mechanism of Chain Collapse of Strongly Charged Polyelectrolytes.

We perform extensive molecular dynamics simulations of a charged polymer in a good solvent in the regime where the chain is collapsed. We analyze the dependence of the gyration radius R_{g} on the reduced Bjerrum length ℓ_{B} and find two different regimes. In the first one, called a weak electrostatic regime, R_{g}∼ℓ_{B}^{-1/2}, which is consistent only with the predictions of the counterion-fluctuation theory. In the second one, called a strong electrostatic regime, we find R_{g}∼ℓ_{B}^{-1/5}. To explain the novel regime we modify the counterion-fluctuation theory.

Size distribution of particles in Saturn's rings from aggregation and fragmentation.

Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative interparticle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, ~r(-q) with q ≈ 3, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent q to be constrained to the interval 2.75 ≤ q ≤ 3.5. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of microstructures seen in Saturn's rings.

Collision of viscoelastic bodies: Rigorous derivation of dissipative force.

We report a new theory of dissipative forces acting between colliding viscoelastic bodies. The impact velocity is assumed not to be large to neglect plastic deformations in the material and propagation of sound waves. We consider the general case of bodies of an arbitrary convex shape and of different materials. We develop a mathematically rigorous perturbation scheme to solve the continuum mechanics equations that deal with both displacement and displacement rate fields and accounts for the dissipation in the bulk of the material. The perturbative solution of these equations allows to go beyond the previously used quasi-static approximation and obtain the dissipative force. The derived force does not suffer from the inconsistencies of the quasi-static approximation, like the violation of the third Newton's law for the case of different materials, and depends on particle deformation and deformation rate.

Velocity distribution function and effective restitution coefficient for a granular gas of viscoelastic particles.

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)). We use ε(v(imp)) as it follows from the simplest first-principles collision model of viscoelastic spheres. Both cases of force-free and uniformly heated gases are studied. We formulate a simplified model of an effective constant restitution coefficient ε(eff), which depends on a current granular temperature, and we compute ε(eff) using the kinetic theory. We develop a theory of the velocity distribution function for driven gases of viscoelastic particles and analyze the evolution of granular temperature and of the Sonine coefficients, which characterize the form of the velocity distribution function. We observe that for not large dissipation the simulation results are in an excellent agreement with the theory for both the homogeneous cooling state and uniformly heated gases. At the same time, a noticeable discrepancy between the theory and MD results for the Sonine coefficients is detected for large dissipation. We analyze the accuracy of the simplified model based on the effective restitution coefficient ε(eff), and we conclude that this model can accurately describe granular temperature. It provides also an acceptable accuracy for the velocity distribution function for small dissipation, but it fails when dissipation is large.

Intermediate regimes in granular Brownian motion: superdiffusion and subdiffusion.

Brownian motion in a granular gas in a homogeneous cooling state is studied theoretically and by means of molecular dynamics. We use the simplest first-principles model for the impact-velocity dependent restitution coefficient, as it follows for the model of viscoelastic spheres. We reveal that for a wide range of initial conditions the ratio of granular temperatures of Brownian and bath particles demonstrates complicated nonmonotonic behavior, which results in a transition between different regimes of Brownian dynamics: It starts from the ballistic motion, switches later to a superballistic one, and turns at still later times into subdiffusion; eventually normal diffusion is achieved. Our theory agrees very well with the molecular dynamics results, although extreme computational costs prevented us from detecting the final diffusion regime. Qualitatively, the reported intermediate diffusion regimes are generic for granular gases with any realistic dependence of the restitution coefficient on the impact velocity.

Diffusive counter dispersion of mass in bubbly media.

We consider a liquid bearing gas bubbles in a porous medium. When gas bubbles are immovably trapped in a porous matrix by surface-tension forces, the dominant mechanism of transfer of gas mass becomes the diffusion of gas molecules through the liquid. Essentially, the gas solution is in local thermodynamic equilibrium with vapor phase all over the system, i.e., the solute concentration equals the solubility. When temperature and/or pressure gradients are applied, diffusion fluxes appear and these fluxes are faithfully determined by the temperature and pressure fields, not by the local solute concentration, which is enslaved by the former. We derive the equations governing such systems, accounting for thermodiffusion and gravitational segregation effects, which are shown not to be neglected for geological systems-marine sediments, terrestrial aquifers, etc. The results are applied for the treatment of non-high-pressure systems and real geological systems bearing methane or carbon dioxide, where we find a potential possibility of the formation of gaseous horizons deep below a porous medium surface. The reported effects are of particular importance for natural methane hydrate deposits and the problem of burial of industrial production of carbon dioxide in deep aquifers.

Negative normal restitution coefficient found in simulation of nanocluster collisions.

The oblique impacts of nanoclusters are studied theoretically and by means of molecular dynamics. In simulations we explore two models--Lennard-Jones clusters and particles with covalently bonded atoms. In contrast with the case of macroscopic bodies, the standard definition of the normal restitution coefficient yields for this coefficient negative values for oblique collisions of nanoclusters. We explain this effect and propose a proper definition of the restitution coefficient which is always positive. We develop a theory of an oblique impact based on a continuum model of particles. A surprisingly good agreement between the macroscopic theory and simulations leads to the conclusion that macroscopic concepts of elasticity, bulk viscosity, and surface tension remain valid for nanoparticles of a few hundred atoms.

Slow dust in Enceladus' plume from condensation and wall collisions in tiger stripe fractures.

One of the spectacular discoveries of the Cassini spacecraft was the plume of water vapour and icy particles (dust) originating near the south pole of Saturn's moon Enceladus. The data imply considerably smaller velocities for the grains than for the vapour, which has been difficult to understand. The gas and dust are too dilute in the plume to interact, so the difference must arise below the surface. Here we report a model for grain condensation and growth in channels of variable width. We show that repeated wall collisions of grains, with re-acceleration by the gas, induce an effective friction, offering a natural explanation for the reduced grain velocity. We derive particle speed and size distributions that reproduce the observed and inferred properties of the dust plume. The gas seems to form near the triple point of water; gas densities corresponding to sublimation from ice at temperatures less than 260 K are generally too low to support the measured particle fluxes. This in turn suggests liquid water below Enceladus' south pole.

Collision dynamics of granular particles with adhesion.

We investigate the collision of adhesive viscoelastic spheres in quasistatic approximation where the adhesive interaction is described by the Johnson, Kendall, and Roberts (JKR) theory. The collision dynamics, based on the dynamic contact force, describes both restitutive collisions quantified by the coefficient of restitution epsilon as well as aggregative collisions, characterized by the critical aggregative impact velocity gcr. Both quantities epsilon and gcr depend sensitively on the impact velocity and particle size. Our results agree well with laboratory experiments.