Showing papers on "Monte Carlo molecular modeling published in 1977"
TL;DR: In this paper, a Monte Carlo simulation method for solving option valuation problems is presented, which simulates the process generating the returns on the underlying asset and invokes the risk neutrality assumption to derive the value of the option.
1,280 citations
TL;DR: In this paper, the Metropolis Monte Carlo method is used to sample the square of an antisymmetric wave function composed of a product of a Jastrow wave function and a number of Slater determinants.
Abstract: The Metropolis Monte Carlo method is used to sample the square of an antisymmetric wave function composed of a product of a Jastrow wave function and a number of Slater determinants. We calculate variational energies for $^{3}\mathrm{He}$ and several models of neutron matter. The first-order Wu-Feenberg expansion is shown always to underestimate the energy, sometimes seriously. The phase diagram for ground-state Yukawa matter is determined. There is a class of Yukawa potentials which do not lead to a crystal phase at any density.
519 citations
TL;DR: The Monte Carlo approach to testing a simple null hypothesis is reviewed briefly and several examples of its application to problems involving spatial distributions are presented, to illustrate the value of the general approach, particularly at a preliminary stage of analysis.
Abstract: The Monte Carlo approach to testing a simple null hypothesis is reviewed briefly and several examples of its application to problems involving spatial distributions are presented. These include spatial point pattern, pattern similarity, space‐time interaction and scales of pattern. The aim is not to present specific “recommended tests” but rather to illustrate the value of the general approach, particularly at a preliminary stage of analysis.
493 citations
TL;DR: A general explicit formulation of Monte Carlo simulation for quantum systems is given in this article on the basis of the previous fundamental proposal by Suzuki, and new interesting physical results on the two-dimensional XY-model are given.
Abstract: A general explicit formulation of Monte Carlo simulation for quantum systems is given in this paper on the basis of the previous fundamental proposal by Suzuki. This paper also demonstrates explicitly the possibility of it and gives new interesting physical results on the two-dimensional XY-model. That is, the present preliminary simulation seems to indicate a phase transition with a divergent susceptibility, and a very weak singularity of specific heat if it exists, and without long-range order.
200 citations
TL;DR: In this article, a mixture of two identical Lennard-Jones liquids in which the interactions between the components are characterized by a range parameter σ12 obeying the Lorentz rule, but an energy parameter e12= (1−α) (e11e22)1/2 violating the Berthelot rule is presented.
Abstract: Recently developed nonphysical sampling methods—umbrella sampling—have been used to obtain the free energy and other properties of a binary liquid mixture exhibiting phase separation with an upper critical solution point. The system is a mixture of two identical Lennard‐Jones liquids in which the interactions between the components are characterized by a range parameter σ12 obeying the Lorentz rule, but an energy parameter e12= (1−α) (e11e22)1/2 violating the Berthelot rule. The sampling methods enable one to cover wide ranges of temperature and composition with few Monte Carlo experiments, successfully sampling the metastable regions and obtaining the coexistence curve. The case α=0.25 is studied in detail, and compared with some theoretical predictions. An estimate is made of the minimum value of α required for phase separation at low pressures.
192 citations
136 citations
IBM1
TL;DR: In this paper, Monte Carlo values for the equation of state of the two-dimensional Lennard-Jones fluid are reported and a semi-empirical correction term to the second-order Barker-Henderson theory is constructed.
Abstract: Monte Carlo values for the equation of state of the two-dimensional Lennard-Jones fluid are reported. The agreement with previous simulations is good, with the exception of the critical point region. However, the estimates of the critical temperature and density given here are lower than those previously reported. The first and second-order Barker-Henderson and first-order Weeks-Chandler-Andersen perturbation theories are applied to this system and are found to be satisfactory only at high densities. A semiempirical correction term to the second-order Barker-Henderson theory is constructed. The resulting parameterization of the Monte Carlo data is found to be accurate and useful at all densities and temperatures for which the Monte Carlo data exist.
127 citations
TL;DR: In this article, a Monte Carlo algorithm is described which concentrates sampling in the neighborhood of the solute molecule in calculations on dilute solutions, which improves the computational efficiency in the determination of many solution properties.
123 citations
TL;DR: The "Exact" and Monte Carlo calculations are in complete agreement, which allows the Monte Carlo results to be used to calibrate other methods and the relatively simple Chernoff bound is in very good agreement.
Abstract: In this paper four approaches to the calculation of error rates for optical fiber system repeaters are compared ("Exact" calculation, Monte Carlo simulation, Chernoff bounds and the Gaussian approximation). We conclude that the "Exact" and Monte Carlo calculations are in complete agreement. This allows the Monte Carlo results to be used to calibrate other methods. The relatively simple Chernoff bound is in very good agreement with the above, and should be used whenever computational facilities allow. For simpler calculations, or analytical expressions for the effects of parameter variations, the Guassian approximation gives a reasonable good estimate of the receiver sensitivity. However, it tends to underestimate the threshold setting and overestimate the optimal avalanche gain.
