Dissipative particle dynamics DPD

In general, the particles in the DPD method are defined by their mass Mi, position r, and momentum pt. The interaction between two particles can be expressed as the sum of a conservative force a dissipative force F j, a random force F, and a harmonic spring force F j for the system  

The positions and the velocities of the particles are solved in accordance with the above equations by implementing Newton s equation of motion and a modified version of the velocity. While the interaction potentials in MD models are high-order polynomials of the distance ry between two particles, in DPD models the potentials are softened in order to approximate the effective potential at microscopic length scales. The form of the conservative force is chosen in particular to 

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Dissipative particle dynamics (DPD) is a technique for simulating the motion of mesoscale beads. The technique is superficially similar to a Brownian dynamics simulation in that it incorporates equations of motion, a dissipative (random) force, and a viscous drag between moving beads. However, the simulation uses a modified velocity Verlet algorithm to ensure that total momentum and force symmetries are conserved. This results in a simulation that obeys the Navier-Stokes equations and can thus predict flow. In order to set up these equations, there must be parameters to describe the interaction between beads, dissipative force, and drag. 

A disadvantage of Langevin thermostats is that they require a (local) reference system. Dissipative particle dynamics (DPD) overcomes this problem by assuming that damping and random forces act on the center-of-mass system of a pair of atoms. The DPD equations of motion read as... 

During the past few decades, various theoretical models have been developed to explain the physical properties and to find key parameters for the prediction of the system behaviors. Recent technological trends focus toward integration of subsystem models in various scales, which entails examining the nanophysical properties, subsystem size, and scale-specified numerical analysis methods on system level performance. Multi-scale modeling components including quantum mechanical (i.e., density functional theory (DFT) and ab initio simulation), atom-istic/molecular (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational... 

Dissipative Particle Dynamics (DPD) is a coarse graining method that groups several atoms into simulation sites whose dynamics is governed by conservative and frictional forces designed to reproduce thermodynamics and hydrodynamics [132,133]. Since the effective interactions are constmcted to reproduce macroscopic properties soft repulsive forces can be used, thereby avoiding the small MD step sizes needed to integrate the system when full interactions are taken into account. In addition, random... 

The molecular dynamics methods that we have discussed in this chapter, and the examples that have been used to illustrate them, fall into the category of atomistic simulations, in that all of the actual atoms (or at least the non-hydrogen atoms) in the core system are represented explicitly. Atomistic simulations can provide very detailed information about the behaviour of the system, but as we have discussed this typically limits a simulation to the nanosecond timescale. Many processes of interest occur over a longer timescale. In the case of processes which occur on a macroscopic timescale (i.e. of the order of seconds) then rather simple models may often be applicable. Between these two extremes are phenomena that occur on an intermediate scale (of the order of microseconds). This is the realm of the mesoscale Dissipative particle dynamics (DPD) is particularly useful in this region, examples include complex fluids such as surfactants and polymer melts. 

Dissipative particle dynamics (DPD) is a simulation technique initially developed for the simulation of complex fluids [18] and later extended for polymers. The DPD model consists of pointlike particles interacting with each other through a set of prescribed forces [19]. From a physical point of view, each dissipative particle is regarded not as a single atom or molecule but rather as a collection of atomic groups (molecules) that move in a coherent fashion. 

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... 

Momentum-Conserving Thermostats and the Dissipative Particle Dynamics (DPD) Method... 

The atomistic methods usually employ atoms, molecules or their group and can be classified into three main categories, namely the quantum mechanics (QM), molecular dynamics (MD) and Monte Carlo (MC). Other atomistic modeling techniques such as tight bonding molecular dynamics (TBMD), local density (LD), dissipative particle dynamics (DPD), lattice Boltzmann (LB), Brownian dynamics (BD), time-dependent Ginzbuig-Lanau method, Morse potential function model, and modified Morse potential fimction model were also applied afterwards. 

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