Simulation efficiency

RNApolymerase molecules are involved in the process. If the system is well stirred so that spatial degrees of freedom play no role, birth-death master equation approaches have been used to describe such reacting systems [33, 34]. The master equation can be simulated efficiently using Gillespie s algorithm [35]. However, if spatial degrees of freedom must be taken into account, then the construction of algorithms is still a matter of active research [36-38]. 

The best way to handle this case is to move the loop-invariant expression out of the loop. This also improves simulation efficiency. This is shown in the following example. 

Pauli group. That is, they map states with compact descriptions to states with compact descriptions. All this may be summarized by the Gottesman-Knill theorem [Gottesman 1997], which may be roughly stated as Theorem Any computation restricted to these gates may be simulated efficiently within the stabilizer formalism. 

We have implicitly assumed that when product molecules are created, they are placed in the locations previously occupied by the reactant molecules used to create the products. This is not a requirement of the RCMC method, but increases the simulation efficiency. Likewise, replacing reactant molecules with product molecules of similar size will enhance the efficiency of the method. If the number of reactant and product molecules is the same then no molecules need be inserted at random locations. The term ppos(v ) is needed forcases where the total number of molecules is not conserved. The quantity is the net number of molecules produced or consumed for the given set of vys and s,... 

There is obviously a need to use more-advanced displacement procedures when a strong macroion-counterion coupUng is present. The simulation efficiency can be improved dramatically by applying a displacement procedure where strongly coupled particles are displaced simultaneously, referred to here as a cluster move. Such ideas have been appHed to MC simulations of... 

Orthogonal collocation in two dimensions has been used to simulate microdisk edge effects. The first paper in a series (5 up till now), by Speiser and Pons (1982) is a formidable tour de force. A two-dimensional set of polynomials is fitted to the grid and it leads, as in one dimension, to an "easily solved" set of ordinary differential equations. In the fifth part of this series of papers, Cassidy et al (1985), applied the method to electrode ensembles. This is obviously not for the occasional simulator, who is advised to use a simple technique and put up with the long computational times or use someone else s program but the method undoubtedly makes two-dimensional simulations efficient and accurate. 

The simulation of component parts exhibiting electromechanical coupling with the aid of commercial finite element packages is subject to some restrictions. Usually the piezoelectric effect is considered only in connection with volume elements, see Freed and Bahuska [76]. For complex structures, the modeling with volume elements often does not represent a viable procedure with respect to implementation and calculation expenditure. A prominent example for this are structures with thin walls made of multiple layers. Their mechanical behavior may be simulated efficiently with layered structural shell elements. 

An analytic and a simulation approaches are presented in this paper. Both of the approaches are aimed at solving the problem of availabiUty and reliability evaluation of redundant systems under periodic maintenance, considering fault detection rate, fault isolation rate and repair rate. Using the simulation tool we have developed, instantaneous availability and MTBCF of the system could be easily obtained, which are of great significance for designers to make and optimize the maintenance policy. The simulation efficiency would be raised in further application to shorten the simulation time. 

In the field of modelling and simulation, multi-domain object-oriented languages are increasingly adopted. They enable an intuitive way of modelling, since objects and their interconnections correspond with real components. Thus, large-scale system models can be created and simulated efficiently. 

Almost every chemical process includes many reaction steps. This means that the reactants will first produce intermediates, which will then be involved in further reactions leading to the final products. Frequently, the final products of the chemical process appear only after several hundreds or thousands of different reaction steps. The products may include those that are desired (e.g. yields of valuable chemicals or energy) and those that are unwanted, such as pollutants. If the stoichiometric equations and the rates of each reaction step are known, then the chemical process can in principle be controlled. In industrial applications this means that the composition of the reacting mixture and the conditions of the reaction process can be selected so that the process operates as efficiently as possible and has low environmental impact. Simulations of detailed reaction mechanisms can therefore be extremely useful within the design phase of new equipment or for the development and control of existing equipment. If a model is accurate and robust, and can be simulated efficiently, then it can be used in place of expensive experiments for process design. Within the book we have tried to address methods that can be used to assess and improve the robustness of kinetic mechanisms, as well as to reduce their impact on the simulation time of models of coupled chemical and physical processes. The aim of all of these methods is to improve the utility of kinetic mechanisms for a range of applications in the real world. 

Abstract In this contribution, we present an overview of the various techniques for combining atomistic molecular dynamics with Monte Carlo simulations, mainly in the context of condensed matter systems, as well as a brief summary of the main accelerated dynamics techniques. Special attention is given to the force bias Monte Carlo technique and its combination with molecular dynamics, in view of promising recent developments, including a definable timescale. Various examples of the application of combined molecular dynamics / Monte Carlo simulations are given, in order to demonstrate the enhanced simulation efficiency with respect to either pure molecular dynamics or Monte Carlo. 

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