Performing Simulations

So far, there have been few published simulation studies of room-temperature ionic liquids, although a number of groups have started programs in this area. Simulations of molecular liquids have been common for thirty years and have proven important in clarifying our understanding of molecular motion, local stmcture and thermodynamics of neat liquids, solutions and more complex systems at the molecular level [1 ]. There have also been many simulations of molten salts with atomic ions [5]. Room-temperature ionic liquids have polyatomic ions and so combine properties of both molecular liquids and simple molten salts. 

There are many molecular dynamics programs available for simulations, and the book by Allen and Tildesley [6] provides a very helpful introduction for anyone who wishes to perform simulations. The key points are  

In a classical simulation a force-field has to be provided. Experience with molecular liquids shows that surprisingly good results can be obtained with intermolecular potentials based on site-site short-range interactions and a number of charged sites 

---

Our discussion so far has considered the calculation of Helmholtz free energies, which a obtained by performing simulations at constant NVT. For proper comparison with expe inental values we usually require the Gibbs free energy, G. Gibbs free energies are obtaini trorn a simulation at constant NPT. 

MAPPS Maintenance Personnel Performance Simulation model NUREG/CR-3fi26. I984... 

Siegel, A.I. et al., Maintenance Personnel Performance Simulation (MAPPS) Model Description of Model Content, Structure and Sensitivity Testing, 1984. 

Kopstein, F. F. and J. J. Wolf, Maintenance Personnel Performance Simulator (MAPPS) Model User s Manual, ORNL, July 1985. 

IDA Indoor Climate and Energy (ICE) is a new generation of building performance simulation tools. The mathematical models are described in terms of equations in a formal language, NMF. Whenever appropriate, models recommended by ASHRAE have been used. Advanced database features support model reuse. 

Before putting a HEX in operation, it is necessary to characterize its properties in terms of heat and mass transfer, pressure drop, and hydrodynamics. A number of experimental methods have been presented and exemplified. These data are important to perform simulations and to define optimal operating conditions. 

Single-event microkinetics describe the hydrocarbon conversion at molecular level. Present day analytical techniques do not allow an identification of industrial feedstocks in such detail. In addition current computational resources are not sufficient to perform simulations at molecular level for industrial feedstock conversion. These issues are addressed using the relumping methodology. 

The goal in this chapter has been to show that it is possible to perform simulations relevant to electrochemistry-based ab initio surface calculations, without including all known physical effects. Focusing on trends and differences rather than absolute values, the approach in some cases yields not only qualitative results, but also (semi)-quantitative predictions. 

In order to check this prediction, Huber et al. performed simulations on a lattice of dimensions 200 x 20 x 20 the lattice constant was taken as 4 A, and a dielectric constant of e = 80 was assumed throughout the system. Since a fair number of ions is needed to obtain good statistics, the ionic concentrations in this study are of the order of 0.1 M. Figure 8 shows the distribution of the ions and Af for two different values of the interactions constant u. The smaller u, the lower is the repulsion of these ions from phase... 

Such models can be used to solve problems from a study of the analytical solutions or by simple arithmetic calculations. However, it is most likely that a computer is needed for performing simulations. 

The simulations were started from an equilibrium Boltzmann distribution on the free energy surface for A = 0. During a time t = 1, A was changed linearly in time from 0 to 1. We also performed simulations in the backward direction. However, because of the symmetry of V with respect to A, backward transformations are equivalent to forward transformations. Along the resulting trajectories, the work ftW was accumulated. Figure 5.2 shows the probability distributions of the work on the forward direction, and on the backward direction multiplied by exp(-fiW). As expected from (5.35) for AA = 0, the two distributions agree nicely. 

The quantity of primary interest in the study of nonuniform fluids is the density profile of the fluid at a surface. Dickman and Hall [28] reported the density profiles of freely jointed hard-sphere chains at hard walls. Their focus was on the equation of state of melts of hard-chain polymers, and they performed simulations of polymers at hard walls because the bulk pressure, P, can be calculated from the value of the density profile at the surface using the wall sum rule ... 

To perform simulations of relatively large systems for relatively long times, it is essential to optimize the computational strategy of discrete particle simulations. Obviously, the larger the time step 5t, the more efficient the simulation method. For the soft-sphere model, the maximum value for 5t is dictated by the duration of a contact. Since there are two different spring-dashpot systems in our current model, it is essential to assume that tcontact>n — tcontacUU so that... 

A final piece of the proof-of-concept calculations is to compare the predictions obtained by solving the filtered TFM equations with highly resolved simulations of the microscopic TFM equations. For this purpose, Andrews and Sundaresan (2005) performed simulations of the microscopic TFM equations in a 16 x 32 cm periodic domain at various resolutions (e.g., see Fig. 29). From these simulations, they extracted domain-average quantities in the statistical steady state (see Agrawal et al., 2001 for a discussion of how these data are gathered). Fig. 33 shows the domain-average slip velocity between the gas and particle phases at various grid resolutions (shown by the squares connected by... 

J Wang and G Yu, Performance Simulation of Active-Matrix OLED Displays, Photonics Asia 2004 Light-Emitting Diode Materials and Devices, Beijing, China, 2004, pp. 32-44. 

For the case of the bias estimation, several runs were performed simulating a known bias in one of the measurements, assuming different initial values of the variance of the bias. From Fig. 4 it can be seen that the convergence and the speed of response are heavily dependent on the initial values of. To help in the interpretation... 

Second virial coefficients represent the first approximation to the system equation of state. Yethiraj and Hall [148] obtained the compressibility factor, i.e., pV/kgTn, for small stars. They found no significant differences with respect to the linear chains in the pressure vs volume behavior. Escobedo and de Pablo [149] performed simulations in the NPT ensemble (constant pressure) with an extended continuum configurational bias algorithm to determine volumetric properties of small branched chains with a squared-well attractive potential... 

---