Simulations, increasing efficiency

Molecular dynamics simulations are efficient for searching the conformational space of medium-sized molecules and peptides. Different protocols can increase the efficiency of the search and reduce the computer time needed to sample adequately the available conformations. 

Owing to the increasing efficiency of computational methods, it has become possible to investigate base pairs in the gas phase and solution simulated by super-molecular approaches with up to six water molecules [98IJQ37, 98JPC(A) 10374, 98JPC(B)9109, 99JST107]. In the cytosine-isocytosine Watson-Crick base pair. 

As computers become faster, the complexity of problem that can be usefully simulated increases. Areas of interest include combining computational fluid dynamics (CFD) modelling with chemical kinetics to investigate (and hence reduce) the effect of flow maldistributions on aftertreatment system efficiency, and simulating catalyst deactivation over the lifetime of the catalyst. 

The dynamics of adsorbed species over MgO(OOl) surface was studied by MD method. The migration of the adsorbed species was found to depend on the morphology of MgO and the thermal vibration of surface atoms in MgO lattice. Further, the situation where the supercritical fluid and adsorbed species exist together was simulated. The collision of supercritical fluid with the adsorbed species was identified as the primary cause of extraction. Additionally, the supercritical fluid form clusters around the desorbed species avoiding the readsorption. Thus, clustering is the secondary cause for the increased efficiency of supercritical extraction even above the critical conditions. The details of these simulation studies are given in the following section. 

Adaptive computations of nonlinear systems of reaction-diffusion equations play an increasingly important role in dynamical process simulation. The efficient adaptation of the spatial and temporal discretization is often the only way to get relevant solutions of the underlying mathematical models. The corresponding methods are essentially based on a posteriori estimates of the discretization errors. Once these errors have been computed, we are able to control time and space grids with respect to required tolerances and necessary computational work. Furthermore, the permanent assessment of the solution process allows us to clearly distinguish between numerical and modelling errors - a fact which becomes more and more important. 

This simplified description has assumed that the exact physical probabilities are utilized to determine the outcome of every decision when this is done, the resulting simulation is termed an analog simulation. More sophisticated statistical treatments are included in modern computer codes that utilize nonphysical distributions with corrections (in a defined parficle weight) to keep the results of the simulation unbiased these can be shown to improve the efficiency of the simulation. These methods are called "variance reduction" methods, although this is somewhat of a misnomer because many of these methods increase efficiency by saving computer time, not by reducing variance. The exact theory and technique for doing this is beyond the scope of this handbook but is well described in Monte Carlo descriptions such as in Lewis and Miller (1993). 

This search for ever-increasing efficiency has led to ingenious simulation algorithms, some of which are fairly removed from reality in that molecules are broken and reconnected, hypothetical and often unphysical thermodynamic paths are constructed, the natural fluctuations of a system are arbitrarily enhanced or suppressed, molecules are created or destroyed, etc. Indeed, half-Jokingly one could almost venture that the efficiency of a Monte Carlo method is inversely proportional to its resemblance to reality. Just as Monte Carlo methods have evolved, however, the power of computers has been steadily increasing it is conceivable that simulators will eventually return to simpler and more transparent simulation techniques that were not possible on smaller and slower machines. 

The CBMC algorithm greatly improves the conformational sampling for molecules with articulated structure and increases the efficiency of chain insertions (required for the calculation of chemical potentials, grand-canonical, and Gibbs ensemble simulations) by several orders of magnitude. To make these simulations more efficient and to use this technique for branched molecules, several extensions are needed ... 

Based on the Monte Carlo simulations, it is seen that the presence of positional disorder causes the mobiUty to decrease with increasing field at low fields (37). This is the case because the introduction of positional disorder into the system provides the carrier with energetically more favorable routes, which occasionally are against the field direction. These detour routes are most efficient at low fields, but are eliminated at high fields. This rationalizes the decrease of hole mobilities with increasing field. 

---