Nonequilibrium-phase transition and 'specific-heat' singularity in the kinetic Ising model: A Monte Carlo study

The nonequilibrium-phase transition has been studied by Monte Carlo simulation in a ferromagnetically interacting (nearest-neighbour) kinetic Ising model in presence of a sinusoidally oscillating magnetic field. The ('specific-heat') temperature derivative of energies (averaged over a full cycle of the oscillating field) diverge near the dynamic transition point.

Methodology for Pavement Design Reliability and Back Analysis Using Markov Chain Monte Carlo Simulation

Given the increasing cost of designing and building new highway pavements, reliability analysis has become vital to ensure that a given pavement performs as expected in the field. Recognizing the importance of failure analysis to safety, reliability, performance, and economy, back analysis has been employed in various engineering applications to evaluate the inherent uncertainties of the design and analysis. The probabilistic back analysis method formulated on Bayes' theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis-Hastings algorithm has proved to be highly efficient to address this issue. It is also quite flexible and is applicable to any type of prior information. In this paper, this method has been used to back-analyze the parameters that influence the pavement life and to consider the uncertainty of the mechanistic-empirical pavement design model. The load-induced pavement structural responses (e.g., stresses, strains, and deflections) used to predict the pavement life are estimated using the response surface methodology model developed based on the results of linear elastic analysis. The failure criteria adopted for the analysis were based on the factor of safety (FOS), and the study was carried out for different sample sizes and jumping distributions to estimate the most robust posterior statistics. From the posterior statistics of the case considered, it was observed that after approximately 150 million standard axle load repetitions, the mean values of the pavement properties decrease as expected, with a significant decrease in the values of the elastic moduli of the expected layers. An analysis of the posterior statistics indicated that the parameters that contribute significantly to the pavement failure were the moduli of the base and surface layer, which is consistent with the findings from other studies. After the back analysis, the base modulus parameters show a significant decrease of 15.8% and the surface layer modulus a decrease of 3.12% in the mean value. The usefulness of the back analysis methodology is further highlighted by estimating the design parameters for specified values of the factor of safety. The analysis revealed that for the pavement section considered, a reliability of 89% and 94% can be achieved by adopting FOS values of 1.5 and 2, respectively. The methodology proposed can therefore be effectively used to identify the parameters that are critical to pavement failure in the design of pavements for specified levels of reliability. DOI: 10.1061/(ASCE)TE.1943-5436.0000455. (C) 2013 American Society of Civil Engineers.

Monte-Carlo estimation of time-dependent statistical characteristics of random dynamical systems

The problem of estimating the time-dependent statistical characteristics of a random dynamical system is studied under two different settings. In the first, the system dynamics is governed by a differential equation parameterized by a random parameter, while in the second, this is governed by a differential equation with an underlying parameter sequence characterized by a continuous time Markov chain. We propose, for the first time in the literature, stochastic approximation algorithms for estimating various time-dependent process characteristics of the system. In particular, we provide efficient estimators for quantities such as the mean, variance and distribution of the process at any given time as well as the joint distribution and the autocorrelation coefficient at different times. A novel aspect of our approach is that we assume that information on the parameter model (i.e., its distribution in the first case and transition probabilities of the Markov chain in the second) is not available in either case. This is unlike most other work in the literature that assumes availability of such information. Also, most of the prior work in the literature is geared towards analyzing the steady-state system behavior of the random dynamical system while our focus is on analyzing the time-dependent statistical characteristics which are in general difficult to obtain. We prove the almost sure convergence of our stochastic approximation scheme in each case to the true value of the quantity being estimated. We provide a general class of strongly consistent estimators for the aforementioned statistical quantities with regular sample average estimators being a specific instance of these. We also present an application of the proposed scheme on a widely used model in population biology. Numerical experiments in this framework show that the time-dependent process characteristics as obtained using our algorithm in each case exhibit excellent agreement with exact results. (C) 2010 Elsevier Inc. All rights reserved.

