Bose-Hubbard models in confining potentials: Inhomogeneous mean-field theory

We present an extensive study of Mott insulator (MI) and superfluid (SF) shells in Bose-Hubbard (BH) models for bosons in optical lattices with harmonic traps. For this we apply the inhomogeneous mean-field theory developed by Sheshadri et al. Phys. Rev. Lett. 75, 4075 (1995)]. Our results for the BH model with one type of spinless bosons agree quantitatively with quantum Monte Carlo simulations. Our approach is numerically less intensive than such simulations, so we are able to perform calculations on experimentally realistic, large three-dimensional systems, explore a wide range of parameter values, and make direct contact with a variety of experimental measurements. We also extend our inhomogeneous mean-field theory to study BH models with harmonic traps and (a) two species of bosons or (b) spin-1 bosons. With two species of bosons, we obtain rich phase diagrams with a variety of SF and MI phases and associated shells when we include a quadratic confining potential. For the spin-1 BH model, we show, in a representative case, that the system can display alternating shells of polar SF and MI phases, and we make interesting predictions for experiments in such systems.

Asymptotics of the invariant measure in mean field models with jumps

We consider the asymptotics of the invariant measure for the process of spatial distribution of N coupled Markov chains in the limit of a large number of chains. Each chain reflects the stochastic evolution of one particle. The chains are coupled through the dependence of transition rates on the spatial distribution of particles in the various states. Our model is a caricature for medium access interactions in wireless local area networks. Our model is also applicable in the study of spread of epidemics in a network. The limiting process satisfies a deterministic ordinary differential equation called the McKean-Vlasov equation. When this differential equation has a unique globally asymptotically stable equilibrium, the spatial distribution converges weakly to this equilibrium. Using a control-theoretic approach, we examine the question of a large deviation from this equilibrium.

Improved quasiparticle wave functions and mean field for G(0)W(0) calculations: Initialization with the COHSEX operator

The GW approximation to the electron self-energy has become a standard method for ab initio calculation of excited-state properties of condensed-matter systems. In many calculations, the G W self-energy operator, E, is taken to be diagonal in the density functional theory (DFT) Kohn-Sham basis within the G0 W0 scheme. However, there are known situations in which this diagonal Go Wo approximation starting from DFT is inadequate. We present two schemes to resolve such problems. The first, which we called sc-COHSEX-PG W, involves construction of an improved mean field using the static limit of GW, known as COHSEX (Coulomb hole and screened exchange), which is significantly simpler to treat than GW W. In this scheme, frequency-dependent self energy E(N), is constructed and taken to be diagonal in the COHSEX orbitals after the system is solved self-consistently within this formalism. The second method is called off diagonal-COHSEX G W (od-COHSEX-PG W). In this method, one does not self-consistently change the mean-field starting point but diagonalizes the COHSEX Hamiltonian within the Kohn-Sham basis to obtain quasiparticle wave functions and uses the resulting orbitals to construct the G W E in the diagonal form. We apply both methods to a molecular system, silane, and to two bulk systems, Si and Ge under pressure. For silane, both methods give good quasiparticle wave functions and energies. Both methods give good band gaps for bulk silicon and maintain good agreement with experiment. Further, the sc-COHSEX-PGW method solves the qualitatively incorrect DFT mean-field starting point (having a band overlap) in bulk Ge under pressure.

Application of principal component analysis to gas sensing characteristics of Cr0.8Fe0.2NbO4 thick film array

The transient changes in resistances of Cr0.8Fe0.2NbO4 thick film sensors towards specified concentrations of H-2, NH3, acetonitrile, acetone, alcohol, cyclohexane and petroleum gas at different operating temperatures were recorded. The analyte-specific characteristics such as slopes of the response and retrace curves, area under the curve and sensitivity deduced from the transient curve of the respective analyte gas have been used to construct a data matrix. Principal component analysis (PCA) was applied to this data and the score plot was obtained. Distinguishing one reducing gas from the other is demonstrated based on this approach, which otherwise is not possible by measuring relative changes in conductivity. This methodology is extended for three Cr0.8Fe0.2NbO4 thick film sensor array operated at different temperatures. (C) 2015 Elsevier B.V. All rights reserved.

