Numerical Simulation of Antennae by Discrete Exterior Calculus

Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes.     

A New Algebraic Method and Its Application to Nonlinear Klein-Gordon Equation

In terms of the solutions of the generalized Riccati equation, a new algebraic method, which contains the terms of radical expression of functions f（ξ）, is constructed to explore the new exact solutions for nonlinear evolution equations. Being concise and straightforward, the method is applied to nonlinear Klein-Gordon equation, and some new exact solutions of the system are obtained. The method is of important significance in exploring exact solutions for other nonlinear evolution equations.     

关于费曼传播子在位形空间的解析式

We correct an inaccurate result of previous work on the Feynman propagator in position space of a free Dirac field in （3 ＋ 1）-dimensional spacetime; we derive the generalized analytic formulas of both the scalar Feynman propagator and the spinor Feynman propagator in position space in arbitrary （D ＋ 1）- dimensional spacetime; and we further find a recurrence relation among the spinor Feynman propagator in （D＋1）-dimensional spacetime and the scalar Feynman propagators in （D＋1）-, （D-1）- and （D＋3）-dimensional spacetimes.     

New homotopy analysis transform method for solving the discontinued problems arising in nanotechnology

We present a new reliable analytical study for solving the discontinued problems arising in nanotechnology.Such problems are presented as nonlinear differential–difference equations.The proposed method is based on the Laplace transform with the homotopy analysis method(HAM).This method is a powerful tool for solving a large amount of problems.This technique provides a series of functions which may converge to the exact solution of the problem.A good agreement between the obtained solution and some well-known results is obtained.     

Groupoids, Discrete Mechanics, and Discrete Variation

After introducing some of the basic definitions and results from the theory of groupoid and Lie algebroid, we investigate the discrete Lagrangian mechanics from the viewpoint of groupoid theory and give the connection between groupoids variation and the methods of the first and second discrete variational principles.     

Electric field distribution around the chain of composite nanoDarticles in ferrofluids

Composite nanoparticles （NPs） have the ability of combining materials with different properties together, thus receiving extensive attention in many fields. Here we theoretically investigate the electric field distribution around core/shell NPs （a type of composite NPs） in ferrofluids under the influence of an external magnetic field. The NPs are made of cobalt （ferromagnetic） coated with gold （metallic）. Under the influence of the external magnetic field, these NPs will align along the direction of this field, thus forming a chain of NPs. According to Laplace＇s equations, we obtain electric fields inside and outside the NPs as a function of the incident wavelength by taking into account the mutual interaction between the polarized NPs. Our calculation results show that the electric field distribution is closely related to the resonant incident wavelength, the metallic shell thickness, and the inter-particle distance. These analytical calculations agree well with our numerical simulation results. This kind of field-induced anisotropic soft-matter systems offers the possibility of obtaining an enhanced Raman scattering substrate due to enhanced electric fields.     

Research on the discrete variational method for a Birkhoffian system

In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.     

Mei Symmetry of General Discrete Holonomic System

The Mei symmetry and conserved quantity of general discrete holonomic system are investigated in this paper. The requirement for an invariant formalism of discrete motion equations is defined to be Mei symmetry. The criterion when a conserved quantity may be obtained from Mei symmetry is also deduced. An example is discussed for applications of the results.     

New Positive and Negative Hierarchies of Integrable Differential-Difference Equations and Conservation Laws

Two hierarchies of nonlinear integrable positive and negative lattice equations are derived from a discrete spectrak problem. The two lattice hierarchies are proved to have discrete zero curvature representations associated with a discrete spectral problem, which also shows that the positive and negative hierarchies correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. Moreover, the integrable lattice models in the positive hierarchy are of polynomial type, and the integrable lattice models in the negative hierarchy are of rational type. Further, we construct infinite conservation laws about the positive hierarchy.     

Integrable Properties Associated with a Discrete Three-by-Three Matrix Spectral Problem

Based on a new discrete three-by-three matrix spectral problem, a hierarchy of integrable lattice equations with three potentials is proposed through discrete zero-curvature representation, and the resulting integrable lattice equation reduces to the classical Toda lattice equation. It is shown that the hierarchy possesses a HamiItonian structure and a hereditary recursion operator. Finally, infinitely many conservation laws of corresponding lattice systems are obtained by a direct way.     

Non-autonomous discrete Boussinesq equation:Solutions and consistency

A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter δ. Tree-dimendional consistency and Lax pair of the obtained equation are discussed.     

