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.

Linearization and Reconstruction of Non-linear Diffuse Optical Tomographic Image

Diffuse optical tomography (DOT) is one of the ways to probe highly scattering media such as tissue using low-energy near infra-red light (NIR) to reconstruct a map of the optical property distribution. The interaction of the photons in biological tissue is a non-linear process and the phton transport through the tissue is modelled using diffusion theory. The inversion problem is often solved through iterative methods based on nonlinear optimization for the minimization of a data-model misfit function. The solution of the non-linear problem can be improved by modeling and optimizing the cost functional. The cost functional is f(x) = x(T)Ax - b(T)x + c and after minimization, the cost functional reduces to Ax = b. The spatial distribution of optical parameter can be obtained by solving the above equation iteratively for x. As the problem is non-linear, ill-posed and ill-conditioned, there will be an error or correction term for x at each iteration. A linearization strategy is proposed for the solution of the nonlinear ill-posed inverse problem by linear combination of system matrix and error in solution. By propagating the error (e) information (obtained from previous iteration) to the minimization function f(x), we can rewrite the minimization function as f(x; e) = (x + e)(T) A(x + e) - b(T)(x + e) + c. The revised cost functional is f(x; e) = f(x) + e(T)Ae. The self guided spatial weighted prior (e(T)Ae) error (e, error in estimating x) information along the principal nodes facilitates a well resolved dominant solution over the region of interest. The local minimization reduces the spreading of inclusion and removes the side lobes, thereby improving the contrast, localization and resolution of reconstructed image which has not been possible with conventional linear and regularization algorithm.

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.

Continuum theory of edge states of topological insulators: variational principle and boundary conditions

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.

Theory and Algorithms for Hop-Count-Based Localization with Random Geometric Graph Models of Dense Sensor Networks

Wireless sensor networks can often be viewed in terms of a uniform deployment of a large number of nodes in a region of Euclidean space. Following deployment, the nodes self-organize into a mesh topology with a key aspect being self-localization. Having obtained a mesh topology in a dense, homogeneous deployment, a frequently used approximation is to take the hop distance between nodes to be proportional to the Euclidean distance between them. In this work, we analyze this approximation through two complementary analyses. We assume that the mesh topology is a random geometric graph on the nodes; and that some nodes are designated as anchors with known locations. First, we obtain high probability bounds on the Euclidean distances of all nodes that are h hops away from a fixed anchor node. In the second analysis, we provide a heuristic argument that leads to a direct approximation for the density function of the Euclidean distance between two nodes that are separated by a hop distance h. This approximation is shown, through simulation, to very closely match the true density function. Localization algorithms that draw upon the preceding analyses are then proposed and shown to perform better than some of the well-known algorithms present in the literature. Belief-propagation-based message-passing is then used to further enhance the performance of the proposed localization algorithms. To our knowledge, this is the first usage of message-passing for hop-count-based self-localization.

A finite population model of mlecular evolution: theory and computation

This article is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work has impacted antiviral treatment and vaccine design strategies. Yet, predictions of the quasispecies model are at best viewed as a guideline, primarily because it assumes an infinite population size, whereas realistic population sizes can be quite small. In this paper we consider a population genetics-based model aimed at understanding the evolution of such organisms with finite population sizes and present a rigorous study of the convergence and computational issues that arise therein. Our first result is structural and shows that, at any time during the evolution, as the population size tends to infinity, the distribution of genomes predicted by our model converges to that predicted by the quasispecies model. This justifies the continued use of the quasispecies model to derive guidelines for intervention. While the stationary state in the quasispecies model is readily obtained, due to the explosion of the state space in our model, exact computations are prohibitive. Our second set of results are computational in nature and address this issue. We derive conditions on the parameters of evolution under which our stochastic model mixes rapidly. Further, for a class of widely used fitness landscapes we give a fast deterministic algorithm which computes the stationary distribution of our model. These computational tools are expected to serve as a framework for the modeling of strategies for the deployment of mutagenic drugs.

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

Ampcalculator (AMPC) is a Mathematica (c) based program that was made publicly available some time ago by Unterdorfer and Ecker. It enables the user to compute several processes at one loop (upto O(p(4))) in SU(3) chiral perturbation theory. They include computing matrix elements and form factors for strong and non-leptonic weak processes with at most six external states. It was used to compute some novel processes and was tested against well-known results by the original authors. Here we present the results of several thorough checks of the package. Exhaustive checks performed by the original authors are not publicly available, and hence the present effort. Some new results are obtained from the software especially in the kaon odd-intrinsic parity non-leptonic decay sector involving the coupling G(27). Another illustrative set of amplitudes at tree level we provide is in the context of tau-decays with several mesons including quark mass effects, of use to the BELLE experiment. All eight meson-meson scattering amplitudes have been checked. The Kaon-Compton amplitude has been checked and a minor error in the published results has been pointed out. This exercise is a tutorial-based one, wherein several input and output notebooks are also being made available as ancillary files on the arXiv. Some of the additional notebooks we provide contain explicit expressions that we have used for comparison with established results. The purpose is to encourage users to apply the software to suit their specific needs. An automatic amplitude generator of this type can provide error-free outputs that could be used as inputs for further simplification, and in varied scenarios such as applications of chiral perturbation theory at finite temperature, density and volume. This can also be used by students as a learning aid in low-energy hadron dynamics.

