A model of fasciculation and sorting in mixed populations of axons

We extend a recently proposed model (Chaudhuri et al., EPL 87, 20003 (2009)) aiming to describe the formation of fascicles of axons during neural development. The growing axons are represented as paths of interacting directed random walkers in two spatial dimensions. To mimic turnover of axons, whole paths are removed and new walkers are injected with specified rates. In the simplest version of the model, we use strongly adhesive short-range inter-axon interactions that are identical for all pairs of axons. We generalize the model to adhesive interactions of finite strengths and to multiple types of axons with type-specific interactions. The dynamic steady state is characterized by the position-dependent distribution of fascicle sizes. With distance in the direction of axon growth, the mean fascicle size and emergent time scales grow monotonically, while the degree of sorting of fascicles by axon type has a maximum at a finite distance. To understand the emergence of slow time scales, we develop an analytical framework to analyze the interaction between neighboring fascicles.Comment: 19 pages, 13 figures; version accepted for publication in Phys Rev

Dynamics of path aggregation in the presence of turnover

We investigate the slow time scales that arise from aging of the paths during the process of path aggregation. This is studied using Monte-Carlo simulations of a model aiming to describe the formation of fascicles of axons mediated by contact axon-axon interactions. The growing axons are represented as interacting directed random walks in two spatial dimensions. To mimic axonal turnover, random walkers are injected and whole paths of individual walkers are removed at specified rates. We identify several distinct time scales that emerge from the system dynamics and can exceed the average axonal lifetime by orders of magnitude. In the dynamical steady state, the position-dependent distribution of fascicle sizes obeys a scaling law. We discuss our findings in terms of an analytically tractable, effective model of fascicle dynamics.Comment: 6 pages, 5 figures; changed the order of presentation, rewritten the abstract and introduction, changed the title, expanded discussions; the main results remain the sam

Dynamical Induction of s-wave Component in d-wave Superconductor Driven by Thermal Fluctuations

We investigated the mutual induction effects between the d-wave and the s-wave components of order parameters due to superconducting fluctuation above the critical temperatures and calculated its contributions to paraconductivity and excess Hall conductivity based on the two-component stochastic TDGL equation. It is shown that the coupling of two components increases paraconductivity while it decreases excess Hall conductivity compared to the cases when each component fluctuates independently. We also found the singular behavior in the paraconductivity and the excess Hall conductivity dependence on the coupling parameter which is consistent with the natural restriction among the coefficients of gradient terms.Comment: 10 pages, 4 figures included, submitted to J.Phys.Soc.Jp

Ordering kinetics of stripe patterns

We study domain coarsening of two dimensional stripe patterns by numerically solving the Swift-Hohenberg model of Rayleigh-Benard convection. Near the bifurcation threshold, the evolution of disordered configurations is dominated by grain boundary motion through a background of largely immobile curved stripes. A numerical study of the distribution of local stripe curvatures, of the structure factor of the order parameter, and a finite size scaling analysis of the grain boundary perimeter, suggest that the linear scale of the structure grows as a power law of time with a craracteristic exponent z=3. We interpret theoretically the exponent z=3 from the law of grain boundary motion.Comment: 4 pages, 4 figure

Induction of non-d-wave order-parameter components by currents in d-wave superconductors

It is shown, within the framework of the Ginzburg-Landau theory for a superconductor with d_{x^2-y^2} symmetry, that the passing of a supercurrent through the sample results, in general, in the induction of order-parameter components of distinct symmetry. The induction of s-wave and d_{xy(x^2-y^2)-wave components are considered in detail. It is shown that in both cases the order parameter remains gapless; however, the structure of the lines of nodes and the lobes of the order parameter are modified in distinct ways, and the magnitudes of these modifications differ in their dependence on the (a-b plane) current direction. The magnitude of the induced s-wave component is estimated using the results of the calculations of Ren et al. [Phys. Rev. Lett. 74, 3680 (1995)], which are based on a microscopic approach.Comment: 15 pages, includes 2 figures. To appear in Phys. Rev.

Defect configurations and dynamical behavior in a Gay-Berne nematic emulsion

To model a nematic emulsion consisting of a surfactant-coated water droplet dispersed in a nematic host, we performed a molecular dynamics simulation of a droplet immersed in a system of 2048 Gay-Berne ellipsoids in a nematic phase. Strong radial anchoring at the surface of the droplet induced a Saturn ring defect configuration, consistent with theoretical predictions for very small droplets. A surface ring configuration was observed for lower radial anchoring strengths, and a pair of point defects was found near the poles of the droplet for tangential anchoring. We also simulated the falling ball experiment and measured the drag force anisotropy, in the presence of strong radial anchoring as well as zero anchoring strength.Comment: 17 pages, 15 figure

Field dynamics and kink-antikink production in rapidly expanding systems

Field dynamics in a rapidly expanding system is investigated by transforming from space-time to the rapidity - proper-time frame. The proper-time dependence of different contributions to the total energy is established. For systems characterized by a finite momentum cut-off, a freeze-out time can be defined after which the field propagation in rapidity space ends and the system decays into decoupled solitons, antisolitons and local vacuum fluctuations. Numerical simulations of field evolutions on a lattice for the (1+1)-dimensional $\Phi^4$ model illustrate the general results and show that the freeze-out time and average multiplicities of kinks (plus antikinks) produced in this 'phase transition' can be obtained from simple averages over the initial ensemble of field configurations. An extension to explicitly include additional dissipation is discussed. The validity of an adiabatic approximation for the case of an overdamped system is investigated. The (3+1)-dimensional generalization may serve as model for baryon-antibaryon production after heavy-ion collisions.Comment: 18 pages, 7 figures. Two references added. New subsection III.E added. Final version accepted for publication in PR

Dynamics of orientational ordering in fluid membranes

We study the dynamics of orientational phase ordering in fluid membranes. Through numerical simulation we find an unusually slow coarsening of topological texture, which is limited by subdiffusive propagation of membrane curvature. The growth of the orientational correlation length $\xi$ obeys a power law $\xi \propto t^w$ with $w < 1/4$ in the late stage. We also discuss defect profiles and correlation patterns in terms of long-range interaction mediated by curvature elasticity.Comment: 5 pages, 3 figures (1 in color); Eq.(9) correcte

Spatial organization in cyclic Lotka-Volterra systems

We study the evolution of a system of $N$ interacting species which mimics the dynamics of a cyclic food chain. On a one-dimensional lattice with N<5 species, spatial inhomogeneities develop spontaneously in initially homogeneous systems. The arising spatial patterns form a mosaic of single-species domains with algebraically growing size, $\ell(t)\sim t^\alpha$, where $\alpha=3/4$ (1/2) and 1/3 for N=3 with sequential (parallel) dynamics and N=4, respectively. The domain distribution also exhibits a self-similar spatial structure which is characterized by an additional length scale, ${\cal L}(t)\sim t^\beta$, with $\beta=1$ and 2/3 for N=3 and 4, respectively. For $N\geq 5$, the system quickly reaches a frozen state with non interacting neighboring species. We investigate the time distribution of the number of mutations of a site using scaling arguments as well as an exact solution for N=3. Some possible extensions of the system are analyzed.Comment: 18 pages, 10 figures, revtex, also available from http://arnold.uchicago.edu/~ebn