Dissipative particle dynamics thermostat

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... 

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

Soddemann, T., Diinweg, B., Kremer, K. Dissipative particle dynamics a useful thermostat for equilibrium and nonequihbrium molecular dynamics simulations. Phys. Rev. E 68(4), 046,702 (2003). doi 10.1103/PhysRevE.68.046702... 

Equation (41) ensures that the time averages resulting from (40) are equivalent to the canonical ensemble averages. The algorithm is rather robust, and very useful if one is just interested in static averages of the model. However, when one considers the dynamics of polymer solutions, one must be aware that the additional terms in (40) seriously disturb the hydrodynamic interactions, for instance. This latter problem can be avoided by using a more complicated form of friction plus random force, the so-caUed dissipative particle dynamics (DPD) thermostat [225-227]. 

The most straightforward modification of the LGV thermostat is to relate the thermostat forces to the relative velocity of interacting particle pairs. Such an approach is based on the dissipative particle dynamics (DPD) method. Originally, DPD was proposed in conjunction with soft interaction potentials, which would represent clusters of atoms, increasing the stability of particle trajectories and allowing the use of larger MD time steps than for hard potentials. It has been applied to various problems, for example, phase separation [161, 164, 166], the flow around complex objects [153], and colloidal [154,162] and polymeric [143,147, 149-151, 157, 158, 167, 170] systems. 

Mb is interpreted as the mass of the heat bath . For appropriate choices of Mb, the kinetic energy of the particles does indeed follow the Maxwell-Boltzmann distribution, and other variables follow the canonical distribution, as it should be for the AfVT ensemble. Note, however, that for some conditions the dynamic correlations of observables clearly must be disturbed somewhat, due to the additional terms in the equation of motion [(38) and (39)] in comparison with (35). The same problem (that the dynamics is disturbed) occurs for the Langevin thermostat, where one adds both a friction term and a random noise term (coupled by a fluctuation-dissipation relation) [75, 78] ... 

This canonical behavior of the system particles is not accounted for by standard Newtonian dynamics (where the system energy is considered to be a constant of motion). In order to perform molecular dynamics (MD) simulations of the system under the influence of thermal fluctuations, the coupling of the system to the heat bath is required. This is provided by a thermostat, i.e., by extending the equations of motion by additional heat-bath coupling degrees of freedom [75]. The introduction of thermostats into the dynamics is a notorious problem in MD and it cannot be considered to be solved satisfactorily to date [76]. In order to take into consideration the stochastic nature of any particle trajectory in the heat bath, a typical approach is to introduce random forces into the dynamics. These forces represent the collisions of system and heat-bath particles on the basis of the fluctuation-dissipation theorem. 

When DPD is applied as a thermostat, dissipative and random forces are added to the total conservative force in a pair-wise form. The sum of thermostat forces acting on a particle pair vanishes such that the microscopic dynamics fulfills Newton s third law. This method provides momentum conservation and Galilean invariance. 

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