102 research outputs found
The Dynamics of Silica Melts under High Pressure: Mode-Coupling Theory Results
The high-pressure dynamics of a computer-modeled silica melt is studied in
the framework of the mode-coupling theory of the glass transition (MCT) using
static-structure input from molecular-dynamics (MD) computer simulation. The
theory reproduces the experimentally known viscosity minimum (diffusivity
maximum) as a function of density or pressure and explains it in terms of a
corresponding minimum in its critical temperature. This minimum arises from a
gradual change in the equilibrium static structure which shifts from being
dominated by tetrahedral ordering to showing the cageing known from
high-density liquids. The theory is in qualitative agreement with computer
simulation results.Comment: Presented at ESF EW Glassy Liquids under Pressure, to be published in
Journal of Physic
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
Tagged-particle dynamics in a hard-sphere system: mode-coupling theory analysis
The predictions of the mode-coupling theory of the glass transition (MCT) for
the tagged-particle density-correlation functions and the mean-squared
displacement curves are compared quantitatively and in detail to results from
Newtonian- and Brownian-dynamics simulations of a polydisperse
quasi-hard-sphere system close to the glass transition. After correcting for a
17% error in the dynamical length scale and for a smaller error in the
transition density, good agreement is found over a wide range of wave numbers
and up to five orders of magnitude in time. Deviations are found at the highest
densities studied, and for small wave vectors and the mean-squared
displacement. Possible error sources not related to MCT are discussed in
detail, thereby identifying more clearly the issues arising from the MCT
approximation itself. The range of applicability of MCT for the different types
of short-time dynamics is established through asymptotic analyses of the
relaxation curves, examining the wave-number and density-dependent
characteristic parameters. Approximations made in the description of the
equilibrium static structure are shown to have a remarkable effect on the
predicted numerical value for the glass-transition density. Effects of small
polydispersity are also investigated, and shown to be negligible.Comment: 20 pages, 23 figure
Structural relaxation of polydisperse hard spheres: comparison of the mode-coupling theory to a Langevin dynamics simulation
We analyze the slow, glassy structural relaxation as measured through
collective and tagged-particle density correlation functions obtained from
Brownian dynamics simulations for a polydisperse system of quasi-hard spheres
in the framework of the mode-coupling theory of the glass transition (MCT).
Asymptotic analyses show good agreement for the collective dynamics when
polydispersity effects are taken into account in a multi-component calculation,
but qualitative disagreement at small when the system is treated as
effectively monodisperse. The origin of the different small- behaviour is
attributed to the interplay between interdiffusion processes and structural
relaxation. Numerical solutions of the MCT equations are obtained taking
properly binned partial static structure factors from the simulations as input.
Accounting for a shift in the critical density, the collective density
correlation functions are well described by the theory at all densities
investigated in the simulations, with quantitative agreement best around the
maxima of the static structure factor, and worst around its minima. A
parameter-free comparison of the tagged-particle dynamics however reveals large
quantiative errors for small wave numbers that are connected to the well-known
decoupling of self-diffusion from structural relaxation and to dynamical
heterogeneities. While deviations from MCT behaviour are clearly seen in the
tagged-particle quantities for densities close to and on the liquid side of the
MCT glass transition, no such deviations are seen in the collective dynamics.Comment: 23 pages, 26 figure
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
Diffusion and Interdiffusion in Binary Metallic Melts
We discuss the dependence of self- and interdiffusion coefficients on
temperature and composition for two prototypical binary metallic melts, Al-Ni
and Zr-Ni, in molecular-dynamics (MD) computer simulations and the
mode-coupling theory of the glass transition (MCT). Dynamical processes that
are mainly entropic in origin slow down mass transport (as expressed through
self diffusion) in the mixture as compared to the ideal-mixing contribution.
Interdiffusion of chemical species is a competition of slow kinetic modes with
a strong thermodynamic driving force that is caused by non-entropic
interactions. The combination of both dynamic and thermodynamic effects causes
qualitative differences in the concentration dependence of self-diffusion and
interdiffusion coefficients. At high temperatures, the thermodynamic
enhancement of interdiffusion prevails, while at low temperatures, kinetic
effects dominate the concentration dependence, rationalized within MCT as the
approach to its ideal-glass transition temperature . The Darken equation
relating self- and interdiffusion qualitatively reproduces the
concentration-dependence in both Zr-Ni and Al-Ni, but quantitatively, the
kinetic contributions to interdiffusion can be slower than the lower bound
suggested by the Darken equation. As temperature is decreased, the agreement
with Darken's equation improves, due to a strong coupling of all kinetic modes
that is a generic feature predicted by MCT.Comment: 16 pages, 12 figure
Slow Dynamics in Ion-Conducting Sodium Silicate Melts: Simulation and Mode-Coupling Theory
A combination of molecular-dynamics (MD) computer simulation and
mode-coupling theory (MCT) is used to elucidate the structure-dynamics relation
in sodium-silicate melts (NSx) of varying sodium concentration. Using only the
partial static structure factors from the MD as an input, MCT reproduces the
large separation in relaxation time scales of the sodium and the silicon/oxygen
components. This confirms the idea of sodium diffusion channels which are
reflected by a prepeak in the static structure factors around 0.95 A^-1, and
shows that it is possible to explain the fast sodium-ion dynamics peculiar to
these mixtures using a microscopic theory.Comment: 4 pages, 4 figure
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
Active and Nonlinear Microrheology in Dense Colloidal Suspensions
We present a first-principles theory for the active nonlinear microrheology
of colloidal model systems: for constant external force on a spherical probe
particle embedded in a dense host dispersion, neglecting hydrodynamic
interactions, we derive an exact expression for the friction. Within
mode-coupling theory (MCT), we discuss the threshold external force needed to
delocalize the probe from a host glass, and its relation to strong nonlinear
velocity-force curves in a host fluid. Experimental microrheology data and
simulations, which we performed, are explained with a simplified model
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