1,168 research outputs found
A normal form for excitable media
We present a normal form for travelling waves in one-dimensional excitable
media in form of a differential delay equation. The normal form is built around
the well-known saddle-node bifurcation generically present in excitable media.
Finite wavelength effects are captured by a delay. The normal form describes
the behaviour of single pulses in a periodic domain and also the richer
behaviour of wave trains. The normal form exhibits a symmetry preserving Hopf
bifurcation which may coalesce with the saddle-node in a Bogdanov-Takens point,
and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We
verify the existence of these bifurcations in numerical simulations. The
parameters of the normal form are determined and its predictions are tested
against numerical simulations of partial differential equation models of
excitable media with good agreement.Comment: 22 pages, accepted for publication in Chao
SciRecSys: A Recommendation System for Scientific Publication by Discovering Keyword Relationships
In this work, we propose a new approach for discovering various relationships
among keywords over the scientific publications based on a Markov Chain model.
It is an important problem since keywords are the basic elements for
representing abstract objects such as documents, user profiles, topics and many
things else. Our model is very effective since it combines four important
factors in scientific publications: content, publicity, impact and randomness.
Particularly, a recommendation system (called SciRecSys) has been presented to
support users to efficiently find out relevant articles
Effect of Leading-edge-flap Deflection on the Wing Loads, Load Distributions, and Flap Hinge Moments of the Douglas X-3 Research Airplane at Transonic Speeds
Flight measurements and calculations of wing loads and load distributions at subsonic, transonic, and supersonic speeds
The effects of intrinsic noise on the behaviour of bistable cell regulatory systems under quasi-steady state conditions
We analyse the effect of intrinsic fluctuations on the properties of bistable
stochastic systems with time scale separation operating under1 quasi-steady
state conditions. We first formulate a stochastic generalisation of the
quasi-steady state approximation based on the semi-classical approximation of
the partial differential equation for the generating function associated with
the Chemical Master Equation. Such approximation proceeds by optimising an
action functional whose associated set of Euler-Lagrange (Hamilton) equations
provide the most likely fluctuation path. We show that, under appropriate
conditions granting time scale separation, the Hamiltonian can be re-scaled so
that the set of Hamilton equations splits up into slow and fast variables,
whereby the quasi-steady state approximation can be applied. We analyse two
particular examples of systems whose mean-field limit has been shown to exhibit
bi-stability: an enzyme-catalysed system of two mutually-inhibitory proteins
and a gene regulatory circuit with self-activation. Our theory establishes that
the number of molecules of the conserved species are order parameters whose
variation regulates bistable behaviour in the associated systems beyond the
predictions of the mean-field theory. This prediction is fully confirmed by
direct numerical simulations using the stochastic simulation algorithm. This
result allows us to propose strategies whereby, by varying the number of
molecules of the three conserved chemical species, cell properties associated
to bistable behaviour (phenotype, cell-cycle status, etc.) can be controlled.Comment: 33 pages, 9 figures, accepted for publication in the Journal of
Chemical Physic
Dynamics of lattice spins as a model of arrhythmia
We consider evolution of initial disturbances in spatially extended systems
with autonomous rhythmic activity, such as the heart. We consider the case when
the activity is stable with respect to very smooth (changing little across the
medium) disturbances and construct lattice models for description of
not-so-smooth disturbances, in particular, topological defects; these models
are modifications of the diffusive XY model. We find that when the activity on
each lattice site is very rigid in maintaining its form, the topological
defects - vortices or spirals - nucleate a transition to a disordered,
turbulent state.Comment: 17 pages, revtex, 3 figure
Limit theorems for weakly subcritical branching processes in random environment
For a branching process in random environment it is assumed that the
offspring distribution of the individuals varies in a random fashion,
independently from one generation to the other. Interestingly there is the
possibility that the process may at the same time be subcritical and,
conditioned on nonextinction, 'supercritical'. This so-called weakly
subcritical case is considered in this paper. We study the asymptotic survival
probability and the size of the population conditioned on non-extinction. Also
a functional limit theorem is proven, which makes the conditional
supercriticality manifest. A main tool is a new type of functional limit
theorems for conditional random walks.Comment: 35 page
Anti-phase synchronization of phase-reduced oscillators using open-loop control
In this letter, we present an elegant method to build and maintain an
anti-phase configuration of two nonlinear oscillators with different natural
frequencies and dynamics described by the sinusoidal phase-reduced model. The
anti-phase synchronization is achieved using a common input that couples the
oscillators and consists of a sequence of square pulses of appropriate
amplitude and duration. This example provides a proof of principle that
open-loop control can be used to create desired synchronization patterns for
nonlinear oscillators, when feedback is expensive or impossible to obtain
Vortex Dynamics in Dissipative Systems
We derive the exact equation of motion for a vortex in two- and three-
dimensional non-relativistic systems governed by the Ginzburg-Landau equation
with complex coefficients. The velocity is given in terms of local gradients of
the magnitude and phase of the complex field and is exact also for arbitrarily
small inter-vortex distances. The results for vortices in a superfluid or a
superconductor are recovered.Comment: revtex, 5 pages, 1 encapsulated postscript figure (included), uses
aps.sty, epsf.te
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