Monte grid-based

V, ip, x, and t) in the PDF transport equation makes it intractable to solve using standard discretization methods. Instead, Lagrangian PDF methods (Pope 1994a) can be used to express the problem in terms of stochastic differential equations for so-called notional particles. In Chapter 7, we will discuss grid-based Eulerian PDF codes which also use notional particles. However, in the Eulerian context, a notional particle serves only as a discrete representation of the Eulerian PDF and not as a model for a Lagrangian fluid particle. The Lagrangian Monte-Carlo simulation methods discussed in Chapter 7 are based on Lagrangian PDF methods. 

Single-Chain-in-Mean-Field Simulations and Grid-Based Monte Carlo Simulation of the Field-Theoretic Hamiltonian... 

The comparison between SCMF simulations and Monte Carlo simulations of our soft, coarse-grained model allows us to quantify the accuracy of the quasi-instantaneous field approximation [41]. For simplicity, we consider a local Monte Carlo move, where one proposes to move an A-segment from position r to position r. The concomitant change in the grid-based A-density, 6 y (c), is of the order 1/q AL. In the Monte Carlo simulations, one calculates the energy change and... 

In Monte Carlo Localization, the space is digitized into some random samples (k). As discussed above, multi modal representation is used because of the global localization. Because of this reason, it requires less memory and is computationally more capable. Grid-based approaches were also used, but more memory was required because of 3-D figures (Oxford, 2012). 

To approximately locate the global minimum i.e., to obtain a good quality crystal structure solution) in a reasonable amount of time, grid search methods should be replaced by the stochastic ones, based on a random sampling of the parameter space. This technique, called Monte Carlo MC), has been widely used in other scientific fields to simulate the behavior of complex systems. Its application to crystal structure determination from powder diffraction data has been developed by many authors the main strategies are outlined below. 

Recent work (Altmann, 2002) has focussed on combining a dynamic Monte Carlo percolation-grid simulation for reaction kinetics and an enthalpy-based group-interaction viscoelastic model to develop a model for the chemorheological and network properties of reactive systems. More emphasis will be placed on this model in Chapter 6. 

Cracial to the simulations presented here is the inclusion of surface reconstmction, together with correct time-dependence of the reactions. As such, the method provides an extension of earlier important computer simulations of CO oxidation on Pt surfaces " . A dynamic Monte Carlo method is used based on the solution of the master equation of the reaction system. The reaction system consists of a regular grid with periodic boundary conditions. The largest grid used in our simulations contained ca. eight million reaction sites. A short description of the model is presented in Fig. 3 and in Table I, that shows the parameters of the rate constants considered. 

---