Monte Carlo Simulation Scheme Research Articles

Kinetic Monte Carlo Simulations of Flow-Assisted Polymerization.

We performed kinetic Monte Carlo simulations on a model of a polymerization process in the presence of a periodic oscillatory flow to explore the role of mixing in polymerization reactors. Application of an oscillatory flow field helps overcome the diffusive limitations that develop during a polymerization process due to an increase in the molecular weights of polymer chains, thereby giving rise to high rates of polymerization. A systematic increase in the flow strength results in a "dynamic" coil-stretch transition, leading to an elongation of polymer chains. Reactive ends of stretched (polymer) chains react more frequently than the reactive ends of coiled chains, which are screened by other monomers of the same chain. There exists a critical flow strength for the efficiency of polymerization processes. The kinetic Monte Carlo simulation scheme developed here exhibit great promise for the study of dynamic properties of polymer systems.

Performance Loss Analysis for Neglecting the Weibull Clutter Texture in Wideband Radar Spread Targets Detection

The problem of adaptive detection of spatially distributed targets or targets embedded in Weibull clutter with unknown covariance matrix is studied. At first, the texture and the speckle of Weibull clutter is researched, the texture expression is proposed base on the property of spherically invariant random vector (SIRV) , then the optimal detection statistics regards the texture of clutter as a certain function is derived, another detector regards the texture as an unknown deterministic parameter as a contrast. Next, the numerical results are presented by means of Monte Carlo simulation strategy. Assume that cells of signal components are available. Those secondary data are supposed to possess either the same covariance matrix or the same structure of the covariance matrix of the cells under test. In this context, the simulation results highlight that the performance loss of the two tests in different shaping parameter, then the influence of the Weibull clutter texture on detection performance of test is given.

Monte Carlo simulation of radionuclide migration in fractured rock for the performance assessment of radioactive waste repositories

The estimation of radionuclide migration within a fractured medium is a fundamental task in any performance assessment aimed at verifying the protection offered by radioactive waste repositories. In this paper, we present a novel application of a dual-permeability, Monte Carlo simulation approach based on Kolmogorov–Dmitriev (KD) theory of branching stochastic processes. The Monte Carlo simulation scheme allows to easily handle the high degree of complexity of the problem, accounting for non-homogeneities both in space and time. Particular attention is devoted here to the inclusion of time-dependencies. An illustration is given with reference to a realistic case study of 239Pu migration.

ANN based inversion of DC resistivity data for groundwater exploration in hard rock terrain of western Maharashtra (India)

Inversion of vertical electrical sounding (VES) data, especially from the crystalline hard rock area, assumes a special significance for groundwater exploration. Here we used a newly developed algorithm based on the Bayesian neural network (BNN) theory combined with Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulation scheme to invert the Direct Current (DC) VES measurements obtained from 30-locations around Tenduli-Vengurla, Sindhudurg district, Maharashtra, India. The inversion results suggest that the top layer is mostly comprised of laterites followed by mixture of clay/clayey sand and garnulites/granite as basement rocks. The source of groundwater appears to be accessible in weathered/semi-weathered layer of laterite/clayey sand that exists within the depth of 10–15 m from the surface. The NW–SE trending major lineaments and its criss-crosses are also identified from the apparent and true resistivity surface map. The pseudo-section at different depths in the western part of the area, near Nivti, shows extensive influence of saltwater intrusion and its impact reaching up to the depth of 30 m from the surface along the coastal area. Our results also show that intrusion of saline water decreases from the western part to the eastern part of the region. Two dimensional modeling of four resistivity profiles from the study region identified two potential groundwater reservoirs; one lying between Path-Tenduli and another in between Mat and Zaraph. The deduced true electrical resistivity section against depth correlates well with available borehole lithology in the area. The results presented here would be useful for interpreting the geological signatures like fractures, major joints and lineaments, which in turn will be helpful for identifying groundwater reservoirs and drainage pattern in the crystalline hard rock area. The newly developed HMC-based BNN method is robust and would provide insights for constraining the geophysical models and criteria for modeling resistivity data.

