Analytical approach to quantile estimation in regional frequency analysis based on fuzzy framework

Regional frequency analysis is widely used for estimating quantiles of hydrological extreme events at sparsely gauged/ungauged target sites in river basins. It involves identification of a region (group of watersheds) resembling watershed of the target site, and use of information pooled from the region to estimate quantile for the target site. In the analysis, watershed of the target site is assumed to completely resemble watersheds in the identified region in terms of mechanism underlying generation of extreme event. In reality, it is rare to find watersheds that completely resemble each other. Fuzzy clustering approach can account for partial resemblance of watersheds and yield region(s) for the target site. Formation of regions and quantile estimation requires discerning information from fuzzy-membership matrix obtained based on the approach. Practitioners often defuzzify the matrix to form disjoint clusters (regions) and use them as the basis for quantile estimation. The defuzzification approach (DFA) results in loss of information discerned on partial resemblance of watersheds. The lost information cannot be utilized in quantile estimation, owing to which the estimates could have significant error. To avert the loss of information, a threshold strategy (TS) was considered in some prior studies. In this study, it is analytically shown that the strategy results in under-prediction of quantiles. To address this, a mathematical approach is proposed in this study and its effectiveness in estimating flood quantiles relative to DFA and TS is demonstrated through Monte-Carlo simulation experiments and case study on Mid-Atlantic water resources region, USA. (C) 2015 Elsevier B.V. All rights reserved.

Markov chain splitting methods in structural reliability integral estimation

Monte Carlo simulation methods involving splitting of Markov chains have been used in evaluation of multi-fold integrals in different application areas. We examine in this paper the performance of these methods in the context of evaluation of reliability integrals from the point of view of characterizing the sampling fluctuations. The methods discussed include the Au-Beck subset simulation, Holmes-Diaconis-Ross method, and generalized splitting algorithm. A few improvisations based on first order reliability method are suggested to select algorithmic parameters of the latter two methods. The bias and sampling variance of the alternative estimators are discussed. Also, an approximation to the sampling distribution of some of these estimators is obtained. Illustrative examples involving component and series system reliability analyses are presented with a view to bring out the relative merits of alternative methods. (C) 2015 Elsevier Ltd. All rights reserved.

Global response sensitivity analysis using probability distance measures and generalization of Sobol's analysis

The study introduces two new alternatives for global response sensitivity analysis based on the application of the L-2-norm and Hellinger's metric for measuring distance between two probabilistic models. Both the procedures are shown to be capable of treating dependent non-Gaussian random variable models for the input variables. The sensitivity indices obtained based on the L2-norm involve second order moments of the response, and, when applied for the case of independent and identically distributed sequence of input random variables, it is shown to be related to the classical Sobol's response sensitivity indices. The analysis based on Hellinger's metric addresses variability across entire range or segments of the response probability density function. The measure is shown to be conceptually a more satisfying alternative to the Kullback-Leibler divergence based analysis which has been reported in the existing literature. Other issues addressed in the study cover Monte Carlo simulation based methods for computing the sensitivity indices and sensitivity analysis with respect to grouped variables. Illustrative examples consist of studies on global sensitivity analysis of natural frequencies of a random multi-degree of freedom system, response of a nonlinear frame, and safety margin associated with a nonlinear performance function. (C) 2015 Elsevier Ltd. All rights reserved.

Evaluation of the Index-Flood Approach Related Regional Frequency Analysis Procedures

