Metropolis Monte Carlo Method Research Articles

Structural and thermodynamic properties ofAg‐Conanoclusters

The Metropolis Monte Carlo and molecular statics methods with a semiempirical embedded atom potential are used to study the structural and thermodynamic equilibrium states of $\mathrm{Ag}\text{\ensuremath{-}}\mathrm{Co}$ isolated nanoparticles. The state parameters considered are size (from 200 to 3000 atoms), temperature (from $0\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1500\phantom{\rule{0.3em}{0ex}}\mathrm{K}$), and composition (from elemental Co to elemental Ag). A lower and an upper limit to the Co concentration is found for the occurrence of a core-shell structure. The lower limit results from a balance between $\mathrm{Co}\text{\penalty1000-\hskip0pt}\mathrm{Co}$ binding energy and the stress of the Ag lattice. The upper limit is a consequence of the wetting of the Co core by Ag. When the core-shell structure takes place, the Ag shell induces an expansion of the Co core of no more than 2% while the Co core induces an average contraction of the Ag lattice which is twice as large and is mainly taken over by the interfacial Ag atomic layer. Co cores melt at a temperature lower than $1500\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, which is not sensitive to the thickness of the Ag shell. Inside the Co cores, coexistence is found possible between a liquid layer surrounding a solid center and the thickness of the liquid layer is an increasing function of temperature. With increasing temperature, depending on its thickness, the Ag shell may undergo a crystal to amorphous transition followed by an amorphous to liquid transition. The former is caused by the Co core but proceeds from the Ag free surface. The melting temperature of the Ag shell is fairly lower than of the Co core, suggesting the possibility of core-shell nanoparticles with a solid core and a liquid shell.

Lattice models of peptide aggregation: Evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.

Density guided importance sampling: application to a reduced model of protein folding

Monte Carlo methods are the most effective means of exploring the energy landscapes of protein folding. The rugged topography of folding energy landscapes causes sampling inefficiencies however, particularly at low, physiological temperatures. A hybrid Monte Carlo method, termed density guided importance sampling (DGIS), is presented that overcomes these sampling inefficiencies. The method is shown to be highly accurate and efficient in determining Boltzmann weighted structural metrics of a discrete off-lattice protein model. In comparison to the Metropolis Monte Carlo method, and the hybrid Monte Carlo methods, jump-walking, smart-walking and replica-exchange, the DGIS method is shown to be more efficient, requiring no parameter optimization. The method guides the simulation towards under-sampled regions of the energy spectrum and recognizes when equilibrium has been reached, avoiding arbitrary and excessively long simulation times. Fortran code available from authors upon request. m.j.parker@leeds.ac.uk.

Statistical fragmentation of small neutral carbon clusters

We present a statistical fragmentation study of the ${\mathrm{C}}_{5}$, ${\mathrm{C}}_{7}$, and ${\mathrm{C}}_{9}$ carbon clusters using the Metropolis Monte Carlo and Weisskopf methods. We show that inclusion of several isomeric forms as well as rotational effects is essential to reproduce the experimental observations. We have found that, for cluster excitation energies around $10\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, several fragmentation channels are efficiently populated, but the dominant one always corresponds to ${\mathrm{C}}_{n\ensuremath{-}3}∕{\mathrm{C}}_{3}$. For high enough excitation energies, we observe first-order phase transitions corresponding to a complete breakup of the cluster.

Prediction of liquid crystalline properties of poly(1,4-phenylene sebacate-oxybenzoate) by Monte Carlo simulation

A Monte Carlo simulation study was undertaken to predict the liquid crystalline potential of a group of poly(1,4-phenylene sebacate-oxybenzoate) polymers. Molecular modelling procedures have been used to determine statistical parameters of isolated chains, with the objective of achieving a description which defines the tendency of a polymer molecule to form a liquid-crystalline phase, its mesogenicity. Initial attention was focused on the persistence length parameter as the most promising in this context to provide a description of mesogenicity which is equally applicable to molecules that consist of rigid segments separated by flexible sequences. A range of known mesogenic molecules has been modelled using RIS Metropolis Monte Carlo (RMMC) method based on carefully determined bond-rotation potentials which enabled the direct estimation of several key structural properties of the polymer chains. Evidence is presented to suggest that for liquid-crystalline polymer (LCP) molecules the nematic to isotropic transition occurs when the ratio of the persistence length to diameter (the persistence ratio) reaches a value of 5. The predictive possibilities of this criterion are explored in the estimation of the nematic–isotropic transition temperatures of the simulated polymers. RMMC was also applied to a well known LCP (poly( p-phenylene terephthalate)) in order to confirm the validity of the simulations. The results provide detailed quantitative information concerning the structural, orientational and liquid crystalline properties of the investigated copolymers as well as qualitative insights into the factors affecting the chain conformation.

