Topological jamming and the glass transition in a frustrated system

The relationship between extended structures, glassy dynamics and an underlying critical point is examined in the context of a lattice model of fluctuating lines. Monte Carlo simulations are used to construct an effective, coarse-grained dynamics for the “order parameter” near the critical point. Analysis of the effective dynamics reveals that the critical point is associated with diverging barriers leading to the observed Vogel-Fulcher divergence of the relaxation times. A direct connection is established between the presence of extended structures and the activated dynamics. Received 15 March 2002     

Complex scaling behavior of nonconserved self-organized critical systems

The Olami-Feder-Christensen earthquake model is often considered the prototype dissipative self-organized critical model. It is shown that the size distribution of events in this model results from a complex interplay of several different phenomena, including limited floating-point precision. Parallels between the dynamics of synchronized regions and those of a system with periodic boundary conditions are pointed out, and the asymptotic avalanche size distribution is conjectured to be dominated by avalanches of size 1, with the weight of larger avalanches converging towards zero as the system size increases.     

Quantitative parameter-free prediction of simulated crystal-nucleation times

We present direct comparisons between simulated crystal-nucleation times and theoretical predictions using a model of aluminum, and demonstrate that a quantitative prediction can be made. All relevant thermodynamic properties of the system are known, making the agreement of our simulation data with nucleation theories free of any adjustable parameters. The role of transient nucleation is included in the classical nucleation theory approach, and shown to be necessary to understand the observed nucleation times. The calculations provide an explanation on why nucleation is difficult to observe in simulations at moderate undercoolings. Even when the simulations are significantly larger than the critical nucleus, and when simulation times are sufficiently long, at moderate undercoolings the small concentration of critical nuclei makes the probability of the nucleation low in molecular dynamics simulations.     

Negativity of Quantumness and Non-Markovianity in a Qubit Coupled to a Thermal Ising Spin Bath System

We propose a scheme to characterize the non-Markovian dynamics and quantify the non-Markovianity via the non-classicality measured by the negativity of quantumness. By considering a qubit in contact with a critical Ising spin bath and introducing an ancilla, we show that revivals of negativity of quantumness indicate the non-Markovian dynamics. Furthermore, a normalized measure of non-Markovianity based on the negativity of quantumness is introduced and the influences of bath criticality, bath temperature and bath size on the non-Markovianity are discussed. It is shown that, at the critical point, the decay of non-Markovianity versus the size of spin bath is the fastest and the non-Markovianity is exactly zero only in the thermodynamic limit. Besides, non-trivial behaviours of negativity of quantumness such as sudden change, double sudden changes and keeping constant are found for different relations between parameters of the initial state. Finally, how the non-classicality of the system is affected by a series of bang-bang pulses is also examined.     

Extremal dynamics and the approach to the critical state: experiments on a three dimensional pile of rice

The evolution of the growth of a ricepile is studied in three dimensions. With time, the pile approaches a critical state with a certain slope. Assuming extremal dynamics in the evolution of the pile, the way the critical state is approached is dictated by the scaling properties of the critical state itself. Experimentally, we determine the envelope of the maximal slope, which is a measure for the distance from the critical state, as well as the growth of the average avalanche size with time. These quantities obey power-law scaling, where the experimental exponents are in good agreement with those obtained from an earlier determination of the critical state properties and extremal dynamics. Furthermore, we discuss the influence of the transient state on the avalanche size distribution, which may have applications in the prevention of large avalanches in natural systems.     

MR measurement of critical phase transition dynamics and supercritical fluid dynamics in capillary and porous media flow

Supercritical fluids (SCF) are useful solvents in green chemistry and oil recovery and are of great current interest in the context of carbon sequestration. Magnetic resonance techniques were applied to study near critical and supercritical dynamics for pump driven flow through a capillary and a packed bed porous media. Velocity maps and displacement propagators measure the dynamics of C(2)F(6) at pressures below, at, and above the critical pressure and at temperatures below and above the critical temperature. Displacement propagators were measured at various displacement observation times to quantify the time evolution of dynamics. In capillary flow, the critical phase transition fluid C(2)F(6) showed increased compressibility compared to the near critical gas and supercritical fluid. These flows exhibit large variations in buoyancy arising from large changes in density due to very small changes in temperature.     