Adsorption isitherms for neutral organic compounds-A hierarchy in modelling: Part IV. Charge of maximum adsorption-Statistical mechanical basis

The charge at which adsorption of orgamc compounds attains a maximum ( \sigma MAX M) at an electrochenucal interface is analysed using several multi-state models in a hierarchical manner The analysis is based on statistical mechamcal results for the following models (A) two-state site parity, (B) two-state muhl-slte, and (C) three-state site parity The coulombic interactions due to permanent and reduced dipole effects (using mean field approximation), electrostatic field effects and specific substrate interactions have been taken into account. The simplest model in the hierarchy (two-state site parity) yields the exphcit dependence of ( \sigma MAX M) on the permanent dipole moment, polarizability of the solvent and the adsorbate, lattice spacing, effective coordination number, etc Other models in the baerarchy bring to hght the influence of the solvent structure and the role of substrate interactions, etc As a result of this approach, the "composition" of oM.x m terms of the fundamental molecular constants becomes clear. With a view to use these molecular results to maxamum advantage, the derived results for ( \sigma MAX M) have been converted into those involving experimentally observable parameters lake Co, C 1, E N, etc Wherever possible, some of the earlier phenomenologlcal relations reported for ( \sigma MAX M), notably by Parsons, Damaskm and Frumkln, and Trasattl, are shown to have a certain molecular basis, vlz a simple two-state sate panty model.As a corollary to the hxerarcbacal modelling, \sigma MAX M and the potential corresponding to at (Emax) are shown to be constants independent of 0max or Corg for all models The lmphcatlon of our analysis f o r OmMa x with respect to that predicted by the generalized surface layer equation (which postulates Om~ and Ema x varlaUon with 0) is discussed in detail Finally we discuss an passing o M. and the electrosorptlon valency an this context.

State Dependent Attempt Rate Modeling of Single Cell IEEE 802.11 WLANs with Homogeneous Nodes and Poisson Arrivals

Analytical models of IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known mean-field approximations proposed by Bianchi for saturated nodes. In this paper, we provide a new approach for modeling the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model M queues (one queue per node) served by the CSMA/CA protocol as standardized in the IEEE 802.11 DCF. The approximation is that, when n of the M queues are non-empty, the attempt probability of the n non-empty nodes is given by the long-term attempt probability of n saturated nodes as provided by Bianchi's model. This yields a coupled queue system. When packets arrive to the M queues according to independent Poisson processes, we provide an exact model for the coupled queue system with SDAR service. The main contribution of this paper is to provide an analysis of the coupled queue process by studying a lower dimensional process and by introducing a certain conditional independence approximation. We show that the numerical results obtained from our finite buffer analysis are in excellent agreement with the corresponding results obtained from ns-2 simulations. We replace the CSMA/CA protocol as implemented in the ns-2 simulator with the SDAR service model to show that the SDAR approximation provides an accurate model for the CSMA/CA protocol. We also report the simulation speed-ups thus obtained by our model-based simulation.

Field Flow Sensitive Pointer and Escape Analysis for Java Using Heap Array SSA

Context sensitive pointer analyses based on Whaley and Lam’s bddbddb system have been shown to scale to large Java programs. We provide a technique to incorporate flow sensitivity for Java fields into one such analysis and obtain an escape analysis based on it. First, we express an intraprocedural field flow sensitive analysis, using Fink et al.’s Heap Array SSA form in Datalog. We then extend this analysis interprocedurally by introducing two new φ functions for Heap Array SSA Form and adding deduction rules corresponding to them. Adding a few more rules gives us an escape analysis. We describe two types of field flow sensitivity: partial (PFFS) and full (FFFS), the former without strong updates to fields and the latter with strong updates. We compare these analyses with two different (field flow insensitive) versions of Whaley-Lam analysis: one of which is flow sensitive for locals (FS) and the other, flow insensitive for locals (FIS). We have implemented this analysis on the bddbddb system while using the SOOT open source framework as a front end. We have run our analysis on a set of 15 Java programs. Our experimental results show that the time taken by our field flow sensitive analyses is comparable to that of the field flow insensitive versions while doing much better in some cases. Our PFFS analysis achieves average reductions of about 23% and 30% in the size of the points-to sets at load and store statements respectively and discovers 71% more “caller-captured” objects than FIS.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Electrochemical phase formation involving multicomponents: hemispherical overlap models for varied nucleation and growth conditions

The phenomenological theory of hemispherical growth in the context of phase formation with more than one component is presented. The model discusses in a unified manner both instantaneous and progressive nucleation (at the substrate) as well as arbitrary growth rates (e.g. constant and diffusion controlled growth rates). A generalized version of Avrami ansatz (a mean field description) is used to tackle the ''overlap'' aspects arising from the growing multicentres of the many components involved, observing that the nucleation is confined to the substrate plane only. The time evolution of the total extent of macrogrowth as well as those of the individual components are discussed explicitly for the case of two phases. The asymptotic expressions for macrogrowth are derived. Such analysis depicts a saturation limit (i.e. the maximum extent of growth possible) for the slower growing component and its dependence on the kinetic parameters which, in the electrochemical context, can be controlled through potential. The significance of this model in the context of multicomponent alloy deposition and possible future directions for further development are pointed out.