Elastic photoelectron scattering effects in the XPS analysis of stratified samples

Two theoretical models describing photoelectron transport in multilayer samples were developed: (i) the Monte Carlo simulation strategy, in which the photoelectron elastic scattering events are accounted for, and (ii) the common x-ray electron spectroscopy (XPS) formalism adjusted to multilayer systems, in which the photoelectron elastic scattering events are ignored. Calculations were performed for Au/Ni and Si/Au multilayer systems with layers of different thicknesses. The emission depth distribution function (EMDDF) calculated for a layer deposited at a surface turns out to be identical to that for the bulk of the layer material; however, it may differ considerably when the layer is buried at a certain depth. The EMDDFs for buried layers are found to be considerably affected by elastic photoelectron scattering, however, in a different way from the EMDDF of the bulk material. The XPS depth profiles calculated for multilayer materials in the considered geometry are noticeably affected by elastic photoelectron collisions. However, in contrast with Auger electron spectroscopy depth profiling, the shape of the profile due to a given layer is not affected by the structure beneath that layer.

Delineation of shallow resistivity structure around Malvan, Konkan region, Maharashtra by neural network inversion using vertical electrical sounding measurements

Modeling resistivity profiles, especially from hard rock areas, is of specific relevance for groundwater exploration. A method based on Bayesian neural network (BNN) theory using a Hybrid Monte Carlo (HMC) simulation scheme is applied to model and interpret direct current vertical electrical sounding measurements from 28 locations around the Malvan region, in the Sindhudurg district, southwest India. The modeling procedure revolves around optimizing the objective function using the HMC based sampling technique which is followed by updating each trajectory by integrating the Hamiltonian differential equations via a second order leapfrog discretization scheme. The inversion results suggest a high resistivity structure in the north-western part of the area, which correlates well with the presence of laterites. In the south-western part, a very high conductive zone is observed near the coast indicating an extensive influence of saltwater intrusion. Our results also show that the effect of intrusion of saline water diminishes from the south-western part to the north-eastern part of the region. Two dimensional modeling of four resistivity profiles shows that the groundwater flow is partly controlled by existing lineaments, fractures, and major joints. Groundwater occurs at a weathered/semi-weathered layer of laterite/clayey sand and the interface of overburden and crystalline basement. The presence of conduits is identified at a depth between 10 and 15 m along the Dhamapur–Kudal and Parule–Oros profiles, which seems to be potential zone for groundwater exploration. The NW–SE trending major lineaments and its criss-cross sections are indentified from the apparent and true resistivity surface map. The pseudo-section at different depths in the western part of the area, near Parule, shows extensive influence of saltwater intrusion and its impact reaching up to a depth of 50 m from the surface along the coastal area. Further, the deduced true electrical resistivity section against depth correlates well with available borehole lithology in the area. Present analyses suggest that HMC-based BNN method is robust for modeling resistivity data especially in hard rock terrains. These results are useful for interpreting fractures, major joints, and lineaments and crystalline basement rock and also for constraining the higher dimensional models.

Computational measurement of void percolation thresholds of oblate particles and thin plate composites

The void percolation thresholds of random oblate particles and thin plate composites are measured computationally using the lattice mapping technique and the Monte Carlo simulation scheme. Two types of spatially uncorrelated inclusions have been investigated: oblate ellipsoids and elliptical thin plates, with which the site and bond percolation systems are developed separately. The results are obtained from the finite-size lattices followed by a mathematical extrapolation to the infinite domains. The computational results are validated by a comparison with the numerical solutions of the limiting cases found in the literature. It is concluded that the void percolation thresholds of oblate inclusions have a much stronger dependence on the geometric aspect ratio of the inclusions compared to those of the prolate counterparts. In the limit, the percolation threshold η is measured to be 22.86 for circular thin disks. Approximate solutions are presented in the form of polynomial functions and Pade approximants. The results have potential applications in composite material designs and molecular diffusion problems.

Experimental and numerical analysis of ballistic and scattered light using femtosecond optical Kerr gating: a way for the characterization of strongly scattering media

We have developed a new experimental setup based on optical Kerr gating in order to isolate either the transmitted or the scattered light going through an optically thick medium. This selectivity can be obtained by finely tuning the focusing of the different laser beams in the Kerr medium. We have developed an experimental setup. A Monte Carlo simulation scheme generates an accurate model of scattering processes taking into account the time of flight, the geometry of the Kerr gating and the polarization. We show that our experimental setup is capable of analyzing the transmitted light with optical densities up to OD = 9.7, and scattered light beyond OD = 347 in poly-disperse silica spheres in water (distribution centered on ~0.9 µm radius) at λ = 550 nm. Strongly positive correlations are obtained with simulations.