Monte Carlo simulation of light transport in turbid medium with embedded object-spherical, cylindrical, ellipsoidal, or cuboidal objects embedded within multilayered tissues

Monte Carlo modeling of light transport in multilayered tissue (MCML) is modified to incorporate objects of various shapes (sphere, ellipsoid, cylinder, or cuboid) with a refractive-index mismatched boundary. These geometries would be useful for modeling lymph nodes, tumors, blood vessels, capillaries, bones, the head, and other body parts. Mesh-based Monte Carlo (MMC) has also been used to compare the results from the MCML with embedded objects (MCML-EO). Our simulation assumes a realistic tissue model and can also handle the transmission/reflection at the object-tissue boundary due to the mismatch of the refractive index. Simulation of MCML-EO takes a few seconds, whereas MMC takes nearly an hour for the same geometry and optical properties. Contour plots of fluence distribution from MCML-EO and MMC correlate well. This study assists one to decide on the tool to use for modeling light propagation in biological tissue with objects of regular shapes embedded in it. For irregular inhomogeneity in the model (tissue), MMC has to be used. If the embedded objects (inhomogeneity) are of regular geometry (shapes), then MCML-EO is a better option, as simulations like Raman scattering, fluorescent imaging, and optical coherence tomography are currently possible only with MCML. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)

Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

An investigation of solid adamantane by a modified isothermal-isobaric ensemble Monte Carlo simulation

Isothermal-isobaric ensemble Monte Carlo simulation studies of adamantane have been carried out at different temperatures. Thermodynamic properties and radial distribution functions calculated by employing a simple potential model based on sitesite interactions show good agreement with experiment and suggest that the solid is orientationally disordered at high temperatures.

Monte Carlo simulation of mictomagnets

Monte Carlo simulations of a binary alloy with impurity concentrations between 20 and 45 at.% have been carried out. The proportion of large clusters relative to that of small clusters increases with the number of MC diffusion steps as well as impurity concentration. Magnetic susceptibility peaks become more prominent and occur at higher temperatures with increasing impurity concentration. The different peaks in the susceptibility and specific heat curves seem to correspond to different sized clusters. A freezing model would explain the observed behaviour with the large clusters freezing first and the small clusters contributing to susceptibility (specific heat) peaks at lower temperatures.

Monte Carlo study of the phase boundary of YBa2Cu3O6 +x

A model hamiltonian previously introduced to study the oxygen ordering is considered. The phase boundary is isolated by studying the relaxation behaviour of the order parameters. Our results are consistent with the published Monte Carlo results except at low temperatures.

Monte Carlo simulation of network formation based on structural fragments in epoxy-anhydride systems

A method combining the Monte Carlo technique and the simple fragment approach has been developed for simulating network formation in amine-catalysed epoxy-anhydride systems. The method affords a detailed insight into the nature and composition of the network, showing the distribution of various fragments. It has been used to characterize the network formation in the reaction of the diglycidyl ester of isophthalic acid with hexahydrophthalic anhydride, catalysed by benzyldimethylamine. Pre-gel properties like number and weight distributions and average molecular weights have been calculated as a function of epoxy conversion, leading to a prediction of the gel-point conversion. Analysis of the simulated network further yields other characteristic properties such as concentration of crosslink points, distribution and concentration of elastically active chains, average molecular weight between crosslinks, sol content and mass fraction of pendent chains. A comparison has been made of the properties obtained through simulation with those predicted by the fragment approach alone, which, however, gives only average properties. The Monte Carlo simulation results clearly show that loops and other cyclic structures occur in the gel. This may account for the differences observed between the results of the simulation and the fragment model in the post-gel phase. Copyright (C) 1996 Elsevier Science Ltd.

Monte Carlo simulation of ion conduction in silver based glassy electrolytes

A simplified structural model to study the ionic transport in silver based glasses has been formulated. The diffusion of silver ion under the influence of coulombic interactions of mobile cation and anions has been studied. Monte Carlo simulations of silver ion hopping in glass have suggested two different kinds of population of silver ions. We discuss the results of variation in diffusion constant with dopant (AgI) concentration using the diffusion path model. (C) 1997 Elsevier-Science S.A.

Uncertainty Quantification in Helicopter Performance Using Monte Carlo Simulations

The effect of structural and aerodynamic uncertainties on the performance predictions of a helicopter is investigated. An aerodynamic model based on blade element and momentum theory is used to predict the helicopter performance. The aeroelastic parameters, such as blade chord, rotor radius, two-dimensional lift-curve slope, blade profile drag coefficient, rotor angular velocity, blade pitch angle, and blade twist rate per radius of the rotor, are considered as random variables. The propagation of these uncertainties to the performance parameters, such as thrust coefficient and power coefficient, are studied using Monte Carlo Simulations. The simulations are performed with 100,000 samples of structural and aerodynamic uncertain variables with a coefficient of variation ranging from 1 to 5%. The scatter in power predictions in hover, axial climb, and forward flight for the untwisted and linearly twisted blades is studied. It is found that about 20-25% excess power can be required by the helicopter relative to the determination predictions due to uncertainties.