Microscopic simulation of the percolation of manganites

The one-orbital double exchange model is studied using the METROPOLIS Monte Carlo method and the microscopic resistor network. The phase competition and percolation are displayed microscopically. As far as the resistivity is concerned, the metal–insulator transition is described by the competition between a fraction p of metallic resistors and a fraction 1−p of insulating resistors. p can be obtained as a function of temperature T, doping percentage x, and external field H. In the present model, systems with different x, T, and H can be unified into a single class of percolation, which is different from the standard picture.

Thin-film polymerization and Metropolis Monte Carlo simulation of thermotropic liquid crystalline poly(ester-amide)s

A series of perfluoroalkyl dicarboxylic acids with different lengths of fluorinated aliphatic segments have been introduced into the 2,6-acetoxynaphthoic acid (ANA) and acetoxy acetanilide (AAA) system and their effects on the evolution of liquid crystal texture and liquid crystallinity have been investigated. The perfluoroalkyl dicarboxylic acids are tetrafluorosuccinic acid (TFSA, n=2), perfluorosuberic acid (PFSUA, n=6) and perfluorosebacic acid (PFSEA, n=8). Novel liquid crystalline polymers (LCPs) made from fluorinated poly(ester-amide)s have been identified; supported by molecular simulation (“RIS” Metropolis Monte Carlo method) and confirmed by the thin film polymerization. Based on computational results, all systems (ANA/AAA/perfluoroalkyl) satisfy the minimum requirement for thermotropic LC formation with persistence ratios larger than 6.42. Moreover, the results obtained also suggest that the chain stiffness and persistence length increase linearly with (CF2)n spacers. The effects of perfluoroalkyl aliphatic spacers on the LC texture evolution, generation and annihilation have been determined by in situ polymerization under a polarizing light microscope. The longest aliphatic perfluoroalkyl spacer (n=8) tends to induce a crystal phase, whereas short aliphatic spacers (n=2 and 6) appear to be more favorable in LC formation. Ternary phase diagrams were plotted to show the relationship among monomer structure, composition, anisotropic and crystalline phases. In addition, Fourier transform infrared spectroscopy (FTIR) results confirm the formation of LCPs, acetoxy group completely disappears after the reaction and ester group forms at the end of the reaction.

Multiple "time step" Monte Carlo simulations: application to charged systems with Ewald summation.

Recently, we have proposed an efficient scheme for Monte Carlo simulations, the multiple "time step" Monte Carlo (MTS-MC) [J. Chem. Phys. 117, 8203 (2002)] based on the separation of the potential interactions into two additive parts. In this paper, the structural and thermodynamic properties of the simple point charge water model combined with the Ewald sum are compared for the MTS-MC real-/reciprocal-space split of the Ewald summation and the common Metropolis Monte Carlo method. We report a number of observables as a function of CPU time calculated using MC and MTS-MC. The correlation functions indicate that speedups on the order of 4.5-7.5 can be obtained for systems of 108-500 waters for n=10 splitting parameter.

An algorithm for simulating the Ising model on a type-II quantum computer

Presented here is an algorithm for a type-II quantum computer which simulates the Ising model in one and two dimensions. It is equivalent to the Metropolis Monte Carlo method and takes advantage of quantum superposition for random number generation. This algorithm does not require the ensemble of states to be measured at the end of each iteration, as is required for other type-II algorithms. Only the binary result is measured at each node which means this algorithm could be implemented using a range of different quantum computing architectures. The Ising model provides an example of how cellular automata rules can be formulated to be run on a type-II quantum computer.

Molecular design of liquid crystalline poly(ester-amide)s with perfluoroalkyl spacers

