Strongly frustrated random antiferromagnets

A high dimensionality calculation (Weiss like) has been carried out for antiferromagnetism (AFM) in structures with many sublattices. By allowing quenched disorder in the exchange interactions our results clearly exhibit the interplay between the effects of lattice frustration and disorder on the system's properties. For given number of sublattices present, there are several possible phases (ordering of the spins) and as many metastable states in the ergodic phases. It is found that the glassy behavior, and metastability, for multi-sublattices systems is substantially enhanced as compared with simple structures, exhibiting structure dependent de Almeida-Thouless lines. Strongly disordered systems have the long-range AFM ordering, ergodic metastable states and glassy phases intermingled in a non-trivial way. Also, even small fluctuations in the exchange parameters do induce sizeable glassy behavior in structures with many sublattices. Spin glass behavior in apparently non-disordered systems as certain pyrochlores may be accounted for within the present context. Received 9 April 1999 and Received in final form 8 June 1999     

Effective temperature and jamming transition in dense, gently sheared granular assemblies

We present extensive computational results for the effective temperature, defined by the fluctuation-dissipation relation between the mean square displacement and the average displacement of grains, under the action of a weak, external perturbation, of a sheared, bi-disperse granular packing of compressible spheres. We study the dependence of this parameter on the shear rate and volume fractions, the type of particle and the observable in the fluctuation-dissipation relation. We find the same temperature for different tracer particles in the system. The temperature becomes independent on the shear rate for slow enough shear suggesting that it is the effective temperature of the jammed packing. However, we also show that the agreement of the effective temperature for different observables is only approximate, for very long times, suggesting that this defintion may not capture the full thermodynamics of the system. On the other hand, we find good agreement between the dynamical effective temperature and a compactivity calculated assuming that all jammed states are equiprobable. Therefore, this definition of temperature may capture an instance of the ergodic hypothesis for granular materials as proposed by theoretical formalisms for jamming. Finally, our simulations indicate that the average shear stress and apparent shear viscosity follow the usual relation with the shear rate for complex fluids. Our results show that the application of shear induces jamming in packings whose particles interact by tangential forces.     

A phenomenological theory of metastable states in disordered Ising magnets

A mechanism of the formation of an exponentially large number of metastable states in magnetic phases of disordered Ising magnets as a result of condensation of fractal delocalized modes near the localization threshold is suggested. The thermodynamic properties of metastable states are studied in the effective-field approximation in the vicinity of transitions in magnets with zero uniform magnetization in the ground state such as dilute antiferromagnets, spin glasses, and dilute ferromagnets with dipole interaction. These properties are shown to determine the parameters of nonequilibrium processes in the glassy phase, namely, the shape of the hysteresis loop, the thermodynamic values in field-cooled and zero-field-cooled regimes, and the thermoremanent and isothermal remanent magnetization values.     

The effects of grain shape and frustration in a granular column near jamming

We investigate the full phase diagram of a column of grains near jamming, as a function of varying levels of frustration. Frustration is modelled by the effect of two opposing fields on a grain, due respectively to grains above and below it. The resulting four dynamical regimes (ballistic, logarithmic, activated and glassy) are characterised by means of the jamming time of zero-temperature dynamics, and of the statistics of attractors reached by the latter. Shape effects are most pronounced in the cases of strong and weak frustration, and essentially disappear around a mean-field point.     

Studies on magnetic-field-induced first-order transitions

We shall discuss magnetization and transport measurements in materials exhibiting a broad first-order transition. The phase transitions would be caused by varying magnetic field as well as temperature, and we concentrate on ferro- to antiferromagnetic transitions in magnetic materials. We distinguish between metastable supercooled phases and metastable glassy phase.     

About the influence of friction and polydispersity on the jamming behavior of bead assemblies

We study the jamming of bead assemblies placed in a cylindrical container whose bottom is pierced with a circular hole. Their jamming behavior is quantified here by the median jamming diameter, that is the diameter of the hole for which the jamming probability is 0.5. Median jamming diameters of monodisperse assemblies are obtained numerically using the Distinct Element Method and experimentally with steel beads. We obtain good agreement between numerical and experimental results. The influence of friction is then investigated. In particular, the formation of concentric bead rings is observed for low frictions. We identify this phenomenon as a boundary effect and study its influence on jamming. Relying on measures obtained from simulation runs, the median jamming diameter of bidisperse bead assemblies is finally found to depend only on the volume-average diameter of their constituting beads. We formulate this as a tentative law and validate it using bidisperse assemblies of steel beads.     

Preparation and relaxation of very stable glassy states of a simulated liquid

We prepare metastable glassy states in a model glass former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose "fast" vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the "slow" structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.     

