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.

A Magnetic Susceptibility Study of Spin-state Transitions in Rare-earth TrioxocobaItates( III)

Rare-earth trioxocobaltates(lll), Ln[CoO,], with Ln = Pr, Nd, Tb, Dy. and Yb exhibit low-spin to high-spin transitions of cobalt characterised by a maximum in the Ax-l against temperature plots where Ax is the cobalt contribution to the magnetic susceptibility. The susceptibility behaviour is distinct from that of La[CoO,] which shows a plateau in the x-I-T curve accompanied by a structural transition. The temperature at which the AX- I-T curve shows a maximum increases with the decrease in the size of the rare-earth ion. The susceptibility behavior of solid solutions of La,,Nd,CoO, has been investigated to see how the behaviour characteristic of Nd[CoO,] changes to that of La[CoO,].

Design of high-order filters with restricted component values

The feasibility of realising a high-order LC filter with a small set of different capacitor values, without sacrificing the frequency response specifications, is indicated. This idea could be conveniently adopted in other filter structures also—for example the FDNR transformed filter realisations.

Unsteady laminar compressible stagnation-point boundary-layer flow over a three-dimensional body: Higher order effects

The unsteady laminar compressible three-dimensional stagnation-point boundary-layer flow with variable properties has been studied when the velocity of the incident stream, mass transfer and wall temperature vary arbitrarily with time. The second-order unsteady boundary-layer equations for all the effects have been derived by using the method of matched asymptotic expansions. Both nodal and saddle point flows as well as cold and hot wall cases have been considered. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. Computations have been carried out for an accelerating stream, a decelerating stream and a fluctuating stream. The results indicate that the unsteady free stream velocity distributions, the nature of the stagnation point, the mass transfer, the wall temperature and the variation of the density-viscosity product across the boundary significantly affect the skin friction and heat transfer. The variation of the wall temperature with time strongly affects the heat transfer whereas its effect is comparatively less on skin friction. Suction increases the skin friction and heat transfer but injection does the opposite. The skin friction in the x direction due to the combined effects of first- and second-order boundary layers is less than the skin-friction in the x direction due to the first-order boundary layers for all the parameters. The overall skin friction in the z direction and heat transfer are more or less than the first-order boundary layers depending upon the values of the various parameters.

Interatomic Auger transitions in transition-metal oxides

Interatomic L3(M)M23(M)V(O) and L3(M)V(O)V(O) Auger transitions of some transition-metal oxides are reported for the first time. The interatomic mode of decay becomes progressively more dominant (relative to the intra-atomic mode) as the metal d level gets depleted or as the oxidation state of the metal increases. The usefulness of interatomic Auger transitions in studying oxidation of metals has been examined.

Sensing Shape Recovery Using Conductivity Noise in Thin Films of NiTi Shape Memory Alloys

Low frequency fluctuations in the electrical resistivity, or noise, have been used as a sensitive tool to probe into the temperature driven martensite transition in dc magnetron sputtered thin films of nickel titanium shape-memory alloys. Even in the equilibrium or static case, the noise magnitude was more than nine orders of magnitude larger than conventional metallic thin films and had a characteristic dependence on temperature. We observe that the noise while the temperature is being ramped is far larger as compared to the equilibrium noise indicating the sensitivity of electrical resistivity to the nucleation and propagation of domains during the shape recovery. Further, the higher order statistics suggests the existence of long range correlations during the transition. This new characterization is based on the kinetics of disorder in the system and separate from existing techniques and can be integrated to many device applications of shape memory alloys for in-situ shape recovery sensing.

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.

