Modified Monte Carlo Algorithm Research Articles

A multi-scale MCCPFEM framework: Modeling of thermal interface grooving and deformation anisotropy of titanium alloy with lamellar colony

Micro-scale thermal interface grooving (TIG), as an important breakdown mechanism of single lamella and the key to spheroidization of lamellar colony, does significant influence on the mechanical response and microstructural evolution of titanium alloy with lamellar colony during hot working. This influence may become remarkable by coupling with meso-scale deformation anisotropy of the colony. The coupled effect across different scales is crucial to the spheroidization of lamellar colony, while rare related research is reported due to the difficulty in experiment. In this work, a multi-scale MCCPFEM framework was proposed to model on the micro-scale TIG and meso-scale deformation anisotropy through the fully coupling of lattice kinetic Monte Carlo (MC) model and crystal plasticity finite element model (CPFEM). During the modeling, the modified MC algorithm was established based on the multiple-integral method (MIM) solution with Mullin's theory, which accounts for the TIG's microstructural evolution. In addition, the deformation anisotropy at different length scales including strain localization at lamella, and strain partitioning at colony was characterized by an explicit CPFEM which includes resistance anisotropy of slip systems, evolution of dislocations and high-fidelity representative lamellar colony. At the same time, geometrically necessary dislocation (GND) was also considered in the CPFEM by developing a new algorithm with mesh-free methodology and re-construct radial basic shape functions. The fully coupling of the multi-scale MCCPFEM was realized through the microstructure-based 2D grids acting as both finite elements and lattice sites. Moreover, re-set ‘zero’ of the deformation gradient of the TIG mesh was proposed to characterize the strain-free state of new TIG nucleation. Then, the TIG-induced changes in the dislocation density, lattice rotation, strain-free state and morphological characteristics were returned to MCCPFEM to determine the heterogeneous deformation and anisotropic mechanical response of the lamellar colony. With this multi-scale model, the coupled effect of the deformation anisotropy (strain localization in beta phase, stress relief in TIG and local internal stress concentration in alpha lamella) and TIG-induced microstructural evolution during the isothermal compression of the IMI834 alloy with lamellar colony is well captured and analyzed.

Geometrical Interruption in the Nerve Anatomical Model of the Foot to Simulate Small Fiber Neuropathy

Diabetic Foot Ulceration (DFU) is a type of Small Fiber Neuropathy (SFN) which usually arises in the unmyelinated smaller Intra-Epidermal Nerve Fibers (IENF) of the foot. Skin biopsy is a diagnostic method to examine quantitatively IENF in the foot but examination is limited to the specific positions of the body. Computational models may provide an alternative approach to examine SFN. Formerly, an anatomical model of Normal IENF (NIENF), based on IENF Density (IENFD) at various locations in the human foot was presented. Therefore, in this study, a geometrically Interrupted IENF (IIENF) model is developed using reduced IENFD, to simulate SFN at miscellaneous locations of the human foot. This IIENF model was then compared with the NIENF model for the same location of the foot and observed reduced IENF network in this IIENF model as compared to NIENF model. Furthermore, approximately 98% of the realistic IENF terminals at the skin were generated using the modified Monte Carlo Algorithm (MCA) and the reduced empirical IENFD at the various locations of the foot. This IIENF model provides a starting platform for evaluating diabetic foot ulceration. The IIENF model may be used in future studies for functional consequences by stimulating the most distal sensory IENF of the skin of the foot.

Free-Space Optical Communications in Vehicular Networks Using Rectangular Guiding Models

This letter introduces Free-Space Optical (FSO) Communication links in vehicular applications using potential guiding structures around a vehicle. An optical wireless communication system simulation is described which delivers received power, bandwidth, root mean square delay spread channel impulse response for purely diffuse and diffuse-specular materials with omnidirectional and directed transmitters. In the former case, a bandwidth of 225 MHz with a power deviation of 25% results at the exit. For the latter, a 75GHz bandwidth is available at best but with a power deviation of over 99% making receiver positioning critical. The impulse response is calculated using a Modified Monte Carlo algorithm taking into account up to 15 reflections. The effect of the pipe bend angle on the path loss is also presented and the simulation is supported with experimental work.

