Convergence Phenomenon with Fourier Series of tg(x2)and Alike

The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .

Coherent phase control in electron argon scattering in a bichromatic laser field

This paper theoretically investigates the coherent phase control in electron-argon scattering assisted by a bichro- matic laser field. The laser field is composed of a fundamental component and its second harmonic. The incoming and out going states of electron are described by the Volkov wave functions, and the electron-target interaction is treated as a screening potential. Numerical results for differential cross section of multiphoton processes vs the phase difference between the two components of laser field are discussed for several scattering angles and impact energies.

Positron-impact ionisation of atomic hydrogen in the presence of a bichromatic laser field

The positron impact-ionisation of atomic hydrogen in the presence of a linearly polarised bichromatic field is investigated in the first Born approximation. The field is composed of a fundamental frequency and its second harmonic. The state of positron in the field is described by the Volkov wavefunction, and the continuum state of the ejected electron is described by the Coulomb-Volkov wavefunction. The dressed ground state of target is a first order time-dependent perturbative wavefunction. The triple differential cross sections and their dependencies on laser field parameters are discussed and compared with the results modified by a monochromatic field. Numerical results show that the coherent phase control is significant and the laser-assisted ionisation cross sections caused by positron and electron are different.

A counterexample of the Euler condition:the Appell-Hamel dynamical system on a horizontally moving plate

As a counterexample of the Euler condition for nonholonomic constraint problems [H. C. Shen, Acta Phys. Sin. 54, 2468 （2005）], we investigate the Apell-Hamel dynamical system on a horizontally moving plate. The inconsistency of the results with Newton mechanics suggests that the Euler condition is not a universal model for nonlinear nonholonomic systems. This is attributed to the fact that the virtual displacements so obtained are not normal to the constraint forces.

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states, we find a link to some entanglement measures through some new parameters （amplitudes of coherent states）. Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of entanglement by applying the formalism of Horodecki et al.

A comparison of approaches in fitting continuum SEDs

We present a detailed comparison of two approaches, the use of a precalculated database and simulated annealing （SA）, for fitting the continuum spectral energy distribution （SED） of astrophysical objects whose appearance is dominated by surrounding dust. While pre-calculated databases are commonly used to model SED data, only a few studies to date employed SA due to its unclear accuracy and convergence time for this specific problem. From a methodological point of view, different approaches lead to different fitting quality, demand on computational resources and calculation time. We compare the fitting quality and computational costs of these two approaches for the task of SED fitting to provide a guide to the practitioner to find a compromise between desired accuracy and available resources. To reduce uncertainties inherent to real datasets, we introduce a reference model resembling a typical circumstellar system with 10 free parameters. We derive the SED of the reference model with our code MC3 D at 78 logarithmically distributed wavelengths in the range [0.3 μm, 1.3 mini and use this setup to simulate SEDs for the database and SA. Our result directly demonstrates the applicability of SA in the field of SED modeling, since the algorithm regularly finds better solutions to the optimization problem than a precalculated database. As both methods have advantages and shortcomings, a hybrid approach is preferable. While the database provides an approximate fit and overall probability distributions for all parameters deduced using Bayesian analysis, SA can be used to improve upon the results returned by the model grid.

Spin manipulations through electrical and thermoelectrical transport in magnetic tunnel junctions

A brief review is presented,which includes the direct current,alternate current,electrical and thermoelectrical transport as well as spin transfer effect in a variety of spin-based nanostructures such as the magnetic tunnel junction(MTJ),ferromagnet(FM)-quantum dot(QD)/FM-FM,double barrier MTJ,FM-marginal Fermi liquid-FM,FM-unconventional superconductor-FM(FUSF),quantum ring and optical spin-field-effect transistor.The magnetoresistances in those structures,spin accumulation effect in FM-QD-FM and FUSF systems,spin injection and spin filter into semiconductor,spin transfer effect,photon-assisted spin transport,magnonassisted tunneling,electron-electron interaction effect on spin transport,laser-controlled spin dynamics,and thermoelectrical spin transport are discussed.

The atomic structure and the properties of Ununbium (Z=112) and Mercury (Z=80)

A super heavy element Uub (z = 112) has been studied theoretically in conjunction with rela-tivistic effects and the effects of electron correlations.The atomic structure and the oscillator strengths of low-lying levels have been calculated,and the ground states have also been determined for the singly and doubly charged ions. The influence of relativity and correlation effects to the atomic properties of such a super heavy element has been investigated in detail. The results have been compared with the properties of an element Hg. Two energy levels at wave numbers 64470 and 94392 are suggested to be of good candidates for experimental observations.

Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force（TBF） . It is shown that the potential energy per nucleon in the isospinsinglet T = 0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities,the TBF effect on the isospin-triplet T = 1 channel contribution turns out to be much larger than that on the T =0 channel contribution. At low densities around and below the normal nuclear matter density,the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T = 1 component is almost independent of isospin asymmetry. As the density increases,the T = 1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T = 0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.

Influence of octupole deformation and orientation on the potential energy surface in the di-nuclear system model

The nuclear and Coulomb potentials between deformed nuclei with octupole deformations and arbitrary orientations are evaluated numerically. The effects of the octupole deformation on the potential between nuclei and the potential energy surface （PES） used in the description of the production of super-heavy nuclei （SHN） by heavy-ion fusion reactions are investigated in the di-nuclear system model. It is found that the nuclear octupole deformation significantly changes the shape of the PES, which may influence the fusion probability of the SHN. Also, PESs in the tip-belly and belly-belly cases are investigated. Finally, the quasi-fission barriers in the tip-tip and belly-belly cases are evaluated. It is found that the quasi-fission barriers of the belly-belly case are generally larger than those of the tip-tip case.

Terahertz emission in tenuous gases irradiated by ultrashort laser pulses

Mechanism of terahertz (THz) pulse generation in gases irradiated by ultrashort laser pulses is investigated theoretically. Quasi-static transverse currents produced by laser field ionization of gases and the longitudinal modulation in formed plasmas are responsible for the THz emission at the electron plasma frequency, as demonstrated by particle-in-cell simulations including field ionization. The THz field amplitude scaling with the laser amplitude within a large range is also discussed.

Photoproduction of the Θ^+ and its vector andaxial-vector structure

We present recent investigations on the vector and axial-vector transitions of the baryon antidecuplet within the framework of the self-consistent SU（3） chiral quark-soliton model, taking into account the 1/No rotational and linear mscorrections. The main contribution to the electric-like transition form factor comes from the wave-function corrections. This is a consequence of the generalized Ademollo-Gatto theorem. It is also found that in general the leading-order contributions are almost canceled by the rotational 1/No corrections. The results are summarized as follows： the vector and tensor K＇NO coupling constants, gK＊N= 0.74--0.87 and fk＊N =0.53--1.16, respectively, and F→KN = 0.71 MeV, based on the result of the KN coupling constant gKne =0.83. We also show the differential cross sections and beam asymmetries, based on the present results. We also discuss the connection of present results with the original work by Diakonov, Petrov, and Polyakov.