Spectral moment sum rules for the retarded Green's function and self-energy of the inhomogeneous Bose-Hubbard model in equilibrium and nonequilibrium

We derive exact expressions for the zeroth and the first three spectral moment sum rules for the retarded Green's function and for the zeroth and the first spectral moment sum rules for the retarded self-energy of the inhomogeneous Bose-Hubbard model in nonequilibrium, when the local on-site repulsion and the chemical potential are time-dependent, and in the presence of an external time-dependent electromagnetic field. We also evaluate these expressions for the homogeneous case in equilibrium, where all time dependence and external fields vanish. Unlike similar sum rules for the Fermi-Hubbard model, in the Bose-Hubbard model case, the sum rules often depend on expectation values that cannot be determined simply from parameters in the Hamiltonian like the interaction strength and chemical potential but require knowledge of equal-time many-body expectation values from some other source. We show how one can approximately evaluate these expectation values for the Mott-insulating phase in a systematic strong-coupling expansion in powers of the hopping divided by the interaction. We compare the exact moment relations to the calculated moments of spectral functions determined from a variety of different numerical approximations and use them to benchmark their accuracy. DOI: 10.1103/PhysRevA.87.013628

Twin peak distribution of electron emission profile and impact ionization of ambient molecules during laser ablation of silver target

Laser-induced plasma generated from a silver target under partial vacuum conditions using the fundamental output of nanosecond duration from a pulsed Nd:yttrium aluminum garnet laser is studied using a Langmuir probe. The time of flight measurements show a clear twin peak distribution in the temporal profile of electron emission. The first peak has almost the same duration as the laser pulse while the second lasts for several microseconds. The prompt electrons are energetic enough ('60 eV) to ionize the ambient gas molecules or atoms. The use of prompt electron pulses as sources for electron impact excitation is demonstrated by taking nitrogen, carbon dioxide, and argon as ambient gases.

Flexural behaviour and design of hollow flange steel beams

The LiteSteel Beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using a patented Dual Electric Resistance Welding technique. The LSB has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. It is commonly used as rafters, floor joists and bearers and roof beams in residential, industrial and commercial buildings. It is on average 40% lighter than traditional hot-rolled steel beams of equivalent performance. The LSB flexural members are subjected to a relatively new Lateral Distortional Buckling mode, which reduces the member moment capacity. Unlike the commonly observed lateral torsional buckling of steel beams, lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist and web distortion. Current member moment capacity design rules for lateral distortional buckling in AS/NZS 4600 (SA, 2005) do not include the effect of section geometry of hollow flange beams although its effect is considered to be important. Therefore detailed experimental and finite element analyses (FEA) were carried out to investigate the lateral distortional buckling behaviour of LSBs including the effect of section geometry. The results showed that the current design rules in AS/NZS 4600 (SA, 2005) are over-conservative in the inelastic lateral buckling region. New improved design rules were therefore developed for LSBs based on both FEA and experimental results. A geometrical parameter (K) defined as the ratio of the flange torsional rigidity to the major axis flexural rigidity of the web (GJf/EIxweb) was identified as the critical parameter affecting the lateral distortional buckling of hollow flange beams. The effect of section geometry was then included in the new design rules using the new parameter (K). The new design rule developed by including this parameter was found to be accurate in calculating the member moment capacities of not only LSBs, but also other types of hollow flange steel beams such as Hollow Flange Beams (HFBs), Monosymmetric Hollow Flange Beams (MHFBs) and Rectangular Hollow Flange Beams (RHFBs). The inelastic reserve bending capacity of LSBs has not been investigated yet although the section moment capacity tests of LSBs in the past revealed that inelastic reserve bending capacity is present in LSBs. However, the Australian and American cold-formed steel design codes limit them to the first yield moment. Therefore both experimental and FEA were carried out to investigate the section moment capacity behaviour of LSBs. A comparison of the section moment capacity results from FEA, experiments and current cold-formed steel design codes showed that compact and non-compact LSB sections classified based on AS 4100 (SA, 1998) have some inelastic reserve capacity while slender LSBs do not have any inelastic reserve capacity beyond their first yield moment. It was found that Shifferaw and Schafer’s (2008) proposed equations and Eurocode 3 Part 1.3 (ECS, 2006) design equations can be used to include the inelastic bending capacities of compact and non-compact LSBs in design. As a simple design approach, the section moment capacity of compact LSB sections can be taken as 1.10 times their first yield moment while it is the first yield moment for non-compact sections. For slender LSB sections, current cold-formed steel codes can be used to predict their section moment capacities. It was believed that the use of transverse web stiffeners could improve the lateral distortional buckling moment capacities of LSBs. However, currently there are no design equations to predict the elastic lateral distortional buckling and member moment capacities of LSBs with web stiffeners under uniform moment conditions. Therefore, a detailed study was conducted using FEA to simulate both experimental and ideal conditions of LSB flexural members. It was shown that the use of 3 to 5 mm steel plate stiffeners welded or screwed to the inner faces of the top and bottom flanges of LSBs at third span points and supports provided an optimum web stiffener arrangement. Suitable design rules were developed to calculate the improved elastic buckling and ultimate moment capacities of LSBs with these optimum web stiffeners. A design rule using the geometrical parameter K was also developed to improve the accuracy of ultimate moment capacity predictions. This thesis presents the details and results of the experimental and numerical studies of the section and member moment capacities of LSBs conducted in this research. It includes the recommendations made regarding the accuracy of current design rules as well as the new design rules for lateral distortional buckling. The new design rules include the effects of section geometry of hollow flange steel beams. This thesis also developed a method of using web stiffeners to reduce the lateral distortional buckling effects, and associated design rules to calculate the improved moment capacities.

