Continuous Damage Fiber Bundle Model for Strongly Disordered Materials

We present an extension of the continuous damage fiber bundle model to describe the gradual degradation of highly heterogeneous materials under an increasing external load. Breaking of a fiber in the model is preceded by a sequence of partial failure events occurring at random threshold values. In order to capture the subsequent propagation and arrest of cracks, furthermore, the disorder of the number of degradation steps of material constituents, the failure thresholds of single fibers are sorted into ascending order and their total number is a Poissonian distributed random variable over the fibers. Analytical and numerical calculations showed that the failure process of the system is governed by extreme value statistics, which has a substantial effect on the macroscopic constitutive behaviour and on the microscopic bursting activity as well.Comment: 10 pages, 13 figure

Scaling behavior in the β\beta-relaxation regime of a supercooled Lennard-Jones mixture

We report the results of a molecular dynamics simulation of a supercooled binary Lennard-Jones mixture. By plotting the self intermediate scattering functions vs. rescaled time, we find a master curve in the $\beta$-relaxation regime. This master curve can be fitted well by a power-law for almost three decades in rescaled time and the scaling time, or relaxation time, has a power-law dependence on temperature. Thus the predictions of mode-coupling-theory on the existence of a von Schweidler law are found to hold for this system; moreover, the exponents in these two power-laws are very close to satisfying the exponent relationship predicted by the mode-coupling-theory. At low temperatures, the diffusion constants also show a power-law behavior with the same critical temperature. However, the exponent for diffusion differs from that of the relaxation time, a result that is in disagreement with the theory.Comment: 8 pages, RevTex, four postscript figures available on request, MZ-Physics-10

A diagrammatic formulation of the kinetic theory of fluctuations in equilibrium classical fluids. VI. Binary collision approximations for the memory function for self correlation functions

We use computer simulation results for a dense Lennard-Jones fluid for a range of temperatures to test the accuracy of various binary collision approximations for the memory function for density fluctuations in liquids. The approximations tested include the moderate density approximation of the generalized Boltzmann-Enskog memory function (MGBE) of Mazenko and Yip, the binary collision approximation (BCA) and the short time approximation (STA) of Ranganathan and Andersen, and various other approximations derived by us using diagrammatic methods. The tests are of twotypes. The first is a comparison of the correlation functions predicted by each approximate memory function with the simulation results, especially for the self longitudinal current correlation function (SLCC). The second is a direct comparison of each approximate memory function with a memory function numerically extracted from the correlation function data. The MGBE memory function is accurate at short times but decays to zero too slowly and gives a poor description of the correlation function at intermediate times. The BCA is exact at zero time, but it predicts a correlation function that diverges at long times. The STA gives a reasonable description of the SLCC but does not predict the correct temperature dependence of the negative dip in the function that is associated with caging at low temperatures. None of the other binary collision approximations is a systematic improvement upon the STA. The extracted memory functions have a rapidly decaying short time part, much like the STA, and a much smaller, more slowly decaying part of the type predicted by mode coupling theory. Theories that use mode coupling commonly include a binary collision term in the memory function but do not discuss in detail the nature of that term. ...Comment: 18 pages, 10 figure