Renormalization of the axial-vector current in QCD

Following the method of Ioffe and Smilga, the propagation of the baryon current in an external constant axial-vector field is considered. The close similarity of the operator-product expansion with and without an external field is shown to arise from the chiral invariance of gauge interactions in perturbation theory. Several sum rules corresponding to various invariants both for the nucleon and the hyperons are derived. The analysis of the sum rules is carried out by two independent methods, one called the ratio method and the other called the continuum method, paying special attention to the nondiagonal transitions induced by the external field between the ground state and excited states. Up to operators of dimension six, two new external-field-induced vacuum expectation values enter the calculations. Previous work determining these expectation values from PCAC (partial conservation of axial-vector current) are utilized. Our determination from the sum rules of the nucleon axial-vector renormalization constant GA, as well as the Cabibbo coupling constants in the SU3-symmetric limit (ms=0), is in reasonable accord with the experimental values. Uncertainties in the analysis are pointed out. The case of broken flavor SU3 symmetry is also considered. While in the ratio method, the results are stable for variation of the fiducial interval of the Borel mass parameter over which the left-hand side and the right-hand side of the sum rules are matched, in the continuum method the results are less stable. Another set of sum rules determines the value of the linear combination 7F-5D to be ≊0, or D/(F+D)≊(7/12). .AE

Composite field approximations for ion traps with apertures on electrodes

This paper presents two approximate analytical expressions for nonlinear electric fields in the principal direction in axially symmetric (3D) and two dimensional (2D) ion trap mass analysers with apertures (holes in case of 3D traps and slits in case of 2D traps) on the electrodes. Considered together (3D and 2D), we present composite approximations for the principal unidirectional nonlinear electric fields in these ion traps. The composite electric field E has the form E = E-noaperture + E-aperture. where E-noaperture is the field within an imagined trap which is identical to the practical trap except that the apertures are missing and E-aperture is the field contribution due to apertures on the two trap electrodes. The field along the principal axis, of the trap can in this way be well approximated for any aperture that is not too large. To derive E-aperture. classical results of electrostatics have been extended to electrodes with finite thickness and different aperture shapes.E-noaperture is a modified truncated multipole expansion for the imagined trap with no aperture. The first several terms in the multipole expansion are in principle exact(though numerically determined using the BEM), while the last term is chosen to match the field at the electrode. This expansion, once Computed, works with any aperture in the practical trap. The composite field approximation for axially symmetric (3D) traps is checked for three geometries: the Paul trap, the cylindrical ion trap (CIT) and an arbitrary other trap. The approximation for 2D traps is verified using two geometries: the linear ion trap (LIT) and the rectilinear ion trap (RIT). In each case, for two aperture sizes (10% and 50% of the trap dimension), highly satisfactory fits are obtained. These composite approximations may be used in more detailed nonlinear ion dynamics Studies than have been hitherto attempted. (C) 2009 Elsevier B.V. All rights reserved.

On the Cubicity of Interval Graphs

A k-cube (or ``a unit cube in k dimensions'') is defined as the Cartesian product R-1 x . . . x R-k where R-i (for 1 <= i <= k) is an interval of the form [a(i), a(i) + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes corresponding to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity of a graph G, denoted as cub(G), is defined as the minimum dimension k such that G has a k-cube representation. An interval graph is a graph that can be represented as the intersection of intervals on the real line - i. e., the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. We show that for any interval graph G with maximum degree Delta, cub(G) <= inverted right perpendicular log(2) Delta inverted left perpendicular + 4. This upper bound is shown to be tight up to an additive constant of 4 by demonstrating interval graphs for which cubicity is equal to inverted right perpendicular log(2) Delta inverted left perpendicular.

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.