Effectiveness factor for zeroth-order catalytic reactions with volume change and nonuniform catalyst activity profiles

Analytical solutions are presented for the effectiveness factor of a zeroth-order reaction with volume change and nonuniform catalyst activity profile in slab, cylinder and spherical pellets. The possibility of shape normalization is considered for a variety of activity profiles and pellet shapes. When the catalyst activity at the external surface of the pellet is non-zero, shape normalization is obtained, which makes the asymptotic behavior of the effectiveness factor identical for small and large values of Thiele modulus, however, the normalization can lead to significant errors, particularly for the case of activity profiles decreasing towards the outer surface of the catalyst.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Electron- Spin-Resonance studies of phase transitions in double propionates

Detailed ESR investigations of Mn2+ substituting for Ca2+ in Ca2Sr(C2H5COO)6, (DSP) and Ca2Pb(C2H5COO)6, (DLP) and Ca2Ba(C2H5COO)6, (DBP), in single crystals and powders, over the temperature range from 300°C to -180°C have been carried out to study the successive phase transitions in these compounds. Spectra have been analyzed in terms of axial spin Hamiltonians and the temperature dependences of the parameters studied. Across the I-II transition, new physically and chemically inequivalent sites appear indicating the disappearance of the diad axes on which the propionate groups are located, bringing out the connection between the motional states of the propionate groups and the occurrence of ferroelectricity. The II-III transition also causes chemically inequivalent sites to develop, indicating that the transitions may not be isomorphous as believed previously. Similarities and dissimilarities of the ESR spectra of DLP, DSP and DBP are discussed in relation to the phase transitions.

Structural studies of analgesics and their interactions. VII. Stereoisomerism and disorder in the structure of oxyphenbutazone monohydrate

Oxyphenbutazone, C19H20N203, a metabolite and perhaps the active form of phenylbutazone, is a widely used non-narcotic analgesic and anti-inflammatory pyrazolidinedione derivative. The monohydrate of the compound crystallizes in the triclinic space group Pi with two molecules in a unit cell of dimensions a -- 9.491 (4), b = 10.261 (5), c = 11.036 (3)A and ¢~ = 72.2 (1), fl = 64.3 (1), 7 = 73.0 (1) °. The structure was solved by direct methods and refined to an R value of 0.107 for 1498 observed reflections. The butyl group in the molecule is disordered. The hydroxyl group occupies two sites with unequal occupancies. On account of the asymmetry at the two N atoms and one of the C atoms in the central five-membered ring, the molecule can exist in eight isomeric states, of which four are sterically unfavourable. The disorder in the position of the hydroxyl group can be readily explained on the basis of the existence, with unequal abundances, of all four sterically favourable isomers.The bond lengths and angles in the molecule are similar to those in phenylbutazone. The crystal structure is stabilized by van der Waals interactions, and O-H... O hydrogen bonds involving the carbonyl and the hydroxyl groups as well as a water molecule.

Universal jellium BCS picture for Peierls and spin-Peierls phase transitions

Both metal-insulator Peierls and antiferromagnetic spin-Peierls dimerized phase transitions are observed to have a BCS electron-phonon interaction parameter which is compatible with the jellium value λ = 2/3π ≈ 0.21.

Pressure-induced first-order transition in layered crystalline semiconductor GeSe to a metallic phase

The electrical resistivity of layerd crystalline GeSe has been investigated up to a pressure of 100 kbar and down to liquid-nitrogen temperature by use of a Bridgman anvil device. A pressure-induced first-order phase transition has been observed in single-crystal GeSe near 6 GPa. The high-pressure phase is found to be quenchable and an x-ray diffraction study of the quenched material reveals that it has the face-centered-cubic structure. Resistivity measurements as a function of pressure and temperature suggest that the high-pressure phase is metallic.

Stability and structural transitions of tomato aspermy virus and cucumber mosaic virus

The properties of the S-strain of cucumber mosaic virus (S-CMV) and the B-strain of tomato aspermy virus (B-TAV) have been studied with respect to their (i) size and sedimentation behavior, (ii) requirement of divalent metal ions for stability, (iii) sensitivity towards chloride salts and the anionic detergent sodium dodecyl sulfate, (iv) solubility in ammonium sulfate-containing buffers, and (v) pH-dependent structural transitions. The results indicate that the coat protein of B-TAV is more hydrophobic than the other well-studied strains of TAV and CMV. Circular dichroism and uv absorption studies reveal pH-dependent structural transitions, although these do not result in particle swelling. These transitions appear to alter the strength of protein-nucleic acid interactions in these viruses.