We propose a model of coupled random walks for stock-stock correlations. The walks in the model are coupled via a mechanism that the displacement (price change) of each walk (stock) is activated by the price gradients over some underlying network. We assume that the network has two underlying structures, describing the correlations among the stocks of the whole market and among those within individual groups, respectively, each with a coupling parameter controlling the degree of correlation. The model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences. We verify that such modeling indeed gives good fitting for the market data of US stocks.

The results of molecular-dynamics studies of surface-tension-dominated spinodal decomposition of initially well-mixed binary fluids in the absence and presence of gravity are presented. The growth exponent for the domain size and the decay exponent of the potential energy of interaction between the two species with time are found to be 0.6+0.1, inconsistent with scaling arguments based on dimensional analysis.

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Using molecular dynamics simulation, we find that the velocity distributions of monomers in the system of non-equilibrium polymer chains and Lennard-Jones molecules in a wide range of simulation time can be well described by Tsallis q-statistics and a single scaling function; the value of q is related to the conformation constraining potential, the interactions with background fluid, or the destruction of chain homogeneity. This approach can be applied to other non-equilibrium systems.

The dynamics offreezing of a Lennard-Jones liquid in narrow channels bounded by molecular walls is studied by computer simulation. We quantify the time development of ordering and observe a novel freezing mechanism. The liquid forms layers and subsequent in-plane ordering within a layer is accompanied by a sharpening of the layer in the transverse direction. The effects of channel size, the methods of quench, the liquid-wall interaction and the roughness of walls on the freezing mechanism are elucidated. Comparison with recent experiments on freezing in confined geometries is presented.

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