879 research outputs found
Kink Localization under Asymmetric Double-Well Potential
We study diffuse phase interfaces under asymmetric double-well potential
energies with degenerate minima and demonstrate that the limiting sharp
profile, for small interface energy cost, on a finite space interval is in
general not symmetric and its position depends exclusively on the second
derivatives of the potential energy at the two minima (phases). We discuss an
application of the general result to porous media in the regime of solid-fluid
segregation under an applied pressure and describe the interface between a
fluid-rich and a fluid-poor phase. Asymmetric double-well potential energies
are also relevant in a very different field of physics as that of Brownian
motors. An intriguing analogy between our result and the direction of the dc
soliton current in asymmetric substrate driven Brownian motors is pointed out
Moving boundary approximation for curved streamer ionization fronts: Solvability analysis
The minimal density model for negative streamer ionization fronts is
investigated. An earlier moving boundary approximation for this model consisted
of a "kinetic undercooling" type boundary condition in a Laplacian growth
problem of Hele-Shaw type. Here we derive a curvature correction to the moving
boundary approximation that resembles surface tension. The calculation is based
on solvability analysis with unconventional features, namely, there are three
relevant zero modes of the adjoint operator, one of them diverging;
furthermore, the inner/outer matching ahead of the front has to be performed on
a line rather than on an extended region; and the whole calculation can be
performed analytically. The analysis reveals a relation between the fields
ahead and behind a slowly evolving curved front, the curvature and the
generated conductivity. This relation forces us to give up the ideal
conductivity approximation, and we suggest to replace it by a constant
conductivity approximation. This implies that the electric potential in the
streamer interior is no longer constant but solves a Laplace equation; this
leads to a Muskat-type problem.Comment: 22 pages, 6 figure
Finite to infinite steady state solutions, bifurcations of an integro-differential equation
We consider a bistable integral equation which governs the stationary
solutions of a convolution model of solid--solid phase transitions on a circle.
We study the bifurcations of the set of the stationary solutions as the
diffusion coefficient is varied to examine the transition from an infinite
number of steady states to three for the continuum limit of the
semi--discretised system. We show how the symmetry of the problem is
responsible for the generation and stabilisation of equilibria and comment on
the puzzling connection between continuity and stability that exists in this
problem
On a Conjecture of Goriely for the Speed of Fronts of the Reaction--Diffusion Equation
In a recent paper Goriely considers the one--dimensional scalar
reaction--diffusion equation with a polynomial reaction
term and conjectures the existence of a relation between a global
resonance of the hamiltonian system and the asymptotic
speed of propagation of fronts of the reaction diffusion equation. Based on
this conjecture an explicit expression for the speed of the front is given. We
give a counterexample to this conjecture and conclude that additional
restrictions should be placed on the reaction terms for which it may hold.Comment: 9 pages Revtex plus 4 postcript figure
The Speed of Fronts of the Reaction Diffusion Equation
We study the speed of propagation of fronts for the scalar reaction-diffusion
equation \, with . We give a new integral
variational principle for the speed of the fronts joining the state to
. No assumptions are made on the reaction term other than those
needed to guarantee the existence of the front. Therefore our results apply to
the classical case in , to the bistable case and to cases in
which has more than one internal zero in .Comment: 7 pages Revtex, 1 figure not include
Dynamical mechanism of atrial fibrillation: a topological approach
While spiral wave breakup has been implicated in the emergence of atrial
fibrillation, its role in maintaining this complex type of cardiac arrhythmia
is less clear. We used the Karma model of cardiac excitation to investigate the
dynamical mechanisms that sustain atrial fibrillation once it has been
established. The results of our numerical study show that spatiotemporally
chaotic dynamics in this regime can be described as a dynamical equilibrium
between topologically distinct types of transitions that increase or decrease
the number of wavelets, in general agreement with the multiple wavelets
hypothesis. Surprisingly, we found that the process of continuous excitation
waves breaking up into discontinuous pieces plays no role whatsoever in
maintaining spatiotemporal complexity. Instead this complexity is maintained as
a dynamical balance between wave coalescence -- a unique, previously
unidentified, topological process that increases the number of wavelets -- and
wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure
Drift- or Fluctuation-Induced Ordering and Self-Organization in Driven Many-Particle Systems
According to empirical observations, some pattern formation phenomena in
driven many-particle systems are more pronounced in the presence of a certain
noise level. We investigate this phenomenon of fluctuation-driven ordering with
a cellular automaton model of interactive motion in space and find an optimal
noise strength, while order breaks down at high(er) fluctuation levels.
Additionally, we discuss the phenomenon of noise- and drift-induced
self-organization in systems that would show disorder in the absence of
fluctuations. In the future, related studies may have applications to the
control of many-particle systems such as the efficient separation of particles.
The rather general formulation of our model in the spirit of game theory may
allow to shed some light on several different kinds of noise-induced ordering
phenomena observed in physical, chemical, biological, and socio-economic
systems (e.g., attractive and repulsive agglomeration, or segregation).Comment: For related work see http://www.helbing.or
Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns
Domain walls in equilibrium phase transitions propagate in a preferred
direction so as to minimize the free energy of the system. As a result, initial
spatio-temporal patterns ultimately decay toward uniform states. The absence of
a variational principle far from equilibrium allows the coexistence of domain
walls propagating in any direction. As a consequence, *persistent* patterns may
emerge. We study this mechanism of pattern formation using a non-variational
extension of Landau's model for second order phase transitions. PACS numbers:
05.70.Fh, 42.65.Pc, 47.20.Ky, 82.20MjComment: 12 pages LaTeX, 5 postscript figures To appear in Phys. Rev.
Avalanche of Bifurcations and Hysteresis in a Model of Cellular Differentiation
Cellular differentiation in a developping organism is studied via a discrete
bistable reaction-diffusion model. A system of undifferentiated cells is
allowed to receive an inductive signal emenating from its environment.
Depending on the form of the nonlinear reaction kinetics, this signal can
trigger a series of bifurcations in the system. Differentiation starts at the
surface where the signal is received, and cells change type up to a given
distance, or under other conditions, the differentiation process propagates
through the whole domain. When the signal diminishes hysteresis is observed
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