Computer simulation hard particle models

It has not proved possible to develop general analytical hard-core models for liquid crystals, just as for nonnal liquids. Instead, computer simulations have played an important role in extending our understanding of the phase behaviour of hard particles. Frenkel and Mulder found that a system of hard ellipsoids can fonn a nematic phase for ratios L/D >2.5 (rods) or L/D <0.4 (discs) [73] however, such a system cannot fonn a smectic phase, as can be shown by a scaling... 

To simulate the particle-particle collision, the hard-sphere model, which is based on the conservation law for linear momentum and angular momentum, is used. Two empirical parameters, a restitution coefficient of 0.9 and a friction coefficient of 0.3, are utilized in the simulation. In this study, collisions between spherical particles are assumed to be binary and quasi-instantaneous. The equations, which follow those of molecular dynamic simulation, are used to locate the minimum flight time of particles before any collision. Compared with the soft-sphere particle-particle collision model, the hard-sphere model accounts for the rotational particle motion in the collision dynamics calculation thus, only the translational motion equation is required to describe the fluid induced particle motion. In addition, the hard-sphere model also permits larger time steps in the calculation therefore, the simulation of a sequence of collisions can be more computationally effective. The details of this approach can be found in the literature (Hoomans et al., 1996 Crowe et al., 1998). 

In spite of the fact that the decay after excitation of the hard-potential itinerant oscillator is similar to the experimental computer simulation result of Figs. 7 and 8, we do not believe that it is the reduced model equivalent to the one-dimensional many-particle model under study. As remarked above, indeed, the e(r) function is not correctly reproduced by this reduced model. The choice of a virtual potential softer than the linear one seems also to be in line with the point of view of Balucani et al. They used an itinerant oscillator with a sinusoidal potential, which is the simplest one (to be studied via the use of CFP) to deal with the soft-potential itinerant oscillator. Note that the choice... 

There are a number of computational models used to investigate granular media. Event-driven or hard-sphere algorithms are based on the calculation of changes from distinct collisions between single grains that are often approximated by spheres, ellipsoids, or polyhedral.MD of soft-particle models are another common way to simulate granular materials. In this approach, the repulsive contact force in normal direction is typically proportional to the particle... 

Ref. [32] includes results from computer simulations of a system composed of spherical particles interacting via a discontinuous potential that includes a hard core, a repulsive square part, and an attractive square well. This model system, with appropriate parameterization, presents a LLCP that is metastable with respect to freezing. The system also shows kt and Cp maximum lines, however, no density anomaly is observed. 

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. 

From Particle-Based Models for Computer Simulations to Self-Consistent Field Theory Hard-Core Models... 

A collection of hard, identical spheres is the simplest possible model system that undergoes a first order phase transition. For low packing fractions the particles are in a liquid state, but when the packing fractions exceeds a value of 49.4% a ordered solid state becomes more stable. This was first shown in computer simulations by Hoover and Ree [27] in 1968. The experimental realization of a colloidal suspension that closely mimics the phase behavior of hard spheres followed about 20 years later and was a milestone in soft matter physics [28, 29]. More recently the phase transition kinetics of hard sphere colloids has been studied extensively in experiments [5, 30, 31]. However as mentioned in the introduction the interpretation of the data with CNT was rather indirect. 

A large body of the computer simulation work has been reported on model systems such as hard discs, spheres or Lennard-Jones particles. Here the interparticle potential is known and can be used to rapidly calculate the configurational energy of the system as required for Monte Carlo studies or the configurational force on a particle as required for molecular dynamics. 

The original models used in MC were highly idealized representations of molecules, such as hard spheres and disks, but nowadays MC simulations are carried out on the basis of more reliable interaction potential. The use of realistic molecule-molecule interaction potential makes it possible to compare data obtained fi om experiments with the computer generated thermodynamic data derived from a model. The particle momenta do not enter the calculation, there is no scale time involved, and the order in which the configurations occur has no special significance. 

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