An extended finite-element model coupled with level set method for analysis of growth of corrosion pits in metallic structures

Mass balance between metal and electrolytic solution, separated by a moving interface, in stable pit growth results in a set of governing equations which are solved for concentration field and interface position (pit boundary evolution). The interface experiences a jump discontinuity in metal concentration. The extended finite-element model (XFEM) handles this jump discontinuity by using discontinuous-derivative enrichment formulation, eliminating the requirement of using front conforming mesh and re-meshing after each time step as in the conventional finite-element method. However, prior interface location is required so as to solve the governing equations for concentration field for which a numerical technique, the level set method, is used for tracking the interface explicitly and updating it over time. The level set method is chosen as it is independent of shape and location of the interface. Thus, a combined XFEM and level set method is developed in this paper. Numerical analysis for pitting corrosion of stainless steel 304 is presented. The above proposed model is validated by comparing the numerical results with experimental results, exact solutions and some other approximate solutions. An empirical model for pitting potential is also derived based on the finite-element results. Studies show that pitting profile depends on factors such as ion concentration, solution pH and temperature to a large extent. Studying the individual and combined effects of these factors on pitting potential is worth knowing, as pitting potential directly influences corrosion rate.

Spectrum of the three-dimensional fuzzy well

We develop the formalism of quantum mechanics on three-dimensional fuzzy space and solve the Schrodinger equation for the free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well are calculated.

Quantum entropy for the fuzzy sphere and its monopoles

Using generalized bosons, we construct the fuzzy sphere S-F(2) and monopoles on S-F(2) in a reducible representation of SU(2). The corresponding quantum states are naturally obtained using the GNS-construction. We show that there is an emergent nonabelian unitary gauge symmetry which is in the commutant of the algebra of observables. The quantum states are necessarily mixed and have non-vanishing von Neumann entropy, which increases monotonically under a bistochastic Markov map. The maximum value of the entropy has a simple relation to the degeneracy of the irreps that constitute the reducible representation that underlies the fuzzy sphere.

Monopoles, Dirac operator, and index theory for fuzzy SU(3) / (U(1) x U(1))

The intersection of the ten-dimensional fuzzy conifold Y-F(10) with S-F(5) x S-F(5) is the compact eight-dimensional fuzzy space X-F(8). We show that X-F(8) is (the analogue of) a principal U(1) x U(1) bundle over fuzzy SU(3) / U(1) x U(1)) ( M-F(6)). We construct M-F(6) using the Gell-Mann matrices by adapting Schwinger's construction. The space M-F(6) is of relevance in higher dimensional quantum Hall effect and matrix models of D-branes. Further we show that the sections of the monopole bundle can be expressed in the basis of SU(3) eigenvectors. We construct the Dirac operator on M-F(6) from the Ginsparg-Wilson algebra on this space. Finally, we show that the index of the Dirac operator correctly reproduces the known results in the continuum.

The Tetrablock as a Spectral Set

The tetrablock, roughly speaking, is the set of all linear fractional maps that map the open unit disc to itself. A formal definition of this inhomogeneous domain is given below. This paper considers triples of commuting bounded operators (A,B,P) that have the tetrablock as a spectral set. Such a triple is named a tetrablock contraction. The motivation comes from the success of model theory in another inhomogeneous domain, namely, the symmetrized bidisc F. A pair of commuting bounded operators (S,P) with Gamma as a spectral set is called a Gamma-contraction, and always has a dilation. The two domains are related intricately as the Lemma 3.2 below shows. Given a triple (A, B, P) as above, we associate with it a pair (F-1, F-2), called its fundamental operators. We show that (A,B,P) dilates if the fundamental operators F-1 and F-2 satisfy certain commutativity conditions. Moreover, the dilation space is no bigger than the minimal isometric dilation space of the contraction P. Whether these commutativity conditions are necessary, too, is not known. what we have shown is that if there is a tetrablock isometric dilation on the minimal isometric dilation space of P. then those commutativity conditions necessarily get imposed on the fundamental operators. En route, we decipher the structure of a tetrablock unitary (this is the candidate as the dilation triple) and a tertrablock isometry (the restriction of a tetrablock unitary to a joint invariant sub-space). We derive new results about r-contractions and apply them to tetrablock contractions. The methods applied are motivated by 11]. Although the calculations are lengthy and more complicated, they beautifully reveal that the dilation depends on the mutual relationship of the two fundamental operators, so that certain conditions need to be satisfied. The question of whether all tetrablock contractions dilate or not is unresolved.

