Showing papers on "Dynamic Monte Carlo method published in 1980"
TL;DR: In this article, a Monte Carlo computer program was developed for determining ion range and damage distributions as well as angular and energy distributions of backscattered and transmitted ions in amorphous targets.
4,204 citations
CERN1
TL;DR: In this article, the authors lay a theoretical basis for both the traditional Monte Carlo and quasi-Monte Carlo methods, and present some practical aspects of when and how to use them.
Abstract: The Monte Carlo method has long been recognised as a powerful technique for performing certain calculations, generally those too complicated for a more classical approach. Since the use of high-speed computers became widespread in the 1950s, a great deal of theoretical investigation has been undertaken and practical experience has been gained in the Monte Carlo approach. The author tries to lay a theoretical basis for both the 'traditional' Monte Carlo and quasi-Monte Carlo methods, and, to present some practical aspects of when and how to use them. An important theme is the comparison of Monte Carlo, quasi-Monte Carlo and numerical quadrature for the integration of functions, especially in many dimensions.
432 citations
Book•
01 Mar 1980
TL;DR: In this article, Monte Carlo methods for solving direct and inverse problems of the theory of radiative transfer in a Spherical Atmosphere were presented. And Monte Carlo algorithms for estimating the Correlation Function of Strong Light Fluctuations in a Turbulent Medium.
Abstract: 1 Introduction- 2 Elements of Radiative-Transfer Theory Used in Monte Carlo Methods- 3 General Questions About the Monte Carlo Technique for Solving Integral Equations of Transfer- 4 Monte Carlo Methods for Solving Direct and Inverse Problems of the Theory of Radiative Transfer in a Spherical Atmosphere- 5 Monte Carlo Algorithms for Solving Nonstationary Problems of the Theory of Narrow-Beam Propagation in the Atmosphere and Ocean- 6 Monte Carlo Algorithms for Estimating the Correlation Function of Strong Light Fluctuations in a Turbulent Medium- References
359 citations
TL;DR: In this article, Monte Carlo calculations in the grand canonical ensemble for coulombic systems were carried out for 1:1, 2:2 and 2:1 aqueous electrolytes in the primitive model with equal ion sizes.
Abstract: Monte Carlo calculations in the grand canonical ensemble are described for coulombic systems, and carried out for 1:1, 2:2, 2:1, and 3:1 aqueous electrolytes in the primitive model with equal ion sizes. Energies and activity coefficients are obtained, and the scope and reliability of the method is discussed.
253 citations
TL;DR: In this article, a modified sampling technique is proposed for use in Monte Carlo calculations in the grand canonical ensemble, called the cavity-biased (T, V, μ) Monte Carlo procedure, attempts insertions of new particles into existing cavities in the system instead of at randomly selected points.
Abstract: A modified sampling technique is proposed for use in Monte Carlo calculations in the grand canonical ensemble. The new method, called the cavity-biased (T, V, μ) Monte Carlo procedure, attempts insertions of new particles into existing cavities in the system instead of at randomly selected points. Calculations on supercritical Lennard-Jones fluid showed an 8-fold increase in the efficiency of the insertion process using the new method. The highest density that can be successfully treated was raised by 35 per cent, making part of the liquid region of the Lennard-Jones fluid now accessible to theoretical study by this method.
214 citations
185 citations
172 citations
TL;DR: In this article, Monte Carlo renormalization group methods were applied to the classical three-component Heisenberg model on a two-dimensional lattice and the expectation values of local correlations of spins and various sized block spins were computed using traditional Monte Carlo methods.
Abstract: Monte Carlo renormalization-group methods were applied to the classical three-component Heisenberg model on a two-dimensional lattice. Expectation values of local correlations of spins and various sized block spins were computed using traditional Monte Carlo methods. By matching quantities at different length scales generated by different Monte Carlo Hamiltonians we directly determined the renormalization of the nearest-neighbor coupling. Using these data and the results of high-temperature expansions and low-temperature renormalization-group calculations we have determined that this model does not have a phase transition. We have also obtained the amplitude for the low-temperature divergence of the susceptibility and the correlation length.
