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PubMed2003

Monte Carlo method for evaluating the quantum real time propagator.

A new exact representation of the quantum propagator is derived in terms of semiclassical initial value representations. The resulting expression may be expanded in a series, of which the leading order term is the semiclassical one. Motion of a Gaussian wave packet on a symmetric double well potential is used to demonstrate numerical convergence of the series and the ability to compute each element in the series using Monte Carlo methods.

Journal Article↗
PubMed2004

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods.

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.

Journal Article↗
PubMed2004

Modelling an extreme water-lung interface using a single pencil beam algorithm and the Monte Carlo method.

The goal of this study was to quantify, in a heterogeneous phantom, the difference between experimentally measured beam profiles and those calculated using both a commercial convolution algorithm and the Monte Carlo (MC) method. This was done by arranging a phantom geometry that incorporated a vertical solid water-lung material interface parallel to the beam axis. At nominal x-ray energies of 6 and 18 MV, dose distributions were modelled for field sizes of 10 x 10 cm(2) and 4 x 4 cm(2) using the CadPlan 6.0 commercial treatment planning system (TPS) and the BEAMnrc-DOSXYZnrc Monte Carlo package. Beam profiles were found experimentally at various depths using film dosimetry. The results showed that within the lung region the TPS had a substantial problem modelling the dose distribution. The (film-TPS) profile difference was found to increase, in the lung region, as the field size decreased and the beam energy increased; in the worst case the difference was more than 15%. In contrast, (film-MC) profile differences were not found to be affected by the material density difference. BEAMnrc-DOSXYZnrc successfully modelled the material interface and dose profiles to within 2%.

Algorithms↗
PubMed1990

On the multiple-minima problem in the conformational analysis of polypeptides. IV. Application of the electrostatically driven Monte Carlo method to the 20-residue membrane-bound portion of melittin.

The conformational space of the membrane-bound portion of melittin has been searched using the electrostatically driven Monte Carlo (EDMC) method with the ECEPP/2 (empirical conformational energy program for peptides) algorithm. The former methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. The algorithm produces a Monte Carlo search in the conformational hyperspace of the polypeptide using electrostatic predictions and a random sampling technique, combined with local minimization of the energy function, to locate low-energy conformations. As a result of 8 test calculations on the 20-residue membrane-bound portion of melittin, starting from six arbitrary and two completely random conformations, the method was able to locate a very low-energy region of the potential with a well-defined structure for the backbone. In all of the cases under study, the method found a cluster of similar low-energy conformations that agree well with the structure deduced from x-ray diffraction experiments and with one computed earlier by the build-up procedure.

Amino Acid Sequence↗
PubMed2001

Clustering and fluidization in a one-dimensional granular system: molecular dynamics and direct-simulation Monte Carlo method.

We study a one-dimensional granular gas of pointlike particles not subject to gravity between two walls at temperatures T(left) and T(right). The system exhibits two distinct regimes, depending on the normalized temperature difference Delta=(T(right)-T(left))/(T(right)+T(left)): one completely fluidized and one in which a cluster coexists with the fluidized gas. When Delta is above a certain threshold, cluster formation is fully inhibited, obtaining a completely fluidized state. The mechanism that produces these two phases is explained. In the fluidized state the velocity distribution function exhibits peculiar non-Gaussian features. For this state, comparison between integration of the Boltzmann equation using the direct-simulation Monte Carlo method and results stemming from microscopic Newtonian molecular dynamics gives good coincidence, establishing that the non-Gaussian features observed do not arise from the onset of correlations.

Journal Article↗
PubMed2003

Investigation of radiosurgical beam profiles using Monte Carlo method.

An accurate determination of the penumbra of radiosurgery profiles is critical to avoid complications in organs at risk adjacent to the tumor. Conventional detectors may not be accurate enough for small field sizes. The Monte Carlo (MC) method was used to study the behavior of radiosurgical beam profiles at the penumbral region; the BEAM code was also used in this work. Two collimators (2.2- and 0.3-cm diameter) were calculated and compared with empirical measurements obtained with the detectors normally used. The differences found between film dosimetry and MC revealed a systematic error in the reading procedure. In the process, a water phantom was simulated with a layer of the same composition as that of the film. MC calculations with film differed by a small amount from those obtained with the water phantom alone. In conclusion, MC may be used as a verification tool to support dosimetrical procedures with conventional detectors, especially in very small beams such as those used in radiosurgery. Furthermore, it has been proved that the film energy dependence is negligible for fields used in radiosurgery.

Brain Neoplasms↗
PubMed2002

A hybrid Monte Carlo method for crystal structure determination from powder diffraction data.