We have introduced a series of perfluoroalkyl dicarboxylic acids with different lengths of fluorinated aliphatic segments into the 2,6-acetoxynaphthoic acid (ANA) and acetoxy acetanilide (AAA) systems; and their effects on the evolution of liquid crystal texture and liquid crystallinity have been investigated. The perfluoroalkyl dicarboxylic acids are tetrafluorosuccinic acid (TFSA, n=2), hexafluoroglutaric acid (HFGA, n=3), perfluorosuberic acid (PFSUA, n=6) and perfluorosebacic acid (PFSEA, n=8). Computational results based on the ‘RIS’ Metropolis Monte Carlo method indicate that the ANA/AAA/perfluoroalkyl system may form thermotropic liquid crystalline polymers (LCPs) because the calculated persistence ratios are greater than 6.42. Computational results also predict that the systems containing even-numbered perfluoroalkyl acids have greater persistence length and molar stiffness than that containing odd-numbered acids. Experiments were carried out using the in situ thin film polymerization technique under a polarizing optical microscope. We observed that systems containing short aliphatic units (n=2, 3) tend to remain in the LC phase, while systems containing a long aliphatic spacer (n=8) tend to crystallize during the late stage of the polycondensation reaction. The liquid crystal domain formed in the early stage has a disclination strength S of +1. Ternary phase diagrams were plotted to show the relationship among monomer structure, composition, anisotropic and crystalline phases. FTIR results confirm the formation of LCPs.

Evaluation of internal structure and morphology of poly(benzyl ether) dendrimers by molecular dynamics simulations

We performed molecular dynamics (MD) simulations at 300 K on a series of poly(benzyl ether) (PBE) dendrimers having a different core functionalities. We used the rotational isomeric state Metropolis Monte Carlo (RMMC) method to construct the initial configuration in a periodic boundary cell (PBC) before the MD simulations were undertaken. To elucidate the effects that the structural features have on the chain dimension, the overall internal structure, and the morphology, we monitored the radii of gyration,Rg, and the conformational changes during the simulations. The PBE dendrimers in a glassy state adopted less-extended structures when compared with the conformations obtained from the RMMC calculations. We found thatRg of the PBE dendrimer depends on the molecular weight,M, according to the relation,R g ∼M 0.22. The radial distributions of the dendrimers were developed identically in the PBC, irrespective of the core functionality. A gradual decrease in radial density resulted from the fact that the terminal branch ends are distributed all over the molecule, except for the core region.

Annealing contour Monte Carlo algorithm for structure optimization in an off-lattice protein model.

We present a space annealing version for a contour Monte Carlo algorithm and show that it can be applied successfully to finding the ground states for an off-lattice protein model. The comparison shows that the algorithm has made a significant improvement over the pruned-enriched-Rosenbluth method and the Metropolis Monte Carlo method in finding the ground states for AB models. For all sequences, the algorithm has renewed the putative ground energy values in the two-dimensional AB model and set the putative ground energy values in the three-dimensional AB model.

Modeling Lipid–Sterol Bilayers: Applications to Structural Evolution, Lateral Diffusion, and Rafts

This chapter describes the off-lattice models for lipid–cholesterol and lipid–lanosterol bilayers. The difference in behavior between the two sterols was modeled on the basis of their specific molecular characteristics and in terms of their differential interactions with lipid molecules. The Metropolis Monte Carlo method and the algorithm used in the MMC simulations of the model are analyzed. The simulated equilibrium phase diagrams for the lipid–cholesterol and the lipid–lanosterol membranes are shown. It is found that the small modification in the lipid–sterol interaction strength leads to considerable differences in the overall topologies of the two-phase diagrams. To characterize quantitatively, the differential effects of the two sterols on the physical properties of lipid–sterol bilayer membranes, the calculated conformational order parameter is presented. The lipid tracer diffusion coefficient in a model lipid–cholesterol binary mixture was calculated as a function of cholesterol concentration and temperature.

CHARACTERISTICS OF MESOSCOPIC PHASE TRANSITIONS IN TWO-DIMENSIONAL SIMPLE NANOSTRUCTURED MATERIALS

In order to study nanostructured materials, a fundamental framework of the theory and the computer-experimental studies is established. The essential characteristics of the mesoscopic phase transitions and critical phenomena in these materials are evaluated by means of this approach. For nanostructured materials consisting of inert gas atoms, we study mesoscopic phase transitions and critical phenomena by generalizing the renormalization theory and the Metropolis Monte Carlo method. The results obtained by the both methods are reported in two papers: computational results in the present paper and the theoretical results in the paper which follows.

Atomic scale modelling of Al and Ni( [formula omitted]) surface erosion under cluster impact

We have studied sputtering of Al and Ni(1 1 1) surfaces under impact of Al N and Ni N clusters (1⩽ N⩽55) at energy E/ N=500 eV/atom by means of atomic scale modeling using many-body potential, which is based on the second moment approximation of the tight binding model. To reach final equilibrium state at non-zero temperature, the molecular dynamics simulation was combined with data sampling in frame of Metropolis Monte-Carlo method. It was demonstrated that contribution of non-linear (“spike”) effects leads to non-additive enhancement of sputtering yields, which raises with N for N⩾13. The pronounced microcraters are formed in the impact region above a threshold cluster size of around N=13. As a sensitivity study, we show that interaction with electronic subsystem of the target has a strong influence on secondary emission, but almost does not affect the features of surface microstructure of irradiated target.