159 citations
TL;DR: In this article, the authors compared various theories of dilute coulombic systems with canonical and grand canonical Monte Carlo data on the thermodynamics and structure of this system: HNC, BGY, MPB, and ORPA+B2.
Abstract: Canonical Monte Carlo results are reported for the 2:2 aqueous electrolyte in the primitive model. The various theories of dilute coulombic systems are compared with canonical and grand canonical Monte Carlo data on the thermodynamics and structure of this system: HNC, BGY, MPB, and ORPA+B2 are comparably successful, most other theories less so. The MC results show that there are many triple ions or larger clusters even at low concentrations. The problem of extrapolating experimental thermodynamic data for 2:2 electrolytes is discussed.
119 citations
TL;DR: In this article, high and low-temperature series, Monte Carlo simulations, mean-field calculations, and renormalization-group ideas are used to analyze the behavior of the Ashkin-Teller model in three dimensions.
Abstract: High- and low-temperature series, Monte Carlo simulations, mean-field calculations, and renormalization-group ideas are used to analyze the behavior of the Ashkin-Teller model in three dimensions. The data generated by series and Monte Carlo methods in the neighborhood of the decoupling point are consistent with the renormalization-group conclusion that this system cannot show a line of continuously varying exponents. Thus the phase diagram for the $d=3$ system is quite different from that in $d=2$. Indeed a new phase (not seen in $d=2$) is observed, one in which the system spontaneously breaks its natural symmetry between its two kinds of Ising spins. A variety of continuous transitions are observed and explained in terms of an analysis which is fully consonant with renormalization-group concepts.
113 citations
TL;DR: In this article, the authors applied the grand canonical ensemble Monte Carlo method to the electrical double layer, using a discrete surface charge distribution and the restricted primitive model for the electrolyte, and compared the results with the Gouy-Chapman theory for bulk electrolyte concentrations up to 0.2 C/m2.
Abstract: The grand canonical ensemble Monte Carlo method is applied to the electrical double layer, using a discrete surface charge distribution and the restricted primitive model for the electrolyte. A systematic examination of the effects of the dimensions of the basic Monte Carlo cell shows that the usual minimum image technique, for determining the potential energy of the system, must be supplemented by long range corrections. Alternatively, very large dimensions or numbers of ions must be employed. The calculated ion distribution functions are compared with the Gouy–Chapman theory for bulk electrolyte concentrations up to 0.2 C/m2. The Gouy–Chapman theory compares very well with the Monte Carlo results for electrolyte concentrations up to 0.1 mole/dm3, but quantitatvive differences appear at 1 mole/dm3. These differences are more pronounced at 2 mole/dm3 for which the Monte Carlo results indicate an inversion of the positive and negative charge distribution functions.
TL;DR: Monte Carlo is used as a tool for the elicitation of a uniform prior on a finite region by making use of several types of prior information in Klein's model I.
TL;DR: In this paper, a dynamic Monte Carlo method was used to investigate the thermodynamics of static and time-dependent properties of the freely jointed polymer chain with Lennard-Jones type intramolecular forces.
Abstract: Using a dynamic Monte Carlo method we investigated the thermodynamics of static and time‐dependent properties of the freely jointed polymer chain with Lennard‐Jones type intramolecular forces. The Θ temperture is calculated to kBΘ/−=3.70±0.01 (− is the Lennard‐Jones energy parameter). We give estimates for the equilibrium values of end‐to‐end distances, radii of gyration, and densities for chains consisting of up to N=63 segments and for various temperatures. The detailed structure of the extended coil state (T≳Θ) and the dense globular state (T<Θ) are demonstrated by their average internal distances and their structure functions. The results seem to confirm the predicted scaling laws. Especially we found that for T=Θ the mean size of the coil is ∼N1/2 but the detailed structure is different from a random walk shape. Although the specific heat exhibits a maximum below the Θ temperature, the finite size effects are too serious to confirm the predicted logarithmic divergency. The dynamics of our Monte Carlo...
TL;DR: In this paper, Monte Carlo simulations for the square-well fluid for 1.125?λ?2, where λ is the width of the well, are presented and compared with perturbation theory and, λ = 1.85, with the BGY theory.
