Simulation particle-based mesoscopic

In addition to these theoretical smdies, particle-based mesoscopic simulation studies on me self-assembly behavior of rod-coil block copolymers have also been performed... 

Since MPC dynamics yields the hydrodynamic equations on long distance and time scales, it provides a mesoscopic simulation algorithm for investigation of fluid flow that complements other mesoscopic methods. Since it is a particle-based scheme it incorporates fluctuations, which are essential in many applications. For macroscopic fluid flow averaging is required to obtain the deterministic flow fields. In spite of the additional averaging that is required the method has the advantage that it is numerically stable, does not suffer from lattice artifacts in the structure of the Navier-Stokes equations, and boundary conditions are easily implemented. 

Moving from particle-based and field-based simulations to continuum mechanics is a further step of coarse-graining, after which the effea of polymer dynamics are described only in a rather unspecific manner by a set of PDEs, employing the conservation laws and phenomenological constitutive relations. Continuum mechanics relies on the fundamental notion of a mesoscopic volume element in which properties averaged over disaete particles obey deterministic relationships. Continuum-level models assume naturally that matter is a continuum that is, it can be subdivided without limit. As a result, continuum simulations can in principle handle systems of any (maaoscopic) size and dynamic processes on long timescales. 

Dissipative particle dynamics (DPD) is a meshless, coarse-grained, particle-based method used to simulate systems at mesoscopic length and timescales (Coveney and Espafiol 1997 Espafiol and Warren 1995). In simple terms, DPD can be interpreted as coarse-grained MD. Atoms, molecules, or monomers are grouped together into mesoscopic clusters, or beads, that are acted on by conservative, dissipative, and random forces. The interaction forces are pairwise additive in nature and act between bead centers. Connections between DPD and the macroscopic (hydrodynamic, Navier-Stokes) level of description (Espanol 1995 Groot and Warren 1997), as well as microscopic (atomistic MD) have been well established (Marsh and Coveney 1998). DPD has been used to model a wide variety of systems such as lipid bilayer membranes (Groot and Rabone 2001), vesicles (Yamamoto et al. 2002), polymersomes (Ortiz et al. 2005), binary immiscible fluids (Coveney and Novik 1996), colloidal suspensions (Boek et al. 1997), and nanotube polymer composites (Maiti etal.2005). 

Simulation techniques suitable for the description of phenomena at each length-scale are now relatively well established Monte Carlo (MC) and Molecular Dynamics (MD) methods at the molecular length-scale, various mesoscopic simulation methods such as Dissipative Particle Dynamics (Groot and Warren, 1997), Brownian Dynamics, or Lattice Boltzmann in the colloidal domain, Computational Fluid Dynamics at the continuum length-scale, and sequential-modular or equation-based methods at the unit operation/process-systems level. 

In order to achieve these goals, we have adopted a multi-scale approach that comprises molecular and mesoscopic models for the liquid crystal. The molecular description is carried out in terms of Monte Carlo simulations of repulsive ellipsoids (truncated and shifted Gay-Berne particles), while the mesoscopic description is based on a dynamic field theory[5] for the orientational tensor order parameter, Q. ... 

Scale matters. We have seen that scale may be used to facilitate reconstruction of structures with nano-components, but it has also shown that scale is important when simulation takes place. When calculated correctly, properly, or if you like, usefully, transport effective coefficients can be determined and even compared to experimental data. However, in some cases new approaches may need to be considered. Here, approaches like mesoscopic physics, or a model of multiple scattering with effective media approximation (EMA) for condensed matter, based on the approach of atomic cluster, may play important roles. Recently, a review (Debe, 2012) was discussed on the different approaches that scientists and fuel cell developers in general, are using in order to have better and cheaper catalysts. Many have made a great impact on CL structures. Some approaches included supporting material but others considered unsupported catalysts too. The aspect ratio of particles has been recognized as a relevant factor. Metallic membranes, meshes, and bulk materials have also been considered of which the structural features will impact on the final structure and functionality of fuel cell technology. Local structures and at different levels of scale are still subjects of interest in many scientific works (Soboleva et al, 2010). 

In this article we will focus on systems which comprise particles, with or without internal degrees of freedom, suspended in a simple fluid. We will first outline the necessary ingredients for a theoretical description of the dynamics, and in particular explain the concept of hydrodynamic interactions (HI). Starting from this background, we will provide a brief overview of the various simulation approaches that have been developed to treat such systems. All of these methods are based upon a description of the solute in terms of particles, while the solvent is taken into account by a simple (but sufficient) model, making use of the fact that it can be described as a Newtonian fluid. Such methods are often referred to as mesoscopic. We will then describe and derive in some detail the algorithms that have been developed by us to couple a particulate system to a LB fluid. The usefulness of these methods will then be demonstrated by applications to colloidal dispersions and polymer solutions. Some of the material presented here is a summary of previously published work. 

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