Monte Carlo Brownian dynamics simulation

Yoshida M, Kikuchi K. Metropolis Monte Carlo Brownian dynamics simulation of the ion atmosphere polarization around a rodlike polyion. J Phys Chem 1994 98 10303-10306. 

Molecular Dynamics simulation is one of many methods to study the macroscopic behavior of systems by following the evolution at the molecular scale. One way of categorizing these methods is by the degree of determinism used in generating molecular positions [134], On the scale from the completely stochastic method of Metropolis Monte Carlo to the pure deterministic method of Molecular Dynamics, we find a multitude and increasingly diverse number of methods to name just a few examples Force-Biased Monte Carlo, Brownian Dynamics, General Langevin Dynamics [135], Dissipative Particle Dynamics [136,137], Colli-sional Dynamics [138] and Reduced Variable Molecular Dynamics [139]. 

Following the construction of the model is the calculation of a sequence of states (or a trajectory of the system). This step is usually referred to as the actual simulation. Simulations can be stochastic (Monte Carlo) or deterministic (Molecular Dynamics) or they can combine elements of both, like force-biased Monte Carlo, Brownian dynamics or general Langevin dynamics (see Ref. 16 for a discussion). It is usually assumed that the physical system can be adequately described by the laws of classical mechanics. This assumption will alsq be made throughout the present work. 

Intensive studies in the area of dendritic macromolecules, which include applied research and are generally interdisciplinary, have created a need for a more systematic approach to dendritic architectures development that employs a multi-scale modeling and simulation approach. A possible way is to determine the atomic-scale characteristics of dendritic molecules using computer simulation and computational approaches. Computer simulation, as a powerful and modem tool for solving scientific problems, can be performed for dendritic architectures without synthesizing them. Computer simulation not only used to reproduce experiment to elucidate the invisible microscopic details and further explain experiments, but also can be used as a useful predictive tool. Currently, Monte Carlo, Brownian dynamics and molecular dynamics are the most widely used simulation methods for molecular systems [5]. 

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]. 

Now that we have settled on a model, one needs to choose the appropriate algorithm. Three methods have been used to study polymers in the continuum Monte Carlo, molecular dynamics, and Brownian dynamics. Because the distance between beads is not fixed in the bead-spring model, one can use a very simple set of moves in a Monte Carlo simulation, namely choose a monomer at random and attempt to displace it a random amount in a random direction. The move is then accepted or rejected based on a Boltzmann weight. Although this method works very well for static and dynamic properties in equilibrium, it is not appropriate for studying polymers in a shear flow. This is because the method is purely stochastic and the velocity of a mer is undefined. In a molecular dynamics simulation one can follow the dynamics of each mer since one simply solves Newton s equations of motion for mer i,... 

Kikuchi K, Yoshida M, Maekawa T, Watanabe H. Monte Carlo method for Brownian dynamics simulation. In Jennings BR, Stoylov SP, eds. Colloid and Molecular Electro-Optics 1991. Bristol IOP Publishing, 1992 7-12. 

There are two main types of computational procedure which have been used to simulate colloidal dispersions the Monte Carlo method and the Brownian dynamics method. A Monte Carlo simulation gives equilibrium behaviour only, whereas a Brownian dynamics simulation gives both equilibrium and time-dependent behaviour. 

The configurations obtained in successive steps of a molecular dynamics, Monte Carlo, or Brownian dynamics simulation are usually not very different from each other. Hence, one should expect the energy, virial, or any other function of the microscopic state obtained from the successive configurations to be correlated. These correlations disappear after some... 

KAPRAL - The results for the equilibrium fractions of clusters in the electrolyte were obtained from long-time averages over the Brownian dynamics simulation. These results could be checked by direct Monte-Carlo simulations on the primitive model electrolyte. Has this been done ... 

But a computer simulation is more than a few clever data structures. We need algorithms to manipulate our system. In some way, we have to invent ways to let the big computer in our hands do things with the model that is useful for our needs. There are a number of ways for such a time evolution of the system the most prominent is the Monte Carlo procedure that follows an appropriate random path through configuration space in order to investigate equilibrium properties. Then there is molecular dynamics, which follows classical mechanical trajectories. There is a variety of dissipative dynamical methods, such as Brownian dynamics. All these techniques operate on the fundamental degrees of freedom of what we define to be our model. This is the common feature of computer simulations as opposed to other numerical approaches. 

Rossky, P.J. Doll, J.D. Friedman, H.L., Brownian dynamics as smart Monte Carlo simulation, J. Chem. Phys. 1978, 69, 4628... 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

The preceding discussion applied implicitly to what we classify as dynamical simulations — namely, those simulations in which all correlations in the final trajectory arise because each configuration is somehow generated from the previous one. This time-correlated picture applies to a broad class of algorithms MD, Langevin and Brownian dynamics, as well as traditional Monte Carlo (MC, also known as Markov-chain Monte Carlo). Even though MC may not lead to true physical dynamics, all the correlations are sequential. 

Abstract We use Nuclear Magnetic Resonance relaxometry (i.e. the frequency variation of the NMR relaxation rates) of quadrupolar nucleus ( Na) and H Pulsed Gradient Spin Echo NMR to determine the mobility of the counterions and the water molecules within aqueous dispersions of clays. The local ordering of isotropic dilute clay dispersions is investigated by NMR relaxometry. In contrast, the NMR spectra of the quadrupolar nucleus and the anisotropy of the water self-diffusion tensor clearly exhibit the occurrence of nematic ordering in dense aqueous dispersions. Multi-scale numerical models exploiting molecular orbital quantum calculations, Grand Canonical Monte Carlo simulations, Molecular and Brownian Dynamics are used to interpret the measured water mobility and the ionic quadrupolar relaxation measurements. 

Simulation techniques suitable for the description of phenomena at each length-scale are now relatively well established Monte Carlo (MC) and Molecular Dynamics (MD) methods at the molecular length-scale, various mesoscopic simulation methods such as Dissipative Particle Dynamics (Groot and Warren, 1997), Brownian Dynamics, or Lattice Boltzmann in the colloidal domain, Computational Fluid Dynamics at the continuum length-scale, and sequential-modular or equation-based methods at the unit operation/process-systems level. 

Sampling of the biomolecular conformations is usually performed using MD simulations or Monte Carlo methods (61, 62). The protonation state of titrateable amino acids can be treated with constant pH dynamics, QM/MM calculations, or continuum electrostatics methods (61, 62). Formation of a protein-protein encounter complex is often studied using Brownian dynamics (63). Studies of protein-protein docking involve electrostatic potential analysis and, more recently, protein flexibility models, for example normal mode analysis (64). 

Computational methods are increasingly valuable supplements to experiments and theories in the quest to understand complex liquids. Simulations and computations can be aimed at either molecular or microstructural length scales. The most widely used molecular-scale simulation methods are molecular dynamics. Brownian dynamics, and Monte Carlo sampling. Computations can also be performed at the continuum level by numerical solutions of field equations or by Stokesian dynamics methods, described briefly below. 

For this reason, computer simulation methods (Monte Carlo and molecular and Brownian dynamic methods) have been developed not only for solving the problems of polymer statistics, but also for the investigation of the dynamic properties and the intramolecular mobility of polymers. 

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