Mesoscale Brownian dynamics

The conceptual forerunner to mesoscale dynamics is Brownian dynamics. Brownian simulations used equations of motion modified by a random force... 

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. 

This is one of the simple and most commonly used method to perform multiscale simulation. By definition calculation of parameters for classical MD simulation from quantum chemical calculation is also a multiscale simulation. Therefore, most of the force filed e.g., OPLS," AMBER, GROMOS available for simulations of liquid, polymers, biomolecules are derived from quantum chemical calculations can be termed as multiscale simulation. To bridge scales from classical MD to mesoscale, different parameter can be calculated and transferred to the mesoscale simulation. One of the key examples will be calculation of solubiUty parameter from all atomistic MD simulations and transferring it to mesoscale methods such dissipative particle dynamics (DPD) or Brownian dynamics (BD) simulation. Here, in this context of multiscale simulation only DPD simulation along with the procedure of calculation of solubility parameter from all atomistic MD simulation will be discussed. 

A second catch is the noise. If one observes the movements of a colloidal particle, the Brownian motion will be evident. There may be a constant drift in the dynamics, but the movement will be irregular. Likewise, if one observes a phase-separating liquid mixture on the mesoscale, the concentration levels would not be steady, but fluctuating. The thermodynamic mean-field model neglects all fluctuations, but they can be restored in the dynamical equations, similar to added noise in particle Brownian dynamics models. The result is a set of stochastic diffusion equations, with an additional random noise source tj [20]. In principle, the value and spectrum of the noise is dictated by a fluctuation dissipation theorem, but usually one simply takes a white noise source. 

In this section we briefly summarize the Brownian dynamics algorithm and its close cousin Stokesian Dynamics. We then outline the motivation and development of several mesoscale methods, some of which are reviewed elsewhere in this series. 

The off-grid particle methods, such as DPD and FPM, can capture easily mesoscopic scales of hundreds of micrometers employing up to 10 fluid particles currently, i.e., the scales in which temperature fluctuations and depletion forces interact with mesoscopic flows. Therefore, gridless particle methods can mimic the complex dynamics of fluid particles in the mesoscale more realistically than LEG. The FPMs also save computational time taken by molecular dynamics for calculating thermal noise. Instead, in DPD and FPM, we introduce the random Brownian force. 

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