Index-flood related regional frequency analysis (RFA) procedures are in use by hydrologists to estimate design quantiles of hydrological extreme events at data sparse/ungauged locations in river basins. There is a dearth of attempts to establish which among those procedures is better for RFA in the L-moment framework. This paper evaluates the performance of the conventional index flood (CIF), the logarithmic index flood (LIF), and two variants of the population index flood (PIF) procedures in estimating flood quantiles for ungauged locations by Monte Carlo simulation experiments and a case study on watersheds in Indiana in the U.S. To evaluate the PIF procedure, L-moment formulations are developed for implementing the procedure in situations where the regional frequency distribution (RFD) is the generalized logistic (GLO), generalized Pareto (GPA), generalized normal (GNO) or Pearson type III (PE3), as those formulations are unavailable. Results indicate that one of the variants of the PIF procedure, which utilizes the regional information on the first two L-moments is more effective than the CIF and LIF procedures. The improvement in quantile estimation using the variant of PIF procedure as compared with the CIF procedure is significant when the RFD is a generalized extreme value, GLO, GNO, or PE3, and marginal when it is GPA. (C) 2015 American Society of Civil Engineers.

Effect of Super-exchange Interaction on Ground state Magnetic Properties of Spin-dependent Falicov-Kimball Model on a Triangular Lattice

Ground state magnetic properties are studied by incorporating the super-exchange interaction (J(se)) in the spin-dependent Falicov-Kimball model (FKM) between localized (f-) electrons on a triangular lattice for half filled case. Numerical diagonalization and Monte-Carlo simulation are used to study the ground state magnetic properties. We have found that the magnetic moment of (d-) and (f-) electrons strongly depend on the value of Hund's exchange (J), super-exchange interaction (J(se)) and also depends on the number of (d-) electrons (N-d). The ground state changes from antiferromagnetic (AFM) to ferromagnetic (FM) state as we decrease (N-d). Also the density of d electrons at each site depends on the value of J and J(se).

Damage assessment of composite plate structures with material and measurement uncertainty

Composite materials are very useful in structural engineering particularly in weight sensitive applications. Two different test models of the same structure made from composite materials can display very different dynamic behavior due to large uncertainties associated with composite material properties. Also, composite structures can suffer from pre-existing imperfections like delaminations, voids or cracks during fabrication. In this paper, we show that modeling and material uncertainties in composite structures can cause considerable problein in damage assessment. A recently developed C-0 shear deformable locking free refined composite plate element is employed in the numerical simulations to alleviate modeling uncertainty. A qualitative estimate of the impact of modeling uncertainty on the damage detection problem is made. A robust Fuzzy Logic System (FLS) with sliding window defuzzifier is used for delamination damage detection in composite plate type structures. The FLS is designed using variations in modal frequencies due to randomness in material properties. Probabilistic analysis is performed using Monte Carlo Simulation (MCS) on a composite plate finite element model. It is demonstrated that the FLS shows excellent robustness in delamination detection at very high levels of randomness in input data. (C) 2016 Elsevier Ltd. All rights reserved.

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.

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.

Elastic property estimation using Ultrasound Assisted Optical Elastography through Remote Palpation - A simulation study - art. no. 61640Q

We propose an effective elastography technique in which an acoustic radiation force is used for remote palpation to generate localized tissue displacements, which are directly correlated to localized variations of tissue stiffness and are measured using a light probe in the same direction of ultrasound propagation. The experimental geometry has provision to input light beam along the ultrasound propagation direction, and hence it can be prealigned to ensure proper interception of the focal region by the light beam. Tissue-mimicking phantoms with homogeneous and isotropic mechanical properties of normal and malignant breast tissue are considered for the study. Each phantom is insonified by a focusing ultrasound transducer (1 MHz). The focal volume of the transducer and the ultrasound radiation force in the region are estimated through solving acoustic wave propagation through medium assuming average acoustic properties. The forward elastography problem is solved for the region of insonification assuming the Lame's parameters and Poisson's ratio, under Dirichlet boundary conditions which gives a distribution of displacement vectors. The direction of displacement, though presented spatial variation, is predominantly towards the ultrasound propagation direction. Using Monte Carlo (MC) simulation we have traced the photons through the phantom and collected the photons arriving at the detector on the boundary of the object in the direction of ultrasound. The intensity correlations are then computed from detected photons. The intensity correlation function computed through MC simulation showed a modulation whose strength is found to be proportional to the amplitude of displacement and inversely related to the storage (elastic) modulus. It is observed that when the storage modulus in the focal region is increased the computed displacement magnitude, as indicated by the depth of modulation in the intensity autocorrelation, decreased and the trend is approximately exponential.

