121 research outputs found
An infinite-period phase transition versus nucleation in a stochastic model of collective oscillations
A lattice model of three-state stochastic phase-coupled oscillators has been
shown by Wood et al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase
transition at a critical value of the coupling parameter, leading to stable
global oscillations. We show that, in the complete graph version of the model,
upon further increase in the coupling, the average frequency of collective
oscillations decreases until an infinite-period (IP) phase transition occurs,
at which point collective oscillations cease. Above this second critical point,
a macroscopic fraction of the oscillators spend most of the time in one of the
three states, yielding a prototypical nonequilibrium example (without an
equilibrium counterpart) in which discrete rotational (C_3) symmetry is
spontaneously broken, in the absence of any absorbing state. Simulation results
and nucleation arguments strongly suggest that the IP phase transition does not
occur on finite-dimensional lattices with short-range interactions.Comment: 15 pages, 8 figure
Application of the Limit Cycle Model to Star Formation Histories in Spiral Galaxies: Variation among Morphological Types
We propose a limit-cycle scenario of star formation history for any
morphological type of spiral galaxies. It is known observationally that the
early-type spiral sample has a wider range of the present star formation rate
(SFR) than the late-type sample. This tendency is understood in the framework
of the limit-cycle model of the interstellar medium (ISM), in which the SFR
cyclically changes in accordance with the temporal variation of the mass
fraction of the three ISM components. When the limit-cycle model of the ISM is
applied, the amplitude of variation of the SFR is expected to change with the
supernova (SN) rate. Observational evidence indicates that the early-type
spiral galaxies show smaller rates of present SN than late-type ones. Combining
this evidence with the limit-cycle model of the ISM, we predict that the
early-type spiral galaxies show larger amplitudes in their SFR variation than
the late-types. Indeed, this prediction is consistent with the observed wider
range of the SFR in the early-type sample than in the late-type sample. Thus,
in the framework of the limit-cycle model of the ISM, we are able to interpret
the difference in the amplitude of SFR variation among the morphological
classes of spiral galaxies.Comment: 12 pages LaTeX, to appear in A
Vortex dynamics in a three-state model under cyclic dominance
The evolution of domain structure is investigated in a two-dimensional voter
model with three states under cyclic dominance. The study focus on the dynamics
of vortices, defined by the points where three states (domains) meet. We can
distinguish vortices and antivortices which walk randomly and annihilate each
other. The domain wall motion can create vortex-antivortex pairs at a rate
which is increased by the spiral formation due to the cyclic dominance. This
mechanism is contrasted with a branching annihilating random walk (BARW) in a
particle antiparticle system with density dependent pair creation rate.
Numerical estimates for the critical indices of the vortex density
() and of its fluctuation () improve an earlier
Monte Carlo study [Tainaka and Itoh, Europhys. Lett. 15, 399 (1991)] of the
three-state cyclic voter model in two dimensions.Comment: 5 pages, 6 figures, to appear in PR
Phase transition and selection in a four-species cyclic Lotka-Volterra model
We study a four species ecological system with cyclic dominance whose
individuals are distributed on a square lattice. Randomly chosen individuals
migrate to one of the neighboring sites if it is empty or invade this site if
occupied by their prey. The cyclic dominance maintains the coexistence of all
the four species if the concentration of vacant sites is lower than a threshold
value. Above the treshold, a symmetry breaking ordering occurs via growing
domains containing only two neutral species inside. These two neutral species
can protect each other from the external invaders (predators) and extend their
common territory. According to our Monte Carlo simulations the observed phase
transition is equivalent to those found in spreading models with two equivalent
absorbing states although the present model has continuous sets of absorbing
states with different portions of the two neutral species. The selection
mechanism yielding symmetric phases is related to the domain growth process
whith wide boundaries where the four species coexist.Comment: 4 pages, 5 figure
Population Uncertainty in Model Ecosystem: Analysis by Stochastic Differential Equation
Perturbation experiments are carried out by contact process and its
mean-field version. Here, the mortality rate is increased or decreased
suddenly. It is known that the fluctuation enhancement (FE) occurs after the
perturbation, where FE means a population uncertainty. In the present paper, we
develop a new theory of stochastic differential equation. The agreement between
the theory and the mean-field simulation is almost perfect. This theory enables
us to find much stronger FE than reported previously. We discuss the population
uncertainty in the recovering process of endangered species.Comment: 16 pages, 4 figure, submitted to J. Phys. Soc. Jp
Competing associations in six-species predator-prey models
