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.

The effect of low intra-sublattice repulsion on phase diagram of YBa2Cu3O6+x: A Monte Carlo simulation study

We report the results of Monte Carlo simulation of the phase diagram and oxygen ordering in YBa2Cu3O6+x for low intra-sublattice repulsion. At low temperatures, apart from tetragonal (T), orthorhombic (OI) and 'double cell' ortho II phases, there is evidence for two additional orthorhombic phases labelled here as OIBAR and OIII. At high temperatures, there was no evidence for the decomposition of the OI phase into the T and OI phases. We find qualitative agreement with experimental observations and cluster-variation method results.

Monte Carlo and molecular dynamics simulation of argon clusters andn-alkanes in the confined regions of zeolites

Geometry and energy of argon clusters confined in zeolite NaCaA are compared with those of free clusters. Results indicate the possible existence of magic numbers among the confined clusters. Spectra obtained from instantaneous normal mode analysis of free and confined clusters give a larger percentage of imaginary frequencies for the latter indicating that the confined cluster atoms populate the saddle points of the potential energy surface significantly. The variation of the percentage of imaginary frequencies with temperature during melting is akin to the variation of other properties. It is shown that confined clusters might exhibit inverse surface melting, unlike medium-to-large-sized free clusters that exhibit surface melting. Configurational-bias Monte Carte (CBMC) simulations of n-alkanes in zeolites Y and A are reported. CBMC method gives reliable estimates of the properties relating to the conformation of molecules. Changes in the conformational properties of n-butane and other longer n-alkanes such as n-hexane and n-heptane when they are confined in different zeolites are presented. The changes in the conformational properties of n-butane and n-hexane with temperature and concentration is discussed. In general, in zeolite Y as well as A, there is significant enhancement of the gauche population as compared to the pure unconfined fluid.

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.

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.

An improved Monte Carlo scheme for simulation of synthesis of nanoparticles in reverse micelles

An improved Monte Carlo technique is presented in this work to simulate nanoparticle formation through a micellar route. The technique builds on the simulation technique proposed by Bandyopadhyaya et al. (Langmuir 2000, 16, 7139) which is general and rigorous but at the same time very computation intensive, so much so that nanoparticle formation in low occupancy systems cannot be simulated in reasonable time. In view of this, several strategies, rationalized by simple mathematical analyses, are proposed to accelerate Monte Carlo simulations. These are elimination of infructuous events, removal of excess reactant postreaction, and use of smaller micelle population a large number of times. Infructuous events include collision of an empty micelle with another empty one or with another one containing only one molecule or only a solid particle. These strategies are incorporated in a new simulation technique which divides the entire micelle population in four classes and shifts micelles from one class to other as the simulation proceeds. The simulation results, throughly tested using chi-square and other tests, show that the predictions of the improved technique remain unchanged, but with more than an order of magnitude decrease in computational effort for some of the simulations reported in the literature. A post priori validation scheme for the correctness of the simulation results has been utilized to propose a new simulation strategy to arrive at converged simulation results with near minimum computational effort.

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.

Monte Carlo simulation of polytypes

Based on the analogy between polytypes and spin-half Ising chains with competing short- and infinite-range interactions, a Monte Carlo simulation of polytypes has been attempted. A general double-layer mechanism connects different states of the polytype chain with about the same probability as the spin-flip mechanism in magnetic Ising chains. It has been possible to simulate various polytypes with periodicities extending up to 12 layers. The Monte Carlo method should be useful in testing different interaction models that may be proposed in the future to describe polytypism.

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.

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.

A Novel Monte-Carlo-Sampling-Based Receiver for Large-Scale Uplink Multiuser MIMO Systems

In this paper, we propose low-complexity algorithms based on Monte Carlo sampling for signal detection and channel estimation on the uplink in large-scale multiuser multiple-input-multiple-output (MIMO) systems with tens to hundreds of antennas at the base station (BS) and a similar number of uplink users. A BS receiver that employs a novel mixed sampling technique (which makes a probabilistic choice between Gibbs sampling and random uniform sampling in each coordinate update) for detection and a Gibbs-sampling-based method for channel estimation is proposed. The algorithm proposed for detection alleviates the stalling problem encountered at high signal-to-noise ratios (SNRs) in conventional Gibbs-sampling-based detection and achieves near-optimal performance in large systems with M-ary quadrature amplitude modulation (M-QAM). A novel ingredient in the detection algorithm that is responsible for achieving near-optimal performance at low complexity is the joint use of a mixed Gibbs sampling (MGS) strategy coupled with a multiple restart (MR) strategy with an efficient restart criterion. Near-optimal detection performance is demonstrated for a large number of BS antennas and users (e. g., 64 and 128 BS antennas and users). The proposed Gibbs-sampling-based channel estimation algorithm refines an initial estimate of the channel obtained during the pilot phase through iterations with the proposed MGS-based detection during the data phase. In time-division duplex systems where channel reciprocity holds, these channel estimates can be used for multiuser MIMO precoding on the downlink. The proposed receiver is shown to achieve good performance and scale well for large dimensions.

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)

Calculation of Chemical Potentials and Occupancies in Clathrate Hydrates through Monte Carlo Molecular Simulations

The flexibility of the water lattice in clathrate hydrates and guest-guest interactions has been shown in previous studies to significantly affect the values of the thermodynamic properties, such as chemical potentials and free energies. Here we describe methods for computing occupancies, chemical potentials, and free energies that account for the flexibility of water lattice and guest-guest interactions in the hydrate phase. The methods are validated for a wide variety of guest molecules, such as methane, ethane, carbon dioxide, and tetrahydrodfuran by comparing the predicted occupancy values of guest molecules with those obtained from isothermal isobaric semigrand Monte Carlo simulations. The proposed methods extend the van der Waals and Platteuw theory for clathrate hydrates, and the Langmuir constant is calculated based on the structure of the empty hydrate lattice. These methods in combination with development of advanced molecular models for water and guest molecules should lead to a more thermodynamically consistent theory for clathrate hydrates.

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.