A hybrid Monte Carlo algorithm for crystal structure determination from powder diffraction data is presented. The algorithm combines the key components of molecular dynamics and Monte Carlo simulations to achieve efficient sampling of phase space, allowing the crystal structure of capsaicin to be determined from powder diffraction data more effectively than by a simulated-annealing approach. The implementation of the algorithm, the choice of the simulation parameters and the performance of the algorithm are discussed.

Journal Article↗
PubMed1992

Folding protein alpha-carbon chains into compact forms by Monte Carlo methods.

A method is presented for generating folded chains of specific amino acid sequences on a simple cubic lattice. Monte Carlo simulations are used to transform extended geometries of simplified alpha-carbon chains for eight small monomeric globular proteins into folded states. Permitted chain transitions are limited to a few types of moves, all restricted to occur on the lattice. Crude residue-residue potentials derived from statistical structure data are used to describe the energies for each conformer. The low resolution structures obtained by this procedure contain many of the correct gross features of the native folded architectures with respect to average residue energy per nonbonded contact, segment density, and location of surface loops and disulfide pairs. Rms deviations between these and the native X-ray structures and percentage of native long-range contacts found in these final folded structures are 7.6 +/- 0.7 A and 48 +/- 3%, respectively. This procedure can be useful for predicting approximate tertiary interactions from amino acid sequence.

Models, Molecular↗
PubMed2006

Genome-wide tagging SNPs with entropy-based Monte Carlo method.

The number of common single nucleotide polymorphisms (SNPs) in the human genome is estimated to be around 3-6 million. It is highly anticipated that the study of SNPs will help provide a means for elucidating the genetic component of complex diseases and variable drug responses. High-throughput technologies such as oligonucleotide arrays have produced enormous amount of SNP data, which creates great challenges in genome-wide disease linkage and association studies. In this paper, we present an adaptation of the cross entropy (CE) method and propose an iterative CE Monte Carlo (CEMC) algorithm for tagging SNP selection. This differs from most of SNP selection algorithms in the literature in that our method is independent of the notion of haplotype block. Thus, the method is applicable to whole genome SNP selection without prior knowledge of block boundaries. We applied this block-free algorithm to three large datasets (two simulated and one real) that are in the order of thousands of SNPs. The successful applications to these large scale datasets demonstrate that CEMC is computationally feasible for whole genome SNP selection. Furthermore, the results show that CEMC is significantly better than random selection, and it also outperformed another block-free selection algorithm for the dataset considered.

Algorithms↗
PubMed2005

A version of diffusion Monte Carlo method based on random grids of coherent states. II. Six-dimensional simulation of electronic states of H2.

We report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrodinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space.

Journal Article↗
PubMed2000

Exact monte carlo method for continuum fermion systems

We offer a new proposal for the Monte Carlo treatment of many-fermion systems in continuous space. It is based upon diffusion Monte Carlo with significant modifications: correlated pairs of random walkers that carry opposite signs, different functions "guide" walkers of different signs, the Gaussians used for members of a pair are correlated, and walkers can cancel so as to conserve their expected future contributions. We report results for free-fermion systems and a fermion fluid with 14 3He atoms, where it proves stable and correct. Its computational complexity grows with particle number, but slowly enough to make interesting physics within the reach of contemporary computers.

Journal Article↗
PubMed2006

High density dental materials and radiotherapy planning: comparison of the dose predictions using superposition algorithm and fluence map Monte Carlo method with radiochromic film measurements.

BACKGROUND AND PURPOSE: During radiotherapy planning high density dental materials create a major challenge in determining correct dose distribution inside patients with head-and-neck tumors. PATIENTS AND METHODS: In this work we investigated the absorbed dose distribution inside a solid water slab phantom with embedded high density material irradiated by a 6MV photon beam of field size 10x10cm. We evaluated the absorbed dose distribution with three different techniques: superposition algorithm, radiochromic film, and the fluence map Monte Carlo (FMMC) method. RESULTS: The results obtained with radiochromic film and FMMC were in good agreement (within +/-5% of the dose) with one another. The superposition algorithm, which is often considered superior to other commercially available dose calculation algorithms, produced appreciably less accurate results than FMMC. In particular, downstream from the high density cerrobend inhomogeneity the superposition algorithm predicts a higher dose than the measurement does by at least 10-16% depending upon the size of the inhomogeneity and the distance from it. Upstream of the high density inhomogeneities the superposition algorithm predicts a lower than measured dose due to its failure to predict the dose enhancement close to the inhomogeneity interface. CONCLUSIONS: The delivered dose downstream from a high density inhomogeneity would be significantly less than the prescribed dose calculated by the superposition algorithm. The FMMC method which is based on a hybrid of the superposition algorithm input fluence data and Monte Carlo can be a useful tool in predicting dose in the presence of high density (e.g. dental) materials.

Algorithms↗