Effects of magma ocean crystallization and overturn on the development of 142Nd and 182W isotopic heterogeneities in the primordial mantle

One possible mechanism to explain the observed variability of the short-lived Sm146→Nd142 and Hf182→W182 systems recorded in some early Earth rocks is crystal–liquid fractionation and overturn in an early magma ocean. This process could also potentially explain the deviation between the 142Nd isotopic composition of the accessible Earth and the chondritic average. To examine these effects, the magma ocean solidification code of Elkins-Tanton (2008) and a modified Monte Carlo algorithm, designed to randomly choose physically reasonable trace element partition coefficients in crystallizing mantle phases, are used to model the isotopic evolution of early Earth reservoirs. This model, also constrained by the 143Nd composition of the accessible Earth, explores the effects of changing the amount of interstitial liquid trapped in cumulates, the half-life of 146Sm, the magnitude of late accretion, and the simplified model of post-overturn reservoir mixing. Regardless of the parameters used, our results indicate the generation of early mantle reservoirs with isotopic characteristics consistent with observed anomalies is a likely outcome of magma ocean crystallization and overturn of shallow, enriched, and dense (i.e., gravitationally unstable) cumulates. The high-iron composition and density of a hypothesized, early-formed enriched mantle reservoir is compatible with seismic observations indicating large, low-shear velocity provinces (LLSVPs) (e.g., Trampert et al., 2004) present in the mantle today. Later melts of an enriched reservoir are likely to have remained isolated deep within the mantle (e.g., Thomas et al., 2012), consistent with the possibility that the presently observed LLSVPs could be partially or fully composed of remnants of an early enriched reservoir.

Transient radiative transfer in a complex refracting medium by a modified Monte Carlo simulation

Abstract A modified Monte Carlo (MMC) method applied with time shift and superposition principle is developed for solving transient radiative transfer in one-dimensional scattering media with arbitrary distributions of refractive index exposed to a collimated short pulse-laser irradiation at one of its boundaries. We consider a multilayer medium and a graded index medium. The accuracy and computational efficiency of the MMC algorithm are examined firstly. Our results are compared with those obtained by the reverse Monte Carlo method (RMC), the modified discrete ordinates method (MDOM) and the lattice Boltzmann method (LBM), and the excellent agreements are achieved. With the time shift and superposition principle, the MMC method can greatly improve the computational efficiency. We have a parametric investigation on the transient radiative transfer in the three-layer systems and graded-index media, illustrating the effects of refractive index distribution, optical thickness, interface/surface reflection mode, scattering phase function and scattering albedo on the time-resolved signals of reflectance and transmittance. Results show that the reflection mode has an important influence on the transient radiative transfer; the specular reflection at interfaces/boundaries can enhance the effects of forward scattering, while the diffuse reflection can enhance the effects of backward scattering.

Comparison of Monte Carlo ray-tracing and photon-tracing methods for calculation of the impulse response on indoor wireless optical channels

We present a comparison between the modified Monte Carlo algorithm (MMCA) and a recently proposed ray-tracing algorithm named as photon-tracing algorithm. Both methods are compared exhaustively according to error analysis and computational costs. We show that the new photon-tracing method offers a solution with a slightly greater error but requiring from considerable less computing time. Moreover, from a practical point of view, the solutions obtained with both algorithms are approximately equivalent, demonstrating the goodness of the new photon-tracing method.

Statistical modelling of laser induced fluorescence in plant cover

A system of mutually coupled radiative transfer equations is proposed as a formal basis for the numerical analysis of a broad range of spectroscopic effects associated with the propagation of laser radiation in the environment. In particular, this concerns the reabsorption of laser induced fluorescence which inevitably occurs in dense disperse media containing two or more fluorophors. One practical application is for the pressing problem of lidar monitoring the state of plant cover, in particular the concentration of chlorophyll, which regulates the vital activity of plants. A new concept for an optical model of plant cover has been developed in which leaves are not treated as separate scattering elements, but as local volumes of a multiphase medium with a complex polydisperse structure. A modified Monte-Carlo algorithm is created for imitating the fluorescence and reabsorption processes. Test calculations confirm the adequacy of this approach.

Driven polymer transport through a nanopore controlled by a rotating electric field: Off-lattice computer simulations

The driven translocation kinetics of a single strand polynucleotide chain through a nanopore is studied using off-lattice Monte Carlo simulations, by which the authors demonstrate a novel method in controlling the driven polymer transport through a nanopore by a rotating electric field. The recorded time series of blockade current from the driven polynucleotide transport are used to determine the sequence of polynucleotides by implementing a modified Monte Carlo algorithm, in which the energy landscape paving technique is incorporated to avoid trapping at deep local minima. It is found that only six-time series of block current are required to completely determine the polynucleotide sequence if the average missing rate (AMR) of current signals in these time series is smaller than 20%. For those time series with AMR greater than 20%, the error rate in sequencing an unknown polynucleotide decreases rapidly by increasing the number of time series. To find the most appropriate experimental conditions, the authors have investigated the dependence of AMR of current signals and qualified rate of measured time series of blockade current on various controllable experimental variables.

