Brownian dynamics methodology

A number of methodologies have been developed and generalized in recent years to quantitatively describe the ion atmosphere around nucleic acids [11, 12, 17, 28, 29]. These include models based on Poisson-Boltzmann equation [11, 12], counterion condensation [17], and simulation methods, such as Monte Carlo, molecular dynamics, and Brownian dynamics [28, 29]. 

Although not rigorously correct, the approximation of water as a structureless homogeneous continuum dielectric medium is used by many simulative methodologies. Both Brownian dynamics (see the section entitled Implicit Solvation Brownian Dynamics) and electrodiffusive approaches (see the section on Flux-Based Simulation) include the water in the electrostatic picture as a continuous dielectric background with polarizability appropriately tuned... 

The concept of using atomistic molecular dynamics simulations for extracting parameters to be used in less-precise but faster Brownian dynamics simulators, or electrodiffusive solvers, has been discussed. This methodology... 

The fact that the NxP necklace model is isomorphic to a classical system is a great help. All the methodology and standard tricks of the trade, developed to simulate classical systems with Monte Carlo and even MD techniques, can be adapted for use within the PI context. The excellent txx)ks by Allen and Tddesley [22] and by Frenkel and Smidt [23] are compulsory reading in this respect. Two main computational frameworks are successfully applied to the study of quantum fluids PI Monte Carlo (PIMC) and PI molecxilar dynamics (PIMD). PIMC is straightforward and more general in that it can deal with dispersion and exchange quantum effects, while PIMD is more efficient (and involved) but appears to be restricted to dispersion effects. Another dynamical technique PI Brownian dynamics (PIBD) was put forward by Singer and Smith [27], but its use has not been favored by the practitioners in this field. 

There is a variety of computer simulation methodologies that have been applied to study the properties of grafted polymer layers. They include Monte-Carlo (MC) simulations, Molecular Dynamics (MD) simulations, and Brownian Dynamics (BD) simulations. These methodologies have been applied on a variety of model systems, including lattice chains, off-lattice chains, and Edwards Hamiltonians. A recent excellent review of the application of simulation methods has been written by Grest and Murat. Here we just discuss the applicability of the simulations methods in general, their advantages and limitations. 

As discussed previously, an important issue that all dynamic multiscale methodologies must deal with is the phonon spectrum mismatch between the atomistic and coarse-grained regions. In the CLS method, this effect is handled by weakly coupling the FE degrees of freedom to a Brownian motion heat bath that is set to the desired temperature. As a last remark, we need to mention that this hybrid scheme is computationally very efficient and reasonably simple to implement, so that several groups other than the original authors have adopted it. 

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