Langevin equation dynamical algorithm

An algorithm for performing a constant-pressure molecular dynamics simulation that resolves some unphysical observations in the extended system (Andersen s) method and Berendsen s methods was developed by Feller et al. [29]. This approach replaces the deterministic equations of motion with the piston degree of freedom added to the Langevin equations of motion. This eliminates the unphysical fluctuation of the volume associated with the piston mass. In addition, Klein and coworkers [30] present an advanced constant-pressure method to overcome an unphysical dependence of the choice of lattice in generated trajectories. 

In order to understand how the algorithm actually works and to construct an explicit expression for the error it is not convenient to work with the metadynamics equations (12) in their full generality. Instead, we notice that the finite temperature dynamics of the collective variables satisfies, under rather general conditions, a stochastic differential equation [54,55]. Furthermore, in real systems the quantitative behavior of metadynamics is perfectly reproduced by the Langevin equation in its strong friction limit [56]. This is due to the fact that all the relaxation times are usually much smaller than the typical diffusion time in the CV space. Hence, we model the CVs evolution with a Langevin t3rpe dynamics ... 

This algorithm has been used in the integration of the Langevin equation applied to the buffer zone atoms in the stochastic boundary molecular dynamics method (Chapt. IV.C), as well as in other stochastic dynamics calculations.102... 

The theory of Brownian motion was developed to describe the dynamics of a massive particle in a medium of small particles. Ermak and McCammon have formulated a Brownian dynamics simulation method suitable for concentrated dispersions. The method follows the traditional deterministic molecular dynamics algorithm used to simulate fluids, except that the set of 3N Newtonian equations is replaced by a set of 3N coupled Langevin equations ... 

In order to describe shear flow effects in a velocity field of the from v (r) = yvy, Kindt and Briels [136] proposed the use of the SLLOD algorithm [140]. Starting with a Langevin equation, such a method results in the following expression for the blob dynamics ... 

A treatment that studies the case of unphysical dynamics of the solvent particles has been carried out in Ref. 31, also using a microscopic approach. This was done in order to discuss if it is justified to replace an MD algorithm in which the solvent particles obey strictly Newton s equations of motion by a Langevin simulation in which every solvent particle is artificially coupled to a weak friction and a weak heat bath (this latter method has some... 

---