3-D kinematical conservation laws (KCL): Evolution of a surface in R-3 - in particular propagation of a nonlinear wavefront

3-D KCL are equations of evolution of a propagating surface (or a wavefront) Omega(t), in 3-space dimensions and were first derived by Giles, Prasad and Ravindran in 1995 assuming the motion of the surface to be isotropic. Here we discuss various properties of these 3-D KCL.These are the most general equations in conservation form, governing the evolution of Omega(t) with singularities which we call kinks and which are curves across which the normal n to Omega(t) and amplitude won Omega(t) are discontinuous. From KCL we derive a system of six differential equations and show that the KCL system is equivalent to the ray equations of 2, The six independent equations and an energy transport equation (for small amplitude waves in a polytropic gas) involving an amplitude w (which is related to the normal velocity m of Omega(t)) form a completely determined system of seven equations. We have determined eigenvalues of the system by a very novel method and find that the system has two distinct nonzero eigenvalues and five zero eigenvalues and the dimension of the eigenspace associated with the multiple eigenvalue 0 is only 4. For an appropriately defined m, the two nonzero eigenvalues are real when m > 1 and pure imaginary when m < 1. Finally we give some examples of evolution of weakly nonlinear wavefronts.

Valence bond analysis of the Kondo chain Hamiltonian

Accurate extrapolations for the ground state energy per site of the one - dimensional Kondo chain system is obtained from exact finite system calculations carried out employing a valence bond scheme. An analysis of the ground state wave function indicates that the localized spin is quenched for all nonzero values of the Kondo exchange constant in one dimension.

An elementary approach to gap theorems

Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension >= 3. Suppose that the sectional curvature K satisfies -1-s(r) <= K <= -1, where r denotes distance to a fixed point in M. If lim(r ->infinity) e(2r) s(r) = 0, then (M, g) has to be isometric to H-n.The same proof also yields that if K satisfies -s(r) <= K <= 0 where lim(r ->infinity) r(2) s(r) = 0, then (M, g) is isometric to R-n, a result due to Greene and Wu.Our second result is a local one: Let (M, g) be any Riemannian manifold. For a E R, if K < a on a geodesic ball Bp (R) in M and K = a on partial derivative B-p (R), then K = a on B-p (R).

Effects of Isothermal and Adiabatic Thermal Loadings on Size and Strain Rate Dependence of Copper Nanowire

In the present paper, the size and strain rate effects on ultra-thin < 100 >/{100} Cu nanowires at an initial temperature of 10 K have been discussed. Extensive molecular dynamics (MD) simulations have been performed using Embedded atom method (EAM) to investigate the structural behaviours and properties under high strain rate. Velocity-Verlet algorithm has been used to solve the equation of motions. Two different thermal loading cases have been considered: (i) Isothermal loading, in which Nose-Hoover thermostat is used to maintain the constant system temperature, and (ii) Adiabatic loading, i.e., without any thermostat. Five different wire cross-sections were considered ranging from 0.723 x 0.723 nm(2) to 2.169 x 2.169 nm(2) The strain rates used in the present study were 1 x 10(9) s(-1), 1 x 10(8) s(-1), and 1 x 10(7) s(-1). The effect of strain rate on the mechanical properties of copper nanowires was analysed, which shows that elastic properties are independent of thermal loading for a given strain rate and cross-sectional dimension of nanowire. It showed a decreasing yield stress and yield strain with decreasing strain rate for a given cross- section. Also, a decreasing yield stress and increasing yield strain were observed for a given strain rate with increasing cross-sectional area. Elastic modulus was found to be similar to 100 GPa, which was independent of processing temperature, strain rate, and size for a given initial temperature. Reorientation of < 100 >/{100} square cross-sectional copper nanowire into a series of stable ultra-thin Pentagon copper nanobridge structures with dia of similar to 1 nm at 10 K was observed under high strain rate tensile loading. The effect of isothermal and adiabatic loading on the formation of such pentagonal nanobridge structure has been discussed.

Kinetic Ising model: Some exact solutions

Exact expressions for the response functions of kinetic Ising models are reported. These results valid for magnetisation in one dimension are based on a general formalism that yield the earlier results of Glauber and Kimball as special cases.

