Mesoscopic N-atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. A multiscale method for simulating these systems in the friction dominated regime from the underlying N-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate to coarse-grained variables constitute a stationary process on the time scale of coarse-grained dynamics. The method is demonstrated for lactoferrin, nudaurelia capensis omega virus, and human papillomavirus to assess its accuracy.

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Molecular dynamics systems evolve through the interplay of collective and localized disturbances. As a practical consequence, there is a restriction on the time step imposed by the broad spectrum of time scales involved. To resolve this restriction, multiscale factorization was introduced for molecular dynamics as a method that exploits the separation of time scales by coevolving the coarse-grained and atom-resolved states via Trotter factorization. Developing a stable time-marching scheme for this coevolution, however, is challenging because the coarse-grained dynamical equations depend on the microstate; therefore, these equations cannot be expressed in closed form. The objective of this paper is to develop an implicit time integration scheme for multiscale simulation of large systems over long periods of time and with high accuracy. The scheme uses Padé approximants to account for both the stochastic and deterministic features of the coarse-grained dynamics. The method is demonstrated for a protein either undergoing a conformational change or migrating under the influence of an external force. The method shows promise in accelerating multiscale molecular dynamics without a loss of atomic precision or the need to conjecture the form of coarse-grained governing equations.

A computational method is suggested for the simulation of Liesegang patterns in two dimensions on structureless meshes. The method is based on a model that incorporates dynamical equations for the nucleation and growth of solid particles of different sizes into reaction-diffusion equations. We find the model cannot be numerically solved with Galerkin-based finite element methods and cell-centered finite volume methods. Instead, the vertex-based finite volume method is used to correctly reproduce the Liesegang pattern on structureless meshes. The numerical solution is then compared with specially designed experiments on Liesegang patterns in various geometries, and it is shown to be in good agreement.

We report a reaction-diffusion system in which two initially separated electrolytes, mercuric chloride (outer) and potassium iodide (inner), interact in a solid hydrogel media to produce a propagating front of mercuric iodide precipitate. The precipitation process is accompanied by a polymorphic transformation of the kinetically favored (unstable) orange, (metastable) yellow, and (thermodynamically stable) red polymorphs of HgI2. The sequence of crystal transformation is confirmed to agree with the Ostwald Rule of Stages. However, a region is found of initial inner iodide concentration, where a stationary pattern of alternating metastable/stable crystals is formed. A theoretical model based on reaction diffusion coupled to a special nucleation and growth mechanism is proposed. Its numerical solution is shown to reproduce the experimental results.