Strong-coupling expansion for the momentum distribution of the Bose-Hubbard model with benchmarking against exact numerical results

A strong-coupling expansion for the Green's functions, self-energies, and correlation functions of the Bose-Hubbard model is developed. We illustrate the general formalism, which includes all possible (normal-phase) inhomogeneous effects in the formalism, such as disorder or a trap potential, as well as effects of thermal excitations. The expansion is then employed to calculate the momentum distribution of the bosons in the Mott phase for an infinite homogeneous periodic system at zero temperature through third order in the hopping. By using scaling theory for the critical behavior at zero momentum and at the critical value of the hopping for the Mott insulator–to–superfluid transition along with a generalization of the random-phase-approximation-like form for the momentum distribution, we are able to extrapolate the series to infinite order and produce very accurate quantitative results for the momentum distribution in a simple functional form for one, two, and three dimensions. The accuracy is better in higher dimensions and is on the order of a few percent relative error everywhere except close to the critical value of the hopping divided by the on-site repulsion. In addition, we find simple phenomenological expressions for the Mott-phase lobes in two and three dimensions which are much more accurate than the truncated strong-coupling expansions and any other analytic approximation we are aware of. The strong-coupling expansions and scaling-theory results are benchmarked against numerically exact quantum Monte Carlo simulations in two and three dimensions and against density-matrix renormalization-group calculations in one dimension. These analytic expressions will be useful for quick comparison of experimental results to theory and in many cases can bypass the need for expensive numerical simulations.

Unsteady compressible second-order boundary layers at the stagnation point of two-dimensional and axisymmetric bodies

The unsteady laminar compressible boundary-layer flow over two-dimensional and axisymmetric bodies at the stagnation point with mass transfer has been studied for all second-order boundary layer effects when the basic potential flow admits selfsimilarity. The solutions for the governing equations are obtained by using an implicit finite-difference scheme. Computations have been carried out for different values of the parameters characterizing the unsteadiness in the free stream velocity, wall temperature, mass transfer rate and variable gas properties. The results are found to be strongly affected by the unsteadiness in the free stream velocity. For large injection rates the second-orderboundary layer effects may prevail over the first-order boundary layer, but reverse is true for suction. The wall temperature and the variation of the density-viscosity product across the boundary layer appreciably change the skin-friction and heat-transfer rates due to second-order boundary-layer effects.

Structural effects of a dimer interface mutation on catalytic activity of triosephosphate isomerase.The role of conserved residues and complementary mutations

The active site of triosephosphate isomerase (TIM, EC: 5.3.1.1), a dimeric enzyme, lies very close to the subunit interface. Attempts to engineer monomeric enzymes have yielded well-folded proteins with dramatically reduced activity. The role of dimer interface residues in the stability and activity of the Plasmodium falciparum enzyme, PfTIM, has been probed by analysis of mutational effects at residue 74. The PfTIM triple mutant W11F/W168F/Y74W (Y74W*) has been shown to dissociate at low protein concentrations, and exhibits considerably reduced stability in the presence of denaturants, urea and guanidinium chloride. The Y74W* mutant exhibits concentration-dependent activity, with an approximately 22-fold enhancement of kcat over a concentration range of 2.5–40 μm, suggesting that dimerization is obligatory for enzyme activity. The Y74W* mutant shows an approximately 20-fold reduction in activity compared to the control enzyme (PfTIM WT*, W11F/W168F). Careful inspection of the available crystal structures of the enzyme, together with 412 unique protein sequences, revealed the importance of conserved residues in the vicinity of the active site that serve to position the functional K12 residue. The network of key interactions spans the interacting subunits. The Y74W* mutation can perturb orientations of the active site residues, due to steric clashes with proximal aromatic residues in PfTIM. The available crystal structures of the enzyme from Giardia lamblia, which contains a Trp residue at the structurally equivalent position, establishes the need for complementary mutations and maintenance of weak interactions in order to accommodate the bulky side chain and preserve active site integrity.

Nature of ``Disorder'' in the Ordered Double Perovskite Sr2FeMoO6

The degree of B/B alternate cation order is known to heavily influence the magnetic properties of A2BB O6 double perovskites although the nature of such disorder has never been critically studied. Our detailed x-ray absorption fine structure studies in conjunction with synchrotron radiation x-ray diffraction experiments on polycrystalline Sr2FeMoO6 samples with various degrees of disorder reveal that a very high degree of short range order is preserved even in samples with highly reduced long range chemical order. Based on these experimental results and with the help of detailed structural simulations, we are able to model the nature of the disorder in this important class of materials and discuss the consequent implications on its physical properties.

Compressible 2nd-order boundary-layers for 3-dimensional stagnation point flows with mass-transfer

All the second-order boundary-layer effects have been studied for the steady laminar compressible 3-dimensional stagnation-point flows with variable properties and mass transfer for both saddle and nodal point regions. The governing equations have been solved numerically using an implicit finite-difference scheme. Results for the heat transfer and skin friction have been obtained for several values of the mass-transfer rate, wall temperature, and also for several values of parameters characterizing the nature of stagnation point and variable gas properties. The second-order effects on the heat transfer and skin friction at the wall are found to be significant and at large injection rates, they dominate over the results of the first-order boundary layer, but the effect of large suction is just the opposite. In general, the second-order effects are more pronounced in the saddle-point region than in the nodal-point region. The overall heat-transfer rate for the 3-dimensional flows is found to be more than that of the 2-dimensional flows.

