Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Theory of freezing in simple systems

The transition parameters for the freezing of two one-component liquids into crystalline solids are evaluated by two theoretical approaches. The first system considered is liquid sodium which crystallizes into a body-centered-cubic (bcc) lattice; the second system is the freezing of adhesive hard spheres into a face-centered-cubic (fcc) lattice. Two related theoretical techniques are used in this evaluation: One is based upon a recently developed bifurcation analysis; the other is based upon the theory of freezing developed by Ramakrishnan and Yussouff. For liquid sodium, where experimental information is available, the predictions of the two theories agree well with experiment and each other. The adhesive-hard-sphere system, which displays a triple point and can be used to fit some liquids accurately, shows a temperature dependence of the freezing parameters which is similar to Lennard-Jones systems. At very low temperature, the fractional density change on freezing shows a dramatic increase as a function of temperature indicating the importance of all the contributions due to the triplet direction correlation function. Also, we consider the freezing of a one-component liquid into a simple-cubic (sc) lattice by bifurcation analysis and show that this transition is highly unfavorable, independent of interatomic potential choice. The bifurcation diagrams for the three lattices considered are compared and found to be strikingly different. Finally, a new stability analysis of the bifurcation diagrams is presented.

Magnetic superconductors: Model theories and experimental properties of rare-earth compounds

Superconducting and magnetically long-range ordered states were believed to be mutually exclusive phenomena. The discovery of rare-earth compounds in recent years, which exhibit both superconductivity and magnetic ordering (ferromagnetic, antiferromagnetic or sinusoidal), has led to considerable theoretical and experimental work on such systems. In the present article, we give a review of various theoretical models and important experimental results. In the theoretical sections, we start with the Abrikosov-Gorkov pair breaking theory for dilute alloys and discuss its improvement in the work of Müller-Hartmann and Zittartz. Then, in the context of magnetic superconductors, various microscopic theories that have been advanced are presented. These predict re-entrant behaviour in some systems (ferromagnetic superconductors) and coexistence regions in others (particularly antiferromagnetic superconductors). Following this, phenomenological generalized Ginzburg-Landau theories for two kinds of orders (superconducting and magnetic) are presented. A section dealing with renormalization group analysis of phase diagrams in magnetic superconductors is given. In experimental sections, the properties of each rare-earth compounds (ternary as well as some tetranery) are reviewed. These involve susceptibility, heat capacity, resistivity, upper critical field, neutron scattering and magnetic resonance measurements. The anomalous behaviour of the upper critical field of antiferromagnetic superconductors near the Néel temperature is discussed both in theory sections and experimental section for various systems.

Size effect on the lattice parameter of KCl during mechanical milling

The size effect on the lattice parameter of ionic KCl nanocrystals was studied systematically during mechanical milling of Pure KCl powder under vacuum. The results suggest anomalous lattice expansion, with the lattice parameter increasing from 6.278 angstrom at d = 6 mu m to 6.30307 angstrom at d = 85 mn. The defects generated during ball milling of KCl and surface stress are deemed to be responsible for this lattice parameter expansion. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Proton Spin-Lattice Relaxation in Sodium Ammonium Selenate Dihydrate:NaNHaSeOa.2He0

Proton spin-lattice relaxation studies in sodium ammonium selenate dihydrate carried out in the temperature range 130 to 300 K at 10 MHz show a continuous change in T, at T, indicating a second order phase transition. This compound is a typical case of a highly hindered solid wherein the thermally activated reorientations of ammonium ions freeze well above 77 K, as seen by NMR.Untersuchimgen der Protonen-Spin-Gitter-Relaxation in Natriuni-Ammoniumselenat-Dihydrat bei 10 MHz im Temperaturbereich 130 bis 300 K zeigen eine kontinuierliche Andernng in TI bei T, und ergeben einen Phasenubergang zweiter Art. Diese Verbindung ist ein typischer Fall eines stark ,,behinderten" Festkarpers, in dein die thermisch aktivierten Reorientierungen der Ammoniumionen weit oberhalb 77 H einfrieren, wie die NMR-Ergebnisse zeigen.

Gauge hierarchy in a supersymmetric model

In a globally supersymmetric gauge theory with two distinct mass scales, the possible limitation on the gauge hierarchy due to the structure of the loop-corrected Higgs potential is shown to be absent. Also it has been demonstrated that the supersymmetry forces the large corrections to the two-point Greens functions of the light fields from the quadratic divergences and the logarithmic divergences with large coefficients to be zeroseparately. This would, therefore, allow a gauge hierarchy as large as desired.

