137 research outputs found
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
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 obeys a
power law with 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 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, , where
(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, , with and 2/3 for N=3 and 4, respectively. For
, 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
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