Tectono-geomorphic and environmental set-up deduced during deposition of Mio-Pleistocene sediments in NW Himalaya, India

Detailed pedofacies characterization along-with lithofacies investigations of the Mio-Pleistocene Siwalik sediments exposed in the Ramnagar sub-basin have been studied so as to elucidate variability in time and space of fluvial processes and the role of intra- and extra-basinal controls on fluvial sedimentation during the evolution of the Himalayan foreland basin (HFB). Dominance of multiple, moderately to strongly developed palaeosol assemblages during deposition of Lower Siwalik (similar to 12-10.8 Ma) sediments suggest that the HFB was marked by Upland set-up of Thomas et al. (2002). Activity of intra-basinal faults on the uplands and deposition of terminal fans at different times caused the development of multiple soils. Further, detailed pedofacies along-with lithofacies studies indicate prevalence of stable tectonic conditions and development of meandering streams with broad floodplains. However, the Middle Siwalik (similar to 10.8-4.92 Ma) sub-group is marked by multistoried sandstones and minor mudstone and mainly weakly developed palaeosols, indicating deposition by large braided rivers in the form of megafans in a Lowland set-up of Thomas et al. (2002). Significant change in nature and size of rivers from the Lower to Middle Siwalik at similar to 10 Ma is found almost throughout of the basin from Kohat Plateau (Pakistan) to Nepal because the Himalayan orogeny witnessed its greatest tectonic upheaval at this time leading to attainment of great heights by the Himalaya, intensification of the monsoon, development of large rivers systems and a high rate of sedimentation, hereby a major change from the Upland set-up to the Lowland set-up over major parts of the HFB. An interesting geomorphic environmental set-up prevailed in the Ramnagar sub-basin during deposition of the studied Upper Siwalik (similar to 4.92 to <1.68 Ma) sediments as observed from the degree of pedogenesis and the type of palaeosols. In general, the Upper Siwalik sub-group in the Ramnagar sub-basin is subdivided from bottom to top into the Purmandal sandstone (4.92-4.49 Ma), Nagrota (4.49-1.68 Ma) and Boulder Conglomerate (<1.68 Ma) formations on the basis of sedimentological characters and change in dominant lithology. Presence of mudstone, a few thin gravel beds and dominant sandstone lithology with weakly to moderately developed palaeosols in the Purmandal sandstone Fm. indicates deposition by shallow braided fluvial streams. The deposition of mudstone dominant Nagrota Fm. with moderately to some well developed palaeosols and a zone of gleyed palaeosols with laminated mudstones and thin sandstones took place in an environment marked by numerous small lakes, water-logged regions and small streams in an environment just south of the Piedmont zone, perhaps similar to what is happening presently in the Upland region/the Upper Gangetic plain. This area is locally called the `Trai region' (Pascoe, 1964). Deposition of Boulder Conglomerate Fm. took place by gravelly braided river system close to the Himalayan Ranges. Activity along the Main Boundary Fault led to progradation of these environments distal-ward and led to development of on the whole a coarsening upward sequence. (C) 2014 Elsevier B.V. All rights reserved.

LANDSCAPE DYNAMICS MODELING THROUGH INTEGRATED MARKOV, FUZZY-AHP AND CELLULAR AUTOMATA

Multi temporal land use information were derived using two decades remote sensing data and simulated for 2012 and 2020 with Cellular Automata (CA) considering scenarios, change probabilities (through Markov chain) and Multi Criteria Evaluation (MCE). Agents and constraints were considered for modeling the urbanization process. Agents were nornmlized through fiizzyfication and priority weights were assigned through Analytical Hierarchical Process (AHP) pairwise comparison for each factor (in MCE) to derive behavior-oriented rules of transition for each land use class. Simulation shows a good agreement with the classified data. Fuzzy and AHP helped in analyzing the effects of agents of growth clearly and CA-Markov proved as a powerful tool in modelling and helped in capturing and visualizing the spatiotemporal patterns of urbanization. This provided rapid land evaluation framework with the essential insights of the urban trajectory for effective sustainable city planning.

Regionalization of extreme rainfall in India

Regionalization of extreme rainfall is useful for various applications in hydro-meteorology. There is dearth of regionalization studies on extreme rainfall in India. In this perspective, a set of 25 regions that are homogeneous in 1-, 2-, 3-, 4- and 5-day extreme rainfall is delineated based on seasonality measure of extreme rainfall and location indicators (latitude, longitude and altitude) by using global fuzzy c-means (GFCM) cluster analysis. The regions are validated for homogeneity in L-moment framework. One of the applications of the regions is in arriving at quantile estimates of extreme rainfall at sparsely gauged/ungauged locations using options such as regional frequency analysis (RFA). The RFA involves use of rainfall-related information from gauged sites in a region as the basis to estimate quantiles of extreme rainfall for target locations that resemble the region in terms of rainfall characteristics. A procedure for RFA based on GFCM-delineated regions is presented and its effectiveness is evaluated by leave-one-out cross validation. Error in quantile estimates for ungauged sites is compared with that resulting from the use of region-of-influence (ROI) approach that forms site-specific regions exclusively for quantile estimation. Results indicate that error in quantile estimates based on GFCM regions and ROI are fairly close, and neither of them is consistent in yielding the least error over all the sites. The cluster analysis approach was effective in reducing the number of regions to be delineated for RFA.

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.

