Multi-scale methods

Li, J., and Kwauk, M., Particle-Fluid Two-Phase Flow, The Energy-Minimization Multi-Scale Method, Metallurgical Industry Press, Beijing (1994)... 

We have presented a multi-scale method to simulate a fibrillar structure such as a collagen tissue equivalent. The method is able to predict macroscopic behavior based on microscopic properties, and it also demonstrates the microscopic restructuring that can occur during deformation. Although the method is computationally demanding, the potential for parallelization is high, and three-dimensional problems should not be out of reach. 

In this chapter we have presented a multi-scale method for molecular dynamics simulations of shock compression and characterized its behaviour. This method attempts to constrain the molecular dynamics system to the sequence of thermodynamic states that occur in a shock wave. While we have presented one particular approach, it is certainly not unique and there are likely a variety of related approaches to multi-scale simulations that have a variety of differing practical properties. These methods open the door to simulations of shock propagation on the longest timescales accessible by molecular d5nnamics and the use of accurate but computationally costly material descriptions like density fimctional theory. It is our belief that this method promises to be a valuable tool for elucidation of new science in shocked condensed matter. 

Ge W, Chen F, Gao J, et al Analytical multi-scale method for multi-phase complex systems in process engineering—bridging reductionism and holism, Chem Eng Sci 62 3346—3377, 2007. 

Li J, Kwauk M Particle-fluid two-phase fow energy-minimization multi-scale method, Beijing, 1994, Metallurgy Industry Press. 

Villa, E., A. Balaeff, L. Mahadevan, and K. Schulten. 2004. Multi-scale method for simulating protein-DNA complexes. Multiscale Modeling and Simulation 2(4) 527-553. 

In this section the available QM/MM methods designed for solution chemistry are reviewed, and the relevant terms are introduced. As we focus on describing a reactive process in solution at the atomistic level, multi-scale methods resorting to coarse-grainingwillnotbedescribed andwerefer the interested readers to recentreviews [24—26]. Similarly, methods targeting gas phase reactions only are omitted [27,28]. 

Spatial multi-scale methods are based on the paradigm that in many real situations the atomic description is only required within small parts of the simulation domain whereas for the majority the continuum model is still valid. This allows one to apply concurrent continuum and molecular simulations for the respective parts of the simulation domain using a coupling scheme that permits to connect between the two domains. The majority of the spatial domain is calculated by continuum solvers (computational fluid dynamics) which are very fast and only the active part is calculated using molecular simulation methods. In some cases several other coarser-grained (mesoscale) methods than the atomic simulations ones are used as interfaces between the molecular simulation and the continuum domains. Such approaches are called hybrid molecular-continuum methods and allow the simulation of problems that are not accessible either by continuum or by pure molecular simulation methods. 

Another class of spatial multi-scale methods concerns the quantum chemistry community where efforts have been focussed on the combination of quantum mechanics (QM) methods with continuum electrostatic theories in order to realistically represent the solvation free energy in a polar environment. These methods have been refined over the years and can now give a reasonable description of solvation properties of an isotropic and homogeneous medium. However, these continuum models are not appropriate to represent the electrostatic and steric interactions of the structured environment with the active site. This is particularly true in the descriptions of complex systems like enzymes or catalysts. An appropriate description of such systems has been developed using a hybrid quantum mechanical/molecular mechanical (QM/MM) approaches where the QM methods are used to describe the active site where chemical reactions or electronic excitations occur, and MM methods are employed to capture the effect of the environment on the active site. 

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