28,539 research outputs found
Diffusion limits for discrete velocity models in a thin gap
We consider discrete kinetic models of a gas moving in a small gap with thickness h. Under an appropriate scaling of the variables, we introduce a formal series expansion to study the limit h --> 0. As a necessary condition for the validity of the expansion we derive a nonlinear diffusion equation
Effects of reduced discrete coupling on filament tension in excitable media
Wave propagation in the heart has a discrete nature, because it is mediated by discrete intercellular connections via gap junctions. Although effects of discreteness on wave propagation have been studied for planar traveling waves and vortexes (spiral waves) in two dimensions, its possible effects on vortexes (scroll waves) in three dimensions are not yet explored. In this article, we study the effect of discrete cell coupling on the filament dynamics in a generic model of an excitable medium. We find that reduced cell coupling decreases the line tension of scroll wave filaments and may induce negative filament tension instability in three-dimensional excitable lattices.Peer Reviewe
Three basic issues concerning interface dynamics in nonequilibrium pattern formation
These are lecture notes of a course given at the 9th International Summer
School on Fundamental Problems in Statistical Mechanics, held in Altenberg,
Germany, in August 1997. In these notes, we discuss at an elementary level
three themes concerning interface dynamics that play a role in pattern forming
systems: (i) We briefly review three examples of systems in which the normal
growth velocity is proportional to the gradient of a bulk field which itself
obeys a Laplace or diffusion type of equation (solidification, viscous fingers
and streamers), and then discuss why the Mullins-Sekerka instability is common
to all such gradient systems. (ii) Secondly, we discuss how underlying an
effective interface description of systems with smooth fronts or transition
zones, is the assumption that the relaxation time of the appropriate order
parameter field(s) in the front region is much smaller than the time scale of
the evolution of interfacial patterns. Using standard arguments we illustrate
that this is generally so for fronts that separate two (meta)stable phases: in
such cases, the relaxation is typically exponential, and the relaxation time in
the usual models goes to zero in the limit in which the front width vanishes.
(iii) We finally summarize recent results that show that so-called ``pulled''
or ``linear marginal stability'' fronts which propagate into unstable states
have a very slow universal power law relaxation. This slow relaxation makes the
usual ``moving boundary'' or ``effective interface'' approximation for problems
with thin fronts, like streamers, impossible.Comment: 48 pages, TeX with elsart style file (included), 9 figure
Nonlinear physics of electrical wave propagation in the heart: a review
The beating of the heart is a synchronized contraction of muscle cells
(myocytes) that are triggered by a periodic sequence of electrical waves (action
potentials) originating in the sino-atrial node and propagating over the atria and
the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF)
or ventricular tachycardia (VT) are caused by disruptions and instabilities of these
electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent
wave patterns (AF,VF). Numerous simulation and experimental studies during the
last 20 years have addressed these topics. In this review we focus on the nonlinear
dynamics of wave propagation in the heart with an emphasis on the theory of pulses,
spirals and scroll waves and their instabilities in excitable media and their application
to cardiac modeling. After an introduction into electrophysiological models for action
potential propagation, the modeling and analysis of spatiotemporal alternans, spiral
and scroll meandering, spiral breakup and scroll wave instabilities like negative line
tension and sproing are reviewed in depth and discussed with emphasis on their impact
in cardiac arrhythmias.Peer ReviewedPreprin
Dynamic Properties of Molecular Motors in Burnt-Bridge Models
Dynamic properties of molecular motors that fuel their motion by actively
interacting with underlying molecular tracks are studied theoretically via
discrete-state stochastic ``burnt-bridge'' models. The transport of the
particles is viewed as an effective diffusion along one-dimensional lattices
with periodically distributed weak links. When an unbiased random walker passes
the weak link it can be destroyed (``burned'') with probability p, providing a
bias in the motion of the molecular motor. A new theoretical approach that
allows one to calculate exactly all dynamic properties of motor proteins, such
as velocity and dispersion, at general conditions is presented. It is found
that dispersion is a decreasing function of the concentration of bridges, while
the dependence of dispersion on the burning probability is more complex. Our
calculations also show a gap in dispersion for very low concentrations of weak
links which indicates a dynamic phase transition between unbiased and biased
diffusion regimes. Theoretical findings are supported by Monte Carlo computer
simulations.Comment: 14 pages. Submitted to J. Stat. Mec
Modeling and Simulation of a Fluttering Cantilever in Channel Flow
Characterizing the dynamics of a cantilever in channel flow is relevant to
applications ranging from snoring to energy harvesting. Aeroelastic flutter
induces large oscillating amplitudes and sharp changes with frequency that
impact the operation of these systems. The fluid-structure mechanisms that
drive flutter can vary as the system parameters change, with the stability
boundary becoming especially sensitive to the channel height and Reynolds
number, especially when either or both are small. In this paper, we develop a
coupled fluid-structure model for viscous, two-dimensional channel flow of
arbitrary shape. Its flutter boundary is then compared to results of
two-dimensional direct numerical simulations to explore the model's validity.
Provided the non-dimensional channel height remains small, the analysis shows
that the model is not only able to replicate DNS results within the parametric
limits that ensure the underlying assumptions are met, but also over a wider
range of Reynolds numbers and fluid-structure mass ratios. Model predictions
also converge toward an inviscid model for the same geometry as Reynolds number
increases
The binding dynamics of tropomyosin on actin
We discuss a theoretical model for the cooperative binding dynamics of
tropomyosin to actin filaments. Tropomyosin binds to actin by occupying seven
consecutive monomers. The model includes a strong attraction between attached
tropomyosin molecules. We start with an empty lattice and show that the binding
goes through several stages. The first stage represents fast initial binding
and leaves many small vacancies between blocks of bound molecules. In the
second stage the vacancies annihilate slowly as tropomyosin molecules detach
and re-attach. Finally the system approaches equilibrium. Using a grain-growth
model and a diffusion-coagulation model we give analytical approximations for
the vacancy density in all regimes.Comment: REVTeX, 10 pages, 9 figures; to appear in Biophysical Journal; minor
correction
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