Copper precipitation in iron: a comparison between metropolis Monte Carlo and lattice kinetic Monte Carlo methods

Several variants are possible in the suite of programs forming multiscale predictive tools to estimate the yield strength increase caused by irradiation in RPV steels. For instance, at the atomic scale, both the Metropolis and the lattice kinetic Monte Carlo methods (MMC and LKMC respectively) allow predicting copper precipitation under irradiation conditions. Since these methods are based on different physical models, the present contribution discusses their consistency on the basis of a realistic case study. A cascade debris in iron containing 0.2% of copper was modelled by molecular dynamics with the DYMOKA code, which is part of the REVE suite. We use this debris as input for both the MMC and the LKMC simulations. Thermal motion and lattice relaxation can be avoided in the MMC, making the model closer to the LKMC (LMMC method). The predictions and the complementarity of the three methods for modelling the same phenomenon are then discussed.

Computer Physics Communications – List of Editors

Mesoscopic phase transitions and the critical behavior of nanostructured materials are summarized for three-dimensional systems (1) of simple particles starting from grains of fcc or hcp and two-dimensional spin-particle systems (2), and generalized q-state (q=3,4) Potts-spin systems (3), interacting magnetoelastically. The interactions are taken into account up to the third nearest neighbors of the Lennard–Jones potential. By generalizing Metropolis Monte Carlo and renormalization methods, the following results are discussed: (1) similarity and difference in nanostructured characteristics inherent in the initial fcc or hcp structure, (2) a lot of local, magnetostructural mesoscopic phase transitions, and (3) the adaptive, intelligent control of phase transition temperatures, in addition to (4) concepts of the bulk, “ordered and disordered phases, magnetic and/or elastic”, completely corrected in the mesoscopic phases, and (5) mesoscopic critical behaviors of N-component systems.

Relationship between the thermal properties and optical emission spectra of the KXeN polyatomic exciplexes

The geometrical structures and optical emission spectra of the K(5S)XeN polyatomic exciplexes are calculated as functions of temperature in the range from 1 to 200 K. The relationships between the emission spectra and the thermal properties are investigated by use of the Metropolis Monte Carlo method. The peak energy values and the linewidths of the transition energy of the calculated emission light spectra of individual exciplexes reflect the structure and the thermal properties of each polyatomic exciplex. As the result of a detailed examination of relationships between the geometrical structure and the optical emission spectra of the KXe3, KXe7, KXe8, and KXe9 polyatomic exciplexes, a change in the structure of a given polyatomic exciplex, or the dissociation into a smaller cluster, can be detected by the discontinuities in the peak energy of the emission light and the linewidth as functions of temperature.

Mesoscopic phase transitions and their critical behavior of nanostructured materials

Abstract Mesoscopic phase transitions and the critical behavior of nanostructured materials are summarized for three-dimensional systems (1) of simple particles starting from grains of fcc or hcp and two-dimensional spin-particle systems (2), and generalized q -state ( q =3,4) Potts-spin systems (3), interacting magnetoelastically. The interactions are taken into account up to the third nearest neighbors of the Lennard–Jones potential. By generalizing Metropolis Monte Carlo and renormalization methods, the following results are discussed: (1) similarity and difference in nanostructured characteristics inherent in the initial fcc or hcp structure, (2) a lot of local, magnetostructural mesoscopic phase transitions, and (3) the adaptive, intelligent control of phase transition temperatures, in addition to (4) concepts of the bulk, “ordered and disordered phases, magnetic and/or elastic”, completely corrected in the mesoscopic phases, and (5) mesoscopic critical behaviors of N-component systems.

Interferometric SAR image restoration using Monte Carlo metropolis method

We present a novel method of interferometric synthetic aperture radar (InSAR) image restoration. An InSAR image is modeled as a complex-valued Markov random field (CMRF). Corrupted parts, which are indicated by residues in phase data, are restored by using the Monte Carlo Metropolis (MM) method based on their uncorrupted neighbor's CMRF parameter values. The system is implemented as a complex-valued neural network. The restoration process reduces the residue number, which is useful in the phase unwrapping process. The advantage of the method is demonstrated in the unwrapping process of an InSAR image that contains highly dense residues.