Thermostat Langevin

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... 

This switches on the Langevin thermostat for the NVT ensemble, with temperature temp and friction coefficient gamma. The skin depth skin is a parameter for the link-cell system which tunes its performance, but cannot be discussed here. 

Today a large variety of methods exist that drive the system into the canonic state, e.g., by introduction of artificial degrees of freedom or by coupling the system to a heat bath via stochastic methods. The reader will find more details in Refs. 12 and 13. The choice for the present work is a Langevin thermostat [14], This means that instead of integrating Newton s equations of motion, one solves a set of Langevin equations,... 

More realistic kinetic behavior in implicit solvent simulations can be obtained with the Langevin thermostat [18] where stochastic collisions and friction forces provide kinetic energy transfer to and from the solute in an analogous fashion to explicit solute-solvent interactions. As a result, kinetic transition rates similar to rates from explicit solvent simulations can be recovered with an appropriate choice of the friction constant [2]. 

In the simulation study of fluorescence anisotropy decay, a generic bead-spring model of the polymer was used. It is schematically shown in Fig. 19. Each bead can represent one or several monomer units in a real polymer. The degree of dissociation, a, is defined as the fraction of monomer units carrying electric charges. The interaction between monomer units of the polymer is modeled by the Lennard-Jones potential and the solvent quality is controlled by the depth of this potential, e. As shown by Micka, Holm and Kremer, 0.34 corresponds to the theta state [146]. The simulation study was performed for several values of > 0.33, i.e., under poor solvent conditions. The simulation technique used was MD coupled to a Langevin thermostat, i.e., the polymer was simulated in an implicit solvent. The counterions were simulated explicitly. A more detailed description of the polymer model can be found in the original paper [87]. 

Fig. 8.4 The computed velocity auto-conelation functions are plotted for Nose-Hoover and Nose-Hoover-Langevin dynamics (left), where we overlay plots from simulations using all possible parameter sets where y 0,0.05,0.5,5,50 and /r 20,2,0.2,0.02. We additionally plot the same result for Langevin dynamics (right), overlaying curves for y 0.05,0.1,0.2,..., 51.2, where high to low friction is plotted from red to blue respectively. The salient qualitative features of the results remain qualitatively unchanged when using different values of the parameters for the Nos6-Hoover thermostats (see inset) whereas the Langevin thermostat has a much harsher effect on the dynamics, with significant differences as the friction is increased...

The MD simulation eoupled with the Langevin thermostat simulates Rouse dynamics of a polymer chain. The Rouse relaxation time scales with the number of monomers on a chain as and it is necessary to perform at least cN (where constant c depends on the value of the integration time step At) integrations of the equation of motion for a ehain to completely renew its eonfiguration. During each time step, At, N N — l)/2 calculations of forces between monomers are performed. The CPU time required to do cN integrations of the equations of motion will grow with the number of monomers on a chain as xmd — N - Thus, the computational efficiency of MD simulation has the same N dependence as a MC simulation with only local moves. 

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] ... 

Adding stochastic forces and/or velocities (Langevin thermostat) ... 

Here /(r) and / are conservative force and random force respectively. is the friction coefficient. The drawback of this thermostat is that momentum transfer is destroyed. So, it is not advisable to use Langevin thermostat in the simulations where one wishes to study the diffusion processes. 

Another popular thermostat used in molecular dynamics simulations is the Langevin thermostat. It covers the heat-bath coupling part of the Langevin equation by friction and Gaussian random forces f. The Langevin equation basically describes the dynamics of a Brownian particle in solvent under the influence of external forces F. Its simplest form therefore reads ... 

The simulations were done at constant temperature, T = 1.2e, using the Langevin thermostat with damping constant T = lr and timestep 0.015r, where r =. The length of the simulation is such that the chains move at least 10 times their contour length. 

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