Closed expression of the interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states

The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived from the Bethe-Salpeter equations satisfied by the quark-antiquark four-point Green's function. The latter equations are established based on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green's function and some other kinds of Green's functions which follow directly from the QCD generating functional. The B-S kernel derived is given an exact and explicit expression which contains only a few types of Green's functions. This expression is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.Comment: 27 pages,no figure

Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states II: calculation of the glueball spectrum

In the preceding paper, a rigorous three-dimensional relativistic equation for two-gluon bound states was derived from the QCD with massive gluons and represented in the angular momentum representation. In order to apply this equation to calculate the glueball spectrum, in this paper, the equation is recast in an equivalent three-dimensional relativistic equation satisfied by the two-gluon positive energy state amplitude. The interaction Hamiltonian in the equation is exactly derived and expressed as a perturbative series. The first term in the series describes the one-gluon exchange interaction which includes fully the retardation effect in it. This term plus the linear confining potential are chosen to be the interaction Hamiltonian and employed in the practical calculation. With the integrals containing three and four spherical Bessel functions in the QCD vertices being analytically calculated, the interaction Hamiltonian is given an explicit expression in the angular momentum representation. Numerically solving the relativistic equation with taking the contributions arising from the retardation effect and the longitudinal mode of gluon fields into account, a set of masses for the $0^{++},0^{-+},1^{++},1^{-+},2^{++}$ and $2^{-+\text{}}$ glueball states are obtained and are in fairly good agreement with the predictions given by the lattice simulatio

Development Of A Cathode Designing Method To Avoid Electrodes’ Interference During Blisk Electrochemical Machining

Electrochemical machining plays a prominent role in blisk (bladed integrated disk) construction process. Since blisk channel is narrow and twisted, interference between electrodes may happen during electrochemical machining. Therefore, this paper develops a cathode designing method to avoid interference. Firstly, according to theory of electrochemical machining, machined channel is predicted by calculation. Second, with this channel, interference analysis is carried out and a cathode is designed. Finally, the cathode is employed in experiment and no interference appears

Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states I: Derivation of the relativistic equation

A rigorous three-dimensional relativistic equation satisfied by two-gluon bound states is derived from the QCD with massive gluons. With the gluon fields and the quark fields being expanded in terms of the gluon multipole fields and the spherical Dirac spinors respectively, the equation is well established in the angular momentum representation and hence is much convenient for solving the problem of two-gluon glueball spectra. In particular, the interaction kernel in the equation is exactly derived and given a closed expression which includes all the interactions taking place in the two-gluon glueballs. The kernel contains only a few types of Green's functions and commutators. Therefore, it is not only easily calculated by the perturbation method, but also provides a suitable basis for nonperturbative investigations

Symmetry Properties on Magnetization in the Hubbard Model at Finite Temperatures

By making use of some symmetry properties of the relevant Hamiltonian, two fundamental relations between the ferromagnetic magnetization and a spin correlation function are derived for the $d (=1,2,3)$-dimensional Hubbard model at finite temperatures. These can be viewed as a kind of Ward-Takahashi identities. The properties of the magnetization as a function of the applied field are discussed. The results thus obtained hold true for both repulsive and attractive on-site Coulomb interactions, and for arbitrary electron fillings.Comment: Latex file, no figur

A novel route to phase formation of cobalt oxyhydrates using KMnO4 as an oxidizing agent

We have first succeefully synthesized the sodium cobalt oxyhydrate superconductors using KMnO4 as a de-intercalating and oxidizing agent. It is a novel route to form the superconductive phase of NaxCoO2.yH2O without resorting to the commonly used Br2/CH3CN solution. The role of the KMnO4 is to de-intercalate the Na+ from the parent compound Na0.7CoO2 and oxidize the Co ion as a result. The higher molar ratio of KMnO4 relative to the sodium content tends to remove more Na+ from the parent compound and results in a slight expansion of the c-axis in the unit cell. The superconducting transition temperature is 4.6-3.8 K for samples treated by the aqueous KMnO4 solution with the molar ratio of KMnO4 relative to the sodium content in the range of 0.3 and 2.29.Comment: 10 pages, 3 figure

