Mesoscale simulation approach

Gompper, G., Ihle, T., Kroll, D.M., and Winkler, R.G. (2009) Multi-partide collision dynamics a partide-based mesoscale simulation approach to the hydrodynamics of complex fluids. Adv. Polym. Sci, 221, 1. 

Multi-Particle Collision Dynamics A Particle-Based Mesoscale Simulation Approach to the Hydrodynamics of Complex Fluids... 

This chapter is organized as follows. In section 1.1, we introduce our notation and present the details of the molecular and mesoscale simulations the expanded ensemble-density of states Monte Carlo method,and the evolution equation for the tensor order parameter [5]. The results of both approaches are presented and compared in section 1.2 for the cases of one or two nanoscopic colloids immersed in a confined liquid crystal. Here the emphasis is on the calculation of the effective interaction (i.e. potential of mean force) for the nanoparticles, and also in assessing the agreement between the defect structures found by the two approaches. In section 1.3 we apply the mesoscopic theory to a model LC-based sensor and analyze the domain coarsening process by monitoring the equal-time correlation function for the tensor order parameter, as a function of the concentration of adsorbed nanocolloids. We present our conclusions in Section 1.4. 

In order to overcome these difficulties, considerable effort has been devoted to the development of mesoscale simulation methods such as Dissipative Particle Dynamics [1-3], Lattice-Boltzmann [4-6], and Direct Simulation Monte Carlo [7-9]. The common approach of all these methods is to average out irrelevant microscopic details in order to achieve high computational efficiency while keeping the essential features of the microscopic physics on the length scales of interest. Applying these ideas to suspensions leads to a simplified, coarse-grained description of the solvent degrees of freedom, in which embedded maaomolecules such as polymers are treated by conventional molecular dynamics simulations. 

Polymers are difficult to model due to the large size of microcrystalline domains and the difficulties of simulating nonequilibrium systems. One approach to handling such systems is the use of mesoscale techniques as described in Chapter 35. This has been a successful approach to predicting the formation and structure of microscopic crystalline and amorphous regions. 

An alternative mesoscale approach for high-level molecular modeling of hydrated ionomer membranes is coarse-grained molecular dynamics (CGMD) simulations. One should notice an important difference between CGMD and DPD techniques. CGMD is essentially a multiscale technique (parameters are directly extracted from classical atomistic MD) and it... 

In this chapter we focus on atomistic predictions of thermophysical and mechanical properties of HMX crystals and liquid important to the development of reliable mesoscale equations of state. The outline of the remainder of the chapter is as follows In section 2 we describe briefly the philosophy and overall approach we have taken to force field development, including the results of quantum chemistry calculations for HMX and smaller model compounds that were used in the force field parameterization. The focus of section 3 is on the properties of liquid HMX, for which experimental data are completely lacking. Structural, thermal, and mechanical properties of the three pure crystal polymorphs of HMX are presented in section 4, where the results are compared to the available experimental data. At the ends of sections 3 and 4 we discuss briefly the importance of the various properties with mesoscale models of high explosives, with an emphasis on conditions relevant to weak shock initiation. We conclude in section 5, and provide our opinions (and justifications, based on our interactions with mesoscale modelers) regarding which HMX properties and phenomena should comprise the next targets for study via atomistic simulation. 

Dzwinel W, Yuen DA (2000b) Matching macroscopic properties of binary fluid to the interactions of dissipative particle dynamics. Int l J Modem Phys C 11 1-25 Dzwinel W, Yuen DA (2000c) A two-level, discrete particle approach for large-scale simulation of colloidal aggregates. Int l J Modem Phys C 11 1037-1061 Dzwinel W, Yuen DA (1999) Dissipative particle dynamics of the thin-film evoluation in mesoscale. Molecular Simul 22 369-395... 

Figure 5 Multiscale approach to understand rate of CO2 diffusion into and CH4 diffusion out of a structure I hydrate, (left) Molecular simulation for individual hopping rates, (middle) Mesoscale kinetic Monte Carlo simulation of hopping on the hydrate lattice to determine dependence of diffusion constants on vacancy, CO2 and CH4 concentrations, (right) Macroscopic coupled non-linear diffusion equations to describe rate of CO2 infusion and methane displacement. Graph from Stockie. ...

The total number of independent variables appearing in Fq. (4.32) is thus quite large, and in fact too large for practical applications. However, as mentioned earlier, by coupling Eq. (4.32) with the Navier-Stokes equation to find the forces on the particles due to the fluid, the Ap-particle system is completely determined. Although not written out explicitly, the reader should keep in mind that the mesoscale models for the phase-space fluxes and the collision term depend on the complete set of independent variables. For example, the surface terms depend on all of the state variables A[p ( x ", ", j/p" j, V ", j/p" ). The only known way to determine these functions is to perform direct numerical simulations of the microscale fluid-particle system using all possible sets of initial conditions. Obviously, such an approach is intractable. We are thus led to reduce the number of independent variables and to introduce mesoscale models that attempt to capture the average effect of multi-particle interactions. 

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