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.

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid-solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading-unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10(6) for stress-free temperature-induced transformation and 10(4) for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress-strain hysteresis loop is observed for mechanical loading with higher rates.

Kinetics of Extraction of Iron(II1) by Bis(2-ethylhexyl Phosphate in a Laminar Liquid-Liquid Jet Reactor

The kinetics of iron(II1) extraction by bis(Zethylhexy1) phosphate (HDEHP, HA) in kerosene from sulfuric acid solutions has been studied in a liquid-liquid laminar jet reactor. The contact time of the interface in this reacting device is of the same order of magnitude as the surface renewal time in dispersion mixing and much less than that obtained in the relatively quiescent condition of the Lewis cell. Yet the analysis of the data in this study suggested a rate-controlling step involving surface saturation quite in conformity with that obtained in the Lewis cell and not with that in dispersion mixing as reported in the literature. Further, the mechanism suggested a weaker dependence of the rate on hydrogen ion concentration which was reported by other workers.

Pulsed laser surface treatment of magnesium alloy: Correlation between thermal model and experimental observations

The effect of deposition of Al +Al2O3 on MRI 153 M Mg alloy processed using a pulsed Nd:YAG laser is presented in this study. A composite coating with metallurgical joint to the substrate was formed. The microstructure and phase constituents were characterized and correlated with the thermal predictions. The laser scan speed had an effect on the average melt depth and the amount of retained and/or reconstituted alumina in the final coating. The coating consisted of alumina particles and highly refined dendrites formed due to the extremely high cooling rates (of the order of 10(8) K/s). The microhardness of the coating was higher and several fold improvement of wear resistance compared to the substrate was observed for the coatings. These microstructural features and physical properties were correlated with the effects predicted by a thermal model.

Weak rectifying behaviour of p-SnS/n-ITO heterojunctions

This work explores the electrical properties of p-SnS/n-ITO heterojunction at different temperatures. The p-type SnS film was deposited on n-type ITO substrate using the thermal evaporation technique and its junction properties were studied using two probe method. The as-grown p-n junction exhibited weak rectifying behaviour with a low Saturation current of the order of similar to 10(-6) A. While increasing temperature, the saturation current of the junction is increased and however, its series resistance decreased. At all temperatures the junction exhibited three types of transport mechanisms depending on applied bias-voltage. At lower voltages the junction showed nearly ideal diode characteristics. The junction behaviour with respect to bias-voltage and temperature is discussed with the help of existing theories and energy band diagram.

Pressure effect on the phase transition of trissarcosine calcium chloride

The dielectric measurement of ferroelectric trissarcosine calcium chloride (TSCC) was made under various pressures up to 6 kbar. A striking decrease in the peak value of the permittivity, epsilon r, at the transition temperature, Tc, was observed with increasing pressure. The value of Tc increases linearly with a pressure coefficient dTc/dp=11.1K kbar-1 at low pressures. This increase in Tc supports the suggestion that the ferroelectric transition is of the pure order-disorder type. It is suggested on the basis of the behaviour of epsilon r with pressure that the order of the ferroelectric transition changes from second to first order on application of pressure.

Kinetics of Chemical Vapor Deposition

A generalized mass transport model is developed for predicting the rate ofdeposition in chemical vapor deposition (CVD) systems. This combines thegeneralized method of obtaining equilibrium composition, with elemental fluxbalance expressions. This procedure avoids the usual problems encountered incalculating the rates in multicomponent systems, like writing overall reactionschemes. The dependence of multicomponent diffusivities on the fluxes is accountedin this model using an iterative procedure. The model developed isapplied to the deposition of titanium carbide on cemented carbide tool bitsfrom a gas mixture of titanium tetrachloride, toluene, and hydrogen. Experimentaldeposition rates were obtained using a thermogravimetric assembly.Mass transport controlled rates give an order of magnitude estimates of theobserved rates.

Insoluble anode of porous lead dioxide for electrosynthesis: preparation and characterization

Preparation of a novel type of titanium-substrate lead dioxide anode with enhanced electrocatalytic activity for electrosynthesis is described. It has been demonstrated that in the presence of a suitable surfactant in the coating solution, an adherent and mainly tetragonal form of lead dioxide is deposited on a platinized titanium surface such that the solution side of the coating is porous while the substrate side is compact. By an analysis of anodic charging curves and steady-state Tafel plots with such porous electrodes in contact with sodium sulphate solution, it has been proved that the electrochemically active area of these anodes is higher by more than an order of magnitude when compared to the area of conventional titanium-substrate lead dioxide anodes. The electrocatalytic activity is also thereby enhanced to a significant degree.

Enhancement of Tunneling Density of States at a Junction of Three Luttinger Liquid Wires

We study the tunneling density of states (TDOS) for a junction of three Tomonaga-Luttinger liquid wires. We show that there are fixed points which allow for the enhancement of the TDOS, which is unusual for Luttinger liquids. The distance from the junction over which this enhancement occurs is of the order of x=v/(2 omega), where v is the plasmon velocity and omega is the bias frequency. Beyond this distance, the TDOS crosses over to the standard bulk value independent of the fixed point describing the junction. This finite range of distances opens up the possibility of experimentally probing the enhancement in each wire individually.

