[Show abstract][Hide abstract] ABSTRACT: We investigate numerically the dynamics of traveling clusters in systems of
phase oscillators, some of which possess positive couplings and others negative
couplings. The phase distribution, speed of traveling, and average separation
between clusters as well as order parameters for positive and negative
oscillators are computed, as the ratio of the two coupling constants and/or the
fraction of positive oscillators are varied. The traveling speed depending on
these parameters is obtained and observed to fit well with the numerical data
of the systems. With the help of this, we describe the conditions for the
traveling state to appear in the systems with or without periodic driving.
[Show abstract][Hide abstract] ABSTRACT: We investigate numerically the dynamic properties of a system of
globally coupled oscillators driven by periodic symmetry-breaking fields
in the presence of noise. The phase distribution of the oscillators is
computed and a dynamic transition is disclosed. It is further found that
the stochastic resonance is closely related to the behavior of the
dynamic order parameter, which is in turn explained by the formation of
a bi-cluster in the system. Here noise tends to symmetrize the motion of
the oscillators, facilitating the bi-cluster formation. The observed
resonance appears to be of the same class as the resonance present in
the two-dimensional Ising model under oscillating fields.
International Journal of Modern Physics B 06/2013; 27(14):50062-. · 0.46 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study, via extensive Monte Carlo calculations, the effects of the range of shortcuts in the dynamic model of neural networks. With the increase of the range of shortcuts, the Mattis-state order parameter grows and the ordered-state region expands in the phase diagram, encroaching upon the mixed-phase region in the phase diagram. In particular, the power spectra of the order parameter at stationarity are observed to exhibit different shapes, depending on the range of shortcuts in the network. The cluster size distribution of the memory-unmatched sites, as well as the distribution of waiting times for neuron firing, possesses strong correlations with the power spectra in their shapes, all exhibiting the most pronounced power-law behaviors when the range of shortcuts is long.
Journal of Physics A Mathematical and Theoretical 04/2010; 43(20):205001. · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study, via extensive Monte Carlo calculations, the effects of connectivity in the dynamic model of neural networks, to observe that the Mattis-state order parameter increases with the number of coupled neurons. Such effects appear more pronounced when the average number of connections is increased by introducing shortcuts in the network. In particular, the power spectra of the order parameter at stationarity are found to exhibit power-law behavior, depending on how the average number of connections is increased. The cluster size distribution of the 'memory-unmatched' sites also follows a power law and possesses strong correlations with the power spectra. It is further observed that the distribution of waiting times for neuron firing fits roughly to a power law, again depending on how neuronal connections are increased.
Journal of Physics A Mathematical and Theoretical 04/2009; 42(20):205003. · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Despite the ubiquitous emergence of skew distributions such as power law, log-normal, and Weibull distributions, there still lacks proper understanding of the mechanism as well as relations between them. It is studied how such distributions emerge in general evolving systems and what makes the difference between them. Beginning with a master equation for general evolving systems, we obtain the time evolution equation for the size distribution function. Obtained in the case of size changes proportional to the current size are the power law stationary distribution with an arbitrary exponent and the evolving distribution, which is of either log-normal or Weibull type asymptotically, depending on production and growth in the system. This master equation approach thus gives a unified description of those three types of skew distribution observed in a variety of systems, providing physical derivation of them and disclosing how they are related.
[Show abstract][Hide abstract] ABSTRACT: We study the phase transitions and dynamic behavior of the dynamic model of neural networks, with an emphasis on the effects of neuronal loss due to external stress. In the absence of loss the overall results obtained numerically are found to agree excellently with the theoretical ones. When the external stress is turned on, some neurons may deteriorate and die; such loss of neurons, in general, weakens the memory in the system. As the loss increases beyond a critical value, the order parameter measuring the strength of memory decreases to zero either continuously or discontinuously, namely, the system loses its memory via a second- or a first-order transition, depending on the ratio of the refractory period to the duration of action potential.
Journal of Physics A Mathematical and Theoretical 08/2008; 41(38):385102. · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: To probe the interplay of different mechanisms for criticality, we study the dynamic failure model, each element of which is allowed to break or to be healed with given conditional probabilities. Under an external load the system evolves to the stationary state, which may exhibit breakages of various sizes. In addition, as the healing parameter is varied, the system undergoes a discontinuous transition between the functioning state and the failed one. In the regimes with appropriate amounts of healing and fluctuations of the surviving fraction, scale invariance in spatial and temporal correlations is observed, manifested by the power spectrum of the breakage rate of elements and by the cluster size distribution of broken elements.
Journal of Physics A Mathematical and Theoretical 03/2008; 41(14):145101. · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study internal and external noise effects on the healthy–unhealthy transition and related phenomena in a dynamic failure model for living organisms. It is found that internal noise makes the system weaker, leading to breakdown under smaller stress. The discontinuous healthy–unhealthy transition in a system with global load sharing below a critical point is naturally explained in terms of the bistability for the health status. External noise present in constant stress gives similar results; further, it induces resonance in response to periodic stress, regardless of load transfer. In the case of local load sharing, such periodic stress is revealed more hazardous than the constant stress.
Journal of Physics A Mathematical and Theoretical 03/2007; 40(13):3319. · 1.77 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We perform extensive numerical simulations on a system of globally coupled rotors with repulsive interactions. By controlling systematically initial conditions, we determine the criterion for the emergence of bicluster motion. It is found that stable bicluster motion emerges at low temperatures, where the initial kinetic energy accounts for less than about 60% of the total energy. Also observed are collective oscillations of the potential energy and the magnetization, which are persistent. With appropriately chosen initial conditions, the system exhibits characteristic motion where biclusters keep forming and disappearing continually. It is argued that such bicluster motion is closely related to the dynamical order suggested recently.
