Sequencing Chess

We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both, the size of the state space and the size of the tree of legal moves, are not unique indicators of the complexity of the game, but that topological considerations are equally important

Intermediate range chemical ordering of cations in simple molten alkali halides

The presence of first sharp diffraction peaks in the partial structure factors is investigated in computer simulations of molten mixtures of alkali halides. An intermediate range ordering appears for the Li+ ions only, which is associated with clustering of this species and is not reflected in the arrangement of other ions. This ordering is surprising in view of the simplicity of the interionic interactions in alkali halides. The clustering reflects an incomplete mixing of the various species on a local length scale, which can be demonstrated by studying the complementary sub-space of cations in the corresponding pure alkali halides by means of a void analysis.Comment: 5 pages, 5 figure

Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory

We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.Comment: 15 pages, 8 figures, to appear in J Phys Condens Matte

Mobile particles in an immobile environment: Molecular Dynamics simulation of a binary Yukawa mixture

Molecular dynamics computer simulations are used to investigate thedynamics of a binary mixture of charged (Yukawa) particles with a size-ratio of 1:5. We find that the system undergoes a phase transition where the large particles crystallize while the small particles remain in a fluid-like (delocalized) phase. Upon decreasing temperature below the transition, the small particles become increasingly localized on intermediate time scales. This is reflected in the incoherent intermediate scattering functions by the appearance of a plateau with a growing height. At long times, the small particles show a diffusive hopping motion. We find that these transport properties are related to structural correlations and the single-particle potential energy distribution of the small particles.Comment: 7 pages, 5 figure

Alpha-Relaxation Processes in Binary Hard-Sphere Mixtures

Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon compressing the liquid into high-density states. Partial-density-fluctuation correlation functions for the two species are reported. Results for the alpha-relaxation process are quantified by parameters for the strength, the stretching, and the time scale, where the latter varies over almost four orders of magnitude upon compression. The parameters exhibit an appreciable dependence on the wave vector; and this dependence is different for the correlation function referring to the smaller and that for the larger species. These features are shown to be in semi-quantitative agreement with those calculated within the mode-coupling theory for ideal liquid-glass transitions.Comment: 14 pages, 20 figures, RevTe

Tests of mode coupling theory in a simple model for two-component miscible polymer blends

We present molecular dynamics simulations on the structural relaxation of a simple bead-spring model for polymer blends. The introduction of a different monomer size induces a large time scale separation for the dynamics of the two components. Simulation results for a large set of observables probing density correlations, Rouse modes, and orientations of bond and chain end-to-end vectors, are analyzed within the framework of the Mode Coupling Theory (MCT). An unusually large value of the exponent parameter is obtained. This feature suggests the possibility of an underlying higher-order MCT scenario for dynamic arrest.Comment: Revised version. Additional figures and citation

Glass Rheology: From mode-coupling theory to a dynamical yield criterion

The mode coupling theory (MCT) of glasses, while offering an incomplete description of glass transition physics, represents the only established route to first-principles prediction of rheological behavior in nonergodic materials such as colloidal glasses. However, the constitutive equations derivable from MCT are somewhat intractable, hindering their practical use and also their interpretation. Here, we present a schematic (single-mode) MCT model which incorporates the tensorial structure of the full theory. Using it, we calculate the dynamic yield surface for a large class of flows

Universal and non-universal features of glassy relaxation in propylene carbonate

It is demonstrated that the susceptibility spectra of supercooled propylene carbonate as measured by depolarized-light-scattering, dielectric-loss, and incoherent quasi-elastic neutron-scattering spectroscopy within the GHz window are simultaneously described by the solutions of a two-component schematic model of the mode-coupling theory (MCT) for the evolution of glassy dynamics. It is shown that the universal beta-relaxation-scaling laws, dealing with the asymptotic behavior of the MCT solutions, describe the qualitative features of the calculated spectra. But the non-universal corrections to the scaling laws render it impossible to achieve a complete quantitative description using only the leading-order-asymptotic results.Comment: 37 pages, 16 figures, to be published in Phys. Rev.

Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene

We have measured depolarized light scattering in liquid benzene over the whole accessible temperature range and over four decades in frequency. Between 40 and 180 GHz we find a susceptibility peak due to structural relaxation. This peak shows stretching and time-temperature scaling as known from $\alpha$ relaxation in glass-forming materials. A simple mode-coupling model provides consistent fits of the entire data set. We conclude that structural relaxation in simple liquids and $\alpha$ relaxation in glass-forming materials are physically the same. A deeper understanding of simple liquids is reached by applying concepts that were originally developed in the context of glass-transition research.Comment: submitted to New J. Phy

Reorientational relaxation of a linear probe molecule in a simple glassy liquid

Within the mode-coupling theory (MCT) for the evolution of structural relaxation in glass-forming liquids, correlation functions and susceptibility spectra are calculated characterizing the rotational dynamics of a top-down symmetric dumbbell molecule, consisting of two fused hard spheres immersed in a hard-sphere system. It is found that for sufficiently large dumbbell elongations, the dynamics of the probe molecule follows the same universal glass-transition scenario as known from the MCT results of simple liquids. The $\alpha$-relaxation process of the angular-index-j=1 response is stronger, slower and less stretched than the one for j=2, in qualitative agreement with results found by dielectric-loss and depolarized-light-scattering spectroscopy for some supercooled liquids. For sufficiently small elongations, the reorientational relaxation occurs via large-angle flips, and the standard scenario for the glass-transition dynamics is modified for odd-j responses due to precursor phenomena of a nearby type-A MCT transition. In this case, a major part of the relaxation outside the transient regime is described qualitatively by the $\beta$-relaxation scaling laws, while the $\alpha$-relaxation scaling law is strongly disturbed.Comment: 40 pages. 10 figures as GIF-files, to be published in Phys. Rev.