System Of Active Particles Research Articles

Pressure and phase equilibria in interacting active brownian spheres.

We derive a microscopic expression for the mechanical pressure P in a system of spherical active Brownian particles at density ρ. Our exact result relates P, defined as the force per unit area on a bounding wall, to bulk correlation functions evaluated far away from the wall. It shows that (i) P(ρ) is a state function, independent of the particle-wall interaction; (ii) interactions contribute two terms to P, one encoding the slow-down that drives motility-induced phase separation, and the other a direct contribution well known for passive systems; and (iii) P is equal in coexisting phases. We discuss the consequences of these results for the motility-induced phase separation of active Brownian particles and show that the densities at coexistence do not satisfy a Maxwell construction on P.

Virial pressure in systems of spherical active Brownian particles.

The pressure of suspensions of self-propelled objects is studied theoretically and by simulation of spherical active Brownian particles (ABPs). We show that for certain geometries, the mechanical pressure as force/area of confined systems can be equally expressed by bulk properties, which implies the existence of a nonequilibrium equation of state. Exploiting the virial theorem, we derive expressions for the pressure of ABPs confined by solid walls or exposed to periodic boundary conditions. In both cases, the pressure comprises three contributions: the ideal-gas pressure due to white-noise random forces, an activity-induced pressure ("swim pressure"), which can be expressed in terms of a product of the bare and a mean effective particle velocity, and the contribution by interparticle forces. We find that the pressure of spherical ABPs in confined systems explicitly depends on the presence of the confining walls and the particle-wall interactions, which has no correspondence in systems with periodic boundary conditions. Our simulations of three-dimensional ABPs in systems with periodic boundary conditions reveal a pressure-concentration dependence that becomes increasingly nonmonotonic with increasing activity. Above a critical activity and ABP concentration, a phase transition occurs, which is reflected in a rapid and steep change of the pressure. We present and discuss the pressure for various activities and analyse the contributions of the individual pressure components.

Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks.

We introduce a kinetic Monte Carlo model for self-propelled hard disks to capture with minimal ingredients the interplay between thermal fluctuations, excluded volume, and self-propulsion in large assemblies of active particles. We analyze in detail the resulting (density, self-propulsion) nonequilibrium phase diagram over a broad range of parameters. We find that purely repulsive hard disks spontaneously aggregate into fractal clusters as self-propulsion is increased and rationalize the evolution of the average cluster size by developing a kinetic model of reversible aggregation. As density is increased, the nonequilibrium clusters percolate to form a ramified structure reminiscent of a physical gel. We show that the addition of a finite amount of noise is needed to trigger a nonequilibrium phase separation, showing that demixing in active Brownian particles results from a delicate balance between noise, interparticle interactions, and self-propulsion. We show that self-propulsion has a profound influence on the dynamics of the active fluid. We find that the diffusion constant has a nonmonotonic behavior as self-propulsion is increased at finite density and that activity produces strong deviations from Fickian diffusion that persist over large time scales and length scales, suggesting that systems of active particles generically behave as dynamically heterogeneous systems.

Numerical simulations of a minimal model for the fluid dynamics of dense bacterial suspensions

Collective behavior is a fascinating phenomenon and ubiquitous in nature. A large variety of complex dynamic structures from swarming to turbulence arise in active particle systems. In recent investigations a set of minimal continuum equations was proposed to model mesoscale bacterial turbulence. Numerical solutions are validated with experimental data of Bacillus subtilis bacteria. In this short paper we present a recently used pseudo-spectral operator splitting method that directly solves the nonlinear equations in the turbulent regime. In two and three spatial dimensions we show the resulting typical velocity and vorticity fields as well as energy spectra to highlight the strong difference between turbulence in ordinary fluids and in bacterial suspensions.

Scaling of cluster growth for coagulating active particles

Cluster growth in a coagulating system of active particles (such as microswimmers in a solvent) is studied by theory and simulation. In contrast to passive systems, the net velocity of a cluster can have various scalings dependent on the propulsion mechanism and alignment of individual particles. Additionally, the persistence length of the cluster trajectory typically increases with size. As a consequence, a growing cluster collects neighboring particles in a very efficient way and thus amplifies its growth further. This results in unusual large growth exponents for the scaling of the cluster size with time and, for certain conditions, even leads to "explosive" cluster growth where the cluster becomes macroscopic in a finite amount of time.