Computer Simulations and Statistical Theory of Normal Grain Growth in Two and Three Dimensions

A modified Monte Carlo algorithm for single-phase normal grain growth is presented, which allows one to simulate the time development of the microstructure of very large grain ensembles in two and three dimensions. The emphasis of the present work lies on the investigation of the interrelation between the local geometric properties of the grain network and the grain size distribution in the quasi-stationary self-similar growth regime. It is found that the topological size correlations between neighbouring grains and the resulting average statistical growth law both in two and three dimensions deviate strongly from the assumptions underlying the classical Lifshitz- Sloyzov-Hillert theory. The average local geometric properties of the simulated grain structures are used in a statistical mean-field theory to calculate the grain size distribution functions analytically. By comparison of the theoretical results with the simulated grain size distributions it is shown how far normal grain growth in two and three dimensions can successfully be described by a mean-field theory and how stochastic fluctuations in the average growth law must be taken into account.

FDS: flexible ligand and receptor docking with a continuum solvent model and soft-core energy function.

The docking of flexible small molecule ligands to large flexible protein targets is addressed in this article using a two-stage simulation-based method. The methodology presented is a hybrid approach where the first component is a dock of the ligand to the protein binding site, based on deriving sets of simultaneously satisfied intermolecular hydrogen bonds using graph theory and a recursive distance geometry algorithm. The output structures are reduced in number by cluster analysis based on distance similarities. These structures are submitted to a modified Monte Carlo algorithm using the AMBER-AA molecular mechanics force field with the Generalized Born/Surface Area (GB/SA) continuum model. This solvent model is not only less expensive than an explicit representation, but also yields increased sampling. Sampling is also increased using a rotamer library to direct some of the protein side-chain movements along with large dihedral moves. Finally, a softening function for the nonbonded force field terms is used, enabling the potential energy function to be slowly turned on throughout the course of the simulation. The docking procedure is optimized, and the results are presented for a single complex of the arabinose binding protein. It was found that for a rigid receptor model, the X-ray binding geometry was reproduced and uniquely identified based on the associated potential energy. However, when side-chain flexibility was included, although the X-ray structure was identified, it was one of three possible binding geometries that were energetically indistinguishable. These results suggest that on relaxing the constraint on receptor flexibility, the docking energy hypersurface changes from being funnel-like to rugged. A further 14 complexes were then examined using the optimized protocol. For each complex the docking methodology was tested for a fully flexible ligand, both with and without protein side-chain flexibility. For the rigid protein docking, 13 out of the 15 test cases were able to find the experimental binding mode; this number was reduced to 11 for the flexible protein docking. However, of these 11, in the majority of cases the experimental binding mode was not uniquely identified, but was present in a cluster of low energy structures that were energetically indistinguishable. These results not only support the presence of a rugged docking energy hypersurface, but also suggest that it may be necessary to consider the possibility of more than one binding conformation during ligand optimization.

Modeling of grain growth kinetics with Read–Shockley grain boundary energy by a modified Monte Carlo algorithm

Grain growth of a single-phase material with Read–Shockley anisotropic grain boundary energy was simulated using a modified Monte Carlo (MC) algorithm in which the local system energy is minimized in every step. The microstructure evolution in the presence of anisotropy is reproduced correctly. Providing that the initial grain orientations are distributed randomly, the parabolic growth law is not affected by the degree of anisotropy, which in turn affects the grain growth rate only. These findings are supported by three arguments rooted in previous theoretical and simulation results.

Ray-tracing algorithms for fast calculation of the channel impulse response on diffuse IR wireless indoor channels

A modified Monte Carlo algorithm for the calculation of the impulse response on infrared wireless indoor channels is presented. As is well known, the characteristics of the room where the IR diffuse channel is implemented can lead to problems in communication, such as a multipath penalty on the maximum baud rate or hidden-station situations. Classical algorithms require large computational effort to calculate the impulse response in an ordinary-size room. Monte Carlo offers the possibility of validating the assumptions made for these classic algorithms (basically, the Lambertian nature of all reflections) with a computational complexity that is determined by the accuracy desired by the user. We have developed a mixed ray-tracing-deterministic algorithm that assures that each ray contributes to the final channel response function as many times as it rebounds with an obstacle. It increases dramatically the number of contributions and reduces, to the same extent, the time required for an accurate simulation. Extensive simulation results are presented and are compared with those of other simulation methods. We demonstrate that the method presented here is much faster than Monte Carlo classical simulation schemes. It can be used as a method of simulation in itself or as a validation algorithm for other comparative studies of pulse broadening.

A new model of three-dimensional grain growth: theory and computer simulation of topology-dependency of individual grain growth rate

A relationship between the growth kinetics and the topology of individual grains in three dimensions, as an equivalent to Von Neumann’s law in two dimensions, was derived theoretically. The relationship depicts that the changing rate of the surface area of an individual three-dimensional grain, other than that of grain volume, is independent of grain size and proportional to ( F−F c ), where F is the number of grain faces, and F c a constant. It should also be pointed out that the new theory is approximate in nature — perhaps an exact three-dimensional law does not exist at all. A modified Monte Carlo algorithm was newly developed by the authors to simulate the three-dimensional normal grain growth process including the quasi-steady stage. The simulated process obeys the power law kinetics with its growth exponent approaching 0.5, and agrees quantitatively well with the experimental observations of topological evolution during the three-dimensional grain growth process in various materials found in the literature. The topology dependency of individual grain growth rate in simulation agrees very well with that predicted by the above-mentioned new three-dimensional theory.