Abstract: Some results of Monte Carlo simulations for the square‐well fluid for 1.125?λ?2, where λ‐1 is the width of the well, are presented and compared with perturbation theory and, λ=1.85, with the BGY theory. In general, we find perturbation theory to be more reliable than the BGY theory. For λ≳1.5, perturbation theory is generally satisfactory. However, for λ<1.5, the pressures calculated from perturbation theory become less satisfactory as λ is decreased.
TL;DR: In this paper, two-dimensional Ising models on a square lattice with competing interactions along one axis or both axes are studied primarily by the Monte Carlo method and several commensurate-incommensurate transitions are found.
Abstract: Two-dimensional Ising models on a square lattice with competing interactions along one axis or both axes are studied primarily by the Monte Carlo method. Several commensurate-incommensurate transitions are found. Dislocation-like configurations are identified near the sinusoidal — paramagnetic transition in accordance with the idea that the transition might be of Kosterlitz-Thouless, XY-like character.
IBM1
TL;DR: Isothermal-isobaric Monte Carlo computer experiments on melting in a two-dimensional Lennard-Jones system indicate that the transition is first order, in contrast to the two-stage, second-order melting behavior suggested as a possibility by Halperin and Nelson as discussed by the authors.
Abstract: Isothermal-isobaric Monte Carlo computer experiments on melting in a two-dimensional Lennard-Jones system indicate that the transition is first order, in contrast to the two-stage, second-order melting behavior suggested as a possibility by Halperin and Nelson
TL;DR: In this article, the structure and phase behavior of 13, 19, 55 and 55 Lennard-Jones clusters were investigated using a Monte Carlo method, which allowed the canonical ensemble to be correctly simulated and all thermodynamic variables to be properly defined.
Abstract: Using a Monte Carlo method, the structure and phase behaviour of Lennard-Jones clusters composed of 13, 19 and 55 particles have been investigated. In contrast to most previous work, the clusters were placed in a hard constraining sphere of varying diameter, which allowed the canonical ensemble to be correctly simulated and all thermodynamic variables to be properly defined. In all the clusters the liquid-solid transition could be readily detected by observing the changes in radial density distribution functions and in thermodynamic quantities. For the 55 atom cluster, a two phase region was observed, characterized by a drastic increase in heat capacity of the system. In this case the cluster was composed of a solid core of 13 atoms, surrounded by a fluid-like shell. At high pressures and low temperatures the 19 and 55 atom clusters underwent a solid-solid transition.
TL;DR: In this paper, a detailed comparison of the theoretical results for aluminum and polymethylmethacrylate (PMMA) with experimental results show that this approach describes the energy distribution of transmitted electrons through thin films of aluminum and PMMA more realistically than the Monte Carlo approaches utilizing Bethe's stopping power equation.
Abstract: Fundamental characteristics of electron penetration in solids, such as energy and angular distributions of transmitted electrons, have been theoretically calculated using a Monte Carlo approach. The essential features of the Monte Carlo approach are the inclusion of the random nature of inelastic scattering events, and also the extension of Gryzinski’s semiempirical expression for core electron excitation to valence electron excitation through the use of an appropriate mean binding energy. A detailed comparison of the theoretical results for aluminum and polymethylmethacrylate (PMMA) with experimental results show that the direct Monte Carlo approach describes electron scattering events in solids very well. It is also shown that this approach describes the energy distribution of transmitted electrons through thin films of aluminum and PMMA more realistically than the Monte Carlo approaches utilizing Bethe’s stopping power equation.
TL;DR: In this article, Monte Carlo techniques are used for a complete study of unipolar semiconducting components for both diffusion noise properties and static characteristics, taking into account space-charge reaction by integration of Poisson's equation.
Abstract: It is shown in this paper that Monte Carlo techniques are available for a complete study of unipolar semiconducting components for both diffusion noise properties and static characteristics. This necessitates taking into account space-charge reaction by integration of Poisson's equation. Two possible methods are proposed and carried out in a unidimensional treatment. Emphasis is given to the various problems which are encountered, especially those concerning the reliability of the solutions. In the first of the two methods (single carrier) the validity of classical electrokinetics equations is investigated, showing the influence of possible relaxation effects in a component. In the second method (multicarrier), it is shown that diffusion noise properties are approachable by observation and spectral analysis of current or voltage fluctuations at the ends of the component.