Invasion-wave-induced first-order phase transition in systems of active particles

An instability near the transition to collective motion of self-propelled particles is studied numerically by Enskog-like kinetic theory. While hydrodynamics breaks down, the kinetic approach leads to steep solitonlike waves. These supersonic waves show hysteresis and lead to an abrupt jump of the global order parameter if the noise level is changed. Thus they provide a mean-field mechanism to change the second-order character of the phase transition to first order. The shape of the wave is shown to follow a scaling law and to quantitatively agree with agent-based simulations.

Diffusion, Subdiffusion, and Trapping of Active Particles in Heterogeneous Media

We study the transport properties of a system of active particles moving at constant speed in a heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles avoid. Obstacle avoidance is characterized by the particle turning speed γ. We show, through simulations and analytical calculations, that the mean square displacement of particles exhibits two regimes as function of the density of obstacles ρ(o) and γ. We find that at low values of γ, particle motion is diffusive and characterized by a diffusion coefficient that displays a minimum at an intermediate obstacle density ρ(o). We observe that in high obstacle density regions and for large γ values, spontaneous trapping of active particles occurs. We show that such trapping leads to genuine subdiffusive motion of the active particles. We indicate how these findings can be used to fabricate a filter of active particles.

Collective dynamics in systems of active Brownian particles with dissipative interactions

We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with an internal energy depot and interactions inspired by the dissipative particle dynamics method, imposing pairwise friction force on the nearest neighbors. We study orientational ordering in a 2D system as a function of energy influx rate and particle density. The model demonstrates a transition into the ordered state on increasing the particle density and increasing the input power. Although both the alignment mechanism and the character of individual motion in our model differ from those in the well-studied Vicsek model, it demonstrates identical statistical properties and phase behavior.

Phase separation and rotor self-assembly in active particle suspensions

Adding a nonadsorbing polymer to passive colloids induces an attraction between the particles via the "depletion" mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory, and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger interparticle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower interparticle attraction show unidirectional rotation. These micro-rotors demonstrate the self-assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self-assembly of rotors are generic features of aggregating swimmers and should therefore occur in a variety of biological and synthetic active particle systems.

Patterns of synchronization in the hydrodynamic coupling of active colloids

A system of active colloidal particles driven by harmonic potentials to oscillate about the vertices of a regular polygon, with hydrodynamic coupling between all particles, is described by a piecewise linear model which exhibits various patterns of synchronization. Analytical solutions are obtained for this class of dynamical systems. Depending only on the number of particles, the synchronization occurs into states in which nearest neighbors oscillate in in-phase, antiphase, or phase-locked (time-shifted) trajectories.

Deep-Conformance Control Improves Sweep Efficiency in Mature Waterfloods of the San Jorge Basin

