Particle-Based Simulation

Since the middle of the 1990s, another computation method, direct simulation Monte Carlo (DSMC), has been employed in analysis of ultra-thin film gas lubrication problems [13-15]. DSMC is a particle-based simulation scheme suitable to treat rarefied gas flow problems. It was introduced by Bird [16] in the 1970s. It has been proven that a DSMC solution is an equivalent solution of the Boltzmann equation, and the method has been effectively used to solve gas flow problems in aerospace engineering. However, a disadvantageous feature of DSMC is heavy time consumption in computing, compared with the approach by solving the slip-flow or F-K models. This limits its application to two- or three-dimensional gas flow problems in microscale. In the... 

It is worth mentioning that in the original work of Hockney and Eastwood on the P M approach, the solution of Poisson s equation is calculated in the reciprocal space with Green s functions. In this chapter, an iterative method to calculate the solution of Poisson s equation in real space is discussed. This approach is not commonly adopted for the particle-based simulation of liquid systems. The rather laborious implementation of robust three-dimensional Poisson solvers is probably one of the reasons for the lack of popularity of this approach, which we advocate nevertheless. For this reason, a section of this tutorial is devoted to the discussion of fast iterative methods for the solution of Poisson s equation in position space. 

A key component of particle-based simulation methods involves the coupling of the dynamics of the charge carriers (ions) with the field of forces generated by the external boundary conditions as well as by the internal electrostatic interactions between the components of the system. This self-consistent coupling approach has been successfully employed for more than three decades in plasma simulations. The adjective self-consistent refers to the fact that the forces caused by the electrostatic interactions within the components of the system depend strictly on the spatial configuration of the components and must be updated continuously as the dynamics of the system evolves. 

Particle-based simulation techniques include atomistic MD and coarse-grained molecular dynamics (CG-MD). Accelerated dynamics methods, such as hyperdynamics and replica exchange molecular dynamics (REMD), are very promising for circumventing the timescale problem characteristic of atomistic simulations. Structure and dynamics at the mesoscale level can be described within the framework of coarse-grained particle-based models using such methods as stochastic dynamics (SD), dissipative particle dynamics (DPD), smoothed-particle hydrodynamics (SPH), lattice molecular dynamics (LMD), lattice Boltzmann method (IBM), multiparticle collision dynamics (MPCD), and event-driven molecular dynamics (EDMD), also referred to as collision-driven molecular dynamics or discrete molecular dynamics (DMD). 

Coarse-Grained Particle-Based Simulations 1.16.4.3.1 Stochastic dynamics... 

Many problems in materials and biological sciences are inherently multiscale. Particle based simulations are very much dependent on the computational power which is directly related to the system size. Therefore,... 

Some of the coarse-grained parameters, i e and can be easily measured by experiments or in simulations. The other two parameters, %N and the suppression of density fluctuations, XqN, are thermodynamic characteristics, which are not directly related to the structure (i.e., they cannot be simply expressed as a function of the molecular coordinates). If density fluctuations of the polymeric liquid are small on the length scale of interest (e.g., width of an interface between domains), then the value of the compressibility has only a minor relevance and decreasing it even further will not significantly affect the behavior of the system. Thus, field-theoretic calculations often take the idealized limit of strict incompressibility. In particle-based simulations, however, one often softens the constraint in order to facilitate the motion of the interaction centers and, thereby, reduces the viscosity of the polymer liquid. The Flory-Huggins parameter, in turn, is a crucial coarse-grained parameter and different methods have been devised to extract it from experiments or simulations [16, 20-25]. We shall briefly discuss this important issue in Section 5.2.3, and further refer the reader to the literature, where computer simulations have been quantitatively compared with mean field predictions and where the role of fluctuations on the coarse-grained parameters is discussed [16, 22]. 

Atomistic and Other Particle-Based Simulations of Glass Melts.327... 

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