Fracture Behavior of Multidirectional DCB Specimen: Higher-Order Beam Theories

Mathematical models, for the stress analysis of symmetric multidirectional double cantilever beam (DCB) specimen using classical beam theory, first and higher-order shear deformation beam theories, have been developed to determine the Mode I strain energy release rate (SERR) for symmetric multidirectional composites. The SERR has been calculated using the compliance approach. In the present study, both variationally and nonvariationally derived matching conditions have been applied at the crack tip of DCB specimen. For the unidirectional and cross-ply composite DCB specimens, beam models under both plane stress and plane strain conditions in the width direction are applicable with good performance where as for the multidirectional composite DCB specimen, only the beam model under plane strain condition in the width direction appears to be applicable with moderate performance. Among the shear deformation beam theories considered, the performance of higher-order shear deformation beam theory, having quadratic variation for transverse displacement over the thickness, is superior in determining the SERR for multidirectional DCB specimen.

Pyrrolidine ring conformations in prolyl peptides from 13C spin-lattice relaxation times

A method was developed in the framework of a bistable jump model to obtain the pyrrolidine ring conformations in proline peptides from 13C spin-lattice relaxation times. Equations are presented expressing the ring torsions in terms of the 13C spin-lattice relaxation times of the ring carbons. This method was applied to 26 pyrrolidine ring systems and acceptable conformations were obtained.

Variability of Indian summer monsoon rainfall in daily data from gauge and satellite

It has long been thought that tropical rainfall retrievals from satellites have large errors. Here we show, using a new daily 1 degree gridded rainfall data set based on about 1800 gauges from the India Meteorology Department (IMD), that modern satellite estimates are reasonably close to observed rainfall over the Indian monsoon region. Daily satellite rainfalls from the Global Precipitation Climatology Project (GPCP 1DD) and the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) are available since 1998. The high summer monsoon (June-September) rain over the Western Ghats and Himalayan foothills is captured in TMPA data. Away from hilly regions, the seasonal mean and intraseasonal variability of rainfall (averaged over regions of a few hundred kilometers linear dimension) from both satellite products are about 15% of observations. Satellite data generally underestimate both the mean and variability of rain, but the phase of intraseasonal variations is accurate. On synoptic timescales, TMPA gives reasonable depiction of the pattern and intensity of torrential rain from individual monsoon low-pressure systems and depressions. A pronounced biennial oscillation of seasonal total central India rain is seen in all three data sets, with GPCP 1DD being closest to IMD observations. The new satellite data are a promising resource for the study of tropical rainfall variability.

Intersoliton forces in weak-coupling quantum field theories

We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional φ4 theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U(R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U(R) between a soliton and an antisoliton of the sine-Gordon theory. When this U(R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U(R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U(R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U(R) is that it seems to give strong intersoliton forces when the coupling constant is small, as distinct from the forces between the ordinary quanta of the theory. We suggest that this is a general feature of a class of theories, and emphasize the possible relevance of this feature to real strongly interacting hadrons.

On walls of marginal stability in N=2 string theories

We study the properties of walls of marginal stability for BPS decays in a class of N = 2 theories. These theories arise in N = 2 string compactifications obtained as freely acting orbifolds of N = 4 theories, such theories include the STU model and the FHSV model. The cross sections of these walls for a generic decay in the axion-dilaton plane reduce to lines or circles. From the continuity properties of walls of marginal stability we show that central charges of BPS states do not vanish in the interior of the moduli space. Given a charge vector of a BPS state corresponding to a large black hole in these theories, we show that all walls of marginal stability intersect at the same point in the lower half of the axion-dilaton plane. We isolate a class of decays whose walls of marginal stability always lie in a region bounded by walls formed by decays to small black holes. This enables us to isolate a region in moduli space for which no decays occur within this class. We then study entropy enigma decays for such models and show that for generic values of the moduli, that is when moduli are of order one compared to the charges, entropy enigma decays do not occur in these models.

Large Low-Frequency Fluctuations in the Velocity of a Driven Vortex Lattice in a Single Crystal of 2H-NbSe2 Superconductor

The driven state of a well-ordered flux line lattice in a single crystal of 2H-NbSe2 in the time domain has revealed the presence of substantial fluctuations in velocity, with large and distinct time periods (similar to seconds). A superposition of a periodic drive in the driven vortex lattice causes distinct changes in these fluctuations. We propose that prior to the onset of the peak effect there exists a heretofore unexplored regime of coherent dynamics, with unexpected behavior in velocity fluctuations.

