Particle Systems Research Articles

Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization

A quasi-steady-state model for accurately predicting the detailed diffusion-dominated dissolution process of polydisperse spheroidal (prolate, oblate and spherical) particle systems was presented in Part I of this study. In the present paper, the dissolution characteristics of typical polydisperse spheroidal particle systems have been extensively investigated. The effects of the distributions of particle size and shape have been studied by examining the detailed dissolution processes, such as the size reduction rates of individual particles, the increase in bulk concentration and the dissolution time of the polydisperse systems. Some important factors controlling the dissolution process, including initial particle concentration, smallest and largest particle sizes, and the smallest and largest Taylor shape parameters, have been identified.

Quasi steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, I: modelling

A quasi steady-state model (QSM) for accurately predicting the detailed diffusion-dominated dissolution process of polydisperse spheroidal (prolate, oblate and spherical) particle systems with a broad range of distributions of particle size and aspect ratio has been developed. A rigorous, mathematics-based QSM of the dissolution of single spheroidal particles has been incorporated into the well-established framework of polydisperse dissolution models based on the assumption of uniform bulk concentration. Validation against experimental results shows that this model can accurately predict the increase in bulk concentration of polydisperse systems with various particle sizes and shape parameters. A series of representative instances involving the dissolution of polydisperse felodipine particles at various concentration ratios is used to demonstrate the model's effectiveness, rendering it a valuable tool for understanding and managing complex systems with diverse particle characteristics.

Influence of anomalous agents on the dynamics of an active system.

Swarming behavior in systems of self-propelled particles, whether biological or artificial, has received increased attention in recent years. Here, we show that even a small number of particles with anomalous behavior can change dramatically collective dynamics of the swarming system and can impose unusual behavior and transitions between dynamic states. Our results pave the way to practical approaches and concepts of multiagent dynamics in groups of flocking animals: birds, insects, and fish, i.e., active and living soft matter.

On the ideal gas law for crowds with high pressure

Active particle systems, such as human crowds, are out of equilibrium posing a significant challenge in identifying a suitable equation of state. However, several previous observations suggest that a crowd’s speed distribution may conform to a two-dimensional Maxwell–Boltzmann distribution under certain yet-to-be-determined conditions. Our research uncovers that the divergence between the fluctuation velocity magnitude’s probability density function and its best 2D Maxwell–Boltzmann fit diminishes in a power-law fashion with decreasing collision time scale between individuals. These findings are robustly supported by both experimental data and simulations with diverse boundary conditions and force potentials. The equilibrium characteristics of crowds are interpreted through a canonical ensemble framework. Furthermore, we show that high pressure indicates equilibrium characteristics in human crowds. Remarkably, we reveal the ideal gas law for human crowds without resorting to any behavior assumption. We demonstrate the predictive capability of the ideal gas law on both observational and modeling data. Our research highlights a new pathway to explore and validate traditional thermodynamic quantities and laws in the setting of high-pressure human crowds, advancing our understanding of active matter systems.

A quantization of interacting particle systems

Interacting particle systems studied in this paper are probabilistic cellular automata with nearest-neighbor interaction including the Domany-Kinzel model. A special case of the Domany-Kinzel model is directed percolation. We regard the interacting particle system as a Markov chain on a graph. Then we present a new quantization of the interacting particle system. After that, we introduce a zeta function of the quantized model and give its determinant expression. Moreover, we calculate the absolute zeta function of the quantized model for the Domany-Kinzel model.

Comparative Study of Fluid Dynamic Stress on Aspergillus niger and Model Systems

AbstractThe productivity of Aspergillus niger cultivations is strongly linked to the pellet morphology. In this article, the agitation‐ and aeration‐induced stress on bio agglomerates is studied. To facilitate investigations, non‐biological particle systems are extensively used to model the actual biological matter. The literature lacks a direct comparison of model systems with the biological system of interest, leaving uncertainties in the applicability of such systems. This work shows that the results for the impellers' stress intensity of three A. niger strains agree qualitatively with the ones of four developed model systems of different nature (s/l, l/l). The findings justify the usage of model systems, despite certain limitations originating from their specific characteristic properties.

Canonical Ensemble vs. Grand Canonical Ensemble in the Description of Multicomponent Bosonic Systems

The thermodynamics of a system of interacting bosonic particles and antiparticles in the presence of the Bose–Einstein condensate is studied in the framework of a Skyrme-like mean-field model. It is assumed that the total charge density (isospin density) is conserved at all temperatures. Two cases are explicitly considered: the zero or nonzero isospin charge of the system. A comparative analysis is carried out using the Canonical Ensemble or the Grand Canonical Ensemble. It is shown that the Grand Canonical Ensemble is not suitable for describing the bosonic systems of particles and antiparticles in the presence of a condensate, but an adequate study can be carried out within the framework of the canonical ensemble, where the chemical potential is a thermodynamic quantity that depends on the canonical free variable.