Probabilistic assessment of herbicide runoff from Japanese rice paddies: The effects of local meteorological conditions and site-specific water management

Free to read Uncertainty assessments of herbicide losses from rice paddies in Japan associated with local meteorological conditions and water management practices were performed using a pesticide fate and transport model, PCPF-1, under the Monte Carlo (MC) simulation scheme. First, MC simulations were conducted for five different cities with a prescribed water management scenario and a 10-year meteorological dataset of each city. The effectiveness of water management was observed regarding the reduction of pesticide runoff. However, a greater potential of pesticide runoff remained in Western Japan. Secondly, an extended analysis was attempted to evaluate the effects of local water management and meteorological conditions between the Chikugo River basin and the Sakura River basin using uncertainty inputs processed from observed water management data. The results showed that because of more severe rainfall events, significant pesticide runoff occurred in the Chikugo River basin even when appropriate irrigation practices were implemented. © Pesticide Science Society of Japan.

Depletion potentials in highly size-asymmetric binary hard-sphere mixtures: Comparison of simulation results with theory

We report a detailed study, using state-of-the-art simulation and theoretical methods, of the effective (depletion) potential between a pair of big hard spheres immersed in a reservoir of much smaller hard spheres, the size disparity being measured by the ratio of diameters q ≡ σ(s)/σ(b). Small particles are treated grand canonically, their influence being parameterized in terms of their packing fraction in the reservoir η(s)(r). Two Monte Carlo simulation schemes--the geometrical cluster algorithm, and staged particle insertion--are deployed to obtain accurate depletion potentials for a number of combinations of q ≤ 0.1 and η(s)(r). After applying corrections for simulation finite-size effects, the depletion potentials are compared with the prediction of new density functional theory (DFT) calculations based on the insertion trick using the Rosenfeld functional and several subsequent modifications. While agreement between the DFT and simulation is generally good, significant discrepancies are evident at the largest reservoir packing fraction accessible to our simulation methods, namely, η(s)(r) = 0.35. These discrepancies are, however, small compared to those between simulation and the much poorer predictions of the Derjaguin approximation at this η(s)(r). The recently proposed morphometric approximation performs better than Derjaguin but is somewhat poorer than DFT for the size ratios and small-sphere packing fractions that we consider. The effective potentials from simulation, DFT, and the morphometric approximation were used to compute the second virial coefficient B(2) as a function of η(s)(r). Comparison of the results enables an assessment of the extent to which DFT can be expected to correctly predict the propensity toward fluid-fluid phase separation in additive binary hard-sphere mixtures with q ≤ 0.1. In all, the new simulation results provide a fully quantitative benchmark for assessing the relative accuracy of theoretical approaches for calculating depletion potentials in highly size-asymmetric mixtures.

Monte Carlo simulation strategies for computing the wetting properties of fluids at geometrically rough surfaces

We introduce Monte Carlo simulation methods for determining the wetting properties of model systems at geometrically rough interfaces. The techniques described here enable one to calculate the macroscopic contact angle of a droplet that organizes in one of the three wetting states commonly observed for fluids at geometrically rough surfaces: the Cassie, Wenzel, and impregnation states. We adopt an interface potential approach in which the wetting properties of a system are related to the surface density dependence of the surface excess free energy of a thin liquid film in contact with the substrate. We first describe challenges and inefficiencies encountered when implementing a direct version of this approach to compute the properties of fluids at rough surfaces. Next, we detail a series of convenient thermodynamic paths that enable one to obtain free energy information at relevant surface densities over a wide range of temperatures and substrate strengths in an efficient manner. We then show how this information is assembled to construct complete wetting diagrams at a temperature of interest. The strategy pursued within this work is general and is expected to be applicable to a wide range of molecular systems. To demonstrate the utility of the approach, we present results for a Lennard-Jones fluid in contact with a substrate containing rectangular-shaped grooves characterized by feature sizes of order ten fluid diameters. For this particular fluid-substrate combination, we find that the macroscopic theories of Cassie and Wenzel provide a reasonable description of simulation data.

The affine Heston model with correlated Gaussian interest rates for pricing hybrid derivatives

In this article we define a multi-factor equity–interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model and we use a Gaussian multi-factor short-rate process. By construction, the model fits in the framework of affine diffusion processes, allowing fast calibration to plain vanilla options. We also provide an efficient Monte Carlo simulation scheme.