We study a set of six-species ecological models where each species has two
predators and two preys. On a square lattice the time evolution is governed by
iterated invasions between the neighboring predator-prey pairs chosen at random
and by a site exchange with a probability Xs between the neutral pairs. These
models involve the possibility of spontaneous formation of different defensive
alliances whose members protect each other from the external invaders. The
Monte Carlo simulations show a surprisingly rich variety of the stable spatial
distributions of species and subsequent phase transitions when tuning the
control parameter Xs. These very simple models are able to demonstrate that the
competition between these associations influences their composition. Sometimes
the dominant association is developed via a domain growth. In other cases
larger and larger invasion processes preceed the prevalence of one of the
stable asociations. Under some conditions the survival of all the species can
be maintained by the cyclic dominance occuring between these associations.Comment: 8 pages, 9 figure
Serial optical coherence microscopy for label-free volumetric histopathology
The observation of histopathology using optical microscope is an essential procedure for examination of tissue biopsies or surgically excised specimens in biological and clinical laboratories. However, slide-based microscopic pathology is not suitable for visualizing the large-scale tissue and native 3D organ structure due to its sampling limitation and shallow imaging depth. Here, we demonstrate serial optical coherence microscopy (SOCM) technique that offers label-free, high-throughput, and large-volume imaging of ex vivo mouse organs. A 3D histopathology of whole mouse brain and kidney including blood vessel structure is reconstructed by deep tissue optical imaging in serial sectioning techniques. Our results demonstrate that SOCM has unique advantages as it can visualize both native 3D structures and quantitative regional volume without introduction of any contrast agents
Evolutionary prisoner's dilemma games with optional participation
Competition among cooperators, defectors, and loners is studied in an
evolutionary prisoner's dilemma game with optional participation. Loners are
risk averse i.e. unwilling to participate and rather rely on small but fixed
earnings. This results in a rock-scissors-paper type cyclic dominance of the
three strategies. The players are located either on square lattices or random
regular graphs with the same connectivity. Occasionally, every player
reassesses its strategy by sampling the payoffs in its neighborhood. The loner
strategy efficiently prevents successful spreading of selfish, defective
behavior and avoids deadlocks in states of mutual defection. On square
lattices, Monte Carlo simulations reveal self-organizing patterns driven by the
cyclic dominance, whereas on random regular graphs different types of
oscillatory behavior are observed: the temptation to defect determines whether
damped, periodic or increasing oscillations occur. These results are compared
to predictions by pair approximation. Although pair approximation is incapable
of distinguishing the two scenarios because of the equal connectivity, the
average frequencies as well as the oscillations on random regular graphs are
well reproduced.Comment: 6 pages, 7 figure
On the critical behavior of a lattice prey-predator model
The critical properties of a simple prey-predator model are revisited. For
some values of the control parameters, the model exhibits a line of directed
percolation like transitions to a single absorbing state. For other values of
the control parameters one finds a second line of continuous transitions toward
infinite number of absorbing states, and the corresponding steady-state
exponents are mean-field like. The critical behavior of the special point T
(bicritical point), where the two transition lines meet, belongs to a different
universality class. The use of dynamical Monte-Carlo method shows that a
particular strategy for preparing the initial state should be devised to
correctly describe the physics of the system near the second transition line.
Relationships with a forest fire model with immunization are also discussed.Comment: 6 RevTex pages, 7 ps figure
Phase Transitions and Oscillations in a Lattice Prey-Predator Model
A coarse grained description of a two-dimensional prey-predator system is
given in terms of a 3-state lattice model containing two control parameters:
the spreading rates of preys and predators. The properties of the model are
investigated by dynamical mean-field approximations and extensive numerical
simulations. It is shown that the stationary state phase diagram is divided
into two phases: a pure prey phase and a coexistence phase of preys and
predators in which temporal and spatial oscillations can be present. The
different type of phase transitions occuring at the boundary of the prey
absorbing phase, as well as the crossover phenomena occuring between the
oscillatory and non-oscillatory domains of the coexistence phase are studied.
The importance of finite size effects are discussed and scaling relations
between different quantities are established. Finally, physical arguments,
based on the spatial structure of the model, are given to explain the
underlying mechanism leading to oscillations.Comment: 11 pages, 13 figure
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