Structure of Argon Solid Phases Formed from the Liquid State at Different Isobaric Cooling Rates

By the method of molecular dynamics, computer simulation of the processes of isobaric cooling of argon particle systems under initial conditions with a temperature of 150 K at pressure values from 0.1 to 4 MPa to a temperature of 40 K with cooling rates of 108, 109, 1010, 1011 and 1012 K/s was performed. As a result of a computer experiment, coordinate arrays of particles were obtained, which were subjected to the procedure of three-dimensional Voronoi partitioning to identify and calculate the number of elementary cells of the crystal structure. Analysis of the structure of argon solid phases formed during isobaric cooling allowed us to deduce an estimated pattern between the concentration of FCC (face-centered cubic) cells in solid argon and the cooling rate from the liquid state. The evaluation of the orientation of the axes of translation of crystal cells in the array of particle coordinates made it possible to classify the solid phases formed as a result of cooling as single crystals, glassy media with the inclusion of clusters and single cells of FCC structures. It was revealed that during isobaric cooling at a rate not exceeding 108 K/s, argon completely crystallizes, at isobaric cooling rates of 109–1010 K/s, the union of elementary cells of the crystal structure into clusters is observed in glassy argon, and at rates of 1011 K/s and higher at pressures of 1 MPa and lower, solid vitreous phases of argon are formed in which no crystal structure cells are detected.

Hydrodynamic and kinetic representation of the microscopic classic dynamics at the transition on the macroscopic scale

An open problem of the derivation of the relativistic Vlasov equation for systems of charged particles moving with velocities up to the speed of light and creating the electromagnetic field in accordance with the full set of the Maxwell equations is considered. Moreover, the method of derivation is illustrated on the non-relativistic kinetic model. Independent derivation of the relativistic hydrodynamics is also demonstrated. The key role of these derivations of the hydrodynamic and kinetic equations includes the explicit operator of averaging on the physically infinitesimal volume suggested by L.S. Kuzmenkov.

Active smectics on a sphere

The dynamics of active smectic liquid crystals confined on a spherical surface is explored through an active phase field crystal model. Starting from an initially randomly perturbed isotropic phase, several types of topological defects are spontaneously formed, and then annihilate during a coarsening process until a steady state is achieved. The coarsening process is highly complex involving several scaling laws of defect densities as a function of time where different dynamical exponents can be identified. In general the exponent for the final stage towards the steady state is significantly larger than that in the passive and in the planar case, i.e. the coarsening is getting accelerated both by activity and by the topological and geometrical properties of the sphere. A defect type characteristic for this active system is a rotating spiral of evolving smectic layering lines. On a sphere this defect type also determines the steady state. Our results can in principle be confirmed by dense systems of synthetic or biological active particles.

Synchronous and Fully Steerable Active Particle Systems for Enhanced Mimicking of Collective Motion in Nature (Adv. Mater. 7/2024)

Synchronous and Fully Steerable Active Particle Systems for Enhanced Mimicking of Collective Motion in Nature (Adv. Mater. 7/2024)

Small mass limit for stochastic interacting particle systems with Lévy noise and linear alignment force.

We study the small mass limit in mean field theory for an interacting particle system with non-Gaussian Lévy noise. When the Lévy noise has a finite second moment, we obtain the limit equation with convergence rate ε+1/εN, by taking first the mean field limit N→∞ and then the small mass limit ε→0. If the order of the two limits is exchanged, the limit equation remains the same but has a different convergence rate ε+1/N. However, when the Lévy noise is α-stable, which has an infinite second moment, we can only obtain the limit equation by taking first the small mass limit and then the mean field limit, with the convergence rate 1/Nα-1+1/Np2+εp/α where p∈(1,α). This provides an effectively limit model for an interacting particle system under a non-Gaussian Lévy fluctuation, with rigorous error estimates.

Directional synchrony among self-propelled particles under spatial influence.

Synchronization is one of the emerging collective phenomena in interacting particle systems. Its ubiquitous presence in nature, science, and technology has fascinated the scientific community over the decades. Moreover, a great deal of research has been, and is still being, devoted to understand various physical aspects of the subject. In particular, the study of interacting active particles has led to exotic phase transitions in such systems which have opened up a new research front-line. Motivated by this line of work, in this paper, we study the directional synchrony among self-propelled particles. These particles move inside a bounded region, and crucially their directions are also coupled with spatial degrees of freedom. We assume that the directional coupling between two particles is influenced by the relative spatial distance which changes over time. Furthermore, the nature of the influence is considered to be both short and long-ranged. We explore the phase transition scenario in both the cases and propose an approximation technique which enables us to analytically find the critical transition point. The results are further supported with numerical simulations. Our results have potential importance in the study of active systems like bird flocks, fish schools, and swarming robots where spatial influence plays a pertinent role.