Stochastic analysis of epidemics on adaptive time varying networks

Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an ``adaptive threshold,'' i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.

Phenotypic characters of rice landraces reveal independent lineages of short-grain aromatic indica rice

Rice landraces are lineages developed by farmers through artificial selection during the long-term domestication process. Despite huge potential for crop improvement, they are largely understudied in India. Here, we analyse a suite of phenotypic characters from large numbers of Indian landraces comprised of both aromatic and non-aromatic varieties. Our primary aim was to investigate the major determinants of diversity, the strength of segregation among aromatic and non-aromatic landraces as well as that within aromatic landraces. Using principal component analysis, we found that grain length, width and weight, panicle weight and leaf length have the most substantial contribution. Discriminant analysis can effectively distinguish the majority of aromatic from non-aromatic landraces. More interestingly, within aromatic landraces long-grain traditional Basmati and short-grain non-Basmati aromatics remain morphologically well differentiated. The present research emphasizes the general patterns of phenotypic diversity and finds out the most important characters. It also confirms the existence of very unique short-grain aromatic landraces, perhaps carrying signatures of independent origin of an additional aroma quantitative trait locus in the indica group, unlike introgression of specific alleles of the BADH2 gene from the japonica group as in Basmati. We presume that this parallel origin and evolution of aroma in short-grain indica landraces are linked to the long history of rice domestication that involved inheritance of several traits from Oryza nivara, in addition to O. rufipogon. We conclude with a note that the insights from the phenotypic analysis essentially comprise the first part, which will likely be validated with subsequent molecular analysis.

Evidence of clustering in an aqueous electrolyte solution: a small-angle X-ray scattering study

The work reported hen was motivated by a desire to verify the existence of structure - specifically MP-rich clusters induced by sodium bromide (NaBr) in the ternary liquid mixture 3-methylpyridine (Mf) + water(W) + NaBr. We present small-angle X-ray scattering (SAXS) measurements in this mixture. These measurements were obtained at room temperature (similar to 298 K) in the one-phase region (below the relevant lower consolute points, T(L)s) at different values of X (i.e., X = 0.02 - 0.17), where X is the weight fraction of NaBr in the mixture. Cluster-size distribution, estimated on the assumption that the clusters are spherical, shows systematic behaviour in that the peak of the distribution shifts rewards larger values of cluster radius as X increases. The largest spatial extent of the clusters (similar to 4.5 nm) is seen at X = 0.17. Data analysis assuming arbitrary shapes and sizes of clusters gives a limiting value of cluster size (- 4.5 nm) that is not very sensitive to X. It is suggested that the cluster size determined may not be the same as the usual critical-point fluctuations far removed from the critical point (T-L). The influence of the additional length scale due to clustering is discussed from the standpoint of crossover from Ising to mean-field critical behaviour, when moving away from the T-L.

Cluster analysis of rainfall stations of the Indian peninsula

Principal component analysis is applied to derive patterns of temporal variation of the rainfall at fifty-three stations in peninsular India. The location of the stations in the coordinate space determined by the amplitudes of the two leading eigenvectors is used to delineate them into eight clusters. The clusters obtained seem to be stable with respect to variations in the grid of stations used. Stations within any cluster occur in geographically contiguous areas.

Theory of the mixed valent state

After briefly discussing the question of a distinct mixed valent state and theoretical models for it, the area of greatest theoretical success, namely the mixed valent impurity, is reviewed. Applications to spectroscopy, energetics and Hall effect are then putlined. The independent impurity approximation is inadequate for many properties of the bulk system, which depend on lattice coherence. A recent auxiliary or slave boson approach with a simple mean field limit and fluctuation corrections is summarized. Finally the mixed valent semiconductor is discussed as an outstanding problem.

Edge-based connected component approach for skew correction of complex document images

Skew correction of complex document images is a difficult task. We propose an edge-based connected component approach for robust skew correction of documents with complex layout and content. The algorithm essentially consists of two steps - an 'initialization' step to determine the image orientation from the centroids of the connected components and a 'search' step to find the actual skew of the image. During initialization, we choose two different sets of points regularly spaced across the the image, one from the left to right and the other from top to bottom. The image orientation is determined from the slope between the two succesive nearest neighbors of each of the points in the chosen set. The search step finds succesive nearest neighbors that satisfy the parameters obtained in the initialization step. The final skew is determined from the slopes obtained in the 'search' step. Unlike other connected component based methods, the proposed method does not require any binarization step that generally precedes connected component analysis. The method works well for scanned documents with complex layout of any skew with a precision of 0.5 degrees.