Finite Size Effects and Metastability in Zero-Range Condensation

We study zero-range processes which are known to exhibit a condensation transition, where above a critical density a non-zero fraction of all particles accumulates on a single lattice site. This phenomenon has been a subject of recent research interest and is well understood in the thermodynamic limit. The system shows large finite size effects, and we observe a switching between metastable fluid and condensed phases close to the critical point, in contrast to the continuous limiting behaviour of relevant observables. We describe the leading order finite size effects and establish a discontinuity near criticality in a rigorous scaling limit. We also characterise the metastable phases using a current matching argument and an extension of the fluid phase to supercritical densities. This constitutes an interesting example where the thermodynamic limit fails to capture essential parts of the dynamics, which are particularly relevant in applications with moderate system sizes such as traffic flow or granular clustering.     

Dynamics of the formation of two-dimensional ordered structures

The growth of ordered domains in lattice gas models, which occurs after the system is quenched from infinite temperature to a state below the critical temperatureT _c, is studied by Monte Carlo simulation. For a square lattice with repulsion between nearest and next-nearest neighbors, which in equilibrium exhibits fourfold degenerate (2×1) superstructures, the time-dependent energy E(t), domain size L(t), and structure functionS(q, t) are obtained, both for Glauber dynamics (no conservation law) and the case with conserved density (Kawasaki dynamics). At late times the energy excess and halfwidth of the structure factor decrease proportional tot ^–x, whileL(t) t ^x, where the exponent x=1/2 for Glauber dynamics and x1/3 for Kawasaki dynamics. In addition, the structure factor satisfies a scaling lawS(k,t)=t ^2xS(kt^x). The smaller exponent for the conserved density case is traced back to the excess density contained in the walls between ordered domains which must be redistributed during growth. Quenches toT>T _c, T=T_c (where we estimate dynamic critical exponents) andT=0 are also considered. In the latter case, the system becomes frozen in a glasslike domain pattern far from equilibrium when using Kawasaki dynamics. The generalization of our results to other lattices and structures also is briefly discussed.     

Cooperative motions in a finite size model of liquid silica: an anomalous behavior

Finite size effects on dynamical heterogeneity are studied in liquid silica with Molecular Dynamics simulations using the BKS potential model. When the system size decreases relaxation times are found to increase in accordance with previous results in finite-size simulations and confined liquids. It has been suggested that this increase may be related to a modification of the spatially heterogeneous dynamics in confined liquids. In agreement with this hypothesis we observe a decrease of the spatially heterogeneous dynamics when the size decreases. The spatially heterogeneous dynamics is usually characterized by the dynamical aggregation of the most or the least mobile atoms. However we find that the decrease of the dynamical aggregation associated to the least mobile atoms is much more important than the decrease associated to the most mobile atoms when the size decreases. This result associated with a slowing down of the liquid is surprising as it is expected that the dynamical aggregation of the least mobile atoms should increase the slowing down of the liquid dynamics. The decrease of the heterogeneous behaviour is also in contradiction with the increase of the spatially heterogeneous dynamics observed in liquids confined inside nanopores. However, an increase of the non-Gaussian parameter appears both for the confinement inside nanopores and for the finite size simulations. As the non-Gaussian parameter is usually associated with the heterogeneous dynamics, the increase of the non-Gaussian parameter together with a decrease of the spatially heterogeneous dynamics is also surprising.     