An Analytical Hybrid Equity and Interest Rate Model

In this article, we introduce a new pricing model for equity and interest rate hybrids that can capture the effects of implied volatility skews and stochastic interest rates simultaneously. The proposed model is a simple modification of an existing hybrid model often used by market practitioners. While both models can be calibrated efficiently and accurately along the lines of Piterbarg (2005), it is shown that the proposed model is analytically solvable leading to an explicit equity price expression. Using this expression, we manage to establish an exact Monte Carlo simulation scheme for generic pricing purposes. In addition, it is shown that a path wise approach along the lines of Glasserman (1996) can be applied to the proposed model in a straightforward manner for the calculation of equity deltas and gammas. For illustration purposes, we apply the results developed in this article to the pricing of conditional trigger swaps or Enmansai structures. Numerical results indicate that the exact simulation scheme developed in this article is both efficient and robust. Moreover, both the proposed model and the existing model lead to similar prices, equity deltas, and equity gammas. However, owing to the exact simulation scheme, the proposed model compares favorably to the existing model due to its superior computational efficiency and robustness in pricing. As a benchmark, with a simulation size of 100K, calculation of price, equity deltas, and equity gammas of a 30-year Enmansai trade with semi-annual coupons typically takes less than 5 seconds under the proposed model, while the existing model can take nearly 100 seconds to achieve a comparable accuracy.

Abstract SY14-03: Inferring causality for oncology drug discovery and development

Abstract Decisions in drug development are made based upon determinations of cause and effect from experimental observations that span all development phases. Despite major advances in our powers of observation due to the advent of multi-omic technologies, the ability to determine disease mechanisms, biomarkers, and effective combination therapies from large-scale and diverse data sets in the context of ill-defined and complex biological systems continues to be a major bottleneck in the drug development process. Current methods of statistical analysis do not allow for causal inferences, leaving this impossible task to the human mind. This major bottleneck can only be overcome by utilizing automated computational learning methods that identify from compound data the circuits and connections between drug-affected molecular constituents and physiological observables. We will present several case studies in oncology drug development where we employ massively parallel machines to reverse engineer populations of models that predict the ‘gearing’ between drug, genetic, and genomic molecular components with respect to oncology phenotypic outcomes. Since a single topology or model cannot capture the reality of a biological system under investigation, Monte Carlo simulation strategies over the population of models reveal how the drug, genetic, gene expression and clinical variables work together to impact phenotypic outcomes. We will show how the marriage of multi-omic technologies within the network inference approach is helping to fill in the missing insights needed to improve drug development success rates. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 102nd Annual Meeting of the American Association for Cancer Research; 2011 Apr 2-6; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2011;71(8 Suppl):Abstract nr SY14-03. doi:10.1158/1538-7445.AM2011-SY14-03

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

Abstract. Koyna region is well-known for its triggered seismic activities since the hazardous earthquake of M=6.3 occurred around the Koyna reservoir on 10 December 1967. Understanding the shallow distribution of resistivity pattern in such a seismically critical area is vital for mapping faults, fractures and lineaments. However, deducing true resistivity distribution from the apparent resistivity data lacks precise information due to intrinsic non-linearity in the data structures. Here we present a new technique based on the Bayesian neural network (BNN) theory using the concept of Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulation scheme. The new method is applied to invert one and two-dimensional Direct Current (DC) vertical electrical sounding (VES) data acquired around the Koyna region in India. Prior to apply the method on actual resistivity data, the new method was tested for simulating synthetic signal. In this approach the objective/cost function is optimized following the Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) sampling based algorithm and each trajectory was updated by approximating the Hamiltonian differential equations through a leapfrog discretization scheme. The stability of the new inversion technique was tested in presence of correlated red noise and uncertainty of the result was estimated using the BNN code. The estimated true resistivity distribution was compared with the results of singular value decomposition (SVD)-based conventional resistivity inversion results. Comparative results based on the HMC-based Bayesian Neural Network are in good agreement with the existing model results, however in some cases, it also provides more detail and precise results, which appears to be justified with local geological and structural details. The new BNN approach based on HMC is faster and proved to be a promising inversion scheme to interpret complex and non-linear resistivity problems. The HMC-based BNN results are quite useful for the interpretation of fractures and lineaments in seismically active region.

Preliminary evaluation of a radioactive waste repository safety performance by a Monte Carlo simulation-based reliability model

Abstract Disposal facilities are designed to provide long-term isolation of the wastes from the human environment by means of a system of barriers, both engineered and natural. In this regard, it is required that the containment function of the multi-barrier system be evaluated by a quantitative risk analysis procedure, also called performance assessment. This entails the implementation of a Probabilistic Safety Assessment model for representing the stochastic failure behavior of the repository barriers, estimating the release rates of radionuclides into the groundwater stream and the doses from subsequent ingestion of drinking water. To this aim, a Monte Carlo simulation scheme is provided within a reliability modelling approach for the safety performance analysis of a repository, accounting also for barrier degradation processes. An application to a case study of the literature is presented to validate the approach and demonstrate its simplicity and flexibility.

