A finite element method for compressible viscous fluid flows

This work presents a mixed three-dimensional finite element formulation for analyzing compressible viscous flows. The formulation is based on the primitive variables velocity, density, temperature and pressure. The goal of this work is to present a `stable' numerical formulation, and, thus, the interpolation functions for the field variables are chosen so as to satisfy the inf-sup conditions. An exact tangent stiffness matrix is derived for the formulation, which ensures a quadratic rate of convergence. The good performance of the proposed strategy is shown in a number of steady-state and transient problems where compressibility effects are important such as high Mach number flows, natural convection, Riemann problems, etc., and also on problems where the fluid can be treated as almost incompressible. Copyright (C) 2010 John Wiley & Sons, Ltd.

Shape optimization of RC flexural members

A natural velocity field method for shape optimization of reinforced concrete (RC) flexural members has been demonstrated. The possibility of shape optimization by modifying the shape of an initially rectangular section, in addition to variation of breadth and depth along the length, has been explored. Necessary shape changes have been computed using the sequential quadratic programming (SQP) technique. Genetic algorithm (Goldberg and Samtani 1986) has been used to optimize the diameter and number of main reinforcement bars. A limit-state design approach has been adopted for the nonprismatic RC sections. Such relevant issues as formulation of optimization problem, finite-element modeling, and solution procedure have been described. Three design examples-a simply supported beam, a cantilever beam, and a two-span continuous beam, all under uniformly distributed loads-have been optimized. The results show a significant savings (40-56%) in material and cost and also result in aesthetically pleasing structures. This procedure will lead to considerable cost saving, particularly in cases of mass-produced precast members and a heavy cast-in-place member such as a bridge girder.

Solutions of cubic equations in quadratic fields

Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equations, which represent elliptic curves defined over Q, in quadratic fields and prove some interesting results regarding the solutions by using elementary tools. As an application we consider the Diophantine equation r + s + t = rst = 1 in O-K. This Diophantine equation gives an elliptic curve defined over Q with finite Mordell-Weil group. Using our study of the solutions of cubic equations in quadratic fields we present a simple proof of the fact that except for the ring of integers of Q(i) and Q(root 2), this Diophantine equation is not solvable in the ring of integers of any other quadratic fields, which is already proved in [4].

Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions

The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate-adsorbate interactions in the Brag-Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with epsilon(aa) as the adsorbate-adsorbate interaction parameter, the comparisons for different values of epsilon(aa)(*)=epsilon(aa)z/2kT, and number of sites per cage, n, illustrate that for -1 0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent epsilon(aa)) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages. (C) 1999 American Institute of Physics. [S0021-9606(99)70333-8].

Unsteady flow and heat transfer on a semi-infinite flat plate with an aligned magnetic field

The unsteady laminar boundary layer flow of an electrically conducting fluid past a semi-infinite flat plate with an aligned magnetic field has been studied when at time t > 0 the plate is impulsively moved with a constant velocity which is in the same or opposite direction to that of free stream velocity. The effect of the induced magnetic field has been included in the analysis. The non-linear partial differential equations have been solved numerically using an implicit finite-difference method. The effect of the impulsive motion of the surface is found to be more pronounced on the skin friction but its effect on the x-component of the induced magnetic field and heat transfer is small. Velocity defect occurs near the surface when the plate is impulsively moved in the same direction as that of the free stream velocity. The surface shear stress, x-component of the induced magnetic field on the surface and the surface heat transfer decrease with an increasing magnetic field, but they increase with the reciprocal of the magnetic Prandtl number. However, the effect of the reciprocal of the magnetic Prandtl number is more pronounced on the x-component of the induced magnetic field. (C) 1999 Elsevier Science Ltd. All rights reserved.

Taxonomic Implications of a Field Study of Morphotypes of Hanuman Langurs (Semnopithecus entellus) in Peninsular India

The Hanuman langur is one of the most widely distributed and morphologically variable non-human primates in South Asia. Even though it has been extensively studied, the taxonomic status of this species remains unresolved due to incongruence between various classification schemes. This incongruence, we believe, is largely due to the use of plastic morphological characters such as coat color in classification. Additionally these classification schemes were largely based on reanalysis of the same set of museum specimens. To bring greater resolution in Hanuman langur taxonomy we undertook a field survey to study variation in external morphological characters among Hanuman langurs. The primary objective of this study is to ascertain the number of morphologically recognizable units (morphotypes) of Hanuman langur in peninsular India and to compare our field observations with published classification schemes. We typed five color-independent characters for multiple adults from various populations in South India. We used the presence-absence matrix of these characters to derive the pair-wise distance between individuals and used this to construct a neighbor-joining (NJ) tree. The resulting NJ tree retrieved six distinct clusters, which we assigned to different morphotypes. These morphotypes can be identified in the field by using a combination of five diagnostic characters. We determined the approximate distributions of these morphotypes by plotting the sampling locations of each morphotype on a map using GIS software. Our field observations are largely concordant with some of the earliest classification schemes, but are incongruent with recent classification schemes. Based on these results we recommend Hill (Ceylon Journal of Science, Colombo 21:277-305, 1939) and Pocock (Primates and carnivora (in part) (pp. 97-163). London: Taylor and Francis, 1939) classification schemes for future studies on Hanuman langurs.