Modification of chemical reactivity by cyclodextrins. Observation of moderate effects on Norrish type I and type II photobehavior

The photochemistry and photophysics of organic molecules in organized assemblies are being studied with great interest in order to understand the features controlling the selectivity in the photoreactions brought about by these media.l These studies have paved the way to an intriguing number of possibilities by which photoreactivity can be modified. In this connection, we have investigated the photobehavior of a number of phenyl alkyl ketones and cu,cu-dimethylphenyl alkyl ketones (Scheme I) incorporated in the hydrophobic interior of cyclodextrin cavities.

Unusual effects of anisotropic bonding in Cu(II) and Ni(II) oxides with K2NiF4 structure

Geometric constraints present in A2BO4 compounds with the tetragonal-T structure of K2NiF4 impose a strong pressure on the B---OII---B bonds and a stretching of the A---OI---A bonds in the basal planes if the tolerance factor is t congruent with RAO/√2 RBO < 1, where RAO and RBO are the sums of the A---O and B---O ionic radii. The tetragonal-T phase of La2NiO4 becomes monoclinic for Pr2NiO4, orthorhombic for La2CuO4, and tetragonal-T′ for Pr2CuO4. The atomic displacements in these distorted phases are discussed and rationalized in terms of the chemistry of the various compounds. The strong pressure on the B---OII---B bonds produces itinerant σ*x2−y2 bands and a relative stabilization of localized dz2 orbitals. Magnetic susceptibility and transport data reveal an intersection of the Fermi energy with the d2z2 levels for half the copper ions in La2CuO4; this intersection is responsible for an intrinsic localized moment associated with a configuration fluctuation; below 200 K the localized moment smoothly vanishes with decreasing temperature as the d2z2 level becomes filled. In La2NiO4, the localized moments for half-filled dz2 orbitals induce strong correlations among the σ*x2−y2 electrons above Td reverse similar, equals 200 K; at lower temperatures the σ*x2−y2 electrons appear to contribute nothing to the magnetic susceptibility, which obeys a Curie-Weiss law giving a μeff corresponding to S = 1/2, but shows no magnetic order to lowest temperatures. These surprising results are verified by comparison with the mixed systems La2Ni1−xCuxO4 and La2−2xSr2xNi1−xTixO4. The onset of a charge-density wave below 200 K is proposed for both La2CuO4 and La2NiO4, but the atomic displacements would be short-range cooperative in mixed systems. The semiconductor-metallic transitions observed in several systems are found in many cases to obey the relation Ea reverse similar, equals kTmin, where varrho = varrho0exp(−Ea/kT) and Tmin is the temperature of minimum resistivity varrho. This relation is interpreted in terms of a diffusive charge-carrier mobility with Ea reverse similar, equals ΔHm reverse similar, equals kT at T = Tmin.

Conformational effects in the hydrogenation of hemimellitic and cyclohex-1-ene-1,2,3-tricarboxylic acids

The three possible isomers of cyclohexane-1,2,3-tricarboxylic acid were synthesised and separated in order to study the regiospecificity and stereoselectivity of the α-C alkylation of their trimethyl esters. No definitive conclusions could be reached on this aspect for reasons which became apparent in the course of the work. However, the three independent methods adopted for the synthesis of the isomeric tricarboxylic acids have given dramatically different isomer compositions. The reasons are explored in this paper.

Effects of mould filling on evolution of the solid-liquid interface during solidification

This work presents a numerical analysis of simultaneous mould filling and phase change for solidification in a two-dimensional rectangular cavity. The role of residual flow strength and temperature gradients within the solidifying domain, caused by the filling process, on the evolution of solidification interface are investigated. An implicit volume of fluid (VOF)-based algorithm has been employed for simulating the free surface flows during the filling process, while the model for solidification is based on a fixed-grid enthalpy-based control volume approach. Solidification modeling is coupled with VOF through User Defined Functions developed in the commercial computational fluid dynamics (CFD) code FLUENT 6.3.26. Comparison between results of the conventional analysis without filling effect and those of the present analysis shows that the residual flow resulting from the filling process significantly influences the progress of the solidification interface. A parametric study is also performed with variables such as cooling rate, filling velocity and filling configuration, in order to investigate the coupled effects of the buoyancy-driven flow and the residual flow on the solidification behavior.

