Mesoscopic dynamics

Van Vlimmeren, B.A.C., Fraaije, J.G.E.M. Calculation of noise distribution in mesoscopic dynamics models for phase-separation of multicomponent complex fluids. Comput. Phys. Comm. 99 (1996) 21-28. 

Maurits, N.M., Fraaije, J.G.E.M. Mesoscopic dynamics of copolymer melts from density dynamics to external potential dynamics using nonlocal kinetic coupling. J. Chem. Phys. 107 (1997) 5879-5889. 

Hybrid MPC-MD schemes may be constructed where the mesoscopic dynamics of the bath is coupled to the molecular dynamics of solute species without introducing explicit solute-bath intermolecular forces. In such a hybrid scheme, between multiparticle collision events at times x, solute particles propagate by Newton s equations of motion in the absence of solvent forces. In order to couple solute and bath particles, the solute particles are included in the multiparticle collision step [40]. The above equations describe the dynamics provided the interaction potential is replaced by Vj(rJVs) and interactions between solute and bath particles are neglected. This type of hybrid MD-MPC dynamics also satisfies the conservation laws and preserves phase space volumes. Since bath particles can penetrate solute particles, specific structural solute-bath effects cannot be treated by this rule. However, simulations may be more efficient since the solute-solvent forces do not have to be computed. 

H. Kitagawa and Y. Shibutani (eds.) IUTAM Symposium on Mesoscopic Dynamics of Fracture Process and Materials Strength. Proceedings of the IUTAM Symposium held in Osaka, Japan, 6-11 July 2003. Volume in celebration of Professor Kitagawa s retirement. 2004... 

Reduction of kinetic theory to fluid mechanics is historically the first example of a successful reduction of a mesoscopic dynamical theory to a more macroscopic dynamical theory. The method (called the Chapman-Enskog method) that was invented by Chapman and Enskog for this particular reduction remains still a principal inspiration for all other types of reduction (see, e.g.,. Gorban and Karlin, 2003, 2005), Yablonskii et al., 1991). In this example we briefly recall the geometrical viewpoint of the Chapman-Enskog method. We shall also illustrate the point (IV)... 

Another method that introduces a very simplified dynamics is the Multi-Particle Collision Model (or Stochastic Rotation Model) [130]. Like DSMC particle positions and velocities are continuous variables and the system is divided into cells for the purpose of carrying out collisions. Rotation operators, chosen at random from a set of rotation operators, are assigned to each cell. The velocity of each particle in the cell, relative to the center of mass velocity of the cell, is rotated with the cell rotation operator. After rotation the center of mass velocity is added back to yield the post-collision velocity. The dynamics consists of free streaming and multi-particle collisions. This mesoscopic dynamics conserves mass, momentum and energy. The dynamics may be combined with full MD for embedded solutes [131] to study a variety of problems such as polymer, colloid and reaction dynamics. 

Grmela, M., Mesoscopic dynamic and thermodynamic application to polymer fluids, Lect. 

Until now we actually proofed the fact that the Lagrangian (5.348) corresponds to a modeling (mesoscopic) dynamics which is described by the Fokker-Planck equation. Next, one will consider this nonequilibrium form of the Euclidian Lagrangian, to be characteristic to the effective electronic evolution, specific to the mesoscopic characterization. 

Besides extensive experiments, many computer simulations have been carried out on polymer blends, primarily, including Monte Carlo (MC) [15-18], molecular dynamics (MD) [12,19-35], mesoscopic dynamics (MesoDyn) [12,24,25], and dissipative particle dynamics (DPD) [33,36,37]. In the area of theoretical polymer physics, MesoDyn and DPD have been used to treat polymeric chains in a coarse-grained (mesoscopic) level by grouping atoms together up to the persistence length of polymers. Recent trends in the use of MD simulations on bulk polymers have led to the calculations of important... 

Dzwinel W, Yuen DA, Boryczko K (2002) Mesoscopic dynamics of colloids simulated with dissipative particle dynamics and fluid particle model. J Mol Model 8 33 3... 

Although calculation of polymer path integrals is computationally very intensive, it allows us to describe mesoscopic dynamics of specific complex polymer liquids [17],... 

We give a short outline of the theory of the mesoscopic dynamics algorithms. For more details see [11]. We consider a system of n Gaussian chains of N beads of several different species (for example,... 

Mesoscopic dynamics can be also affected by competition between different mesoscales which can generate a coupling between different dynamic modes. 

Abstract. The lectures review the statics and dynamics of the gas-liquid-solid contact line, with the emphasis on the role of intermolecular forces and mesoscopic dynamics in the immediate vicinity of the three-phase boundary. We discuss paradoxes of the existing hydrodynamic theories and ways to resoluve them by taking account of intermoleculr forces, activated slip in the first molecular layer, diffuse character of the gas-liquid interface and interphase transport. 

Stochastic models are also able to capture complicated pattern formation seen in chemically reacting media and can be used to study the effects of fluctuations on chemical patterns and wave propagation. The mesoscopic dynamics of the FHN model illustrates this point. In order to formulate a microscopically based stochastic model for this system, it is first necessary to provide a mechanism whose mass action law is the FHN kinetic equation. Some features of the FHN kinetics seem to preclude such a mechanistic description for example, the production of u is inhibited by a term linear in V, a contribution not usually encountered in mass action kinetics. However, if each local region of space is assumed to be able to accommodate only a maximum number m of each chemical species, then such a mechanism may be written. We assume that the chemical reactions depend on the local number of molecules of the species as well as the number of vacancies corresponding to each species, in analogy with the dependence of some surface reactions on the number of vacant surface sites or biochemical reactions involving complexes of allosteric enzymes that depend on the number of vacant active sites. 

The goal of the modeling is the design of a mesoscopic dynamics that possesses many features of the real non-reactive and reactive collision events in the system. We now turn to a description of some of the general principles involved in the construction of these cellular automaton models. 

Substitution of this reaction probability matrix in the automaton mean-field equations (7) yields the Willamowski-Rbssler rate law (24). Since the full automaton dynamics is not mean field, we can now use the automaton to investigate the mesoscopic dynamics of this reacting system. In the simulations presented below we take the diffusion coefficients of all of the species to be the same thus, henceforth we dispense with the species label and refer to this common diffusion coefficient as D. 

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