65 research outputs found
Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems
Reaction-diffusion systems can describe a wide class of rhythmic
spatiotemporal patterns observed in chemical and biological systems, such as
circulating pulses on a ring, oscillating spots, target waves, and rotating
spirals. These rhythmic dynamics can be considered limit cycles of
reaction-diffusion systems. However, the conventional phase-reduction theory,
which provides a simple unified framework for analyzing synchronization
properties of limit-cycle oscillators subjected to weak forcing, has mostly
been restricted to low-dimensional dynamical systems. Here, we develop a
phase-reduction theory for stable limit-cycle solutions of infinite-dimensional
reaction-diffusion systems. By generalizing the notion of isochrons to
functional space, the phase sensitivity function - a fundamental quantity for
phase reduction - is derived. For illustration, several rhythmic dynamics of
the FitzHugh-Nagumo model of excitable media are considered. Nontrivial phase
response properties and synchronization dynamics are revealed, reflecting their
complex spatiotemporal organization. Our theory will provide a general basis
for the analysis and control of spatiotemporal rhythms in various
reaction-diffusion systems.Comment: 19 pages, 6 figures, see the journal for a full versio
Coupled Map Modeling for Cloud Dynamics
A coupled map model for cloud dynamics is proposed, which consists of the
successive operations of the physical processes; buoyancy, diffusion,
viscosity, adiabatic expansion, fall of a droplet by gravity, descent flow
dragged by the falling droplet, and advection. Through extensive simulations,
the phases corresponding to stratus, cumulus, stratocumulus and cumulonimbus
are found, with the change of the ground temperature and the moisture of the
air. They are characterized by order parameters such as the cluster number,
perimeter-to-area ratio of a cloud, and Kolmogorov-Sinai entropy.Comment: 9 pages, 4 figure, LaTeX, mpeg simulations available at
http://aurora.elsip.hokudai.ac.jp
Electron acceleration with improved Stochastic Differential Equation method: cutoff shape of electron distribution in test-particle limit
We develop a method of stochastic differential equation to simulate electron
acceleration at astrophysical shocks. Our method is based on It\^{o}'s
stochastic differential equations coupled with a particle splitting, employing
a skew Brownian motion where an asymmetric shock crossing probability is
considered. Using this code, we perform simulations of electron acceleration at
stationary plane parallel shock with various parameter sets, and studied how
the cutoff shape, which is characterized by cutoff shape parameter , changes
with the momentum dependence of the diffusion coefficient . In the
age-limited cases, we reproduce previous results of other authors,
. In the cooling-limited cases, the analytical expectation
is roughly reproduced although we recognize deviations to
some extent. In the case of escape-limited acceleration, numerical result fits
analytical stationary solution well, but deviates from the previous asymptotic
analytical formula .Comment: corrected typos, 10 pages, 4 figures, 2 tables, JHEAp in pres
Slow relaxation to equipartition in spring-chain systems
In this study, one-dimensional systems of masses connected by springs, i.e.,
spring-chain systems, are investigated numerically. The average kinetic energy
of chain-end particles of these systems is larger than that of other particles,
which is similar to the behavior observed for systems made of masses connected
by rigid links. The energetic motion of the end particles is, however,
transient, and the system relaxes to thermal equilibrium after a while, where
the average kinetic energy of each particle is the same, that is, equipartition
of energy is achieved. This is in contrast to the case of systems made of
masses connected by rigid links, where the energetic motion of the end
particles is observed in equilibrium. The timescale of relaxation estimated by
simulation increases rapidly with increasing spring constant. The timescale is
also estimated using the Boltzmann-Jeans theory and is found to be in quite
good agreement with that obtained by the simulation
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