Delayed transitions between fluid-like and solid-like granular states

Analysis of granular flows has been a significant theoretical challenge over the past several decades. These flows are difficult to analyze largely because they exhibit both solid-like and fluid-like behaviors side-by-side in single experiments. In this paper, we examine two experiments in which the co-existence between these states is especially marked and leads to unique patterns that may serve as signatures for underlying granular dynamics deserving of further scrutiny. In these experiments, we find that when fluidization of grains is prolonged — as can be expected to occur for example under reduced gravity environments or under conditions of strong kinetic forcing (e.g. during earthquakes) — grains can produce residual depositional patterns that are difficult to distinguish from fluvial deposits. This suggests that geological landforms under low gravity (for example on Mars) or influenced by strong forcing (for example during earthquakes) may behave in a fluid-like manner despite being entirely dry.     

Metastable states in two-lane traffic flow models with slow-to-start rule

Using computer simulations, we show that metastable states still occur in two-lane traffic models with slow to start rules. However, these metastable states no longer exist in systems where aggressive drivers (which do not look back before changing lanes) are present. Indeed, the presence of only one aggressive driver in the circuit, triggers the breakdown of the high flow states. In these systems, the steady state is unique and its relaxation dynamics should depend on the lane changing probability p_ch and the number of aggressive drivers present in the circuit. It is found also that the relaxation time τ diverges as the form of a power-law: τ∝p_ch ^-β, β=1. 89.40.+k     

亚稳相的高压暴露

 很久以前,便有人指出,气态冷凝成固态时,要连续经历液相及各种高温相,才达到平衡结晶相。但是,液态及高温相往往需靠很大的冷却速度才能冻结下来,这在当时对绝大多数合金,是不可能的。近些年,随着超急冷等技术的进步,关于非晶等亚稳相得研究十分活跃。当超过一定临界冷却速度时,液态合金可固化为非晶态。虽然,亚稳结晶相较非晶应更容易冻结,但是,由于产生各种亚稳相所需的过冷条件各不相同,以及对冷却速度的选择不能是任意的,因此有时它们较非晶还难于形成。与液相凝固过程相似,非晶合金的晶化也服从构型最小重排原理,即在晶化完成之前,存在某些亚稳相变态阶段。但是,限于热力学上的不稳定性及动力学因素,在常压下这些亚稳相同样是难以发现的。作者根据对多种合金系的研究,提出高压暴露亚稳相的设想,并利用非晶等亚稳相的高压变态过程,将进行液态急冷时的速度控制方式,改为便于掌握的高压退火方式,来获得新亚稳相。本文对压力暴露亚稳相的原理和实践,加以论述。     

Time dependent local field distribution and metastable states in the SK-spin-glass

Different sets of metastable states can be reached in glassy systems below some transition temperature depending on initial conditions and details of the dynamics. This is investigated for the Sherrington-Kirkpatrick spin glass model with long ranged interactions. In particular, the time dependent local field distribution and energy are calculated for zero temperature. This is done for a system quenched to zero temperature, slow cooling or simulated annealing, a greedy algorithm and repeated tapping. Results are obtained from Monte-Carlo simulations and a Master-Fokker-Planck approach. A comparison with replica symmetry broken theory, evaluated in high orders, shows that the energies obtained via dynamics are higher than the ground state energy of replica theory. Tapping and simulated annealing yield on the other hand results which are very close to the ground state energy. The local field distribution tends to zero for small fields. This is in contrast to the Edwards flat measure hypothesis. The distribution of energies obtained for different tapping strengths does again not follow the canonical form proposed by Edwards.     

The influence of grain shape,friction and cohesion on granular compaction dynamics

This article is a review of our recent and new experimental works on granular compaction. The effects of various microscopic parameters on the compaction dynamics are addressed, in particular the influence of the grain shape, the friction and the cohesion between the grains. Two dimensionnal and three dimensionnal systems are analysed. And the role of dimensionality will be emphasized. Theoretical and numerical investigations provide additional informations about that phenomenon. Indeed numerical models permit us to study the influence of some parameters not easily accessible experimentally. Our results show that the above mentioned parameters have a deep impact on the compaction dynamics. Anisotropic grains lead to two different compaction regimes separated by a “burst" of the packing fraction. Friction is observed to modify how the grains are arranged in the pile. This is confirmed by numerical simulations. Cohesive forces between particles inhibit compaction and lead to extremely low values of the packing fraction.     

Metastable states,the adiabatic theorem and parity violating geometric phases I

A system of metastable plus unstable states is discussed. The mass matrix governing the time development of the system is supposed to vary slowly with time. The adiabatic limit for this case is studied and it is shown that only the metastable states obtain the analogs of the dynamical and geometrical phase factors familiar from stable states. Abelian and non-Abelian geometric phase factors for metastable states are defined.     

Periodic states, local effects and coexistence in the BML traffic jam model

The Biham-Middleton-Levine (BML) model is simple lattice model of traffic flow, self-organization and jamming. Rather than a sharp phase transition between free-flow and jammed, it was recently shown that there is a region where stable intermediate states exist, with details dependent on the aspect ratio of the underlying lattice. Here we investigate square aspect ratios, focusing on the region where random, disordered intermediate (DI) states and conventional global jam (GJ) states coexist, and show that DI states dominate for some densities and timescales. Moreover, we show that periodic intermediate (PI) states can also coexist. PI states converge to periodic limit cycles with short recurrence times and were previously conjectured to arise from idiosyncrasies of relatively prime aspect ratios. The observed coexistence of DI, PI and GJ states shows that global parameters, density together with aspect ratio, are not sufficient to determine the full jamming outcome. We investigate additional features that lead towards jamming and show that a strategic perturbation of a few selected bits can change the nature of the flow, nucleating a global jam.     

