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We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform populations, on the degree of quenched disorder. Hence, in a relatively simple setting this class of models exhibits the qualitative behaviors characteristic of a variety of considerably more complicated models. In addition, we study the microscopic basis of synchronization above threshold and detail the counterintuitive subtleties relating measurements of time averaged frequencies and mean field oscillations. Most notably, we observe a state of suprathreshold partial synchronization in which time-averaged frequency measurements from individual oscillators do not correspond to the frequency of macroscopic oscillations observed in the population.

We show, through a refinement of the work theorem, that the average dissipation, upon perturbing a Hamiltonian system arbitrarily far out of equilibrium in a transition between two canonical equilibrium states, is exactly given by $ = < W > -\Delta F =kT D(\rho\|\widetilde{\rho})= kT < \ln (\rho/\widetilde{\rho})>$, where $\rho$ and $\widetilde{\rho}$ are the phase space density of the system measured at the same intermediate but otherwise arbitrary point in time, for the forward and backward process. $D(\rho\|\widetilde{\rho})$ is the relative entropy of $\rho$ versus $\widetilde{\rho}$. This result also implies general inequalities, which are significantly more accurate than the second law and include, as a special case, the celebrated Landauer principle on the dissipation involved in irreversible computations., Comment: 4 pages, 3 figures (4 figure files), accepted for PRL

We derive an exact expression for entropy production during effusion of an ideal gas driven by momentum transfer in addition to energy and particle flux. Following the treatment in Phys. Rev. E Vol. 74, 021117 (2006), we construct a master equation formulation of the process and explicitly verify the thermodynamic fluctuation theorem, thereby directly exhibiting its extended applicability to particle flows and hence to hydrodynamic systems.

We study synchronization in populations of phase-coupled stochastic three-state oscillators characterized by a distribution of transition rates. We present results on an exactly solvable dimer as well as a systematic characterization of globally connected arrays of N types of oscillators (N=2, 3, 4) by exploring the linear stability of the nonsynchronous fixed point. We also provide results for globally coupled arrays where the transition rate of each unit is drawn from a uniform distribution of finite width. Even in the presence of transition rate disorder, numerical and analytical results point to a single phase transition to macroscopic synchrony at a critical value of the coupling strength. Numerical simulations make possible the further characterization of the synchronized arrays.

The probability distribution of the entropy production for the effusion of an ideal gas between two compartments is calculated explicitly. The fluctuation theorem is verified. The analytic results are in good agreement with numerical data from hard disk molecular dynamics simulations., Comment: 11 pages, 10 figures, 2 tables

Synchronization of stochastic phase-coupled oscillators is known to occur but difficult to characterize because sufficiently complete analytic work is not yet within our reach, and thorough numerical description usually defies all resources. We present a discrete model that is sufficiently simple to be characterized in meaningful detail. In the mean field limit, the model exhibits a supercritical Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, we explicitly rule out multistability and show that that the onset of global synchrony is marked by signatures of the XY universality class. Our numerical results cover dimensions d=2, 3, 4, and 5 and lead to the appropriate XY classical exponents \beta and \nu, a lower critical dimension d_{lc} = 2, and an upper critical dimension d_{uc}=4.

Onsager symmetry implies that a Brownian motor, driven by a temperature gradient, will also perform a refrigerator function upon loading. We analytically calculate the corresponding heat flux for an exactly solvable microscopic model and compare it with molecular dynamics simulations., Comment: 4 pages, 4 figures

We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a critical value. When coupling between units is strictly local, the model undergoes a continuous phase transition which we characterize numerically using finite-size scaling analysis. In particular, the onset of global synchrony is marked by signatures of the XY universality class, including the appropriate classical exponents $\beta$ and $\nu$, a lower critical dimension $d_{lc} = 2$, and an upper critical dimension $d_{uc}=4$., Comment: 4 pages, 4 figures

We elucidate the connection between various fluctuation theorems by a microcanonical version of the Crooks relation. We derive the microscopically exact expression for the work distribution in an idealized Joule experiment, namely for an object, convex but otherwise of arbitrary shape, moving at constant speed through an ideal gas. Analytic results are compared with molecular dynamics simulations of a hard disk gas., Comment: 5 pages, 3 figures

We illustrate the Jarzynski equality on the exactly solvable model of a one-dimensional ideal gas in uniform expansion or compression. The analytical results for the probability density $P(W)$ of the work $W$ performed by the gas are compared with the results of molecular dynamics simulations for a two-dimensional dilute gas of hard spheres., Comment: 7 pages, 4 figures, submitted to Europhys. Lett

Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a stable process while, in long time, it approximates another stable (possibly Gaussian) process. We also investigate the absolute continuity of a layered stable process with respect to its short time limiting stable process. A series representation of layered stable processes is derived, giving insights into both the structure of the sample paths and of the short and long time behaviors. This series is further used for sample paths simulation., Comment: 22 pages, 9 figures

Fractional tempered stable motion (fTSm)} is defined and studied. FTSm has the same covariance structure as fractional Brownian motion, while having tails heavier than Gaussian but lighter than stable. Moreover, in short time it is close to fractional stable L\'evy motion, while it is approximately fractional Brownian motion in long time. A series representation of fTSm is derived and used for simulation and to study some of its sample path properties., Comment: 25 pages, 6 figures

Stochastic Stokes' drift and hypersensitive transport driven by dichotomous noise are theoretically investigated. Explicit mathematical expressions for the asymptotic probability density and drift velocity are derived including the situation in which particles cross unstable fixed points. The results are confirmed by numerical simulations., Comment: 28 pages, 6 figures, submitted to Fluct. Noise Lett

We study a genuine Brownian motor by hard disk molecular dynamics and calculate analytically its properties, including its drift speed and thermal conductivity, from microscopic theory., Comment: 4 pages, 5 figures

Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In addition using this approach we investigate patially-extended systems with two degrees of freedom per site. For this system, the analytic solution of the stationary Fokker-Planck equation is not available and a standard mean field approach cannot be used to find noise induced phase transitions. A new approach based on cumulant dynamics predicts a noise-induced phase transition through a Hopf bifurcation leading to a macroscopic limit cycle motion, which is confirmed by numerical simulation., Comment: 8 pages, 8 figures

We derive explicit results for the asymptotic probability density and drift velocity in systems driven by dichotomous Markov noise, including the situation in which the asymptotic dynamics crosses {\em unstable} fixed points. The results are illustrated on the problem of the rocking ratchet., Comment: 24 pages, 6 figures, submitted to Physical Review E

Dichotomous noise appears in a wide variety of physical and mathematical models. It has escaped attention that the standard results for the long time properties cannot be applied when unstable fixed points are crossed in the asymptotic regime. We show how calculations have to be modified to deal with these cases and present as a first application full analytic results for hypersensitive transport., Comment: To be published in Phys. Rev. E, Rapid Communications; 3 figures; corrected typos in eq.(14); improved Fig. 3

We revisit the mean field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is a detailed characterization of the motions underlying these instabilities. This presentation includes regimes not identified in earlier work [I. Bena and C. Van den Broeck, Europhys. Lett. {\bf 48}, 498 (1999)]. In addition to the familiar parametric instability of individual oscillators, two kinds of collective instabilities are identified. In one the mean amplitude diverges monotonically while in the other the divergence is oscillatory. The frequencies of collective oscillatory instabilities in general bear no simple relation to the eigenfrequencies of the individual oscillators nor to the frequency of the external modulation. Numerical simulations show that systems with only nearest neighbor coupling have collective instabilities similar to those of the mean field model. Many of the mean field results are already apparent in a simple dimer [M. Copelli and K. Lindenberg, to appear in Phys. Rev. E]., Comment: 17 figures, including color figures. A version of the paper with better quality figures (but much larger files) can be obtained by emailing the posting author

A new method of solution to the local spin density approximation to the electronic Schr\"{o}dinger equation is presented. The method is based on an efficient, parallel, adaptive multigrid eigenvalue solver. It is shown that adaptivity is both necessary and sufficient to accurately solve the eigenvalue problem near the singularities at the atomic centers. While preliminary, these results suggest that direct real space methods may provide a much needed method for efficiently computing the forces in complex materials., Comment: 6 pages, Latex with SIAM proceeding macro, 5 postscript figures included, a full postscript file including figures available at ftp://ftp.phy.uab.edu/pub/publications/kawai/RK-94.04.ps To appear in the proceedings of the 7th SIAM Conference on Parallel Processing for Scientific Computing (San Francisco, 1995)

A conceptual study was conducted to determine the benefit potential of an Intermodal Transport in which quick change payload modules are used to reduce the cost of air travel by increasing daily utilization. Three basic concepts varying the degree of modularity were investigated for a 122,000 pounds payload 3,000 NM range regional wide body transport. The profit potential for operating as a passenger transport during the day and as a freighter at night was assessed. Assuming current levels of profitability, Intermodal operations could offer an operating cost reduction potential up to 20%. Enabling technology needs are identified as very quiet aircraft for expanded night operations, distributed load carrying quick disconnect latching, and configuration dependent safety issues. Recommendations are made to explore if additional benefits are possible from alternative mission and usage modules.