An Optical How Feature and McFIS Based Approach for 3-Dimensional Human Action Recognition

We propose to develop a 3-D optical flow features based human action recognition system. Optical flow based features are employed here since they can capture the apparent movement in object, by design. Moreover, they can represent information hierarchically from local pixel level to global object level. In this work, 3-D optical flow based features a re extracted by combining the 2-1) optical flow based features with the depth flow features obtained from depth camera. In order to develop an action recognition system, we employ a Meta-Cognitive Neuro-Fuzzy Inference System (McFIS). The m of McFIS is to find the decision boundary separating different classes based on their respective optical flow based features. McFIS consists of a neuro-fuzzy inference system (cognitive component) and a self-regulatory learning mechanism (meta-cognitive component). During the supervised learning, self-regulatory learning mechanism monitors the knowledge of the current sample with respect to the existing knowledge in the network and controls the learning by deciding on sample deletion, sample learning or sample reserve strategies. The performance of the proposed action recognition system was evaluated on a proprietary data set consisting of eight subjects. The performance evaluation with standard support vector machine classifier and extreme learning machine indicates improved performance of McFIS is recognizing actions based of 3-D optical flow based features.

Multiobjective fuzzy optimization for sustainable groundwater management using particle swarm optimization and analytic element method

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright (c) 2015 John Wiley & Sons, Ltd.

Intramolecular hydrogen bond: Can it be part of the basis set of valence internal coordinates in normal mode analysis?

It has been shown earlier1] that the relaxed force constants (RFCs) could be used as a measure of bond strength only when the bonds form a part of the complete valence internal coordinates (VIC) basis. However, if the bond is not a part of the complete VIC basis, its RFC is not necessarily a measure of bond strength. Sometimes, it is possible to have a complete VIC basis that does not contain the intramolecular hydrogen bond (IMHB) as part of the basis. This means the RFC of IMHB is not necessarily a measure of bond strength. However, we know that IMHB is a weak bond and hence its RFC has to be a measure of bond strength. We resolve this problem of IMHB not being part of the complete basis by postulating `equivalent' basis sets where IMHB is part of the basis at least in one of the equivalent sets of VIC. As long as a given IMHB appears in one of the equivalent complete VIC basis sets, its RFC could be used as a measure of bond strength parameter.

Parameterized Algorithms and Kernels for 3-Hitting Set with Parity Constraints

The 3-Hitting Set problem involves a family of subsets F of size at most three over an universe U. The goal is to find a subset of U of the smallest possible size that intersects every set in F. The version of the problem with parity constraints asks for a subset S of size at most k that, in addition to being a hitting set, also satisfies certain parity constraints on the sizes of the intersections of S with each set in the family F. In particular, an odd (even) set is a hitting set that hits every set at either one or three (two) elements, and a perfect code is a hitting set that intersects every set at exactly one element. These questions are of fundamental interest in many contexts for general set systems. Just as for Hitting Set, we find these questions to be interesting for the case of families consisting of sets of size at most three. In this work, we initiate an algorithmic study of these problems in this special case, focusing on a parameterized analysis. We show, for each problem, efficient fixed-parameter tractable algorithms using search trees that are tailor-made to the constraints in question, and also polynomial kernels using sunflower-like arguments in a manner that accounts for equivalence under the additional parity constraints.

Reservoir Operation with Fuzzy State Variables for Irrigation of Multiple Crops

This paper presents the development and application of a stochastic dynamic programming model with fuzzy state variables for irrigation of multiple crops. A fuzzy stochastic dynamic programming (FSDP) model is developed in which the reservoir storage and soil moisture of the crops are considered as fuzzy numbers, and the reservoir inflow is considered as a stochastic variable. The model is formulated with an objective of minimizing crop yield deficits, resulting in optimal water allocations to the crops by maintaining storage continuity and soil moisture balance. The standard fuzzy arithmetic method is used to solve all arithmetic equations with fuzzy numbers, and the fuzzy ranking method is used to compare two or more fuzzy numbers. The reservoir operation model is integrated with a daily-based water allocation model, which results in daily temporal variations of allocated water, soil moisture, and crop deficits. A case study of an existing Bhadra reservoir in Karnataka, India, is chosen for the model application. The FSDP is a more realistic model because it considers the uncertainty in discretization of state variables. The results obtained using the FSDP model are found to be more acceptable for the case study than those of the classical stochastic dynamic model and the standard operating model, in terms of 10-day releases from the reservoir and evapotranspiration deficit. (C) 2015 American Society of Civil Engineers.

Interplay of vector-like top partner multiplets in a realistic mixing set-up

The ATLAS and CMS collaborations at the LHC have performed analyses on the existing data sets, studying the case of one vector-like fermion or multiplet coupling to the standard model Yukawa sector. In the near future, with more data available, these experimental collaborations will start to investigate more realistic cases. The presence of more than one extra vector-like multiplet is indeed a common situation in many extensions of the standard model. The interplay of these vector-like multiplet between precision electroweak bounds, flavour and collider phenomenology is a important question in view of establishing bounds or for the discovery of physics beyond the standard model. In this work we study the phenomenological consequences of the presence of two vector-like multiplets. We analyse the constraints on such scenarios from tree-level data and oblique corrections for the case of mixing to each of the SM generations. In the present work, we limit to scenarios with two top-like partners and no mixing in the down-sector.