VFT performance of a 180/110 mm co-axial gap in SF6 up to 4 bar absolute

Disconnector switch operation in GIS generates VFT voltages in the system. It is important, for insulation co-ordination purposes, to obtain accurate VFT V-t data for typical gap geometries found in GIS. This paper presents experimentally obtained VFT V-t data for a 180/1 lOmm co-axial gap. The VFT has a time to first peak of 35 ns and a oscillation frequency of 13,6 MHz. Due to the location of the voltage divider in a compartment adjacent to the gap, a correction factor of 1.1 is used to relate the measured breakdown voltage to that in the gap. Positive polarity VFT V-t data is presented for 1, 2, 3 and 4 bar absolute and negative polarity VFT data for 3 and 4 bar absolute. Two methods of generating the VFT's are used. The first is to power up the test transformer at power frequency. The second is to generate a switching impulse by discharging a capacitor into the primary of the test transformer.

Estimation of growth parameters from multiple-recapture data

This article develops a method for analysis of growth data with multiple recaptures when the initial ages for all individuals are unknown. The existing approaches either impute the initial ages or model them as random effects. Assumptions about the initial age are not verifiable because all the initial ages are unknown. We present an alternative approach that treats all the lengths including the length at first capture as correlated repeated measures for each individual. Optimal estimating equations are developed using the generalized estimating equations approach that only requires the first two moment assumptions. Explicit expressions for estimation of both mean growth parameters and variance components are given to minimize the computational complexity. Simulation studies indicate that the proposed method works well. Two real data sets are analyzed for illustration, one from whelks (Dicathais aegaota) and the other from southern rock lobster (Jasus edwardsii) in South Australia.

Number and proportion of selenocucleosides in the transfer RNA of escherichia-coli

tRNA isolated from escherichia-coli grown in a medium containing [75Se] sodium selenosulfate was converted to nucleosides and analysed for selenonucleosides on a phosphocellulose column. Upon chromatography of the nucleosides on phosphocellulose column, the radioactivity resolved into three peaks. The first peak consisted of free selenium and traces of undigested nucleotides. The second peak was identified as 4-selenouridine by co-chromatographing with an authentic sample of 4-selenouridine. The identity of the third peak was not established. The second and third peaks represented 93% and 7% of the selenium present in nucleosides respectively.

