1,621 research outputs found
Diffusive Boundary Layers in the Free-Surface Excitable Medium Spiral
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a
great variety of excitable systems. In the limit of a large separation in
timescale between fast excitation and slow recovery, one can reduce the spiral
problem to one involving the motion of a free surface separating the excited
and quiescent phases. In this work, we study the free surface problem in the
limit of small diffusivity for the slow field variable. Specifically, we show
that a previously found spiral solution in the diffusionless limit can be
extended to finite diffusivity, without significant alteration. This extension
involves the creation of a variety of boundary layers which cure all the
undesirable singularities of the aforementioned solution. The implications of
our results for the study of spiral stability are briefly discussed.Comment: 6 pages, submitted to PRE Rapid Com
Mechanisms underlying sequence-independent beta-sheet formation
We investigate the formation of beta-sheet structures in proteins without
taking into account specific sequence-dependent hydrophobic interactions. To
accomplish this, we introduce a model which explicitly incorporates both
solvation effects and the angular dependence (on the protein backbone) of
hydrogen bond formation. The thermodynamics of this model is studied by
comparing the restricted partition functions obtained by "unfreezing"
successively larger segments of the native beta-sheet structure. Our results
suggest that solvation dynamics together with the aforementioned angular
dependence gives rise to a generic cooperativity in this class of systems; this
result explains why pathological aggregates involving beta-sheet cores can form
from many different proteins. Our work provides the foundation for the
construction of phenomenological models to investigate the competition between
native folding and non-specific aggregation.Comment: 20 pages, 5 figures, Revtex4, simulation mpeg movie available at
http://www-physics.ucsd.edu/~guochin/Images/sheet1.mp
The Universal Gaussian in Soliton Tails
We show that in a large class of equations, solitons formed from generic
initial conditions do not have infinitely long exponential tails, but are
truncated by a region of Gaussian decay. This phenomenon makes it possible to
treat solitons as localized, individual objects. For the case of the KdV
equation, we show how the Gaussian decay emerges in the inverse scattering
formalism.Comment: 4 pages, 2 figures, revtex with eps
Adinkras From Ordered Quartets of BC Coxeter Group Elements and Regarding 1,358,954,496 Matrix Elements of the Gadget
We examine values of the Adinkra Holoraumy-induced Gadget representation
space metric over all possible four-color, four-open node, and four-closed node
adinkras. Of the 1,358,954,496 gadget matrix elements, only 226,492,416 are
non-vanishing and take on one of three values: , , or and thus a
subspace isomorphic to a description of a body-centered tetrahedral molecule
emerges.Comment: LaTeX twice, 56pp, 30 tables, 5 figures, latest version includes link
to updated code, minor corrections, and additional support about inequivalent
representations and tetrahedral geometry comments added along with
observations about similarity with results previously found by Nekraso
Solution of an infection model near threshold
We study the Susceptible-Infected-Recovered model of epidemics in the
vicinity of the threshold infectivity. We derive the distribution of total
outbreak size in the limit of large population size . This is accomplished
by mapping the problem to the first passage time of a random walker subject to
a drift that increases linearly with time. We recover the scaling results of
Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales
as , with the average scaling as , with an explicit form for
the scaling function
Nonlinear lattice model of viscoelastic Mode III fracture
We study the effect of general nonlinear force laws in viscoelastic lattice
models of fracture, focusing on the existence and stability of steady-state
Mode III cracks. We show that the hysteretic behavior at small driving is very
sensitive to the smoothness of the force law. At large driving, we find a Hopf
bifurcation to a straight crack whose velocity is periodic in time. The
frequency of the unstable bifurcating mode depends on the smoothness of the
potential, but is very close to an exact period-doubling instability. Slightly
above the onset of the instability, the system settles into a exactly
period-doubled state, presumably connected to the aforementioned bifurcation
structure. We explicitly solve for this new state and map out its
velocity-driving relation
Microscopic Selection of Fluid Fingering Pattern
We study the issue of the selection of viscous fingering patterns in the
limit of small surface tension. Through detailed simulations of anisotropic
fingering, we demonstrate conclusively that no selection independent of the
small-scale cutoff (macroscopic selection) occurs in this system. Rather, the
small-scale cutoff completely controls the pattern, even on short time scales,
in accord with the theory of microscopic solvability. We demonstrate that
ordered patterns are dynamically selected only for not too small surface
tensions. For extremely small surface tensions, the system exhibits chaotic
behavior and no regular pattern is realized.Comment: 6 pages, 5 figure
Analytic approach to the evolutionary effects of genetic exchange
We present an approximate analytic study of our previously introduced model
of evolution including the effects of genetic exchange. This model is motivated
by the process of bacterial transformation. We solve for the velocity, the rate
of increase of fitness, as a function of the fixed population size, . We
find the velocity increases with , eventually saturated at an which
depends on the strength of the recombination process. The analytical treatment
is seen to agree well with direct numerical simulations of our model equations
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