Simulation of precipitation reactions in reverse micelles

Precipitation involving mixing of two sets of reverse micellar solutions-containing a reactant and precipitant respectively-has been analyzed. Particle formation in such systems has been simulated by a Monte Carlo (MC) scheme (Li, Y.; Park, C. W. Langmuir 1999, 15, 952), which however is very restrictive in its approach. We have simulated particle formation by developing a general Monte Carlo scheme, using the interval of quiescence technique (IQ). It uses Poisson distribution with realistic, low micellar occupancies of reactants, Brownian collision of micelles with coalescence efficiency, fission of dimers with binomial redispersion of solutes, finite nucleation rate of particles with critical number of molecules, and instantaneous particle growth. With the incorporation of these features, the previous work becomes a special case of our simulation. The present scheme was then used to predict experimental data on two systems. The first is the experimental results of Lianos and Thomas (Chem. Phys. Lett. 1986, 125, 299, J. Colloid Interface Sci. 1987, 117, 505) on formation of CdS nanoparticles. They reported the number of molecules in a particle as a function of micellar size and reactant concentrations, which have been predicted very well. The second is on the formation of Fe(OH)(3) nanoparticles, reported by Li and Park. Our simulation in this case provides a better prediction of the experimental particle size range than the prediction of the authors. The present simulation scheme is general and can be applied to explain nanoparticle formation in other systems.

Simulation of magnetovolume effects in Fe65Ni35 nanoparticles

We compare magnetovolume effects in bulk and nanoparticles by performing Monte Carlo simulations of a spin-analogous model with coupled spatial and magnetic degrees of freedom and chemical disorder. We find that correlations between surface and bulk atoms lead with decreasing particle size to a substantial modification of the magnetic and elastic behavior at low temperatures.

Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

We present results from numerical simulations using a ‘‘cell-dynamical system’’ to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (Φ2)2 model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].

Orientational glassy phases of C60 and neopentane. A Monte Carlo study

Based on an isothermal, isobaric simulation the structure and properties of the plastic crystalline phases of C60 and neopentane have been examined. Instantaneous cooling of the plastic crystalline phases of both C60 and neopentane leads to orientational glassy phases. These are accompanied by significant slowing down of reorientational motion. Constant pressure quench experiments on C60 yield a glass transition temperature of around 80 K.

Simulation and experimental study on compositional evolution of Li-Co in LiCoO(2) thin films during sputter deposition

The compositional evolution in sputter deposited LiCoO(2) thin films is influenced by process parameters involved during deposition. The electrochemical performance of these films strongly depends on their microstructure, preferential orientation and stoichiometry. The transport process of sputtered Li and Co atoms from the LiCoO(2) target to the substrate, through Ar plasma in a planar magnetron configuration, was investigated based on the Monte Carlo technique. The effect of sputtering gas pressure and the substrate-target distance (d(st)) on Li/Co ratio, as well as, energy and angular distribution of sputtered atoms on the substrate were examined. Stable Li/Co ratios have been obtained at 5 Pa pressure and d(st) in the range 5 11 cm. The kinetic energy and incident angular distribution of Li and Co atoms reaching the substrate have been found to be dependent on sputtering pressure. Simulations were extended to predict compositional variations in films prepared at various process conditions. These results were compared with the composition of films determined experimentally using x-ray photoelectron spectroscopy (XPS). Li/Co ratio calculated using XPS was in moderate agreement with that of the simulated value. The measured film thickness followed the same trend as predicted by simulation. These studies are shown to be useful in understanding the complexities in multicomponent sputtering. (C) 2011 American Institute of Physics. doi:10.1063/1.3597829]

Filtered density function for large eddy simulation of turbulent reacting flows

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Itô-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results. © 1998 American Institute of Physics.