Monte Carlo simulations, computational development

What has been developed within the last 20 years is the computation of thermodynamic properties including free energy and entropy [12, 13, 14]. But the ground work for free energy perturbation was done by Valleau and Torrie in 1977 [15], for particle insertion by Widom in 1963 and 1982 [16, 17] and for umbrella sampling by Torrie and Valleau in 1974 and 1977 [18, 19]. These methods were primarily developed for use with Monte Carlo simulations continuous thermodynamic integration in MD was first described in 1986 [20]. 

The temperature, pore width and average pore densities were the same as those used by Snook and van Megen In their Monte Carlo simulations, which were performed for a constant chemical potential (12.). Periodic boundary conditions were used In the y and z directions. The periodic length was chosen to be twice r. Newton s equations of motion were solved using the predictor-corrector method developed by Beeman (14). The local fluid density was computed form... 

Efforts have been made to develop EOS for detonation products based on direct Monte Carlo simulations instead of on analytical approaches.35-37 This approach is promising given recent increases in computational capabilities. One of the greatest advantages of direct simulation is the ability to go beyond van der Waals 1-fluid theory, which approximately maps the equation of state of a mixture onto that of a single component fluid.38... 

Probabilistic approaches take advantage of current computational capabilities to combine all of the data in a pesticide residue distribution (rather than a single expected value) with food consumption data to develop a distribution of daily exposure. This approach is called a Monte Carlo simulation, although there are many ways to conduct this type of analysis. 

The estimation of the jamming coverage for the RSA of monodisperse disks is not an important issue, because its value is already accurately known from Monte Carlo simulations [12], However, it is of interest to develop a procedure that can predict the available area and the jamming coverage for a mixture of disks, for which much Less information is available. Even at equilibrium, for which reasonable accurate equations of state for binary mixtures of hard disks are known for low densities [ 19,20], the available area vanishes only for the unphysical total coverage 9 = 9 +0p = 1 (where the subscripts S and L stand for small and large disk radii, respectively), hence there is no jamming . Exact analytical expressions are known only for the first three virial coefficients of a binary mixture of disks [21], The fourth and fifth coefficients were computed numerically for some diameter ratios and molar fractions for an equilibrium gas [22], However, there are no such calculations for the RSA model. 

In the current paper, we discuss some of the new approaches and results that have been developed and obtained recently within the context of such molecular modeling research, and in particular with the mean field and Monte Carlo studies of a lattice model. The next section describes the Gaussian random field method (Woo et al, 2001), which provides a computationally efficient route to generate realistic representations of the disordered mesoporous glasses. Application of the mean field theory, and Monte Carlo simulations are described in Secs. 3 and 4, respectively. 

In spite of the great success of the computer simulation methods in the determination of the microscopic properties of the solutions, the capacity of the traditional MD and MC simulations is always limited by the choice of the suitable potential functions to describe the interatomic interactions. The potentials are most often checked by comparison of the structural properties calculated from the simulation with those determined experimentally. The reverse Monte Carlo (RMC) method, developed by McGreevy and Pusztai [41] does not rely upon knowledge of any interaction potential, instead it generates a large set of atomic configurations on the condition that the difference between the experimental and calculated structure functions (or pair-distribution functions) should be minimum. The same structural... 

The studies of intermolecular quadnipolar relaxation with MD simulations (and Monte Carlo simulations) was initiated by Engstrom et al. [49] in the beginning of the eighties [50-54]. The problem then concerned the nuclear spin relaxation of ions in water. Very successful and well accepted theoretical models of the electrostatic mechanism had been developed, and with computer simulations it was possible to examine some of the assumptions of these models [37,38]. Furthermore, the performance of the electrostatic models could be compared to that of theoretical models of the collision induced mechanism [36,55]. 

By the 1970s, larger computers permitted the statistical mechanical treatment of molecules with complicated (other than spherical) potentials. By using potentials similar to MM2, molecular dynamics and Monte Carlo methods were developed, and calculations could be carried out on whole assemblies of molecules. A successful simulation of the molecular dynamics of water by Rahman and Stillinger allowed the calculation of properties such as dielectric constants. The hydrogen bonding structure of water was finally revealed. Thus, some early approximate developments had begun to pay off. 

Ken Jordan received his Ph.D. in physical chemistry in 1974 under the direction of Bob Silbey at MIT. He then joined the Department of Engineering and Applied Science, Yale University, as a J.W. Gibbs Instructor, being promoted to Assistant Professor in 1976. In 1978 Professor Jordan moved to the Chemistry Department at the University of Pittsburgh where he is now Professor and Director of the Center for Molecular and Materials Simulations. His interest in the application of computers to chemical problems stems from his graduate student days. Professor Jordan s recent research has focused on the properties of hydrogen-bonded clusters, modeling chemical reactions on surfaces, electron-induced chemistry and the development of new methods for Monte Carlo simulations. 

To address these problems, this paper presents a mass balance technique specifically developed for evaluating the resource-in-place potential of basin-centred gas prospects. This paper begins with a general overview of basin-centred gas systems (BCGS), including a summary of common attributes identified from a literature survey. A derivation of the mass balance technique and an explanation of its elements foUow this summary. Application of the technique is illustrated with an example from the Bossier tight gas sand play in the East Texas Basin located in eastern Texas, USA. Uncertainty in resource-in-place estimates are quantified by incorporating a Monte Carlo simulation technique with the mass balance computations. 

Dembo et al. [1988] developed a model based on the ideas of Evans [1985] and Bell [1978]. In this model, a piece of membrane is attached to the wall, and a pulling force is exerted on one end while the other end is held fixed. The cell membrane is modeled as a thin inextensible membrane. The model of Dembo et al. [1988] was subsequentlyextended via a probabilistic approach for the formation of bonds by Coezens-Roberts et al. [1990]. Other authors used the probabilistic approach and Monte Carlo simulation to study the adhesion process as reviewed by Zhu [ 2000]. Dembo s model has also been extended to account for the distribution of microvilli on the surface of the cell and to simulate the rolling and the adhesion of a cell on a surface under shear flow. Hammer and Apte [1992] modeled the cell as a microvilli-coated hard sphere covered with adhesive springs. The binding and breakage of bonds and the distribution of the receptors on the tips of the microvilli are computed using a probabilistic approach. 

---