A Huge Effect of Weak dc Electrical Fields on Grain Growth in Zirconia

We show that the application of a modest dc electrical field, about 4 V/cm, can significantly reduce grain growth in yttria-stabilized polycrystalline zirconia. These measurements were made by annealing samples, for 10 h at 1300°C, with and without an electrical field. The finding adds a new dimension to the role of applied electrical fields in sintering and superplasticity, phenomena that are critical to the net-shape processing of ceramics. Grain-growth retardation will considerably enhance the rates of sintering and superplasticity, leading to significant energy efficiencies in the processing of ceramics.

Shape-Dependent Confinement in Ultrasmall Zero-, One-, and Two-Dimensional PbS Nanostructures

Spatial dimensionality affects the degree of confinement when an electron-hole pair is squeezed from one or more dimensions approaching the bulk exciton Bohr radius (alpha(B)) limit. The etectron-hole interaction in zero-dimensional (0D) dots, one-dimensional (1D) rods/wires, and two-dimensional (2D) wells/sheets should be enhanced by the increase in confinement dimensions in the order 0D > 1D > 2D. We report the controlled synthesis of PbS nanomateriats with 0D, 1D, and 2D forms retaining at least one dimension in the strongly confined regime far below alpha(B) (similar to 10 nm for PbS) and provide evidence through varying the exciton-phonon coupling strength that the degree of confinement is systematically weakened by the loss of confinement dimension. Geometry variations show distinguishable far-field optical polarizations, which could find useful applications in polarization-sensitive devices.

An inhomogeneity problem in couple stress theory

Using Hilbert theory and Mindlin's couple stress theory, the problem of two-dimensional circular inhomogeneity (when the inserted material is of different size than the size of the cavity and having different elastic constants) is studiedin this paper. Stress could be bounded at infinity. The formulation is valid also for regions other then the circular ones when the matrix is finite has also been tackled. Numerical results are in conformity with the fact that the effect of couple stresses is negligible when the ratio of the smallest dimension of the body to the cahracteristic length is large.

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.

Effects of environment on surface-wave characteristics of a dielectric-coated conductor .4.

The problem of excitation of 11zultilayercd-graded-dielectric-coatedc onductor by a magnetic ring source is fornzulated in the ,form of a contour integrul which is rolved by using the method of steepest descent. Numerical evaluation of launching efiiency shows that high value of about 90 percent can be attained by choosing proper dimensions of the launcher with respect to the dimension of the surface wave line.

Acetylation of Transition Protein 2 (TP2) by KAT3B (p300) Alters Its DNA Condensation Property and Interaction with Putative Histone Chaperone NPM3

The hallmark of mammalian spermiogenesis is the dramatic chromatin remodeling process wherein the nucleosomal histones are replaced by the transition proteins TP1, TP2, and TP4. Subsequently these transition proteins are replaced by the protamines P1 and P2. Hyperacetylation of histone H4 is linked to their replacement by transition proteins. Here we report that TP2 is acetylated in vivo as detected by anti-acetylated lysine antibody and mass spectrometric analysis. Further, recombinant TP2 is acetylated in vitro by acetyltransferase KAT3B (p300) more efficiently than by KAT2B (PCAF). In vivo p300 was demonstrated to acetylate TP2. p300 acetylates TP2 in its C-terminal domain, which is highly basic in nature and possesses chromatin-condensing properties. Mass spectrometric analysis showed that p300 acetylates four lysine residues in the C-terminal domain of TP2. Acetylation of TP2 by p300 leads to significant reduction in its DNA condensation property as studied by circular dichroism and atomic force microscopy analysis. TP2 also interacts with a putative histone chaperone, NPM3, wherein expression is elevated in haploid spermatids.Interestingly, acetylation of TP2 impedes its interaction with NPM3. Thus, acetylation of TP2 adds a new dimension to its role in the dynamic reorganization of chromatin during mammalian spermiogenesis.