Correlations of vaporization performance of conventional and biofuel sprays in a crossflow heated chamber

Pre-vaporization and pre-mixing are the two main features of LPP type of combustor that operate on liquid fuels. The pre-vaporization length scale is one of its most important design parameters. In this study, the goal is to put forward a simulation based correlation for fuel vaporization performance as a function of dimensionless parameters for crossflow type of injections. Two types of fuels are studied here: jet-A and one of its potential biofuel substitutes, RME. Different sets of spray simulations are considered for crossflow type of injections. Correlations are provided for both jet-A and RME's vaporization performance as a function of non-dimensional inlet air temperature, fuel/air momentum flux ratio and normalized spray traverse distance. (C) 2012 Elsevier Ltd. All rights reserved.

Pattern clustering using cooperative game theory

In this paper, we approach the classical problem of clustering using solution concepts from cooperative game theory such as Nucleolus and Shapley value. We formulate the problem of clustering as a characteristic form game and develop a novel algorithm DRAC (Density-Restricted Agglomerative Clustering) for clustering. With extensive experimentation on standard data sets, we compare the performance of DRAC with that of well known algorithms. We show an interesting result that four prominent solution concepts, Nucleolus, Shapley value, Gately point and \tau-value coincide for the defined characteristic form game. This vindicates the choice of the characteristic function of the clustering game and also provides strong intuitive foundation for our approach.

Wheeler-Feynman absorber revisited: a useful technique to calculate decay rates and lifetimes in small scale optical systems

The Wheeler-Feynman (WF) absorber theory of radiation though no more of interest in explaining self interaction of an electron, can be very useful in today's research in small scale optical systems. The significance of the WF absorber is the use of time-symmetrical solution of Maxwell's equations as opposed to only the retarded solution. The radiative coupling of emitters to nano wires in the near field and change in their lifetimes due to small mode volume enclosures have been elucidated with the retarded solutions before. These solutions have also been shown to agree with quantum electrodynamics, thus allowing for classical electromagnetic approaches in such problems. It is here assumed that the radiative coupling of the emitter with a body is in proportion to its contribution to the classical force of radiative reaction as derived in the WF absorber theory. Representing such nano structures as a partial WF absorber acting on the emitter makes the computations considerably easier than conventional electromagnetic solutions for full boundary conditions.

Vibrational spectroscopy and density functional theory analysis of 3-O-caffeoylquinic acid

Density functional theory (DFT) calculations are being performed to investigate the geometric, vibrational, and electronic properties of the chlorogenic acid isomer 3-CQA (1R,3R,4S,5R)-3-{(2E)-3-(3,4-dihydroxyphenyl)prop-2-enoyl]oxy}-1,4, 5-trihydroxycyclohexanecarboxylic acid), a major phenolic compound in coffee. DFT calculations with the 6-311G(d,p) basis set produce very good results. The electrostatic potential mapped onto an isodensity surface has been obtained. A natural bond orbital analysis (NBO) has been performed in order to study intramolecular bonding, interactions among bonds, and delocalization of unpaired electrons. HOMO-LUMO studies give insights into the interaction of the molecule with other species. The calculated HOMO and LUMO energies indicate that a charge transfer occurs within the molecule. (C) 2012 Elsevier B.V. All rights reserved.

A Comparison of mechanical and tribological behavior of nanostructured and conventional WC-12Co detonation-sprayed coatings

In the present study, WC-12Co coatings were deposited by detonation-spraying technique using conventional and nanostructured WC-12Co feedstock at four different oxy/fuel ratios (OF ratio). The coatings exhibited the presence of phases like W2C and W due to the decarburization of the WC phase, and the proportions of these phases were higher in the nano WC-12Co coatings compared with conventional WC-12Co coatings. Coating hardness and fracture toughness were measured. The tribological performance of coatings was examined under dry sand rubber wheel abrasion wear, and solid particle erosion wear conditions. The mechanical and wear properties of coatings were influenced by degree of decarburization and more so in the case of nanostructured WC-Co coatings. The results indicate that the extent of decarburization has a substantial influence on the elastic modulus of the coating which in turn is related to the extent of intersplat cracking of the coating.

Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be mu h/4 pi k(B), when h and k(B) are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In,addition, certain optically thin, hot, accretion flows, of temperature greater than or similar to 10(9) K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.

Analytical theory and stability analysis of an elongated nanoscale object under external torque

We consider the rotational motion of an elongated nanoscale object in a fluid under an external torque. The experimentally observed dynamics could be understood from analytical solutions of the Stokes equation, with explicit formulae derived for the dynamical states as a function of the object dimensions and the parameters defining the external torque. Under certain conditions, multiple analytical solutions to the Stokes equations exist, which have been investigated through numerical analysis of their stability against small perturbations and their sensitivity towards initial conditions. These experimental results and analytical formulae are general enough to be applicable to the rotational motion of any isolated elongated object at low Reynolds numbers, and could be useful in the design of non-spherical nanostructures for diverse applications pertaining to microfluidics and nanoscale propulsion technologies.