arXiv subjects

M. R. Mayr

Publications and source records attributed to M. R. Mayr.

5 recordsLinked to original sources

arXiv2001

The mean-squared displacement of a molecule moving in a glassy system

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the $α$-process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The $α$-process for molecules with a large elongation is shown to exhibit an anomalously wide cross-over interval between the end of the von-Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary non-monotonically as function of its elongation.

cond-mat.soft↗

arXiv1999

The evolution of vibrational excitations in glassy systems

The equations of the mode-coupling theory (MCT) for ideal liquid-glass transitions are used for a discussion of the evolution of the density-fluctuation spectra of glass-forming systems for frequencies within the dynamical window between the band of high-frequency motion and the band of low-frequency-structural-relaxation processes. It is shown that the strong interaction between density fluctuations with microscopic wave length and the arrested glass structure causes an anomalous-oscillation peak, which exhibits the properties of the so-called boson peak. It produces an elastic modulus which governs the hybridization of density fluctuations of mesoscopic wave length with the boson-peak oscillations. This leads to the existence of high-frequency sound with properties as found by X-ray-scattering spectroscopy of glasses and glassy liquids. The results of the theory are demonstrated for a model of the hard-sphere system. It is also derived that certain schematic MCT models, whose spectra for the stiff-glass states can be expressed by elementary formulas, provide reasonable approximations for the solutions of the general MCT equations.

cond-mat.soft↗

arXiv1999

Aspects of the dynamics of colloidal suspensions: Further results of the mode-coupling theory of structural relaxation

Results of the idealized mode-coupling theory for the structural relaxation in suspensions of hard-sphere colloidal particles are presented and discussed with regard to recent light scattering experiments. The structural relaxation becomes non-diffusive for long times, contrary to the expectation based on the de Gennes narrowing concept. A semi-quantitative connection of the wave vector dependences of the relaxation times and amplitudes of the final $α$-relaxation explains the approximate scaling observed by Segr{è} and Pusey [Phys. Rev. Lett. {\bf 77}, 771 (1996)]. Asymptotic expansions lead to a qualitative understanding of density dependences in generalized Stokes-Einstein relations. This relation is also generalized to non-zero frequencies thereby yielding support for a reasoning by Mason and Weitz [Phys. Rev. Lett {\bf 74}, 1250 (1995)]. The dynamics transient to the structural relaxation is discussed with models incorporating short-time diffusion and hydrodynamic interactions for short times.

cond-mat.soft↗

arXiv1998

Structure and structure relaxation

A discrete--dynamics model, which is specified solely in terms of the system's equilibrium structure, is defined for the density correlators of a simple fluid. This model yields results for the evolution of glassy dynamics which are identical with the ones obtained from the mode-coupling theory for ideal liquid--glass transitions. The decay of density fluctuations outside the transient regime is shown to be given by a superposition of Debye processes. The concept of structural relaxation is given a precise meaning. It is proven that the long-time part of the mode-coupling-theory solutions is structural relaxation, while the transient motion merely determines an overall time scale for the glassy dynamics.

cond-mat.dis-nn↗

arXiv1998

Asymptotic laws for tagged-particle motion in glassy systems

Within the mode-coupling theory for structural relaxation in simple systems the asymptotic laws and their leading-asymptotic correction formulas are derived for the motion of a tagged particle near a glass-transition singularity. These analytic results are compared with numerical ones of the equations of motion evaluated for a tagged hard sphere moving in a hard-sphere system. It is found that the long-time part of the two-step relaxation process for the mean-squared displacement can be characterized by the $α$-relaxation-scaling law and von Schweidler's power-law decay while the critical-decay regime is dominated by the corrections to the leading power-law behavior. For parameters of interest for the interpretations of experimental data, the corrections to the leading asymptotic laws for the non-Gaussian parameter are found to be so large that the leading asymptotic results are altered qualitatively by the corrections. Results for the non-Gaussian parameter are shown to follow qualitatively the findings reported in the molecular-dynamics-simulations work by Kob and Andersen [Phys. Rev. E 51, 4626 (1995)].

cond-mat.dis-nn↗