Time-Dependent Spintronic Transport and Current-Induced Spin Transfer Torque in Magnetic Tunnel Junctions

The responses of the electrical current and the current-induced spin transfer torque (CISTT) to an ac bias in addition to a dc bias in a magnetic tunnel junction are investigated by means of the time-dependent nonquilibrium Green function technique. The time-averaged current (time-averaged CISTT) is formulated in the form of a summation of dc current (dc CISTT) multiplied by products of Bessel functions with the energy levels shifted by $m\hbar \omega _{0}$. The tunneling current can be viewed as to happen between the photonic sidebands of the two ferromagnets. The electrons can pass through the barrier easily under high frequencies but difficultly under low frequencies. The tunnel magnetoresistance almost does not vary with an ac field. It is found that the spin transfer torque, still being proportional to the electrical current under an ac bias, can be changed by varying frequency. Low frequencies could yield a rapid decrease of the spin transfer torque, while a large ac signal leads to both decrease of the electrical current and the spin torque. If only an ac bias is present, the spin transfer torque is sharply enhanced at the particular amplitude and frequency of the ac bias. A nearly linear relation between such an amplitude and frequency is observed.Comment: 13 pages,8 figure

Modeling water waves beyond perturbations

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein-Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.Comment: 15 pages, 1 figure, 39 references. This document is a contributed chapter to an upcoming volume to be published by Springer in Lecture Notes in Physics Series. Other author's papers can be downloaded at http://www.denys-dutykh.com

Technical Note: Calibration and validation of geophysical observation models

We present a method to calibrate and validate observational models that interrelate remotely sensed energy fluxes to geophysical variables of land and water surfaces. Coincident sets of remote sensing observation of visible and microwave radiations and geophysical data are assembled and subdivided into calibration (Cal) and validation (Val) data sets. Each Cal/Val pair is used to derive the coefficients (from the Cal set) and the accuracy (from the Val set) of the observation model. Combining the results from all Cal/Val pairs provides probability distributions of the model coefficients and model errors. The method is generic and demonstrated using comprehensive matchup sets from two very different disciplines: soil moisture and water quality. The results demonstrate that the method provides robust model coefficients and quantitative measure of the model uncertainty. This approach can be adopted for the calibration/validation of satellite products of land and water surfaces, and the resulting uncertainty can be used as input to data assimilation schemes

Vitamin D deficiency in traumatic brain injury and its relationship with severity of injury and quality of life: a prospective, observational study

This single-centre prospective observational study aims to describe the prevalence of vitamin D deficiency (VDD) in the traumatic brain injury (TBI) population and identify any relationship between vitamin D and severity of head injury or quality of life. 124 TBI patients had serum vitamin D (25-OHD) levels measured at the local post-TBI endocrine screening clinic over 20 months. Quality of Life after Brain Injury (QOLIBRI) questionnaires were completed by the patient concurrently. A multivariate regressional analysis was performed, controlling for age, season, ethnicity, time since injury, TBI severity and gender. 34% (n=42) of the cohort were vitamin D deficient (25-OHD <25nmol/L) with a further 23% (n=29) having insufficient levels (25-OHD 25-50nmol/L). Vitamin D was significantly lower in severe TBI compared to mild TBI (n=95, p=0.03, CI 95% -23.60 to -1.21, mean effect size 12.40 nmol/L). There was a trend for self-reported quality of life to be better in patients with optimum vitamin D levels compared to patients with deficient vitamin D levels, controlling for severity of injury (n=81, p=0.05, CI 95% -0.07 to 21.27). This is the first study to identify a significant relationship between vitamin D levels and severity of head injury. Clinicians should actively screen for and treat VDD in head injured patients to reduce the risk of further morbidity such as osteomalacia and cardiovascular disease. Future research should establish the natural history of vitamin D levels following TBI to identify at which stage VDD develops and whether vitamin D replacement could have a beneficial effect on recovery and quality of life