Papers by Keyword: Mean-Field Theory

Abstract: In the present work it is revealed by modified Potts model simulations and theoretical considerations that self-similarity is a feature of junction controlled grain growth as it can be found in nanocrystalline materials. To this aim the influence of the grain junctions – boundary faces, triple lines and quadruple points – on grain growth is analyzed by attributing each type of junction an own specific energy and mobility yielding nine types of growth kinetics, each characterized by a self-similar scaling form of the growth law and a corresponding self-similar grain size distribution.

Abstract: In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

Abstract: Size effects observed in nanocrystalline grain growth are modeled by attributing each type of grain boundary junction an own specific energy and finite mobility. By considering grain growth as a dissipative process that is driven by the reduction of the Gibbs free interface and junction energy a general grain evolution equation is derived that separates into nine types of possible growth kinetics. The corresponding self-similar grain size distributions are derived and compared with results from modified Monte Carlo Potts model simulations taking into account size effects in triple and quadruple junction limited grain growth.

Abstract: The standard Monte Carlo (MC) Potts model is modified regarding the mobility of grain boundaries and their junctions allowing the simulation of a size effect observed in nanocrystalline grain growth. In large simulation studies different properties are measured. For initially very small grains the early growth regime corresponds to a separate coarsening state, which is characterised by an average growth law and a self-similar grain size distribution that both show strong deviations from the parabolic normal grain growth behaviour. The simulation results can be described by a theoretical model based on a statistical mean-field theory for nanocrystalline grain growth.

Abstract: We studied the plastic behavior of lotus-type porous iron with unidirectional long cylindrical pores. Lotus-type porous iron with different porosities was fabricated by the continuous zone melting method in a pressurized hydrogen and helium atmosphere. To calculate the stress-strain curves for lotus iron, we applied a modified Qiu-Weng’s micromechanical mean-field theory that has recently been proposed by the present authors [J. Mater. Res., in press], and compared the results with those of compression tests. We experimentally found that the deformation resistance and work hardening rate depend on the sample porosity and loading direction. They decrease with an increase in porosity, and their values in the loading along the direction perpendicular to the longitudinal axis of pores are smaller than those in the parallel-direction loading. Our micromechanical calculations reproduce well the stress-strain curves experimentally obtained and express the experimental trends successfully.