TL;DR: The molecular dynamics method is shown to be more efficient than either of the Monte Carlo methods, and an acceptance ratio close to 1/6 yields optimum efficiency for the Metropolis method, in contrast to what is often assumed.
Abstract: Three numerical techniques for generating thermally accessible configurations of globular proteins are considered; these techniques are the molecular dynamics method, the Metropolis Monte Carlo method, and a modified Monte Carlo method which takes account of the forces acting on the protein atoms. The molecular dynamics method is shown to be more efficient than either of the Monte Carlo methods. Because it may be necessary to use Monte Carlo methods in certain important types of sampling problems, the behavior of these methods is examined in some detail. It is found that an acceptance ratio close to 1/6 yields optimum efficiency for the Metropolis method, in contrast to what is often assumed. This result, together with the overall inefficiency of the Monte Carlo methods, appears to arise from the anisotropic forces acting on the protein atoms due to their covalent bonding. Possible ways of improving the Monte Carlo methods are suggested.
TL;DR: The role played by the truncation of the intermolecular potential is analysed using two different truncations, the spherical cutoff and the cubic cut-off, in particular for ST2 water, with 27, 125 and 216 water molecules as discussed by the authors.
Abstract: The structural and thermodynamic properties of water are studied using the force bias Monte Carlo simulation. In particular for ST2 water, the effect of system size is examined with 27, 125 and 216 water molecules. The role played by the truncation of the intermolecular potential is analysed using two different truncations, the spherical cut-off and the cubic cut-off. Also a recent simulation with the Watts potential using Ewald summation by McDonald and Klein is compared with one employing the spherical cut-off. In all cases the angular correlation functions show a strong dependence on the type of boundary condition used, whereas the usual radial functions g oo(r), g oh(r) and g hh(r) do not depend much on the boundary conditions. Because of this dependence of angular correlations on the boundary conditions, care must be exercised in comparing simulation results from small systems to real experiments.
TL;DR: In this article, a Monte Carlo simulation of a dilute aqueous solution of argon has been performed in the canonical (T,V,N) ensemble and the argon-water pair potential energy function was obtained, with a best fitting procedure, from a set of 85 ab initio SCF energy values calculated with an extended basis set.
Abstract: A Monte Carlo simulation of a dilute aqueous solution of argon has been performed in the canonical (T,V,N) ensemble. The argon–water pair potential energy function has been obtained, with a best fitting procedure, from a set of 85 ab initio SCF energy values calculated with an extended basis set. Both energetic and structural evidences supporting the hypothesis of water structure promotion by nonpolar solutes are provided. Water molecules close to argon are oriented in a way similar to that of a crystalline clathrate cage. This analogy however is restricted to a local environment, which suggests that only parts of a real clathrate cage are present at a given time in this solution.
TL;DR: In this article, the authors proposed an adiabatic volume fluctuation model for the Lennard-Jones fluid, which treated the volume as an additional dynamic variable having its own equation of motion.
Abstract: Equilibrium molecular dynamics simulations of the Lennard‐Jones fluid have been performed to serve as tests of a method recently suggested by Andersen for obtaining results in the isoenthalpic–isobaric ensemble. The method involves the introduction of adiabatic volume fluctuations into the simulation by treating the volume as an additional dynamic variable having its own equation of motion. Our findings are that (a) it is a simple task to modify an existing molecular dynamics program to the new method and (b) results for the static properties of the fluid are the same as those obtained by other Monte Carlo and molecular dynamics techniques. At this stage the method still needs refinement in order to produce the correct dynamic properties of the fluid.
TL;DR: In this article, an empirical formula for the beam length distribution that enables the total exchange areas to be calculated for any gas absorption model (i.e., which is not restricted to an exponential absorption law) from the view factors in a diatherm medium is proposed.
TL;DR: The Monte Carlo technique can be used to study the solvent structure around a small peptide and the effect of the aqueous environment on the conformational equilibria of the peptide.
