Langevin dynamic simulations

R. W. Pastor. Techniques and applications of Langevin dynamics simulations. In G. R. Luckhurst and C. A. Veracini, editors. The Molecular Dynamics of Liquid Crystals, pages 85-138. Kluwer Academic, Dordrecht, The Netherlands, 1994. 

G. Ramachandran and T. Schlick. Solvent effects on supercoiled DNA dynamics explored by Langevin dynamics simulations. Phys. Rev. E, 51 6188-6203, 1995. 

Langevin dynamics simulates the effect of molecular collisions and the resulting dissipation of energy that occur in real solvents, without explicitly including solvent molecules. This is accomplished by adding a random force (to model the effect of collisions) and a frictional force (to model dissipative losses) to each atom at each time step. Mathematically, this is expressed by the Langevin equation of motion (compare to Equation (22) in the previous chapter) ... 

In general, Langevin dynamics simulations run much the same as molecular dynamics simulations. There are differences due to the presence of additional forces. Most of the earlier discussions (see pages 69-90 and p. 310-327 of this manual) on simulation parameters and strategies for molecular dynamics also apply to Langevin dynamics exceptions and additional considerations are noted below. 

We first summarize the salient features of the Langevin dynamics simulation results followed by a theoretical analysis. 

As reported in [22] and [29], Fig. 2 shows a typical sequence of images depicting nucleation of a lamella by a single chain of N = 700 beads as obtained from Langevin dynamics simulations. The chain is quenched to T = 9.0... 

The lamellae grown in these Langevin dynamics simulations are very small in comparison with experimentally investigated lamellae. In view of this, we have developed the coarse-grained anisotropic adsorption model described... 

In the Langevin dynamics simulations [33], there is an additional force Sr, acting on the zth bead, where r, is its position and... 

In the Langevin dynamics simulations, the polymer crystallization is modeled by following the competition between the attraction among nonbonded... 

The main results derived from Langevin dynamics simulations and theoretical considerations are as follows. 

It is based on Langevin dynamics simulations of an off-lattice heteropolymer-like model of the polypeptide chain which is characterized by a a well-... 

The major computational effort in a molecular or Langevin dynamic simulation is the calculation of the forces on all particles at each time step. In principle, any type of energy function can be used force field, semi-empirical, ab initio electronic structure... 

C. Liu and M. Muthukumar, Langevin dynamics simulations of early-stage polymer nucleation and crystalhzation, J. Chem. Phys. 109, 2536-2542 (1998). 

A nice application of Eq. (14), which compares simulations for poly(ethyleneoxide) in the explicit solvents water and benzene with Langevin dynamics simulations, can be found in [27,28], The authors use a modified Stokes relation, i = 14nRieffr]lmi, where 2 is a parameter... 

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