Number and proportion of selenocucleosides in the transfer RNA of Image Image

tRNA isolated from . grown in a medium containing [75Se] sodium selenosulfate was converted to nucleosides and analysed for selenonucleosides on a phosphocellulose column. Upon chromatography of the nucleosides on phosphocellulose column, the radioactivity resolved into three peaks. The first peak consisted of free selenium and traces of undigested nucleotides. The second peak was identified as 4-selenouridine by co-chromatographing with an authentic sample of 4-selenouridine. The identity of the third peak was not established. The second and third peaks represented 93% and 7% of the selenium present in nucleosides respectively.

Step function response of non-linear spring mass systems in the presence of Coulomb damping

The transient response of non-linear spring mass systems with Coulomb damping, when subjected to a step function is investigated. For a restricted class of non-linear spring characteristics, exact expressions are developed for (i) the first peak of the response curves, and (ii) the time taken to reach it. A simple, yet accurate linearization procedure is developed for obtaining the approximate time required to reach the first peak, when the spring characteristic is a general function of the displacement. The results are presented graphically in non-dimensional form.

A note on the measurement of travel times using bender and extender elements

By using the bender and extender elements tests, the travel times of the shear (S) and the primary (P) waves were measured for dry sand samples at different relative densities and effective confining pressures. Three methods of interpretations, namely, (i) the first time of arrival, (ii) the first peak to peak, and (iii) the cross-correlation method, were employed. All the methods provide almost a unique answer associated with the P-wave measurements. On contrary, a difference was noted in the arrival times obtained from the different methods for the S-wave due to the near field effect. The resonant column tests in the torsional mode were also performed to check indirectly the travel time of the shear wave. The study reveals that as compared to the S-wave, it is more reliable to depend on the arrival times' measurement for the P-wave. (C) 2010 Elsevier Ltd. All rights reserved.

A note on the measurement of travel times using bender and extender elements

By using the bender and extender elements tests, the travel times of the shear (S) and the primary (P) waves were measured for dry sand samples at different relative densities and effective confining pressures. Three methods of interpretations, namely, (i) the first time of arrival, (ii) the first peak to peak, and (iii) the cross-correlation method, were employed. All the methods provide almost a unique answer associated with the P-wave measurements. On contrary, a difference was noted in the arrival times obtained from the different methods for the S-wave due to the near field effect. The resonant column tests in the torsional mode were also performed to check indirectly the travel time of the shear wave. The study reveals that as compared to the S-wave, it is more reliable to depend on the arrival times’ measurement for the P-wave.

Density-wave theory of dislocations in crystals

The density-wave theory of Ramakrishnan and Yussouff is extended to provide a scheme for describing dislocations and other topological defects in crystals. Quantitative calculations are presented for the order-parameter profiles, the atomic configuration, and the free energy of a screw dislocation with Burgers vector b=(a/2, a/2, a/2) in a bcc solid. These calculations are done using a simple parametrization of the direct correlation function and a gradient expansion. It is conventional to express the free energy of the dislocation in a crystal of size R as (λb2/4π)ln(αR/‖b‖), where λ is the shear elastic constant, and α is a measure of the core energy. Our results yield for Na the value α≃1.94a/(‖c1’’‖)1/2 (≃1.85) at the freezing temperature (371 K) and α≃2.48a/(‖c1’’‖)1/2 at 271 K, where c1’’ is the curvature of the first peak of the direct correlation function c(q). Detailed results for the density distribution in the dislocation, particularly the core region, are also presented. These show that the dislocation core has a columnar character. To our knowledge, this study represents the first calculation of dislocation structure, including the core, within the framework of an order-parameter theory and incorporating thermal effects.

Thermal Fluctuation Spectroscopy of DNA Thermal Denaturation

We have developed the technique of thermal fluctuation spectroscopy to measure the thermal fluctuations in a system. This technique is particularly useful to study the denaturation dynamics of biomolecules like DNA. Here we present a study of the thermal fluctuations during the thermal denaturation (or melting) of double-stranded DNA. We find that the thermal denaturation of heteropolymeric DNA is accompanied by large, non-Gaussian thermal fluctuations. The thermal fluctuations show a two-peak structure as a function of temperature. Calculations of enthalpy exchanged show that the first peak comes from the denaturation of AT rich regions and the second peak from denaturation of GC rich regions. The large fluctuations are almost absent in homopolymeric DNA. We suggest that bubble formation and cooperative opening and closing dynamics of basepairs causes the additional fluctuation at the first peak and a large cooperative transition from a partially molten DNA to a completely denatured state causes the additional fluctuation at the second peak.

