Using molecular dynamics computer simulations we investigate how the relaxation dynamics of a simple supercooled liquid with Newtonian dynamics differs from the one with a stochastic dynamics. We find that, apart from the early b-relaxation regime, the two dynamics give rise to the same relaxation behavior. The increase of the relaxation times of the system upon cooling, the details of the a relaxation, as well as the wave-vector dependence of the Edwards-Anderson parameters, are independent of the microscopic dynamics. [S0031-9007(98)07644-3] PACS numbers: 61.20.Lc, 61.20.Ja, 64.70.Pf If the logarithm of a transport quantity, such as the viscosity, of a good glass former is plotted versus T g ͞T , where T is temperature and T g is the glass transition temperature, it becomes obvious that this temperature dependence is not universal, since some materials show essentially an Arrhenius behavior whereas others show a strong non-Arrhenius behavior [1]. Also more microscopic dynamical properties, such as the Raman spectrum, depend strongly on the material, in that, i.e., the so-called boson peak is much more pronounced in strong glass formers than in fragile glass formers [2]. Thus we can say that it is well established that the macroscopic as well as the microscopic dynamics of supercooled liquids is not universal at all and must be considered as a material specific property. This insight is, of course, not surprising, since the materials differ in their structure, the masses of the individual atoms, etc., and thus it can be expected that these microscopic quantities will give rise to a different relaxational and vibrational dynamics.What is much less obvious, however, is how the microscopic dynamics affects the vibrational and relaxational dynamics of the system, i.e., whether the relaxational dynamics is different if the microscopic dynamics is, e.g., a Newtonian one or a Brownian one. The answer to this question is most important since it will allow us to gain insight to understand which aspects of the relaxation behavior are, for a given system, universal and which ones are not. This information is in turn relevant for testing the applicability of theories that attempt to describe the slowing down of the system upon cooling, i.e., the mechanism for the glass transition.In real experiments it is of course difficult to investigate how the microscopic dynamics affects the dynamics of the system at long times, since usually it is not possible to change the former without also influencing other microscopic quantities like, e.g., the masses of the particles or the interaction between the atoms. Experimentally a Brownian type dynamics can be realized, e.g., by colloidal fluids [3], while atomic liquids have a Newtonian dynamics. However, the structure and interparticle forces in these two types of systems are quite distinct from each other, and thus it is not surprising that the two corresponding dynamics are different. For computer simulations it is, however, most simple to change, for a given system, the dynamics, ...
We present a detailed analysis of the β-relaxation dynamics of a simple glass former, a Lennard-Jones system with a stochastic dynamics. By testing the various predictions of mode-coupling theory, including the recently proposed corrections to the asymptotic scaling laws, we come to the conclusion that in this time regime the dynamics is described very well by this theory.
Summary We consider time‐dependent thermal fluid structure interaction. The respective models are the compressible Navier–Stokes equations and the nonlinear heat equation. A partitioned coupling approach via a Dirichlet–Neumann method and a fixed point iteration is employed. As a reference solver, a previously developed efficient time‐adaptive higher‐order time integration scheme is used. To improve on this, we work on reducing the number of fixed point coupling iterations. Using the idea of extrapolation based on data given from the time integration by deriving such methods for SDIRK2, it is possible to reduce the number of fixed point iterations further by up to a factor of two with linear extrapolation performing better than quadratic. This leads to schemes that can use less than two iterations per time step. Furthermore, widely used vector extrapolation methods for convergence acceleration of the fixed point iteration are tested, namely Aitken relaxation, minimal polynomial extrapolation and reduced rank extrapolation. These have no beneficial effects. Copyright © 2015 John Wiley & Sons, Ltd.
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