A study of void size growth in nonequilibrium stochastic systems of point defects

We study properties of voids growth dynamics in a stochastic system of point defects insolids under nonequilibrium conditions (sustained irradiation). It is shown thatfluctuations of defect production rate (external noise) increase the critical void radiuscomparing to a deterministic system. An automodel regime of void size growth in astochastic system is studied in detail. Considering a homogeneous system, it is found thatexternal noise does not change the universality of the void size distribution function;the mean void size evolves according to classical nucleation theory. The noise increasesthe mean void size and spreads the void size distribution. Studying dynamics of spatiallyextended systems it was shown that vacancies remaining in a matrix phase are able toorganize into vacancy enriched domains due to an instability caused by an elastic latticedeformation. It is shown that dynamics of voids growth is defined by void sinks strengthwith void size growth exponent varying from 1/3 up to 1/2.     

Superheating in metal nanoparticles with non-melting surfaces

We construct microcanonical caloric curves for aluminium nanoparticles with non-melting surface facets and diameters of up to 11 nm using molecular dynamics simulations. We find that fcc aluminium particles can be superheated above the bulk melting temperature, but only for a finite range of particle sizes i.e. diameters between 5–9 nm. We also observe a critical particle size where solid-liquid phase coexistence becomes stable, and a second larger critical size where premelted (100) facets can coexist with solid (111) facets. Ultimately, it is the premelting of the (100) facets that appears to limit the superheating effect in these particles.     

铜晶体中类层错四面体的结构及其演化

运用分子动力学方法,研究了金属铜单晶中不同形状的Frank位错环演化形成的各种类层错四面体稳定构型.对其形成过程的细致分析表明,这些稳定构型都可以用统一的位错分解和位错反应过程来解释.模拟结果表明,在零温下各种Frank位错环存在各自的临界尺寸,小于临界尺寸的Frank位错环不能长成类层错四面体结构.对梯形、六边形等Frank位错环演化过程的模拟表明,在形成稳定类层错四面体的过程中,存在位错生长和回缩的振荡现象.振荡现象是由于位错间的排斥和吸引相互作用不同步或弹性波传播的延迟效应引起的. 关键词： 层错四面体 位错 分子动力学     

Absence of logarithmic scaling in the ageing behaviour of the 4D spherical model

The non-equilibrium dynamics of the kinetic spherical model with a non-conserved order-parameter, quenched to T≤T_c from a fully disordered initial state, is studied at its upper critical dimension d=d^*=4. In the scaling limit where both the waiting time s and the observation time t are large and the ratio y=t/s>1 is fixed, the scaling functions of the two-time autocorrelation and autoresponse functions do not contain any logarithmic correction factors and the typical size of correlated domains scales for large times as L(t)∼t^1/2.     

Transitions to Equilibrium State in Classical φ4 Lattice

Statistical behavior of a classical φ⁴ Hamiltonian lattice is investigated from microscopic dynamics. The largest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system. It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitions to equipartitions, and the scaling behaviors of these lower and upper critical couplings vs. the system size are numerically obtained.     

Transitions to Equilibrium State in Classical φ4 Lattice

Statistical behavior of a classical φ4 Hamiltonian lattice is investigated from microscopic dynamics. Thelargest Lyapunov exponent and entropies are considered for manifesting chaos and equipartition behaviors of the system.It is found, for the first time, that for any large while finite system size there exist two critical couplings for the transitionsto equipartitions, and the scaling behaviors of these lower and upper critical couplings vs. the system size are numericallyobtained.     

Thermodynamics and molecular dynamics investigation of a possible new critical size for surface and inner cohesive energy of Al nanoparticles

In this study, the authors first review the previously developed, thermodynamics-based theory for size dependency of the cohesion energy of free-standing spherically shaped Al nanoparticles. Then, this model is extrapolated to the cubic and truncated octahedron Al nanoparticle shapes. A series of computations for Al nanoparticles with these two new shapes are presented for particles in the range of 1–100 nm. The thermodynamics computational results reveal that there is a second critical size around 1.62 and 1 nm for cubes and truncated octahedrons, respectively. Below this critical size, particles behave as if they consisted only of surface-energy-state atoms. A molecular dynamics simulation is used to verify this second critical size for Al nanoparticles in the range of 1–5 nm. MD simulation for cube and truncated octahedron shapes shows the second critical point to be around 1.63 and 1.14 nm, respectively. According to the modeling and simulation results, this second critical size seems to be a material property characteristic rather than a shape-dependent feature.     