Importance of orientational rearrangement during vitrification of hydrocarbons: dependence on molecular shape

On the basis of Monte Carlo calculations of 2,2-dimethylpropane (neopentane), n-pentane, and 2,2-dimethylbutane (neohexane) at several temperatures, thermodynamic properties and radial distribution functions as well as dimerization and bonding energy distribution functions are reported for both liquid and glassy states. Changes in the radial distribution functions on cooling depend on whether the groups are accessible (peripheral) or inaccessible. Peaks in the radial distribution functions corresponding to peripheral groups do not shift to lower distances on cooling and at times display a large increase in the intensity of the first peak. The peaks due to inaccessible groups, on the other hand, shift to lower distances on cooling. The magnitude of the reorientational contribution in determining the resulting structure of the glass is estimated for the different hydrocarbon molecules investigated. The reorientational contribution is highest for neopentane (26%) followed by isopentane (24%), neohexane (22%), and n-pentane (0%). It appears that molecular geometry has an important role in determining the magnitude of the reorientational contribution to the structure of the glass.

Interaction of sheep liver apo-serine hydroxymethyltransferase with pyridoxal-5'-phosphate: A physicochemical, kinetic, and thermodynamic study

Sheep liver serine hydroxymethyltransferase (EC 2.1.2.1) is a homotetramer of M(r) 213,000 requiring pyridoxal-5'-phosphate (PLP) as cofactor, Removal of PLP from the holoenzyme converted the enzyme to the apo form which, in addition to being inactive, was devoid of the characteristic absorption spectrum. Upon the addition of PLP to the apoenzyme, complete activity was restored and the visible absorption spectrum with a maximum at 425 nm was regained. The interaction of PLP with the apoenzyme revealed two phases of reaction with pseudo-first-order rate constants of 20 +/- 5 s(-1) and 12.2 +/- 2.0 x 10(-3) s(-1), respectively. However, addition of PLP to the apoenzyme did not cause gross conformational changes as evidenced by circular dichroic and fluorescence spectroscopy. Although conformationally apoenzyme and holoenzyme were indistinguishable, they had distinct apparent melting temperatures of 51 +/- 2 and 58 +/- 2 degrees C, respectively, and the reconstituted holoenzyme was thermally as stable as the native holoenzyme. These results suggested that there was no apparent difference in the secondary structure of holoenzyme, apoenzyme, and reconstituted holoenzyme, However, sedimentation analysis of the apoenzyme revealed the presence of two peaks of S-20,S-w values of 8.7 +/- 0.5 and 5.7 +/- 0.3 S, respectively. A similar pattern was observed when the apoenzyme was chromatographed on a calibrated Sephadex G-150 column. The first peak corresponded to the tetrameric form (M(r) 200,000 +/- 15,000) while the second peak had a M(r) of 130,000 +/- 10,000. Reconstitution experiments revealed that only the tetrameric form of the apoenzyme could be converted into an active holoenzyme while the dimeric form could not be reconstituted into an active enzyme. These results demonstrate that PLP plays an important role in maintaining the structural integrity of the enzyme by preventing the dissociation of the enzyme into subunits, in addition to its function in catalysis. (C) 1996 Academic Press, Inc.

Lightning Induced Voltages on a Rocket and its Exhaust Plume

A preliminary attempt has been made to study the time domain characteristics of the induced voltage and current on the rocket and its exhaust plume (ionized trail) when it is coupled with the transient electromagnetic field generated by a nearby lightning discharge. For the computation, finite difference time domain (FDTD) technique has been used where the object is assumed to be a finite vertical nonuniform transmission line above a perfectly conducting ground. It is seen that the amplitude of the first peak of the induced voltage and current at the mid point of the object is 23.5 kV and 4.9 kA respectively.