116 citations
TL;DR: This paper presents a new Monte Carlo method to estimate the reliability of a large complex system represented by a reliability block diagram or by a fault tree and proves that it gives a reliability estimate with a smaller variance than that of the crude Monte Carlo methods.
Abstract: This paper presents a new Monte Carlo method to estimate the reliability of a large complex system represented by a reliability block diagram or by a fault tree. Two binary functions are introduced; one dominates the system structure function and the other is dominated by the structure function. These functions can be constructed easily by using part of path sets and cut sets of the system. Through the use of these binary functions, two variance-reducing techniques (control variate and importance sampling) are applied to the Monte Carlo evaluation of the system reliability. We prove that the new Monte Carlo method gives a reliability estimate with a smaller variance than that of the crude Monte Carlo method.
106 citations
TL;DR: In this article, simple Monte Carlo multiple-trapping model simulations of the observed anomalous transit-time dispersion have been made and the model employs multiple trapping from an exponential distribution.
Abstract: Simple Monte Carlo multiple-trapping model simulations of the observed anomalous transit-time dispersion have been made. The model employs multiple trapping from an exponential distribution. Our results simulate the features of the experimental observations as well as provide a rational explanation for the transition from nondispersive to dispersive transients as a function of temperature. Comparisons with recent results in $a\ensuremath{-}\mathrm{Se}$ show excellent agreement.
TL;DR: In this article, the authors used the molecular dynamics method to compute the compressibility factor, orientational order parameter, velocity autocorrelation function, and diffusion constants for a system of 256 hard spherocylinders at two densities in the liquid region.
Abstract: Using the molecular dynamics method we have computed the compressibility factor, orientational order parameter, velocity autocorrelation function, and diffusion constants for a system of 256 hard spherocylinders at two densities in the liquid region. The equation of state is in agreement with that found by the Monte Carlo method and that predicted by the scaled particle theory. The calculated orientational order parameter was near the expected value of (1/N)1/2 for an isotropic system.
TL;DR: In this article, a theoretical study of the statistical mechanical description of a system composed of interaction-site molecules is made using the site-site correlation function approach, and the problem of excluded volume of a pair of spheres embedded in the dumb-bells is solved.
Abstract: A theoretical study of the statistical mechanical description of a system composed of interaction-site molecules is made using the site-site correlation function approach The system of hard dumb-bells is then studied in detail The problem of excluded volume of a pair of spheres embedded in the dumb-bells is solved, which enables one to evaluate the second virial coefficient and to derive an approximate equation of state in a closed analytical form The equation of state obtained shows good agreement with Monte Carlo data
TL;DR: In this paper, the radial distribution function of a hardsphere solid is given, along with a simple analytic approximation for that function, which is useful over a wider range of densities than that developed earlier by one of us.
Abstract: New Monte Carlo estimates of the radial distribution function of a hardsphere solid are given, along with a simple analytic approximation for that function. The approximation is useful over a wider range of densities than that developed earlier by one of us.
TL;DR: In this paper, a method for extrapolation of distribution functions obtained from Monte Carlo or molecular dynamics simulations is presented, which assumes a zero direct correlation function at large and assumes that the distribution functions have no direct correlation at large.
Abstract: A method is presented for the extrapolation of distribution functions obtained from Monte Carlo or Molecular Dynamics simulations. The procedure assumes a zero direct correlation function at large ...
TL;DR: In this paper, the solutions of the RISM integral equation are compared with Monte Carlo results for three hard core diatomics, including both homonuclear and heteronuclear models.
Abstract: The solutions of the RISM integral equation are compared with Monte Carlo results for three hard‐core diatomics, including both homonuclear and heteronuclear models. The comparison shows that the RISM theory is qualitatively reliable and that the sizes of quantitative errors in the theory are predicted accurately by internal consistency tests.
TL;DR: In this article, Monte Carlo studies of the classical XY -model on 20 × 20 and 30 × 30 square lattices with periodic boundary conditions and nearest neighbor interactions are presented, and preliminary results on the temperature-dependence of the pair correlation functions, susceptibility and specific heat are given.
01 May 1977
TL;DR: In this paper, a concise model has been developed to analyze uncertainties in stratospheric perturbations, yet uses a minimum of computer time and is complete enough to represent the results of more complex models.
Abstract: A concise model has been developed to analyze uncertainties in stratospheric perturbations, yet uses a minimum of computer time and is complete enough to represent the results of more complex models. The steady state model applies iteration to achieve coupling between interacting species. The species are determined from diffusion equations with appropriate sources and sinks. Diurnal effects due to chlorine nitrate formation are accounted for by analytic approximation. The model has been used to evaluate steady state perturbations due to injections of chlorine and NO(X).