Simulating STEM Imaging of Nanoparticles in Micrometers-Thick Substrates

Scanning transmission electron microscope (STEM) images of three-dimensional (3D) samples were simulated. The samples consisted of a micrometer(s)-thick substrate and gold nanoparticles at various vertical positions. The atomic number (Z) contrast as obtained via the annular dark-field detector was generated. The simulations were carried out using the Monte Carlo method in the CASINO software (freeware). The software was adapted to include the STEM imaging modality, including the noise characteristics of the electron source, the conical shape of the beam, and 3D scanning. Simulated STEM images of nanoparticles on a carbon substrate revealed the influence of the electron dose on the visibility of the nanoparticles. The 3D datasets obtained by simulating focal series showed the effect of beam broadening on the spatial resolution and on the signal-to-noise ratio. Monte Carlo simulations of STEM imaging of nanoparticles on a thick water layer were compared with experimental data by programming the exact sample geometry. The simulated image corresponded to the experimental image, and the signal-to-noise levels were similar. The Monte Carlo simulation strategy described here can be used to calculate STEM images of objects of an arbitrary geometry and amorphous sample composition. This information can then be used, for example, to optimize the microscope settings for imaging sessions where a low electron dose is crucial for the design of equipment, or for the analysis of the composition of a certain specimen.

A new scheme developed for the numerical simulation of the Boltzmann equation using the direct simulation monte-carlo scheme for the flow about a sphere

A new scheme, the modified direct simulation Monte-Carlo (MDSMC), for the numerical simulation of the Boltzmann equation for rarefied gas flow about a sphere is developed. The Taylor series expansion is used to obtain the modified equation of the first-order time discretization of the collision equation and the new scheme, MDSMC, is implemented to simulate the collision equation in the Boltzmann equation. In the new scheme (MDSMC) there exists a new extra term which takes into account the effect of the second-order collision. In the new scheme (MDSMC) there also exists a second-order term in time step in the probabilistic coefficients which has the effect of simulation with higher accuracy than the previous DSMC scheme. The results of the drag coefficient of the sphere using the MDSMC scheme show better agreement in comparison with the experimental data of Wegener (1961) than the results of the drag coefficient of the sphere using the DSMC scheme.

Information-theory-based solution of the inverse problem in classical statistical mechanics

We present a procedure for the determination of the interaction potential from the knowledge of the radial pair distribution function. The method, realized inside an inverse Monte Carlo simulation scheme, is based on the application of the maximum entropy principle of information theory and the interaction potential emerges as the asymptotic expression of the transition probability. Results obtained for high density monoatomic fluids are very satisfactory and provide an accurate extraction of the potential, despite a modest computational effort.

Monte-Carlo Simulation with Boundary Conditions (with Applications to Stress Testing, CEV and Variance-Gamma Simulation)

In this paper we discuss how to incorporate analytic boundary conditions into a Monte-Carlo simulation framework and discuss their applications. The method introduced can dramatically improve the stability, robustness and accuracy of the valuation, calculation of sensitivities and stress testing, i.e., valuation under stressed model parameters. We propose a Monte-Carlo simulation scheme which features boundary conditions for the underlying value process. The boundary conditions are analogous to the boundary conditions of a PDE. The Monte-Carlo simulation will then be modified to generate paths only within the boundaries and generate the corresponding Monte-Carlo weights. In addition, the valuation algorithm is adjusted to incorporate the analytic boundary conditions, using given or estimated boundary values for the value process. The complete setup consists of four parts: The definition of a boundary and the corresponding in-bound and out-bound regime. This is done for each time step. The definition of a Monte-Carlo scheme for which all paths remain within the boundary. The definition of a boundary condition which defines the value process on the out-bound region and its valuation conditional to being in the in-bound region at the previous time-step. A modified pricing algorithm which allows to evaluate the product using the Monte-Carlo scheme within the boundary conditions, adding the boundary value process. We present four different methods for calculating the product specific boundary value process: analytic, super-hedge, sub-hedge and numeric. Among the applications of the method we specifically lock at its behavior under stressed data.