Analysis of Parameter Values in the van der Waals and Platteeuw Theory for Methane Hydrates Using Monte Carlo Molecular Simulations

The van der Waals and Platteuw (vdVVP) theory has been successfully used to model the thermodynamics of gas hydrates. However, earlier studies have shown that this could be due to the presence of a large number of adjustable parameters whose values are obtained through regression with experimental data. To test this assertion, we carry out a systematic and rigorous study of the performance of various models of vdWP theory that have been proposed over the years. The hydrate phase equilibrium data used for this study is obtained from Monte Carlo molecular simulations of methane hydrates. The parameters of the vdWP theory are regressed from this equilibrium data and compared with their true values obtained directly from simulations. This comparison reveals that (i) methane-water interactions beyond the first cage and methane-methane interactions make a significant contribution to the partition function and thus cannot be neglected, (ii) the rigorous Monte Carlo integration should be used to evaluate the Langmuir constant instead of the spherical smoothed cell approximation, (iii) the parameter values describing the methane-water interactions cannot be correctly regressed from the equilibrium data using the vdVVP theory in its present form, (iv) the regressed empty hydrate property values closely match their true values irrespective of the level of rigor in the theory, and (v) the flexibility of the water lattice forming the hydrate phase needs to be incorporated in the vdWP theory. Since methane is among the simplest of hydrate forming molecules, the conclusions from this study should also hold true for more complicated hydrate guest molecules.

Monte Carlo simulation of light transport in tissue for optimizing light delivery in photoacoustic imaging of the sentinel lymph node

Noninvasive or minimally invasive identification of sentinel lymph node (SLN) is essential to reduce the surgical effects of SLN biopsy. Photoacoustic (PA) imaging of SLN in animal models has shown its promise for clinical use in the future. Here, we present a Monte Carlo simulation for light transport in the SLN for various light delivery configurations with a clinical ultrasound probe. Our simulation assumes a realistic tissue layer model and also can handle the transmission/reflectance at SLN-tissue boundary due to the mismatch of refractive index. Various light incidence angles show that for deeply situated SLNs the maximum absorption of light in the SLN is for normal incidence. We also show that if a part of the diffused reflected photons is reflected back into the skin using a reflector, the absorption of light in the SLN can be increased significantly to enhance the PA signal. (C) 2013 Society of Photo-Optical Instrumentation Engineers (SPIE)

Prediction of the stiffness of nanoclay-polypropylene composites using a monte carlo finite element analysis approach

The present work deals with the prediction of stiffness of an Indian nanoclay-reinforced polypropylene composite (that can be termed as a nanocomposite) using a Monte Carlo finite element analysis (FEA) technique. Nanocomposite samples are at first prepared in the laboratory using a torque rheometer for achieving desirable dispersion of nanoclay during master batch preparation followed up with extrusion for the fabrication of tensile test dog-bone specimens. It has been observed through SEM (scanning electron microscopy) images of the prepared nanocomposite containing a given percentage (3–9% by weight) of the considered nanoclay that nanoclay platelets tend to remain in clusters. By ascertaining the average size of these nanoclay clusters from the images mentioned, a planar finite element model is created in which nanoclay groups and polymer matrix are modeled as separate entities assuming a given homogeneous distribution of the nanoclay clusters. Using a Monte Carlo simulation procedure, the distribution of nanoclay is varied randomly in an automated manner in a commercial FEA code, and virtual tensile tests are performed for computing the linear stiffness for each case. Values of computed stiffness modulus of highest frequency for nanocomposites with different nanoclay contents correspond well with the experimentally obtained measures of stiffness establishing the effectiveness of the present approach for further applications.

Glass-Transition In Isopentane - A Monte-Carlo Study

Monte Carlo simulations with realistic interaction potentials have been carried out on isopentane to investigate the glass transition. Intermolecular pair-correlation functions of the glass show distinct differences from those of the liquid, the CH-CH pair-correlation function being uniquely different from the other pair-correlation functions. The coordination number of the glass is higher than that of the liquid, and the packing in the glass seems to be mainly governed by the geometrical constraints of the molecule. Annealing affects the properties of the glass significantly.