Multiparticle collision dynamics

MULTIPARTICLE COLLISION DYNAMICS SIMULATION OF COMPLEX SYSTEMS ON MESOSCALES... 

We begin with a description of multiparticle collision dynamics and discuss its important properties. We show how it can be combined with full molecular dynamics (MD) to construct a hybrid MPC-MD method that can be used to... 

Multiparticle collision dynamics can be generalized to treat systems with different species. While there are many different ways to introduce multiparticle collisions that distinguish between the different species [16, 17], all such rules should conserve mass, momentum, and energy. We suppose that the A-particle system contains particles of different species a=A,B,... with masses ma. Different multiparticle collisions can be used to distinguish the interactions among the species. For this purpose we let V 1 denote the center of mass velocity of particles of species a in the cell i ,3... 

Multiparticle collision dynamics can be combined with full molecular dynamics in order to describe the behavior of solute molecules in solution. Such hybrid MPC-MD schemes are especially useful for treating polymer and colloid dynamics since they incorporate hydrodynamic interactions. They are also useful for describing reactive systems where diffusive coupling among solute species is important. 

Most descriptions of the dynamics of molecular or particle motion in solution require a knowledge of the frictional properties of the system. This is especially true for polymer solutions, colloidal suspensions, molecular transport processes, and biomolecular conformational changes. Particle friction also plays an important role in the calculation of diffusion-influenced reaction rates, which will be discussed later. Solvent multiparticle collision dynamics, in conjunction with molecular dynamics of solute particles, provides a means to study such systems. In this section we show how the frictional properties and hydrodynamic interactions among solute or colloidal particles can be studied using hybrid MPC-MD schemes. 

Multiparticle collision dynamics provides an ideal way to simulate the motion of small self-propelled objects since the interaction between the solvent and the motor can be specified and hydrodynamic effects are taken into account automatically. It has been used to investigate the self-propelled motion of swimmers composed of linked beads that undergo non-time-reversible cyclic motion [116] and chemically powered nanodimers [117]. The chemically powered nanodimers can serve as models for the motions of the bimetallic nanodimers discussed earlier. The nanodimers are made from two spheres separated by a fixed distance R dissolved in a solvent of A and B molecules. One dimer sphere (C) catalyzes the irreversible reaction A + C B I C, while nonreactive interactions occur with the noncatalytic sphere (N). The nanodimer and reactive events are shown in Fig. 22. The A and B species interact with the nanodimer spheres through repulsive Lennard-Jones (LJ) potentials in Eq. (76). The MPC simulations assume that the potentials satisfy Vca = Vcb = Vna, with c.,t and Vnb with 3- The A molecules react to form B molecules when they approach the catalytic sphere within the interaction distance r < rc. The B molecules produced in the reaction interact differently with the catalytic and noncatalytic spheres. 

Multiparticle collision dynamics as formulated earlier has an ideal gas equation of state. Ihle, Tiizel, and Kroll [118] have generalized the collision rule to... 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

M. Ripoll, K. Mussawisade, R. G. Winkler, and G. Gompper, Dynamic regimes of fluids simulated by multiparticle-collision dynamics, Phys. Rev. E 72, 016701 (2005). 

E. Allahyarov and G. Gompper, Mesoscopic solvent simulations multiparticle-collision dynamics of three-dimensional flows, Phys. Rev. E 66, 036702 (2002). 

K. Tucci and R. Kapral, Mesoscopic multiparticle collision dynamics of reaction-diffusion fronts, J. Phys. Chem. B 109, 21300 (2005). 

B-particle momentum, multiparticle collision dynamics, single-particle friction and diffusion, 115-118... 

Brownian motion, multiparticle collision dynamics, hydrodynamic interactions, 118—121... 

Coarse-grained approaches, multiparticle collision dynamics, 90-92 Coarse velocity, linear thermodynamics, regression theorem, 18-20 Coherence spectroscopy, two-pathway excitation ... 

Discrete-time velocity correlation function, multiparticle collision dynamics, macroscopic laws and transport coefficients, 103-104 Dissipative structures ... 

Dynamic structure factor, multiparticle collision dynamics, polymers, 124... 

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