Extensive chaos in the Lorenz-96 model

We explore the high-dimensional chaotic dynamics of the Lorenz-96 model by computing the variation of the fractal dimension with system parameters. The Lorenz-96 model is a continuous in time and discrete in space model first proposed by Lorenz to study fundamental issues regarding the forecasting of spatially extended chaotic systems such as the atmosphere. First, we explore the spatiotemporal chaos limit by increasing the system size while holding the magnitude of the external forcing constant. Second, we explore the strong driving limit by increasing the external forcing while holding the system size fixed. As the system size is increased for small values of the forcing we find dynamical states that alternate between periodic and chaotic dynamics. The windows of chaos are extensive, on average, with relative deviations from extensivity on the order of 20%. For intermediate values of the forcing we find chaotic dynamics for all system sizes past a critical value. The fractal dimension exhibits a maximum deviation from extensivity on the order of 5% for small changes in system size and the deviation from extensivity decreases nonmonotonically with increasing system size. The length scale describing the deviations from extensivity is consistent with the natural chaotic length scale in support of the suggestion that deviations from extensivity are due to the addition of chaotic degrees of freedom as the system size is increased. We find that each wavelength of the deviation from extensive chaos contains on the order of two chaotic degrees of freedom. As the forcing is increased, at constant system size, the dimension density grows monotonically and saturates at a value less than unity. We use this to quantify the decreasing size of chaotic degrees of freedom with increased forcing which we compare with spatial features of the patterns.     

Detailed balance and critical slowing down for classical lattice systems

For classical lattice systems we prove rigorously a relation between the fluctuations and the relaxation times for a dynamics given by a detailed balance semigroup. In particular we give a rigorous proof of the conventional theory of critical slowing down.On leave of absence from Institute of Theoretical Physics and Astrophysics, Gdansk University, Poland.     

Dynamic Crossover in Metallic Glass Nanoparticles

We report the dynamic crossover behavior in metallic glass nanoparticles(MGNs)with the size reduction based on the extensive molecular dynamics(MD)simulations combined with the activation-relaxation technique(ART).The fragile-to-strong transition of dynamics can be achieved by just modulating the characteristic size of MGNs.It can be attributed to the abnormal fast surface dynamics enhanced by the surface curvature.By determining the potential energy surface,we reveal the hierarchy-to-flat transition of potential energy landscape(PEL)in MGNs,and demonstrate the intrinsic flat potential landscape feature of the MGN with size smaller than a critical size.Our results provide an important piece of the puzzle about the size-modulated potential energy landscape and shed some lights on the unique properties of MGs in nanoscale.     

Size distribution control of metal nanoparticles using femtosecond laser pulse train: a molecular dynamics simulation

Microscopic mechanisms and optimization of metal nanoparticle size distribution control using femtosecond laser pulse trains are studied by molecular dynamics simulations combined with the two-temperature model. Various pulse train designs, including subpulse numbers, separations, and energy distributions are compared, which demonstrate that the minimal mean nanoparticle sizes are achieved at the maximal subpulse numbers with uniform energy distributions. Femtosecond laser pulse trains significantly alter the film thermodynamical properties, adjust the film phase change mechanisms, and hence control the nanoparticle size distributions. As subpulse numbers and separations increase, alternation of film thermodynamical properties suppresses phase explosion, favors critical point phase separation, and significantly reduces mean nanoparticle size distributions. Correspondingly, the relative ratio of two phase change mechanisms causes two distinct nanoparticle size control regimes, where phase explosion leads to strong nanoparticle size control, and increasing ratio of critical point phase separation leads to gentle nanoparticles size control.