[Show abstract][Hide abstract] ABSTRACT: We apply the dynamic model for failures to a living organism under periodic stress and study how the health status of the organism evolves. It is found that without healing, the average fraction of intact cells decays either stepwise to zero or to a constant value far from zero, depending on the peak value of the periodic stress. As the parameter measuring the healing probability is raised from zero, the fraction exhibits oscillating behavior, reminiscent of periodic synchronization. The power spectrum at the stress frequency at first increases with the healing parameter, then decreases, which may be called healing resonance. We also study the time evolution of the system in the case that the healing parameter varies periodically with time and observe a transition from the unhealthy state to the healthy one as the healing frequency increases. This suggests how to adjust the frequency of medical treatment to the optimum.
[Show abstract][Hide abstract] ABSTRACT: We study motion of domain wall defects in a fully frustrated Josephson-unction ladder system, driven by small applied currents. For small system sizes, the energy barrier E_B to the defect motion is computed analytically via symmetry and topological considerations. More generally, we perform numerical simulations directly on the equations of motion, based on the resistively-shunted junction model, to study the dynamics of defects, varying the system size. Coherent motion of domain walls is observed for large system sizes. In the thermodynamical limit, we find E_B=0.1827 in units of the Josephson coupling energy. Comment: 7 pages, and to apear in Phys. Rev. B
[Show abstract][Hide abstract] ABSTRACT: A dynamic model for failures in biological organisms is proposed and studied both analytically and numerically. Each cell in the organism becomes dead under sufficiently strong stress, and is then allowed to be healed with some probability. It is found that unlike the case of no healing, the organism in general does not completely break down even in the presence of noise. Revealed is the characteristic time evolution that the system tends to resist the stress longer than the system without healing, followed by sudden breakdown with some fraction of cells surviving. When the noise is weak, the critical stress beyond which the system breaks down increases rapidly as the healing parameter is raised from zero, indicative of the importance of healing in biological systems. Comment: To appear in Europhys. Lett
[Show abstract][Hide abstract] ABSTRACT: A system of globally coupled rotors is studied in a unified framework of microcanonical and canonical ensembles. We consider the Fokker-Planck equation governing the time evolution of the system, and examine various stationary as well as non-stationary solutions. The canonical distribution, describing equilibrium, provides a stationary solution also in the microcanonical ensemble, which leads to order in a system with ferromagnetic coupling at low temperatures. On the other hand, the microcanonical ensemble admits additional stationary and non-stationary solutions; the latter allows dynamical order, characterized by multiple degrees of clustering, for both ferromagnetic and antiferromagnetic interactions. We present a detailed stability analysis of these solutions: In a ferromagnetic system, the canonical distribution is observed stable down to a certain temperature, which tends to get lower as the number of Fourier components of the perturbed distribution is increased in the analysis. The non-stationary solution remains neutrally stable below the critical temperature, indicating inequivalence between the two ensembles. For antiferromagnetic systems, all solutions are found to be neutrally stable at all temperatures, suggesting that dynamical ordering is relatively easy to observe at low temperatures compared with ferromagnetic systems. Comment: To appear in J. Phys. A
[Show abstract][Hide abstract] ABSTRACT: We study numerically the motion of vortices in two-dimensional arrays of resistively shunted Josephson junctions. An extra vortex is created in the ground states by introducing novel boundary conditions and made mobile by applying external currents. We then measure critical currents and the corresponding pinning energy barriers to vortex motion, which in the unfrustrated case agree well with previous theoretical and experimental findings. In the fully frustrated case our results also give good agreement with experimental ones, in sharp contrast with the existing theoretical prediction. A physical explanation is provided in relation with the vortex motion observed in simulations. Comment: To appear in Physical Review B
[Show abstract][Hide abstract] ABSTRACT: We consider a two-dimensional fully frustrated Josephson-junction array driven by combined direct and alternating currents. Interplay between the mode locking phenomenon, manifested by giant Shapiro steps in the current-voltage characteristics, and the dynamic phase transition is investigated at finite temperatures. Melting of Shapiro steps due to thermal fluctuations is shown to be accompanied by the dynamic phase transition, the universality class of which is also discussed.
[Show abstract][Hide abstract] ABSTRACT: A realistic continuous-time dynamics for fiber bundles is introduced and studied both analytically and numerically. The equation of motion reproduces known stationary-state results in the deterministic limit while the system under non-vanishing stress always breaks down in the presence of noise. Revealed in particular is the characteristic time evolution that the system tends to resist the stress for considerable time, followed by sudden complete rupture. The critical stress beyond which the complete rupture emerges is also obtained.
[Show abstract][Hide abstract] ABSTRACT: We consider a system of globally coupled rotors, described by a set of Langevin equations, and examine the stability of the incoherent phase. The corresponding Fokker-Planck equation, providing a unified description of microcanonical and canonical ensembles, bears a few solutions, depending upon the ensemble. It is found that the stability of each solution varies differently with the temperature, revealing the inequivalence between the two ensembles. This also suggests a physical explanation of the quasistationarity observed in recent numerical results.
[Show abstract][Hide abstract] ABSTRACT: We consider the conductivity quantization in two-dimensional arrays of mesoscopic Josephson junctions, and examine the associated degeneracy in various regimes of the system. The filling factor of the system may be controlled by the gate voltage as well as the magnetic field, and its appropriate values for quantization is obtained by employing the Jain hierarchy scheme both in the charge description and in the vortex description. The duality between the two descriptions then suggests the possibility that the system undergoes a change in degeneracy while the quantized conductivity remains fixed. Comment: To appear in Phys. Rev. B