TL;DR: In this article, the direct simulation Monte Carlo method is extended to cover molecular dissociation and recombination reactions, including internal degrees of freedom with separate relaxation times for rotation and vibration, and a finite difference procedure is used to extend this program to cover the dissociation relaxation zone behind strong normal shock waves.
TL;DR: In this article, Monte Carlo computations for the thermodynamic properties and pair distribution function of a one-component system of charged hard spheres in a uniform neutralizing background are compared with perturbation theories.
Abstract: Monte Carlo computations for the thermodynamic properties and pair distribution function of a one-component system of charged hard spheres in a uniform neutralizing background are compared with perturbation theories. These are the ‘mixed’ integral equation approach proposed by Lado, the exponential approximation of Andersen and Chandler, a higher-order cluster expansion approximation due to Stell and Verlet and Weis and the mean spherical approximation (MSA). It is shown that, while none of these approximations gives satisfactory results for the pair distribution function, both the MSA and the mixed integral equation approach give internal energies in excellent agreement with the Monte Carlo results.
TL;DR: In this paper, the Monte Carlo technique and the Kadanoff block transformation are combined for the Ising model in two and three dimensions, and the critical point and critical indices are obtained.
Abstract: A program combining the Monte Carlo technique and the Kadanoff block transformation is carried out for the Ising model in two and three dimensions, and the critical point and the critical indices $\ensuremath{
u}$ and $\ensuremath{\delta}$ are obtained. A sequence of approximations seems to converge to the exact Onsager result in two dimensions, although the convergence of $\ensuremath{
u}$ is rather slow. In three dimensions, the numbers obtained seem to tend towards the results from exact series expansions.
TL;DR: Verdier and Kranbuehl as discussed by the authors used two-bead crankshaft motions in contrast to earlier kinetic models that included only single-branch motions.
Abstract: Recently, Verdier and Kranbuehl (VK) have examined by Monte Carlo simulation the relaxation times for the end‐to‐end vector of a polymer, with excluded volume, on a lattice. The kinetic model employed by VK includes two‐bead crankshaft motions in contrast to earlier kinetic models that included only single‐bead motions. It is shown that the new VK model contains constraints similar to those discussed by Hilhorst and Deutch for the single‐bead model. These constraints lead to artificially long relaxation times not due to the long‐range excluded‐volume effect.
01 Jan 1977
TL;DR: In this article, a new criterion for selecting a subset of k populations and also two subset selection procedures introduced by Gupta, Desu, and Sobel in terms of this criterion are described.
Abstract: Publisher Summary The extensive literature on ranking and selection procedures depends heavily on the use of two alternative criteria that are philosophically out of tune with the decision theoretic framework. This chapter describes a new criterion for selecting a subset of k populations and also describes two subset selection procedures introduced by Gupta, Desu, and Sobel in terms of this criterion. Results based on a Monte Carlo studies show that the Gupta procedure is highly efficient. The criterion used in the chapter is advanced in terms of a natural loss function for only one potential application and is not intended to be universally relevant. Calculations are carried out in an invariant Bayesian framework using normal distributions and normal priors. Comparisons are based on Monte Carlo simulations for the case of k = 8 populations.
TL;DR: In this paper, the tracer diffusion coefficient in β-alumina using the path probability method is assessed using a Monte Carlo method, where two interpenetrating non-equivalent triangular sublattices make up the honeycomb lattice on which sodium ions are distributed subject to nearest neighbour repulsion.
Abstract: The calculation by SaAo and Kikuchi (1971) of the sodium tracer diffusion coefficient in β-alumina using the path probability method is assessed using a Monte Carlo method. Two interpenetrating non-equivalent triangular sub-lattices make up the honeycomb lattice on which sodium ions are distributed subject to nearest neighbour repulsion. The Monte Carlo results for the vacancy availability factor and the effective jump frequency factor are in excellent agreement with the calculations of Sato and Kikuchi (1971). Results for the tracer correlation factor differ significantly because of the limitations of the pair-approximation to the path probability method.
01 Dec 1977
TL;DR: A method of calculating potentials and fields that is particularly suited to engineering problems with complicated 3-dimensional geometries that solves Laplace's equation numerically using a floating random-walk technique is concerned.
Abstract: The paper is concerned with a method of calculating potentials and fields that is particularly suited to engineering problems with complicated 3-dimensional geometries. The method solves Laplace's equation numerically using a floating random-walk technique. The efficiency of the basic method can be improved substantially by some simple generalisations, and potential gradients can be calculated directly, as well as the potentials themselves. Examples are given of problems that have arisen in high-voltage engineering for which the potentials and fields have been calculated using a computer program based on the generalised method.
TL;DR: In this paper, a new type of phase transition has been found in the two-dimensional XY-model using Monte Carlo simulations, which show a divergence of susceptibility, but no divergence of specific heat.