Pathwise large deviations for the pure jump k-nary interacting particle systems

Pathwise large deviations for the pure jump k-nary interacting particle systems

Variational Structures Beyond Gradient Flows: a Macroscopic Fluctuation-Theory Perspective

Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the density of the particle system. While large deviations can be studied in considerable generality, these variational structures are often restricted to systems in detailed balance. Using insights from macroscopic fluctuation theory, in this work we aim to generalise this variational connection beyond dissipative systems by augmenting densities with fluxes, which encode non-dissipative effects. Our main contribution is an abstract theory, which for a given flux-density cost and a quasipotential, provides a decomposition into dissipative and non-dissipative components and a generalised orthogonality relation between them. We then apply this abstract theory to various stochastic particle systems—independent copies of jump processes, zero-range processes, chemical-reaction networks in complex balance and lattice-gas models—without assuming detailed balance. For macroscopic equations arising out of these particle systems, we derive new variational formulations that generalise the classical gradient-flow formulation.

Harnessing synthetic active particles for physical reservoir computing

The processing of information is an indispensable property of living systems realized by networks of active processes with enormous complexity. They have inspired many variants of modern machine learning, one of them being reservoir computing, in which stimulating a network of nodes with fading memory enables computations and complex predictions. Reservoirs are implemented on computer hardware, but also on unconventional physical substrates such as mechanical oscillators, spins, or bacteria often summarized as physical reservoir computing. Here we demonstrate physical reservoir computing with a synthetic active microparticle system that self-organizes from an active and passive component into inherently noisy nonlinear dynamical units. The self-organization and dynamical response of the unit are the results of a delayed propulsion of the microswimmer to a passive target. A reservoir of such units with a self-coupling via the delayed response can perform predictive tasks despite the strong noise resulting from the Brownian motion of the microswimmers. To achieve efficient noise suppression, we introduce a special architecture that uses historical reservoir states for output. Our results pave the way for the study of information processing in synthetic self-organized active particle systems.

Stochastic differential equations for infinite particle systems of jump type with long range interactions

Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a Lévy process, and the interaction between particles is determined by the long-range interaction potential. The potential is of Ruelle's class or logarithmic. We discuss the existence and uniqueness of strong solutions of the ISDEs.

Investigating the Emergence of Collective States Within Rugby Sevens Gameplay

ABSTRACT Rugby sevens is a small-sided variant of rugby union characterised by fast-moving, high-intensity gameplay and is an example of a team invasion sport, where players work together to achieve a shared goal of attacking and defending as a cohesive unit. The dynamics of such sports can be viewed as self-organizing systems, where individual players form collective patterns without a centralized mechanism of control. Inspired by the analysis of collective movement in animals, this novel study investigates the emergent patterns of order and disorder in sub-elite female rugby sevens using order parameters (typically used to analyse particle systems) to characterize the team’s collective state during different phases of play. The findings demonstrate that defensive gameplay is more ordered, with more compact formations, compared to attacking play, and there is a correlation between alignment/order in player motion and group speed. The work further suggests that the collective states formed differ between sequences of play with different levels of ground gained by the attacking team. These observations provide a sound justification for player training with a focus on cohesive defensive movements to resist disruptions from opposing attackers, while employing attacking tactics that disrupt the cohesion and order of opposing teams.

In situ investigation of the thermal characteristics of microwave resonance-induced focused hotspots in dimers for improving microwave heating uniformity

Microwave hotspots or thermal runaway is a long-standing challenge that severely limits the uniformity of microwave heating. In particular, the evolvement process and suppression methods of focused hotspots in high permittivity dimers are still not clear. In this work, thermal imaging was used to in situ track the microwave hotspots of grape dimers with different gaps and shapes in a multi-mode microwave oven. Two thermal characteristics of microwave resonance-induced focused hotspots, gap sensitivity and shape selectivity, were found. Finite element simulation verified the experimental results and calculated the influence of different conditions on the heating uniformity and the enhanced electric field. The results indicated that gap can gradually weaken the enhanced electric field between grapes and rapidly improve the heating uniformity by approximately 30 times. For dimers of different shapes in contact, the sharper the contact area, the more pronounced the focused hotspots. Moreover, the heating uniformity raises with increasing shape factor n, and when n = ∞, it is improved by about 35 times compared with n = 1. In addition, the enhanced electric field, which exhibits complexity due to microwave scattering interaction between grapes, was analyzed. These findings provide two strategies for improving the heating homogeneity of dimers or particle systems.

Concentration of measure for graphon particle system

Abstract We study heterogeneously interacting diffusive particle systems with mean-field-type interaction characterized by an underlying graphon and their finite particle approximations. Under suitable conditions, we obtain exponential concentration estimates over a finite time horizon for both 1- and 2-Wasserstein distances between the empirical measures of the finite particle systems and the averaged law of the graphon system.