Showing papers on "Monte Carlo molecular modeling published in 1968"
TL;DR: In this article, the Monte Carlo method was adapted to the calculation of the equation of state and radial distribution function for hard disks, and the results obtained for a small system (12 hard disks), as an example of the method, were presented.
Abstract: The N p T ensemble for hard disks is formulated as an equivalent N V T ensemble for a pseudopotential interaction in a reduced configuration space, with exact relations for small periodic systems emphasized. The Monte Carlo method originally devised by Metropolis et al. is then adapted to the calculation of the equation of state and radial distribution function. The present paper then describes some results obtained for a small system (12 hard disks), as an example of the method, and with emphasis upon the statistical reliability of the results and on the effect of different pseudorandom‐number‐generating procedures. At least for such small systems it is possible to obtain, as a byproduct, the N V T ‐ensemble equation of state over a range of densities from an N p T ‐ensemble calculation at a single pressure. Subsequent papers will describe results already in hand for larger systems, including reasonably reliable extrapolations to the “thermodynamic” limit.
198 citations
168 citations
TL;DR: In this paper, non-self-intersecting walks on the simple cubic and face-centered cubic lattices are used as a model for the linear polymer chain with excluded volume and nearest-neighbor interactions between the chain elements.
Abstract: Non‐self‐intersecting walks on the simple cubic and face‐centered cubic lattices are used as a model for the linear polymer chain with excluded volume and nearest‐neighbor interactions between the chain elements. The statistical properties of this model are investigated using the modified Monte Carlo technique for inversely restricted sampling. The following properties are investigated: the limiting distribution function of chain dimensions, the dependence of mean square length of the chain on the number of chain elements, and the thermodynamic properties of the chain. The results of these investigations are presented by a set of parametric representations. Each of these representations includes a parameter which is descriptive of long‐range interactions in the polymer chain. These parameters are investigated for their dependence on the nearest‐neighbor interaction parameter. A particular value for the nearest‐neighbor interaction parameter is found, in which long‐range interaction parameters reduce to the values they would attain were the chain simulated by an equivalent Markovian chain model. Thus, the conditions are found which uniquely define the Flory's theta point of the single chain. It is also found that an infinitely long single chain undergoes a phase transition which is associated with abrupt changes in the thermodynamic properties of the chain at a critical range of the nearest‐neighbor interaction parameter.
122 citations
TL;DR: The first section of this paper is a mathematical construction of a certain Monte Carlo procedure for sampling from the distribution by defining a particular random variable.
Abstract: The first section of this paper is a mathematical construction of a certain Monte Carlo procedure for sampling from the distributionThe construction begins by defining a particular random variable ...
120 citations
TL;DR: The proper justification of Monte Carlo integration must be based not on the randomness of the procedure, which is spurious, but on equidistribution properties of the sets of points at which the integrand values are computed as discussed by the authors.
Abstract: The proper justification of the normal practice of Monte Carlo integration must be based not on the randomness of the procedure, which is spurious, but on equidistribution properties of the sets of points at which the integrand values are computed. Besides the discrepancy, which it is proposed to call henceforth extreme discrepancy, another concept, that of mean square discrepancy, can be regarded as a measure of the lack of equidistribution of a sequence of points in a multidimensional cube. Determinate upper bounds can be obtained, in terms of either discrepancy, for the absolute value of the error in the computation of the integral. There exist sequences of points yielding, for sufficiently smooth functions, errors of a much smaller order of magnitude than that which is claimed by the Monte Carlo method. In the case of two dimensions, sequences with optimum properties can be generated with the help of Fibonacci numbers. The previous arguments do not apply to domains of integration which cannot be reduced to multidimensional intervals. Difficult questions arising in this connection still await an answer.
96 citations
01 Jan 1968
55 citations
38 citations
TL;DR: The functional integration techniques of Kac are shown to be applicable to an evaluation of Anderson's relaxation function in this paper, and the evaluation is worked through for the rotational diffusion model, and the essential features of the Monte Carlo calculation by Saunders and Johnson are confirmed.
Abstract: The functional integration techniques of Kac are shown to be applicable to an evaluation of Anderson's relaxation function. The evaluation is worked through for the rotational diffusion model, and the essential features of the Monte Carlo calculation by Saunders and Johnson are confirmed.
26 citations
TL;DR: In this paper, a Monte Carlo simulation technique is described that can be used to determine the cumulative distribution functions of stochastic variables such as ultimate strength, factor of safety and region of safety.