Abstract: Applications of Monte Carlo and molecular dynamics computer simulation techniques indicate that they are potentially powerful tools for understanding biological systems at the molecular level. The Monte Carlo technique can be used to study the solvent structure around a small peptide and the effect of the aqueous environment on the conformational equilibria of the peptide.
TL;DR: The power law correction equation (Batho equation) describing the dose distribution in the presence of tissue inhomogeneities is derived in its most general form and is validated for routine patient dosimetry and other analytic correction techniques are shown to be less accurate.
Abstract: A Monte Carlo computer program has been used to calculate axial and off-axis depth dose distributions arising from the interaction of an external beam of 60Co radiation with a medium containing inhomogeneities. An approximation for applying the Monte Carlo data to the configuration where the lateral extent of the inhomogeneity is less than the beam area, is also presented. These new Monte Carlo techniques rely on integration over the dose distributions from constituent sub-beams of small area and the accuracy of the method is thus independent of beam size. The power law correction equation (Batho equation) describing the dose distribution in the presence of tissue inhomogeneities is derived in its most general form. By comparison with Monte Carlo reference data, the equation is validated for routine patient dosimetry. It is explained why the Monte Carlo data may be regarded as a fundamental reference point in performing these tests of the extension to the Batho equation. Other analytic correction techniques, e.g. the equivalent radiological path method, are shown to be less accurate. The application of the generalised power law equation in conjunction with CT scanner data is discussed. For ease of presentation, the details of the Monte Carlo techniques and the analytic formula have been separated into appendices.
IBM1
TL;DR: In this article, the authors assume that the charge collection problem can be reduced to the classical transport of minority carriers, and use the Monte Carlo method to solve the transport equation, which is capable of handling the realistic charge collection environments found in integrated circuits.
Abstract: We are modeling the collection process of ionizing radiation created carriers. We assume that the charge collection problem can be reduced to the classical transport of minority carriers, and use the Monte Carlo method to solve the transport equation. This technique, with modest computational requirements, is capable of handling the realistic charge collection environments found in integrated circuits. To test the simulated results, we carried out charge collection experiments on simple layouts to α-particle radiation. Although a small deviation was found from the assumed classical transport, with a slight modification on the simulation this effect could be taken into account. The final agreement between theory and experiment is excellent.
TL;DR: In this article, Monte Carlo methods are used to calculate density profiles of a dense simple fluid, interacting through a pair potential containing a hard-sphere core and truncated Lennard-Jones attractive tail, near a hard repulsive wall.
Abstract: Monte Carlo methods are used to calculate density profiles of a dense simple fluid, interacting through a pair potential containing a hard‐sphere core and truncated Lennard‐Jones attractive tail, near a hard repulsive wall. The results are compared with integral–equation calculations based on the wall‐particle Ornstein–Zernike equation, with closure approximations such as EXP. The integral equations fail to show several features of the Monte Carlo results, namely dependence on the distance at which the Lennard‐Jones attraction is truncated, and the accumulation of conjugate vapor phase near the wall, which tends to suppress oscillations in the profiles.
TL;DR: In this paper, three-body ion-ion recombination is studied, for Kr+ and F− ions in Ar and Xe+ and Cl− ion in Ne, at temperatures from 300 to 600 K and pressures from 0.5 to 8 atmospheres.
TL;DR: In this article, two new approaches for describing the dynamics of energy transfer in solids have been developed and are described in terms of propagator expansion and Born approximation in the interaction strength.
Abstract: Two new approaches for describing the dynamics of energy transfer in solids have been developed and are described here. The first is a method for treating the case in which weak direct sensitizer-activator interaction acts as a small perturbation on energy transfer by diffusion among sensitizers. A technique involving a propagator expansion and the Born approximation in the interaction strength is used to solve this problem. The second approach is a Monte Carlo technique to simulate the migration of energy on a random distribution of sensitizers. The predictions of both these models are compared to experimental results and to the predictions of other theoretical models. In their regions of validity they predict significantly different results than those of the models commonly used. The models developed here are applicable to many important materials such as those used for rare-earth lasers.