Update statistics in conservative parallel discrete event simulations of asynchronous systems

We model the performance of an ideal closed chain of L processing elements that work in parallel in an asynchronous manner. Their state updates follow a generic conservative algorithm. The conservative update rule determines the growth of a virtual time surface. The physics of this growth is reflected in the utilization (the fraction of working processors) and in the interface width. We show that it is possible to nake an explicit connection between the utilization and the macroscopic structure of the virtual time interface. We exploit this connection to derive the theoretical probability distribution of updates in the system within an approximate model. It follows that the theoretical lower bound for the computational speed-up is s=(L+1)/4 for L>3. Our approach uses simple statistics to count distinct surface configuration classes consistent with the model growth rule. It enables one to compute analytically microscopic properties of an interface, which are unavailable by continuum methods.Comment: 15 pages, 12 figure

Glass Transition of Hard Sphere Systems: Molecular Dynamics and Density Functional Theory

The glass transition of a hard sphere system is investigated within the framework of the density functional theory (DFT). Molecular dynamics (MD) simulations are performed to study dynamical behavior of the system on the one hand and to provide the data to produce the density field for the DFT on the other hand. Energy landscape analysis based on the DFT shows that there appears a metastable (local) free energy minimum representing an amorphous state as the density is increased. This state turns out to become stable, compared with the uniform liquid, at some density, around which we also observe sharp slowing down of the $alpha$ relaxation in MD simulations.Comment: 5 pages, 5 figure

Constraint optimization and landscapes

We describe an effective landscape introduced in [1] for the analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring. This geometric construction reexpresses these problems in the more familiar terms of optimization in rugged energy landscapes. In particular, it allows one to understand the puzzling fact that unsophisticated programs are successful well beyond what was considered to be the `hard' transition, and suggests an algorithm defining a new, higher, easy-hard frontier.Comment: Contribution to STATPHYS2

Kinetic Roughening in Deposition with Suppressed Screening

Models of irreversible surface deposition of k-mers on a linear lattice, with screening suppressed by disallowing overhangs blocking large gaps, are studied by extensive Monte Carlo simulations of the temporal and size dependence of the growing interface width. Despite earlier finding that for such models the deposit density tends to increase away from the substrate, our numerical results place them clearly within the standard KPZ universality class.Comment: nine pages, plain TeX (4 figures not included

Absence of First-order Transition and Tri-critical Point in the Dynamic Phase Diagram of a Spatially Extended Bistable System in an Oscillating Field

It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is on the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures

Segregation of granular binary mixtures by a ratchet mechanism

We report on a segregation scheme for granular binary mixtures, where the segregation is performed by a ratchet mechanism realized by a vertically shaken asymmetric sawtooth-shaped base in a quasi-two-dimensional box. We have studied this system by computer simulations and found that most binary mixtures can be segregated using an appropriately chosen ratchet, even when the particles in the two components have the same size, and differ only in their normal restitution coefficient or friction coefficient. These results suggest that the components of otherwise non-segregating granular mixtures may be separated using our method.Comment: revtex, 4 pages, 4 figures, submitte

Interfaces with a single growth inhomogeneity and anchored boundaries

The dynamics of a one dimensional growth model involving attachment and detachment of particles is studied in the presence of a localized growth inhomogeneity along with anchored boundary conditions. At large times, the latter enforce an equilibrium stationary regime which allows for an exact calculation of roughening exponents. The stochastic evolution is related to a spin Hamiltonian whose spectrum gap embodies the dynamic scaling exponent of late stages. For vanishing gaps the interface can exhibit a slow morphological transition followed by a change of scaling regimes which are studied numerically. Instead, a faceting dynamics arises for gapful situations.Comment: REVTeX, 11 pages, 9 Postscript figure

Liquid-Solid Transition of Hard Spheres Under Gravity

We investigate the liquid-solid transition of two dimensional hard spheres in the presence of gravity. We determine the transition temperature and the fraction of particles in the solid regime as a function of temperature via Even-Driven molecular dynamics simulations and compare them with the theoretical predictions. We then examine the configurational statistics of a vibrating bed from the view point of the liquid-solid transition by explicitly determining the transition temperature and the effective temperature, T, of the bed, and present a relation between T and the vibration strength.Comment: 14 total pages, 4 figure

Transitions in the Horizontal Transport of Vertically Vibrated Granular Layers

Motivated by recent advances in the investigation of fluctuation-driven ratchets and flows in excited granular media, we have carried out experimental and simulational studies to explore the horizontal transport of granular particles in a vertically vibrated system whose base has a sawtooth-shaped profile. The resulting material flow exhibits novel collective behavior, both as a function of the number of layers of particles and the driving frequency; in particular, under certain conditions, increasing the layer thickness leads to a reversal of the current, while the onset of transport as a function of frequency occurs gradually in a manner reminiscent of a phase transition. Our experimental findings are interpreted here with the help of extensive, event driven Molecular Dynamics simulations. In addition to reproducing the experimental results, the simulations revealed that the current may be reversed as a function of the driving frequency as well. We also give details about the simulations so that similar numerical studies can be carried out in a more straightforward manner in the future.Comment: 12 pages, 18 figure

Dynamics of an Intruder in Dense Granular Fluids

We investigate the dynamics of an intruder pulled by a constant force in a dense two-dimensional granular fluid by means of event-driven molecular dynamics simulations. In a first step, we show how a propagating momentum front develops and compactifies the system when reflected by the boundaries. To be closer to recent experiments \cite{candelier2010journey,candelier2009creep}, we then add a frictional force acting on each particle, proportional to the particle's velocity. We show how to implement frictional motion in an event-driven simulation. This allows us to carry out extensive numerical simulations aiming at the dependence of the intruder's velocity on packing fraction and pulling force. We identify a linear relation for small and a nonlinear regime for high pulling forces and investigate the dependence of these regimes on granular temperature