Abstract: Probabilistic concepts of structural safety are reviewed. A Monte Carlo simulation technique is described that can be used to determine the cumulative distribution functions of stochastic variables such as ultimate strength, factor of safety and region of safety. In a worked example, the variability in strength of an axially loaded short reinforced concrete column is investigated using the Monte Carlo technique and the results are compared with a closed form solution. Short cut methods of selective sampling are also described and demonstrated.
25 citations
TL;DR: The present study has verified Kimura's formula and showed that linkage does not affectu(AB) under initial linkage equilibrium and showed some cases of additive × additive epistasis were studied.
Abstract: The probability of ultimate fixation was studied for 2 loci small populations by the method of Monte Carlo simulation and also partly by analytical treatment. The analytical solutions for fixation probability known at present and the difficulty of their application to more complex situations were discussed. Monte Carlo experiments were carried out for large values ofNes1,Nes2 andNee, for which the analytical solutions have not been obtained.
20 citations
TL;DR: In this article, a Monte Carlo calculation of the nucleonic cascade in the atmosphere has been carried out and preliminary results are presented and compared with measurements of the secondary proton spectrum at sea level.
Abstract: A Monte Carlo calculation of the nucleonic cascade in the atmosphere has been carried out. Preliminary results are presented and compared with measurements of the secondary proton spectrum at sea level.
DOI•
02 Dec 1968
TL;DR: A brief survey of the existing methods for determining when to stop sampling in Monte Carlo simulations is presented and the distinction is made between stopping rules for simulations using independent samples and those using correlated samples.
Abstract: A brief survey of the existing methods for determining when to stop sampling in Monte Carlo simulations is presented. The distinction is made between stopping rules for simulations using independent samples and those using correlated samples. Possible avenues for further research are mentioned.
TL;DR: In this paper, the authors performed the calculation of time independent spin correlation function for a Ising ferromagnet with a Monte Carlo method in the case of a simple cubic lattice, S = ∞ and interactions only between nearest neighbours.
TL;DR: In this paper, a Monte Carlo study of the configurational and statistical thermodynamic properties of ring systems generated on the tetrahedral lattice is presented, and it is shown that the above parameters obtained are in close agreement with those found for open walks.
Abstract: A Monte Carlo study of the configurational and statistical thermodynamic properties of ring systems generated on the tetrahedral lattice is presented. It is shown that the above parameters obtained are in close agreement with those found for open walks. It is suggested that a number of ratios of configurational parameters may be fruitful quantities for studying a variety of systems.
TL;DR: In this paper, an extensive series of numerical studies directed toward understanding and evaluating the various errors in the Boltzmann collision integral solutions of the Nordsieck equation are presented.
TL;DR: In this article, the authors present a method for conducting a Monte Carlo simulation of a space mission when nonlinear effects must be considered and accounted for, which can be used in the analysis of a multiphase mission.
Abstract: This paper presents a method for conducting a Monte Carlo simulation of a space mission when nonlinear effects must be considered and accounted for. The simulation uses precomputed relationships between variables to generate the Monte Carlo samples from which the appropriate statistical information is computed. The method reduces the computing time required for the Monte Carlo simulation to just about that required to perform a standard root-sum-square analysis. The results, however, are considerably greater in information content, allow definitive probabilistic statements to be made about the performance of the vehicle, and can be used in the analysis of a multiphase mission. Thus, a very realistic assessment of the over-all performance of a space vehicle can be made at a reasonable computing cost.
TL;DR: In this article, the authors give a general description of a class of formulas which combine the Monte Carlo and classical approaches to get a lower bound on quadrature errors, and show that for the class D * the error of any non-random (e.g. Newton-Cotes, Gaussian) method is Q(N-) ; for random methods the best he could show was (r = Ö(i\\M) and he showed that there in fact exist methods for which
Abstract: /Ytf, X, ' • • , X) (Ox)*\" • • • (da?)* is continuous on G8 whenever mf ^2, • • • , n8^n. N. S. Bahvalov [ l ] , in a study of lower bounds on quadrature errors showed that for the class D\" the error of any nonrandom (e.g. Newton-Cotes, Gaussian) quadrature method is Q(N-) ; for random methods the best he could show was (r = Ö(i\\M) and he showed that for the set of periodic functions in D* there in fact exist methods for which
TL;DR: In this paper, algebraic Monte Carlo method was used to determine simultaneous effect of several input statistical variables on the output variable, and the authors constructed a histogram based on the simultaneous effect.
Abstract: Histogram construction via algebraic Monte Carlo method, determining simultaneous effect of several input statistical variables on output variable
Journal Article•
Journal Article•