Cuprous oxide catalyzed air oxidation of thiosulfate and tetrathionate

Thiosulfate (S2O32−) and tetrathionate (S4O62−)are oxidized to sulfate by air at atmospheric pressure and 50–70°C in the presence of cuprous oxide (Cu2O) as catalyst. Sulfate is produced from S2O32− by series-parallel reaction paths involving S4O62− as an intermediate. The rate data obtained for air oxidation of S2O32− on Cu2O agree well with a pseudo-homogeneous first order kinetic scheme, yielding values of rate constants for series parallel reaction paths which have been used in modelling the catalyzed air oxidation of S2O32−. Air oxidation of S4O62− on Cu2O proceeds at a higher rate in the presence of S2O32− than in its absence. Cu2O is less active than Cu2S for the air oxidation of S2O32−, as shown by the rate constant values which for Cu2O catalyzed oxidation are an order of magnitude smaller than those for the Cu2S catalyzed oxidation.

Three-dimensional elastic analysis of cracked thick plates under bending fields

A three-dimensional analysis is presented for the bending problem of finite thick plates with through-the-thickness cracks. A general solution is obtained for Navier's equations of the theory of elasticity. It is found that the in-plane stresses and the transverse normal stress at the crack front are singular with an inverse square root singularity, while the transverse shear stresses are of the order of unity. Results from a numerical study indicate that the stress intensity factor, which varies across the thickness, is influenced by the thickness ratio in a significant manner. Results from a parametric study and those from a comparative study with existing finite element values are presented.

Theoretical studies of lithium bonding in lithium chloride/aliphatic amine complexes

In the systematic study of amine … LiCl [amines = NH3, CH3NH2, (CH3)2NH] complexes the possibility of an ion-pair structure and the effect of methylation on the stabilization energy is investigated. ΔEis evaluated by the SCF/4-31G method and augmented by the approximate dispersion energy calculated perturbationally. The interaction energy decreases with the increasing number of methyl groups in the amine. The dispersion energy plays a negligible role in the stabilization of complexes. None of the systems studied are ion pairs; their Li bonds are of a so-called molecular type. Due to the divergence of the multipole expansion, the attempt to correct the 4-31G stabilization energies via the electrostatic energy fails. The relative order of the ΔE in the series of complexes is verified instead in the extended basis set calculation. The lithium bonds are compared with their H-bonded analogues.

Influence of deamidation(s) in the 67-74 region of ribonuclease on its refolding

The influence of chemical mutation featuring the selective conversion of asparagine or glutamine to aspartic or glutamic acid, respectively, on the kinetics of refolding of reduced RNase has been studied. The monodeamidated derivatives of RNase A, viz. RNase Aa1a, Aa1b, and Aa1c having their deamidations in the region 67-74, were found to regain nearly their original enzymatic activity. However, a marked difference in the kinetics of refolding is seen, the order of regain of enzymic activity being RNase A greater than Aa1c congruent to Aa1a greater than Aa1b. The similarities in the distinct elution positions on Amberlite XE-64, gel electrophoretic mobilities, and u.v. spectra of reoxidized and native derivatives indicated that the native structures are formed. The slower rate of reappearance of enzymic activity in the case of the monodeamidated derivatives appears to result from altered interactions in the early stages of refolding. The roles of some amino acid residues of the 67-74 region in the pathway of refolding of RNase A are discussed.

Irreversible Thermal Denaturation Of Bovine Pancreatic Ribonuclease-A

The isolation and characterization of the products formed during the irreversible thermal denaturation of enzyme RNAase-A are described. RNAase-A, when maintained in aqueous solution at pH 7.0 and 70° for 2 h, gives soluble products which have been fractionated by gel filtration on Sephadex G-75 into four components. These components are designated RNAase-At1, RNAase-At2, RNAase-At3 and RNAase-At4 according to the order of their elution from Sephadex G-75. RNAase-At4 shows the same specific activity towards yeast RNA as native RNAase-A and is virtually indistinguishable from it by the physical methods employed. However, chromatography on CM-cellulose separates it into three components that show the same u.v. spectra and specific activity towards yeast RNA as native RNAase-A. RNAase-At1, RNAase-At2and RNAase-At3 are all structurally altered derivatives of RNAase-A and they exhibit low specific activity (5–10%) towards yeast RNA. In the presence of added S-protein, all these derivatives show greatly enhanced enzymic activity. RNAase-At1 and RNAase-At2 are polymers, covalently crosslinked by intermolecular disulfide bridges; whereas RNAase-At3 is a monomer. Physical studies such as 1H-n.m.r., sedimentation analysis, u.v. absorption spectra and CD spectra reveal that RNAase-At3 is a unfolded derivative of RNAase-A. However, it is seen to possess sufficient residual structure which gives rise to a low but easily detectable enzymic activity.

Multiaction learning automata possessing ergodicity of the mean

Multiaction learning automata which update their action probabilities on the basis of the responses they get from an environment are considered in this paper. The automata update the probabilities according to whether the environment responds with a reward or a penalty. Learning automata are said to possess ergodicity of the mean if the mean action probability is the state probability (or unconditional probability) of an ergodic Markov chain. In an earlier paper [11] we considered the problem of a two-action learning automaton being ergodic in the mean (EM). The family of such automata was characterized completely by proving the necessary and sufficient conditions for automata to be EM. In this paper, we generalize the results of [11] and obtain necessary and sufficient conditions for the multiaction learning automaton to be EM. These conditions involve two families of probability updating functions. It is shown that for the automaton to be EM the two families must be linearly dependent. The vector defining the linear dependence is the only vector parameter which controls the rate of convergence of the automaton. Further, the technique for reducing the variance of the limiting distribution is discussed. Just as in the two-action case, it is shown that the set of absolutely expedient schemes and the set of schemes which possess ergodicity of the mean are mutually disjoint.