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Register a new userLattice Model of Sweeping Interface for Drying Process in Water-Granule Mixture
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Based on the invasion percolation model, a lattice model for the sweeping interface dynamics is constructed to describe the pattern forming process by a sweeping interface upon drying the water-granule mixture. The model is shown to produce labyrinthine patterns similar to those found in the experiment[Yamazaki and Mizuguchi, J. Phys. Soc. Jpn. textbf{69} (2000) 2387]. Upon changing the initial granular density, resulting patterns undergo the percolation transition, but estimated critical exponents are different from those of the conventional percolation. Loopless structure of clusters in the patterns produced by the sweeping dynamics seems to influence the nature of the transition.
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Motivated by the drying pattern experiment by Yamazaki and Mizuguchi[J. Phys. Soc. Jpn. {bf 69} (2000) 2387], we propose the dynamics of sweeping interface, in which material distributed over a region is swept by a moving interface. A model based on a phase field is constructed and results of numerical simulations are presented for one and two dimensions. Relevance of the present model to the drying experiment is discussed.
Water modeling is a challenging problem. Its anomalies are difficult to reproduce, promoting the proliferation of a large number of computational models, among which researchers select the most appropriate for the property they study. In this chapter, we introduce a coarse-grained model introduced by Franzese and Stanley (FS) that accounts for the many-body interactions of water. We review mean-field calculations and Monte Carlo simulations on water monolayers for a wide range of pressures and temperatures, including extreme conditions. The results show the presence of two dynamic crossovers and explain the origin of diffusion anomalies. Moreover, the model shows that all the different scenarios, proposed in the last decades as alternative explanations of the experimental anomalies of water, can be related by the fine-tuning of the many-body (cooperative) interaction. Once this parameter is set from the experiments, the FS model predicts a phase transition between two liquids with different densities and energies in the supercooled water region, ending in a liquid-liquid critical point. From this critical point stems a liquid-liquid Widom line, i.e., the locus of maxima of the water correlation length, that in the FS model can be directly calculated. The results are consistent with the extrapolations from experiments. Furthermore, they agree with those from atomistic models but make predictions over a much wider thermodynamic region, allowing for a better interpretation of the available experimental data. All these findings provide a coherent picture of the properties of water and confirm the validity of the FS model that has proved to be useful for large-scale simulations of biological systems.
Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a classical binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Changing one interaction parameter allows to continuously switch from a liquid-liquid transition, terminated by a critical point, to a singularity-free scenario, exhibiting water-like anomalies but without polyamorphism. This resolves a controversy about how a liquid-liquid critical point can be found or not in simulations. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with water-like anomalies.
A general strategy is described for finding which amino acid sequences have native states in a desired conformation (inverse design). The approach is used to design sequences of 48 hydrophobic and polar aminoacids on three-dimensional lattice structures. Previous studies employing a sequence-space Monte-Carlo technique resulted in the successful design of one sequence in ten attempts. The present work also entails the exploration of conformations that compete significantly with the target structure for being its ground state. The design procedure is successful in all the ten cases.
We simulate the motion of spherical particles in a phase-separating binary mixture. By combining cell dynamical equations with Langevin dynamics for particles, we show that the addition of hard particles significantly changes both the speed and the morphology of the phase separation. At the late stage of the spinodal decomposition process, particles significantly slow down the domain growth, in qualitative agreement with earlier experimental data.
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