Solid state polymorphism of liquid crystals in confined geometries

Solid polymorphism of 4-alkyl-4'-cyanobiphenyl (nCB) was studied so far as a function of thermal history. In this paper we show that metastable solid phases of 4-octyl-4'-cyanobiphenyl (8CB) are also formed when the mesogens are confined in porous silica matrices and we study their structure by neutron diffraction and by Raman spectroscopy. Three metastable solid states are identified: one crystalline phase K', two frozen-in smectic-like phases K(s) and K'(s). We discuss the relation between the structure of the metastable solid phases and that of the mesomorph phases.     

Crystalline thiophene. II: a comprehensive study of stable and metastable phases by means of heat capacity,thermally stimulated currents and raman spectroscopy measurements

This calorimetric study of crystalline thiophene between 77 and 250 K reveals the existence of four phase transitions at 174.50, 170.49, 136.8 and 111.26 K, respectively. The transition II-III (170.49 K) is easily avoided during cooling, leading to metastable phases, which, in turn, exhibit their own phase transitions.These findings explain previously confused observations. The existence of stable and metastable phases was confirmed by thermally stimulated current measurements. Intermolecular Raman spectra were observed between 10 and 300 K and assigned to the observed phases. Some predictions are made concerning the low-temperature behaviour of thiophene. Tentative rules are proposed to number metastable phases relative to stable ones.     

Supercooled superfluids in Monte Carlo simulations

We perform path integral Monte Carlo simulations to study the imaginary time dynamics of metastable supercooled superfluid states and nearly superglassy states of a one component fluid of spinless bosons square wells. Our study shows that the identity of the particles and the exchange symmetry is crucial for the frustration necessary to obtain metastable states in the quantum regime. Whereas the simulation time has to be chosen to determine whether we are in a metastable state or not, the imaginary time dynamics tells us if we are or not close to an arrested glassy state.     

Phase equilibria,metastable states,and critical points in a simple one-component system

Stability of metastable phase states against infinitesimal perturbations in a simple one-component system is considered. The method of molecular dynamics simulation was used to determine the boundaries of essential instability of supersaturated vapor, a superheated liquid, and a superheated crystal. The absence of a spinodal from a supercooled liquid and the dependence of the boundary of essential instability of a superheated crystal on the character of deformation were established. It is shown that each of the three lines of phase equilibria in a one-component system has an endpoint of termination of phase coexistence. As distinct from the liquid–gas critical point, which is the point of phase identity and is located in the region of stable states, the endpoints of melting and sublimation lines are located in the region ofmetastable states. At these points, a critical (spinodal) state is achieved only for one of the coexisting phases.     

Statistical mechanics of two-dimensional Euler flows and minimum enstrophy states

A simplified thermodynamic approach of the incompressible 2D Euler equation is considered based on the conservation of energy, circulation and microscopic enstrophy. Statistical equilibrium states are obtained by maximizing the Miller-Robert-Sommeria (MRS) entropy under these sole constraints. We assume that these constraints are selected by properties of forcing and dissipation. We find that the vorticity fluctuations are Gaussian while the mean flow is characterized by a linear [`(w)]-y\overline{\omega}-\psi relationship. Furthermore, we prove that the maximization of entropy at fixed energy, circulation and microscopic enstrophy is equivalent to the minimization of macroscopic enstrophy at fixed energy and circulation. This provides a justification of the minimum enstrophy principle from statistical mechanics when only the microscopic enstrophy is conserved among the infinite class of Casimir constraints. Relaxation equations towards the statistical equilibrium state are derived. These equations can serve as numerical algorithms to determine maximum entropy or minimum enstrophy states. We use these relaxation equations to study geometry induced phase transitions in rectangular domains. In particular, we illustrate with the relaxation equations the transition between monopoles and dipoles predicted by Chavanis and Sommeria [J. Fluid Mech. 314, 267 (1996)]. We take into account stable as well as metastable states and show that metastable states are robust and have negative specific heats. This is the first evidence of negative specific heats in that context. We also argue that saddle points of entropy can be long-lived and play a role in the dynamics because the system may not spontaneously generate the perturbations that destabilize them.     

Theoretical vs. empirical classification and prediction of congested traffic states

Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss the terminology of traffic phases and give empirical evidence for the existence of a phase diagram of traffic states. In contrast to previously presented phase diagrams, it is shown that “widening synchronized patterns” are possible, if the maximum flow is located inside of a metastable density regime. Moreover, for various kinds of traffic models with different instability diagrams it is discussed, how the related phase diagrams are expected to approximately look like. Apart from this, it is pointed out that combinations of on- and off-ramps create different patterns than a single, isolated on-ramp.