Grain growth in metals with strong textures: Three-dimensional Monte Carlo simulations

The commonly used Monte Carlo technique has been applied to simulate normal as well as texture-controlled grain growth on 100 3-square lattices. For the case of normal grain growth the simulations yield a grain growth exponent of n ≈ 0.5, provided the modifications of Radhakrishnan and Zacharia [B. Radhakrishnan, T. Zacharia, Simulation of curvature-driven grain growth by using a modified Monte Carlo algorithm, Metall. Mater. Trans. A 26A (1995) 167.] are implemented into the algorithm. Microstructures with a strong initial texture exhibit texture changes if the grain boundaries have anisotropic mobilities.

Three‐Dimensional Model of a Selective Theophylline‐Binding RNA Molecule

We propose a three-dimensional (3D) model for an RNA molecule that selectively binds theophylline but not caffeine. This RNA, which was found using SELEX [Jenison, R.D., et al., Science (1994) 263:1425] is 10,000 times more specific for theophylline (Kd=320 nM) than for caffeine (Kd=3.5 mM), although the two ligands are identical except for a methyl group substituted at N7 (present only in caffeine). The binding affinity for ten xanthine-based ligands was used to derive a Comparative Molecular Field Analysis (CoMFA) model (R{sup 2} = 0.93 for 3 components, with cross-validated R{sup 2} of 0.73), using the SYBYL and GOLPE programs. A pharmacophoric map was generated to locate steric and electrostatic interactions between theophylline and the RNA binding site. This information was used to identify putative functional groups of the binding pocket and to generate distance constraints. Based on a model for the secondary structure (Jenison et al., idem), the 3D structure of this RNA was then generated using the following method: each helical region of the RNA molecule was treated as a rigid body; single-stranded loops with specific end-to-end distances were generated. The structures of RNA-xanthine complexes were studied using a modified Monte Carlo algorithm. The detailed structure of an RNA-ligand complex model, as well as possible explanations for the theophylline selectivity will be discussed.

Three-dimensional model of a selective theophylline-binding RNA molecule

A three-dimensional (3D) model for an RNA molecule that selectively binds theophylline but not caffeine is proposed. This RNA, which was found using SELEX (Jenison et al., 1994), is 10,000 times more specific for theophylline (Kn = 320 nM) than for caffeine (KD = 3.5 mM), although the two ligands are identical except for a methyl group substituted at N7 (present only in caffeine). The binding affinity for ten xanthine-based ligands was used to derive a comparative molecular field analysis model (R2 = 0.93 for three components, with cross-validated R2 of 0.73), using the SYBYL and GOLPE programs. A pharmacophoric map was generated to locate steric and electrostatic interactions between theophylline and the RNA binding site. This information was used to identify putative functional groups of the binding pocket and to generate distance constraints. On the basis of a model for the secondary structure (Jenison et al., 1994), the 3D structure of this RNA was then generated using the following method: each helical region of the RNA molecule was treated as a rigid body; single-stranded loops with specific end-to-end distances were generated. The structures of RNA-xanthine complexes were studied using a modified Monte Carlo algorithm. The detailed structure of an RNA-ligand complex model, as well as possible explanations for the theophylline selectivity are discussed.

Simulation of curvature-driven grain growth by using a modified monte carlo algorithm

The Monte Carlo (MC) algorithm that currently exists in the literature for simulating curvature-driven grain growth has been modified. The modified algorithm results in an acceleration of the simulated grain growth and an early estimate of the grain growth exponent that is close to the theoretical value of 0.5. The upper limit of grain size distributions obtained with the new algorithm is significantly lower than that obtained with the old, because the new algorithm eliminates grain coalescence during grain growth. The log-normal function provides an excellent fit to the grain size distribution data obtained with the new algorithm, after taking into account the anisotropy in grain boundary energy.

Simulation of the adhesive-hard-sphere model

Monte Carlo simulations of the three-dimensional sticky-hard-sphere system are presented. A new modified Monte Carlo algorithm has been developed which makes it possible to explore the phase diagram for a large region of both the packing fraction and the stickiness parameter τ. The phase diagram is calculated, as well as pair distribution functions and structure factors. Cluster percolation has been studied and its relation to the phase diagram. The simulation results are compared with predictions, obtained from the Percus-Yevick approximation, which can be solved analytically for this model. The potential relevance of the present simulation results for experiments on clustering in neutral colloids is discussed.