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 129732, ’Deep-Conformance Control by a Novel Thermally Activated Particle System To Improve Sweep Efficiency in Mature Waterfloods of the San Jorge Basin,’ by J.L. Mustoni, SPE, Pan-American Energy; C.A. Norman, SPE, Tiorco; and P. Denyer, BP plc, prepared for the 2010 SPE Improved Oil Recovery Symposium, Tulsa, 24-28 April. The paper has not been peer reviewed. Six pilot applications of a thermally-activated-particle (TAP) system were applied in mature waterfloods in the San Jorge basin (SJB), Argentina. Injected water preferentially flows along the center of the channel, which becomes a “thief zone,” and breaks through to the producers prematurely, leaving much of the oil unswept. Particle technology has blocked thief zones deep in the reservoir. This blocking creates a new pressure gradient in the reservoir that promotes diversion of injected water toward zones with higher oil saturation. Introduction SJB waterfloods are characterized by low recovery efficiency because of an adverse mobility ratio and the reservoir-rock spatial anisotropy. This heterogeneity is typical of fluvial systems with high contrasts of rock properties inside the same channel body. A permeability contrast of 5:1 between the center and the edge of the channel is typical. The three operating contracts are in southern Argentina and cover approximately 3500 km2 and include 3,800 active oil and gas wells producing from an average depth of 2200 m. As of June 2009, production totaled 17 800 m3/d of oil and almost 9×106 m3/d of gas. Approximately one-half of the oil production is attributable to a massive secondary-recovery (waterflooding) operation that injects 27 000 m3/d of water through 620 water-injection wells. Reservoir heterogeneities and the adverse mobility ratio typically increase the water/oil ratio (WOR) to greater than 10 within a few years of startup. Substantial oil is bypassed by injection water and is the target for a new technology to improve sweep efficiency. Complexity of SJB Reservoirs Sand bodies are separate hydraulic units with distinct reservoir pressures and fluid and rock properties. Depending on well location, the total column thickness varies from 400 to 3500 m and can include up to 30 separate reservoirs that are segregated vertically by water-saturated sandstone layers or impermeable shales. Each hydrocarbon trap is relatively small volumetrically, and most channels are 200 to 700 m wide and 3 to 10 m thick. Because areal continuity is limited, adjacent wells are likely to contact different reservoirs or the same reservoir with different petrophysical characteristics. Therefore, pattern configuration is irregular in an attempt to follow the geometry of the productive reservoirs. The injector/producer flow model is unique for each pattern, depending on reservoir heterogeneities, rock/fluid properties, location of the wellbore within the contacted reservoirs, and the number of productive reservoirs present in the injector and associated producers.

Modelling taxation and redistribution: A discrete active particle kinetic approach

In this paper a general framework is proposed, suitable for the modelling of the taxation and redistribution process in a closed society. This framework arises within a discrete kinetic approach for active particle systems, and is expressed by a system of nonlinear ordinary differential equations. It is intended to describe the evolution of the wealth distribution over the population, based on the interactions of single individuals. The framework is then employed towards the construction of a toy model, which is analytically and computationally investigated.

From the discrete kinetic theory to modelling open systems of active particles

This work deals with a methodological development of the kinetic theory for open systems of active particles with discrete states. It essentially refers to the derivation of mathematical tools which provide the guidelines for modelling open systems in different fields of applied sciences. After a description of closed systems, mathematical frameworks suitable for depicting the evolution of open systems are proposed. Finally, some research perspectives towards modelling are outlined.

HYBRID TWO SCALES MATHEMATICAL TOOLS FOR ACTIVE PARTICLES MODELLING COMPLEX SYSTEMS WITH LEARNING HIDING DYNAMICS

This paper deals with the derivation of hybrid mathematical structures to describe the behavior of large systems of active particles by ordinary differential equations with stochastic coefficients whose evolution is modelled by equations of the mathematical kinetic theory. A preliminary analysis shows how the above tools can be used to model complex systems of interest in applied sciences, with special attention to the immune competition.

Discrete active models and applications

Optimization processes based on “active models” play central roles in many areas of computational vision as well as computational geometry. Unfortunately, current models usually require highly complex and sophisticated mathematical machinery and at the same time they suffer from a number of limitations which impose restrictions on their applicability. In this paper a simple class of discrete active models, called migration processes (MPs), is presented. The processes are based on iterated averaging over neighborhoods defined by constant geodesic distance. It is demonstrated that the MP model-a system of self-organizing active particles—has a number of advantages over previous models, both parametric active models (“snakes”) and implicit (contour evolution) models. Due to the generality of the MP model, the process can be applied to derive natural solutions to a variety of optimization problems,including defining (minimal) surface patches given their boundary curves; finding shortest paths joining sets of points; and decomposing objects into “primitive” parts.

Vectorization of the Monte Carlo program dicon

A complex Monte Carlo program simulating the behaviour of neutral particles in the divertor chamber of a Tokamak fusion reactor has been vectorized. Nearly 50% of all the 5000 Fortran statements of the original program were modified. On the vector-processing computer FACOM VP-100, the revised program was able to be executed in less than one half of the execution time of the original program. The particle-packing method and the management system of active particles are described.