Higher-Dimensional Lie Algebra and New Integrable Coupling of Discrete KdV Equation

Based on semi-direct sums of Lie subalgebra G, a higher-dimensional 6 × 6 matrix Lie algebra sμ（6） is constructed. A hierarchy of integrable coupling KdV equation with three potentials is proposed, which is derived from a new discrete six-by-six matrix spectral problem. Moreover, the Hamiltonian forms is deduced for lattice equation in the resulting hierarchy by means of the discrete variational identity -- a generalized trace identity. A strong symmetry operator of the resulting hierarchy is given. Finally, we prove that the hierarchy of the resulting Hamiltonian equations is Liouville integrable discrete Hamiltonian systems.     

An Integrable Symplectic Map Related to Discrete Nonlinear SchrSdinger Equation

The method of nonlinearization of spectral problem is developed and applied to the discrete nonlinear Schr6dinger （DNLS） equation which is a reduction of the Ablowitz-Ladik equation with a reality condition. A new integable symplectic map is obtained and its integrable properties such as the Lax representation, r-matrix, and invariants are established.     

Hamiltonian Forms for a Hierarchy of Discrete Integrable Coupling Systems

A semi-direct sum of two Lie algebras of four-by-four matrices is presented, and a discrete four-by-four matrix spectral problem is introduced. A hierarchy of discrete integrable coupling systems is derived. The obtained integrable coupling systems are all written in their Hamiltonian forms by the discrete variational identity. Finally, we prove that the lattice equations in the obtained integrable coupling systems are all Liouville integrable discrete Hamiltonian systems.     

Status of KLOE-2

In a few months the KLOE-2 detector is expected to start data taking at the upgraded DAФNE φ-factory of INFN Laboratori Nazionali di Frascati. It aims to collect 25 fb^-1 at the φ（1020） peak, and about 5 fb^-1 in the energy region between 1 and 2.5 GeV. We review the status and physics program of the project.     

Test particle simulations of resonant interactions between energetic electrons and discrete,multi-frequency artificial whistler waves in the plasmasphere

Modulated high frequency(HF) heating of the ionosphere provides a feasible means of artificially generating extremely low frequency(ELF)/very low frequency(VLF) whistler waves, which can leak into the inner magnetosphere and contribute to resonant interactions with high energy electrons. Combining the ray tracing method and test particle simulations, we evaluate the effects of energetic electron resonant scattering driven by the discrete, multi-frequency artificially generated ELF/VLF waves. The simulation results indicate a stochastic behavior of electrons and a linear profile of pitch angle and kinetic energy variations averaged over all test electrons. These features are similar to those associated with single-frequency waves. The computed local diffusion coefficients show that, although the momentum diffusion of relativistic electrons due to artificial ELF/VLF whistlers with a nominal amplitude of ～ 1 pT is minor, the pitch angle scattering can be notably efficient at low pitch angles near the loss cone, which supports the feasibility of artificial triggering of multi-frequency ELF/VLF whistler waves for the removal of high energy electrons from the magnetosphere. We also investigate the dependences of diffusion coefficients on the frequency interval(△f) of the discrete, multi-frequency waves.We find that there is a threshold value of △f for which the net diffusion coefficient of multi-frequency whistlers is inversely proportional to △f(proportional to the frequency components Nw) when △f is below the threshold value but it remains unchanged with increasing △f when △f is larger than the threshold value. This is explained as being due to the fact that the resonant scattering effect of broadband waves is the sum of the effects of each frequency in the ‘effective frequency band’. Our results suggest that the modulation frequency of HF heating of the ionosphere can be appropriately selected with reasonable frequency intervals so that better performance of controlled precipitation of high energy electrons in the plasmasphere by artificial ELF/VLF whistler waves can be achieved.     

Isospectral and Nonisospectral Lattice Hierarchies Associated with a Discrete Spectral Problem and Their Infinitely Many Conservation Laws

In this paper, based on the discrete zero curvature representation, isospectrai and nonisospectrai lattice hierarchies are proposed. By means of solving corresponding discrete spectral equations, we demonstrate the existence of infinitely many conservation laws for this two hierarchies and obtain the formulae of the corresponding conserved densities and associated fluxes.     

Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product

It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally.     

Study of electronic structures and absorption bands of BaMgF4 crystal with F colour centre

The electronic structures of BaMgF 4 crystals containing an F colour centre are studied within the framework of the fully relativistic self-consistent Direc-Slater theory,using a numerically discrete variational (DV-Xα) method. It is concluded from the calculated results that the energy levels of the F colour centre are located in the forbidden band. The optical transition energy from the ground state to the excited state for the F colour centre is about 5.12 eV,which corresponds to the 242-nm absorption band. These calculated results can explain the origin of the absorption bands.