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 ($\beta=0.29(4)$) and of its fluctuation ($\gamma=0.34(6)$) 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