12 research outputs found
Nucleation-induced transition to collective motion in active systems
While the existence of polar ordered states in active systems is well
established, the dynamics of the self-assembly processes are still elusive. We
study a lattice gas model of self-propelled elongated particles interacting
through excluded volume and alignment interactions, which shows a phase
transition from an isotropic to a polar ordered state. By analyzing the
ordering process we find that the transition is driven by the formation of a
critical nucleation cluster and a subsequent coarsening process. Moreover, the
time to establish a polar ordered state shows a power-law divergence
Crossover from Isotropic to Directed Percolation
Percolation clusters are probably the simplest example for scale--invariant
structures which either are governed by isotropic scaling--laws
(``self--similarity'') or --- as in the case of directed percolation --- may
display anisotropic scaling behavior (``self--affinity''). Taking advantage of
the fact that both isotropic and directed bond percolation (with one preferred
direction) may be mapped onto corresponding variants of (Reggeon) field theory,
we discuss the crossover between self--similar and self--affine scaling. This
has been a long--standing and yet unsolved problem because it is accompanied by
different upper critical dimensions: for isotropic, and
for directed percolation, respectively. Using a generalized
subtraction scheme we show that this crossover may nevertheless be treated
consistently within the framework of renormalization group theory. We identify
the corresponding crossover exponent, and calculate effective exponents for
different length scales and the pair correlation function to one--loop order.
Thus we are able to predict at which characteristic anisotropy scale the
crossover should occur. The results are subject to direct tests by both
computer simulations and experiment. We emphasize the broad range of
applicability of the proposed method.Comment: 19 pages, written in RevTeX, 12 figures available upon request (from
[email protected] or [email protected]), EF/UCT--94/2, to be
published in Phys. Rev. E (May 1994
Kinetic Theory of Flux Line Hydrodynamics:LIQUID Phase with Disorder
We study the Langevin dynamics of flux lines of high--T superconductors
in the presence of random quenched pinning. The hydrodynamic theory for the
densities is derived by starting with the microscopic model for the flux-line
liquid. The dynamic functional is expressed as an expansion in the dynamic
order parameter and the corresponding response field. We treat the model within
the Gaussian approximation and calculate the dynamic structure function in the
presence of pinning disorder. The disorder leads to an additive static peak
proportional to the disorder strength. On length scales larger than the line
static transverse wandering length and at long times, we recover the
hydrodynamic results of simple frictional diffusion, with interactions
additively renormalizing the relaxational rate. On shorter length and time
scales line internal degrees of freedom significantly modify the dynamics by
generating wavevector-dependent corrections to the density relaxation rate.Comment: 61 pages and 6 figures available upon request, plain TEX using
Harvard macro
Polar pattern formation: hydrodynamic coupling of driven filaments
How order can emerge spontaneously from a disordered system has always fascinated scientists from numerous disciplines. Especially in active systems like flocks animals, self-propelled microorganisms or the cytoskeleton, a unifying understanding of the pattern formation remains elusive. This is attributed to the inherent complexity of most model systems that prevents a thorough identification of the fundamental mechanisms that are responsible for the intriguing self-organizing phenomena in active systems. Here we show that long ranged hydrodynamic interactions play a crucial role in the pattern forming mechanisms in the high density motility assay, a precisely controllable minimal model system consisting of highly concentrated filaments that are driven on the nanoscale. Stability and size of the patterns depend on long ranged hydrodynamic interactions that are self-induced by the coherently moving filaments. The hydrodynamic interactions not only influence the spatial and temporal scale of the patterns but also affect the dynamics of a particular cluster in close proximity to confining boundaries or other surrounding clusters
Random bursts determine dynamics of active filaments
Constituents of living or synthetic active matter have access to a local energy supply that serves to keep the system out of thermal equilibrium. The statistical properties of such fluctuating active systems differ from those of their equilibrium counterparts. Using the actin filament gliding assay as a model, we studied how nonthermal distributions emerge in active matter. We found that the basic mechanism involves the interplay between local and random injection of energy, acting as an analog of a thermal heat bath, and nonequilibrium energy dissipation processes associated with sudden jump-like changes in the system’s dynamic variables. We show here how such a mechanism leads to a nonthermal distribution of filament curvatures with a non-Gaussian shape. The experimental curvature statistics and filament relaxation dynamics are reproduced quantitatively by stochastic computer simulations and a simple kinetic model
Polar pattern formation in driven filament systems requires non-binary particle collisions
Living matter has the extraordinary ability to behave in a concerted manner, which is exemplified throughout nature ranging from the self-organisation of the cytoskeleton to flocks of animals [1–4]. The microscopic dynamics of constituents have been linked to the system’s meso- or macroscopic behaviour in silico via the Boltzmann equation for propelled particles [5–10]. Thereby, simplified binary collision rules between the constituents had to be assumed due to the lack of experimental data. We report here experimentally determined binary collision statistics by studying the recently introduced molecular system, the high density actomyosin motility assay [11–13]. We demonstrate that the alignment effect of the binary collision statistics is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, which indicates that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. The presented findings demonstrate that the unique properties of biological active matter systems require a description that goes well beyond a gas-like picture developed in the framework of kinetic theories
Cytoskeletal Bundle Mechanics
The mechanical properties of cytoskeletal actin bundles play an essential role in numerous physiological processes, including hearing, fertilization, cell migration, and growth. Cells employ a multitude of actin-binding proteins to actively regulate bundle dimensions and cross-linking properties to suit biological function. The mechanical properties of actin bundles vary by orders of magnitude depending on diameter and length, cross-linking protein type and concentration, and constituent filament properties. Despite their importance to cell function, the molecular design principles responsible for this mechanical behavior remain unknown. Here, we examine the mechanics of cytoskeletal bundles using a molecular-based model that accounts for the discrete nature of constituent actin filaments and their distinct cross-linking proteins. A generic competition between filament stretching and cross-link shearing determines three markedly different regimes of mechanical response that are delineated by the relative values of two simple design parameters, revealing the universal nature of bundle-bending mechanics. In each regime, bundle-bending stiffness displays distinct scaling behavior with respect to bundle dimensions and molecular composition, as observed in reconstituted actin bundles in vitro. This mechanical behavior has direct implications on the physiological bending, buckling, and entropic stretching behavior of cytoskeletal processes, as well as reconstituted actin systems. Results are used to predict the bending regimes of various in vivo cytoskeletal bundles that are not easily accessible to experiment and to generate hypotheses regarding implications of the isolated behavior on in vivo bundle function