Possible conversion of a neutron star to a quark star in the presence of high magnetic field

Recent results and data suggest that high magnetic fields in neutron stars (NS) strongly affect the characteristics (radius, mass) of the star. Such stars are even separated into a class known as magnetars, for which the surface magnetic field is greater than 10(14) G. In this work we discuss the effect of such a high magnetic field on the phase transition of a NS to a quark star (QS). We study the effect of magnetic field on the transition from NS to QS including the magnetic-field effect in the equation of state (EoS). The inclusion of the magnetic field increases the range of baryon number densities for which the flow velocities of the matter in the respective phase are finite. The magnetic field helps in initiation of the conversion process. The velocity of the conversion front, however, decreases due to the presence of the magnetic field, as the presence of the magnetic field reduces the effective pressure (P). The magnetic field of the star is decreased by the conversion process, and the resultant QS has lower magnetic field than the initial NS.

Unsteady mixed convection flow from a rotating vertical cone with a magnetic field

An analysis is developed to study the unsteady mixed convection flow over a vertical cone rotating in an ambient fluid with a time-dependent angular velocity in the presence of a magnetic field. The coupled nonlinear partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The local skin friction coefficients in the tangential and azimuthal directions and the local Nusselt number increase with the time when the angular velocity of the-cone increases, but the reverse trend is observed for decreasing angular velocity. However, these are not mirror reflection of each other. The magnetic field reduces the skin friction coefficient in the tangential direction and also the Nusselt number, but it increases the skin friction coefficient in the azimuthal direction. The skin friction coefficients and the Nusselt number increase with the buoyancy force.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Testing concordance in species boundaries using acoustic, morphological, and molecular data in the field cricket genus Itaropsis (Orthoptera: Grylloidea, Gryllidae: Gryllinae)

In most taxa, species boundaries are inferred based on differences in morphology or DNA sequences revealed by taxonomic or phylogenetic analyses. In crickets, acoustic mating signals or calling songs have species-specific structures and provide a third data set to infer species boundaries. We examined the concordance in species boundaries obtained using acoustic, morphological, and molecular data sets in the field cricket genus Itaropsis. This genus is currently described by only one valid species, Itaropsis tenella, with a broad distribution in western peninsular India and Sri Lanka. Calling songs of males sampled from four sites in peninsular India exhibited significant differences in a number of call features, suggesting the existence of multiple species. Cluster analysis of the acoustic data, molecular phylogenetic analyses, and phylogenetic analyses combining all data sets suggested the existence of three clades. Whatever the differences in calling signals, no full congruence was obtained between all the data sets, even though the resultant lineages were largely concordant with the acoustic clusters. The genus Itaropsis could thus be represented by three morphologically cryptic incipient species in peninsular India; their distributions are congruent with usual patterns of endemism in the Western Ghats, India. Song evolution is analysed through the divergence in syllable period, syllable and call duration, and dominant frequency.

Thermally induced secondary atomization of droplet in an acoustic field

We study the thermal effects that lead to instability and break up in acoustically levitated vaporizing fuel droplets. For selective liquids, atomization occurs at the droplet equator under external heating. Short wavelength [Kelvin-Helmholtz (KH)] instability for diesel and bio-diesel droplets triggers this secondary atomization. Vapor pressure, latent heat, and specific heat govern the vaporization rate and temperature history, which affect the surface tension gradient and gas phase density, ultimately dictating the onset of KH instability. We develop a criterion based on Weber number to define a condition for the inception of secondary atomization. (C) 2012 American Institute of Physics. [doi:10.1063/1.3680257]

Surface pressure and heat transfer measurements in the unsteady separated hypersonic flow field over double cones

Reliable bench mark experimental database in the separated hypersonic flow regime is necessary to validate high resolution CFD codes. In this paper we report the surface pressure and heat transfer measurements carried out on double cones (first cone semi-apex angle = 15, 25 deg.; second cone semi-apex angle= 35, 68 deg.) at hypersonic speeds that will be useful for CFD code validation studies. The surface pressure measurements are carried out at nominal Mach number of 8.35 in the IISc hypersonic wind tunnel. On the other hand the surface heat transfer measurements are carried out at a nominal Mach number of 5.75 in the IISc hypersonic shock tunnel. The flow separation point on the first cone, flow reattachment on the second cone and the wild fluctuation of the transmitted shock on the second cone surface (25/68 deg. double cone) in the presence of severe adverse pressure gradient are some of the flow features captured in the measurements. The results from the CFD studies indicate good agreement with experiments in the attached flow regime while considerable differences are noticeable in the separated flow regime.

The inhomogeneous extended Bose-Hubbard model: A mean-field theory

We develop an inhomogeneous mean-field theory for the extended Bose-Hubbard model with a quadratic, confining potential. In the absence of this potential, our mean-field theory yields the phase diagram of the homogeneous extended Bose-Hubbard model. This phase diagram shows a superfluid (SF) phase and lobes of Mott-insulator (MI), density-wave (DW), and supersolid (SS) phases in the plane of the chemical potential mu and on-site repulsion U; we present phase diagrams for representative values of V, the repulsive energy for bosons on nearest-neighbor sites. We demonstrate that, when the confining potential is present, superfluid and density-wave order parameters are nonuniform; in particular, we obtain, for a few representative values of parameters, spherical shells of SF, MI, DW, and SS phases. We explore the implications of our study for experiments on cold-atom dipolar condensates in optical lattices in a confining potential.

High sensitivity low field magnetically gated resistive switching in CoFe2O4/La0.66Sr0.34MnO3 heterostructure

The phenomenon of resistive switching (RS) has been demonstrated in several non-magnetic and some magnetic oxide systems, however the ``magnetic'' aspect of magnetic oxides has not been emphasized especially in terms of low field tunability. In our work, we examined the CoFe2O4/La0.66Sr0.34MnO3 all-magnetic oxide interface system for RS and discovered a very sharp (bipolar) transition at room temperature that can be gated with high sensitivity by low magnetic fields (similar to 0-100 mT). By using a number of characterizations, we show that this is an interface effect, which may open up interesting directions for manipulation of the RS phenomenon. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4707373]

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.