The non-linear response of a gyrostabilized platform: Effects of correction torque time delay and of random inputs

First, the non-linear response of a gyrostabilized platform to a small constant input torque is analyzed in respect to the effect of the time delay (inherent or deliberately introduced) in the correction torque supplied by the servomotor, which itself may be non-linear to a certain extent. The equation of motion of the platform system is a third order nonlinear non-homogeneous differential equation. An approximate analytical method of solution of this equation is utilized. The value of the delay at which the platform response becomes unstable has been calculated by using this approximate analytical method. The procedure is illustrated by means of a numerical example. Second, the non-linear response of the platform to a random input has been obtained. The effects of several types of non-linearity on reducing the level of the mean square response have been investigated, by applying the technique of equivalent linearization and solving the resulting integral equations by using laguerre or Gaussian integration techniques. The mean square responses to white noise and band limited white noise, for various values of the non-linear parameter and for different types of non-linearity function, have been obtained. For positive values of the non-linear parameter the levels of the non-linear mean square responses to both white noise and band-limited white noise are low as compared to the linear mean square response. For negative values of the non-linear parameter the level of the non-linear mean square response at first increases slowly with increasing values of the non-linear parameter and then suddenly jumps to a high level, at a certain value of the non-linearity parameter.

Nonlocal scale effects on wave propagation in multi-walled carbon nanotubes

This paper represents the effect of nonlocal scale parameter on the wave propagation in multi-walled carbon nanotubes (MWCNTs). Each wall of the MWCNT is modeled as first order shear deformation beams and the van der Waals interactions between the walls are modeled as distributed springs. The studies shows that the scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or group speed tends to zero). The frequency at which this phenomenon occurs is called the ``Escape frequency''. The analysis shows that, for a given N-walled carbon nanotube (CNT). the nonlocal scaling parameter has a significant effect on the shear wave modes of the N - 1 walls. The escape frequencies of the flexural and shear wave modes of the N-walls are inversely proportionl to the nonlocal scaling parameter. It is also shown that the cut-off frequencies are independent of the nonlocal scale parameter. (C) 2009 Elsevier B.V. All rights reserved.

Synthetic arabinomannan glycolipids and their effects on growth and motility of the Mycobacterium smegmatis

Arabinomannan-containing glycolipids, relevant to the mycobacterial cell-wall component lipoarabinomannan, were synthesized by chemical methods. The glycolipids were presented with tri- and tetrasaccharide arabinomannans as the sugar portion and a double alkyl chain as the lyophilic portion. Following synthesis, systematic biological and biophysical studies were undertaken in order to identify the effects of the glycolipids during mycobacterium growth. The studies included mycobacterial growth, biofilm formation and motility assays. From the studies, it was observed that the synthetic glycolipid with higher arabinan residues inhibited the mycobacterial growth, lessened the biofilm formation and impaired the motility of mycobacteria. A surface plasmon resonance study involving the immobilized glycan surface and the mycobacterial crude lysates as analytes showed specificities of the interactions. Further, it was found that cell lysates from motile bacteria bound oligosaccharide with higher affinity than non-motile bacteria.

Boundary-layer effects on internal flow choking in dual-thrust solid rocket motors

Theoretical studies have been carried out to examine internal flow choking in the inert simulators of a dual-thrust motor. Using a two-dimensional k-omega turbulence model, detailed parametric studies have been carried out to examine aerodynamic choking and the existence of a fluid throat at the transition region during the startup transient of dual-thrust motors. This code solves standard k-omega turbulence equations with shear flow corrections using a coupled second-order-implicit unsteady formulation. In the numerical study, a fully implicit finite volume scheme of the compressible, Reynolds-averaged, Navier-Stokes equations is employed. It was observed that, at the subsonic inflow conditions, there is a possibility of the occurrence of internal flow choking in dual-thrust motors due to the formation of a fluid throat at the beginning of the transition region induced by area blockage caused by boundary-layer-displacement thickness. It has been observed that a 55% increase in the upstream port area of the dual-thrust motor contributes to a 25% reduction in blockage factor at the transition region, which could negate the internal How choking and supplement with an early choking of the dual-thrust motor nozzle. If the height of the upstream port relative to the motor length is too small, the developing boundary layers from either side of the port can interact, leading to a choked,flow. On the other hand, if the developing boundary layers are far enough apart, then choking does not occur. The blockage factor is greater in magnitude for the choked case than for the unchoked case. More tangible explanations are presented in this paper for the boundary-layer blockage and the internal flow choking in dual-thrust motors, which hitherto has been unexplored.

Charge transport in a Tomonaga-Luttinger liquid: Effects of pumping and bias

We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, pointlike impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the dc and ac components of the current have power-law dependences on the bias and pumping frequencies with an exponent 2K-1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current grows large for special values of the bias. For noninteracting electrons with K=1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.

Theory of the unusual doping and temperature dependence of photoemission spectra in manganites

A recent, major, puzzle in the core-level photoemission spectra of doped manganites is the observation of a 1–2 eV wide shoulder with intensity varying with temperature T as the square of the magnetization over a T scale of order 200 K, an order of magnitude less than electronic energies. This is addressed and resolved here, by extending a recently proposed two-fluid polaron–mobile electron model for these systems to include core-hole effects. The position of the shoulder is found to be determined by Coulomb and Jahn-Teller energies, while its spectral weight is determined by the mobile electron energetics which is strongly T and doping dependent, due to annealed disorder scattering from the polarons and the t2g core spins. Our theory accounts quantitatively for the observed T dependence of the difference spectra, and furthermore, explains the observed correspondence between spectral changes due to increasing doping and decreasing T.