Particle-dynamic simulations classes

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles and allow particles to travel ballistically between collisions. This class of... 

Two of the most common classes of particle-dynamic simulations are termed hard-particle and soft-particle methods. Hard-particle methods calculate particle trajectories in response to instantaneous, binary collisions between particles, and allow particles to follow ballistic trajectories between collisions. This class of simulation permits only instantaneous contacts and is consequently often used in rapid flow situations such as are found in chutes, fluidized beds, and energetically agitated systems. Soft-particle methods, on the other hand, allow each particle to deform elastoplastically and compute responses using standard models from elasticity and tribology theory. This approach permits enduring particle contacts and is therefore the method of choice for mmbler apphcations. The simulations described in this chapter use soft-particle methods and have been validated and found to agree in detail with experiments. 

The CG method not only provides general models for studying a class of block copolymers but also conducts efficient algorithms for simulation. In this chapter, we overview the theoretical and computational approaches toward the simulations of dynamics of microphase separation of block copolymers with the focus on the recent contributions applying Monte Carlo (MC), dissipation particle dynamics... 

Hybrid particle-field models combine single-cbain simulations with an appropriate field-theoretical approach. The corresponding class of multiscale techniques includes the single-chain-in-mean-field (SCMF) method, the theoretically informed coarse-grain (TICG) simulation scheme, self-consistent Brownian dynamics (SCBD), and the MD-SCF method, in which self-consistent field theory (SOFT) and particle-based MD are combined. 

Whereas in mixed MD/MC simulations, some of the atoms are moved by pure MD, and other particles are moved by pure MC, it is also possible to constmct algorithms in which the displacement itself is determined in part by a deterministic factor and in part by a stochastic factor. In this class, we can further distinguish essentially three techniques Langevin or stochastic dynamics, hybrid Monte Carlo, and force bias Monte Carlo and related techniques. 

Historically there are two distinct classes of problems in chemistry to which discrete microscopic simulations have been applied widely and with considerable success At one extreme the bulk physical properties of atomic and molecular fluids are studied as the "exact" dynamical evolution of a collection of representative particles is followed in "computer experiments" using the well-established method of molecular dynamics (1-10). 

In the first problem class mentioned above (hereinafter called class A), a collection of particles (atoms and/or molecules) is taken to represent a small region of a macroscopic system. In the MD approach, the computer simulation of a laboratory experiment is performed in which the "exact" dynamics of the system is followed as the particles interact according to the laws of classical mechanics. Used extensively to study the bulk physical properties of classical fluids, such MD simulations can yield information about transport processes and the approach to equilibrium (See Ref. 9 for a review) in addition to the equation of state and other properties of the system at thermodynamic equilibrium (2., for example). Current activities in this class of microscopic simulations is well documented in the program of this Symposium. Indeed, the state-of-the-art in theoretical model-building, algorithm development, and computer hardware is reflected in applications to relatively complex systems of atomic, molecular, and even macromolecular constituents. From the practical point of view, simulations of this type are limited to small numbers of particles (hundreds or thousands) with not-too-complicated inter-particle force laws (spherical syrmetry and pairwise additivity are typically invoked) for short times (of order lO" to 10 second in liquids and dense gases). 

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