Collective behavior of interacting self-propelled particles

We discuss biologically inspired, inherently non-equilibrium self-propelled particle models, in which the particles interact with their neighbours by choosing at each time step the local average direction of motion. We summarize some of the results of large scale simulations and theoretical approaches to the problem

Alternating steady state in one-dimensional flocking

We study flocking in one dimension, introducing a lattice model in which particles can move either left or right. We find that the model exhibits a continuous nonequilibrium phase transition from a condensed phase, in which a single `flock' contains a finite fraction of the particles, to a homogeneous phase; we study the transition using numerical finite-size scaling. Surprisingly, in the condensed phase the steady state is alternating, with the mean direction of motion of particles reversing stochastically on a timescale proportional to the logarithm of the system size. We present a simple argument to explain this logarithmic dependence. We argue that the reversals are essential to the survival of the condensate. Thus, the discrete directional symmetry is not spontaneously broken.Comment: 8 pages LaTeX2e, 5 figures. Uses epsfig and IOP style. Submitted to J. Phys. A (Math. Gen.

Anomalous segregation dynamics of self-propelled particles

A number of novel experimental and theoretical results have recently been obtained on active soft matter, demonstrating the various interesting universal and anomalous features of this kind of driven systems. Here we consider a fundamental but still unexplored aspect of the patterns arising in the system of actively moving units, i.e., their segregation taking place when two kinds of them with different adhesive properties are present. The process of segregation is studied by a model made of self-propelled particles such that the particles have a tendency to adhere only to those which are of the same kind. The calculations corresponding to the related differential equations can be made in parallel, thus a powerful GPU card allows large scale simulations. We find that the segregation kinetics is very different from the non-driven counterparts and is described by the new scaling exponents $z\simeq 1$ and $z\simeq 0.8$ for the 1:1 and the non-equal ratio of the two constituents, respectively. Our results are in agreement with a recent observation of segregating tissue cells \emph{in vitro}

Az embrionális érhálózat önszerveződése = Self-organization of the embryonic vascular network

Kutatásaink az önszervezően, sok hasonló sejt kölcsönhatása révén létrejövő biológiai rendszerek, ezen belül elsősorban az embriófejlődés során kialakuló érhálózat és extracelluláris mátrix (ECM) tulajdonságainak vizsgálatára irányultak. A kutatómunka szerves része volt a sejtek viselkedésének megfigyelését lehetővé tevő mikroszkópos és statisztikai elemzés technikák kidolgozása is. Bevezettünk, és madárembriókon végzett kísérletekkel alátámasztottuk a fejlődő szöveteknek egy olyan képét, amelyben a szövet deformációira szuperponálódik a szövetbe ágyazott sejtek aktív (és korrelálatlanabb) mozgása. Megmutattuk, hogy a kezdeti érhálózat -- számos korábbi elképzeléssel ellentétben -- egy, az axonnövekedéshez nagyon hasonló sejtinvázióval történik. Sejttenyészetek in vitro viselkedésének analizálásával rámutattunk, hogy a lineáris szegmensek kialakításának egyik fontos mozgatóeleme a sejtek megváltozott mozgása erősen anizotróp környezetben. Ezekre az emprikus megfigyeléseinkre alapozva felállítottuk a vaszkulogenezis egy új elméleti modelljét. Feltérképeztük a korai embriogenezist jellemző szövetmozgásokat madárembriókban. Megmutattuk, hogy a gasztruláció folyamatát kísérő szövetmozgások jól leírhatók egy olyan tovaterjedő mintázatként, ami az embrió mindkét oldalán egy-egy, ellentétes irányban forgó örvényt tartalmaz. Mint a szövetalkotás egyik fő lépését, elemeztük a sejt-ECM kölcsönhatások szerepét a mintázatképzésben. | The research investigated self-organization phenomena in multicellular systems, especially the formation of blood vessel network during embryogenesis. Improvements in automatic microscopy techniques as well as image processing algorithms were also integral part of the research. Based on experimental analysis of delepoing bird embryos we introduced a mechanicl framwork desribing embryonic tissues, where cell autonomous motion is superimposed upon large-scale (convective) tissue movements. We showed that the early vascular network forms through a multicellular sprouting proess, somewhat reminescent to axon growth. Using in vitro cell cultures we showed that the formation of linear segment is a consequence of altered cell behavior in anisotropic environments. Based on these observations, we created a new theoretical model for vasculogenesis. We also mapped the large-scale tissue movements during embryogenesis. In bird embryos tissue movements during gastrulation form a travelling wave-like pattern containing a vortex on either side of the embryo. As a crucial step during tissue formation, we analyzed cell motion-mediated patterning of the extracellular matrix

Modeling the Role of the Cell Cycle in Regulating Proteus mirabilis Swarm-Colony Development

We present models and computational results which indicate that the spatial and temporal regularity seen in Proteus mirabilis swarm-colony development is largely an expression of a sharp age of dedifferentiation in the cell cycle from motile swarmer cells to immotile dividing cells (also called swimmer or vegetative cells.) This contrasts strongly with reaction-diffusion models of Proteus behavior that ignore or average out the age structure of the cell population and instead use only density-dependent mechanisms. We argue the necessity of retaining the explicit age structure, and suggest experiments that may help determine the underlying mechanisms empirically. Consequently, we advocate Proteus as a model organism for a multiscale understanding of how and to what extent the life cycle of individual cells affects the macroscopic behavior of a biological system

Collective motion of organisms in three dimensions

We study a model of flocking in order to describe the transitions during the collective motion of organisms in three dimensions (e.g., birds). In this model the particles representing the organisms are self-propelled, i.e., they move with the same absolute velocity. In addition, the particles locally interact by choosing at each time step the average direction of motion of their neighbors and the effects of fluctuations are taken into account as well. We present the first results for large scale flocking in the presence of noise in three dimensions. We show that depending on the control parameters both disordered and long-range ordered phases can be observed. The corresponding phase diagram has a number of features which are qualitatively different from those typical for the analogous equilibrium models.Comment: 3 pages, 4 figure

Diffusion in a continuum model of self-propelled particles with alignment interaction

In this paper, we provide the $O(\epsilon)$ corrections to the hydrodynamic model derived by Degond and Motsch from a kinetic version of the model by Vicsek & coauthors describing flocking biological agents. The parameter $\epsilon$ stands for the ratio of the microscopic to the macroscopic scales. The $O(\epsilon)$ corrected model involves diffusion terms in both the mass and velocity equations as well as terms which are quadratic functions of the first order derivatives of the density and velocity. The derivation method is based on the standard Chapman-Enskog theory, but is significantly more complex than usual due to both the non-isotropy of the fluid and the lack of momentum conservation

Coupled map gas: structure formation and dynamics of interacting motile elements with internal dynamics

A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing parameter is changed, the model exhibits successive phase changes with novel pattern dynamics, including spatial clustering, fusion and fission of clusters and intermittent diffusion of elements. We explain the manner in which the interplay between internal dynamics and interaction leads to this behavior by employing certain quantities characterizing diffusion, correlation, and the information cascade of synchronization. Keywords: collective motion, coupled map system, interacting motile elementsComment: 27 pages, 12 figures; submitted to Physica