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

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

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

Non-Fickian diffusion and the accumulation of methane bubbles in deep-water sediments

In the absence of fractures, methane bubbles in deep-water sediments can be immovably trapped within a porous matrix by surface tension. The dominant mechanism of transfer of gas mass therefore becomes the diffusion of gas molecules through porewater. The accurate description of this process requires non-Fickian diffusion to be accounted for, including both thermal diffusion and gravitational action. We evaluate the diffusive flux of aqueous methane considering non-Fickian diffusion and predict the existence of extensive bubble mass accumulation zones within deep-water sediments. The limitation on the hydrate deposit capacity is revealed; too weak deposits cannot reach the base of the hydrate stability zone and form any bubbly horizon

Aggregation Kinetics in Sedimentation: Effect of Diffusion of Particles

Abstract: The aggregation kinetics of settling particles is studied theoretically and numerically using the advection–diffusion equation. Agglomeration caused by these mechanisms (diffusion and advection) is important for both small particles (e.g., primary ash or soot particles in the atmosphere) and large particles of identical or close size, where the spatial inhomogeneity is less pronounced. Analytical results can be obtained for small and large Péclet numbers, which determine the relative importance of diffusion and advection. For small numbers (spatial inhomogeneity is mainly due to diffusion), an expression for the aggregation rate is obtained using an expansion in terms of Péclet numbers. For large Péclet numbers, when advection is the main source of spatial inhomogeneity, the aggregation rate is derived from ballistic coefficients. Combining these results yields a rational approximation for the whole range of Péclet numbers. The aggregation rates are also estimated by numerically solving the advection–diffusion equation. The numerical results agree well with the analytical theory for a wide range of Péclet numbers (extending over four orders of magnitude)

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

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

Atomistic Mechanism of Friction-Force Independence on the Normal Load and Other Friction Laws for Dynamic Structural Superlubricity

We explore dynamic structural superlubricity for the case of a relatively large contact area, where the friction force is proportional to the area (exceeding ∼100 nm2) experimentally, numerically, and theoretically. We use a setup composed of two molecular smooth incommensurate surfaces: graphene-covered tip and substrate. The experiments and molecular dynamic simulations demonstrate independence of the friction force on the normal load for a wide range of normal loads and relative surface velocities. We propose an atomistic mechanism for this phenomenon, associated with synchronic out-of-plane surface fluctuations of thermal origin, and confirm it by numerical experiments. Based on this mechanism, we develop a theory for this type of superlubricity and show that friction force increases linearly with increasing temperature and relative velocity for velocities larger than a threshold velocity. The molecular dynamic results are in a fair agreement with predictions of the theory

Steady oscillations in aggregation-fragmentation processes

We report surprising steady oscillations in aggregation-fragmentation processes. Oscillating solutions are observed for the class of aggregation kernels Ki,j = iν jμ + j ν iμ homogeneous in masses i and j of merging clusters and fragmentation kernels, Fij = λKij , with parameter λ quantifying the intensity of the disruptive impacts. We assume a complete decomposition (shattering) of colliding partners into monomers. We show that an assumption of a steady-state distribution of cluster sizes, compatible with governing equations, yields a power law with an exponential cutoff. This prediction agrees with simulation results when θ ≡ ν − μ < 1. For θ = ν − μ > 1, however, the densities exhibit an oscillatory behavior. While these oscillations decay for not very small λ, they become steady if θ is close to 2 and λ is very small. Simulation results lead to a conjecture that for θ < 1 the system has a stable fixed point, corresponding to the steady-state density distribution, while for any θ > 1 there exists a critical value λc, such that for λ<λc, the system has an attracting limit cycle. This is rather striking for a closed system of Smoluchowski-like equations, lacking any sinks and sources of mass