Origin of activation of Lattice Oxygen and Synergistic Interaction in Bimetal-Ionic Ce0.89Fe0.1Pd0.01O2-delta Catalyst

Flourite-type nanocrystalline Ce0.9Fe0.1O2-delta and Ce0.89Fe0.1Pd0.01O2-delta solid solutions have been synthesized by solution combustion method,'.which show higher oxygen storage/release property (OSC) compared to CeO2 and Ce0.8Zr0.2O2. Temperature programmed reduction an XPS study reveal that the presence of Pd ion in Ce0.9Fe0.1O2-delta facilitates complete reduction of Fe3+ to Fe2+ state and partial reduction of Ce4+ to Ce3+ state at.temperatures as low as 105 degrees C compared to 400 degrees C for monometal-ionic Ce0.9Fe0.1O2-delta. Fe3+ ion is reduced to Fe2+ and not to Feo due to favorable redox potential for Ce4+ + Fe2+ -> Ce3+ + Fe3+ reaction. Using first-principles density functional theory calculation we determine M-O (M = Pd, Fe, Ce) bond lengths, and find that bond lengths vary from shorter (2.16 angstrom) to longer (2.9 angstrom) bond distances compared to mean Ce-O bond distance of 2.34 angstrom. for CeO2. Using these results in bond valence analysis, we show that oxygen with bond valences as low as -1.55 are created, leading to activation of lattice oxygen in the bimetal ionic catalyst. Temperatures of CO oxidation and NO reduction by CO/H-2 are lower with the bimetalionic Ce0.89Fe0.1Pd0.01O2-delta catalyst compared to monometal-ionic Ce0.9Fe0.1O2-delta and Ce0.99Pd0.01O2-delta catalysts. From XPS studies of Pd impregnated on CeO2 and Fe2O3 oxides, we show that the synergism leading to low temperature activation of lattice oxygen in bimetal-ionic catalyst Ce0.89Fe0.1Pd0.01O2-delta is due to low-temperature reduction of Pd2+ to Pd-0, followed by Pd-0 + 2Fe(3+) -> Pd2+ + 2Fe(2+), Pd-0 + 2Ce(4+) -> Pd2+ + 2Ce(3+) redox reaction.

Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method

Purpose - The purpose of this paper is to apply lattice Boltzmann equation method (LBM) with multiple relaxation time (MRT) model, to investigate lid-driven flow in a three-dimensional (3D), rectangular cavity, and compare the results with flow in an equivalent two-dimensional (2D) cavity. Design/methodology/approach - The second-order MRT model is implemented in a 3D LBM code. The flow structure in cavities of different aspect ratios (0.25-4) and Reynolds numbers (0.01-1000) is investigated. The LBM simulation results are compared with those from numerical solution of Navier-Stokes (NS) equations and with available experimental data. Findings - The 3D simulations demonstrate that 2D models may predict the flow structure reasonably well at low Reynolds numbers, but significant differences with experimental data appear at high Reynolds numbers. Such discrepancy between 2D and 3D results are attributed to the effect of boundary layers near the side-walls in transverse direction (in 3D), due to which the vorticity in the core-region is weakened in general. Secondly, owing to the vortex stretching effect present in 3D flow, the vorticity in the transverse plane intensifies whereas that in the lateral plane decays, with increase in Reynolds number. However, on the symmetry-plane, the flow structure variation with respect to cavity aspect ratio is found to be qualitatively consistent with results of 2D simulations. Secondary flow vortices whose axis is in the direction of the lid-motion are observed; these are weak at low. Reynolds numbers, but become quite strong at high Reynolds numbers. Originality/value - The findings will be useful in the study of variety of enclosed fluid flows.

Structural Investigation of Activated Lattice Oxygen in Ce1-xSnxO2 and Ce1-x-ySnxPdyO2-delta by EXAFS and DFT calculation

Substitution of Sn4+ ion in CeO2 creates activated oxygen in Ce0.8Sn0.2O2 leading to higher oxygen storage capacity compared to Ce0.8Zr0.2O2. With Pd ion substitution in Ce0.8Sn0.2O2,activation of oxygen is further enhanced as observed from the H-2/TPR study. Both EXAFS analysis and DFT calculation reveal that in the solid solution Ceexhibits 4 + 4 coordination, Sri exhibits 4 + 2 + 2 coordination and Pd has 4 + 3 coordination. While the oxygen in the First four coordination with short M-O bonds are strongly held in the lattice, the oxygens in the second and higher coordinations with long M-O bonds are weakly bound, and they are the activated oxygen ill the lattice. Bond valence analysis shows that oxygen with valencies as low its 1.65 are created by the Sn and Pd ion Substitution. Another interesting observation is that H-2/TPR experiment of Ce1-xSnxO2 shows a broad peak starting from 200 to 500 degrees C, while the same reduction is achieved in a single step at similar to 110 degrees C in presence Pd2+ on. Substitution of Pd2+ ion thus facilitates synergistic reduction of the catalyst at lower temperature. We have shown that simultaneous reduction of the Ce4+ and Sr4+ ions by Pd-0 is the synergistic interaction leading to high oxygen storage capacity at low temperature.