Birkhoffian symplectic algorithms derived from Hamiltonian symplectic algorithms

In this paper, we focus on the construction of structure preserving algorithms for Birkhoffian systems, based on existing symplectic schemes for the Hamiltonian equations. The key of the method is to seek an invertible transformation which drives the Birkhoffian equations reduce to the Hamiltonian equations. When there exists such a transformation,applying the corresponding inverse map to symplectic discretization of the Hamiltonian equations, then resulting difference schemes are verified to be Birkhoffian symplectic for the original Birkhoffian equations. To illustrate the operation process of the method, we construct several desirable algorithms for the linear damped oscillator and the single pendulum with linear dissipation respectively. All of them exhibit excellent numerical behavior, especially in preserving conserved quantities.     

Multi-symplectic variational integrators for nonlinear Schrdinger equations with variable coefficients

In this paper, we propose a variational integrator for nonlinear Schrdinger equations with variable coefficients. It is shown that our variational integrator is naturally multi-symplectic. The discrete multi-symplectic structure of the integrator is presented by a multi-symplectic form formula that can be derived from the discrete Lagrangian boundary function. As two examples of nonlinear Schrdinger equations with variable coefficients, cubic nonlinear Schrdinger equations and Gross–Pitaevskii equations are extensively studied by the proposed integrator. Our numerical simulations demonstrate that the integrator is capable of preserving the mass, momentum, and energy conservation during time evolutions. Convergence tests are presented to verify that our integrator has second-order accuracy both in time and space.     

Exciton-polaritons in lattices: A non-linear photonic simulator

Microcavity polaritons are mixed light–matter quasiparticles with extraordinary nonlinear properties, which can be easily accessed in photoluminescence experiments. Thanks to the possibility of designing the potential landscape of polaritons, this system provides a versatile photonic platform to emulate 1D and 2D Hamiltonians. Polaritons allow transposing to the photonic world some of the properties of electrons in solid-state systems, and to engineer Hamiltonians for photons with novel transport properties. Here we review some experimental implementations of polariton Hamiltonians using lattice geometries.     

热传导方程的一类无网格方法

构造求解热传导方程的一类无网格方法,只要选择好每个节点的适当的邻点集合,便可利用节点信息顺利进行计算.作为特殊情形,也可在各种结构或非结构网格上进行计算.在矩形或均匀平行四边形网格上进行计算时具有二阶精度,当在任意的不规则四边形或三角形网格上计算时仍然是守恒的和相容的,且至少具有一阶精度.作为数值试验,将该方法用于在不规则四边形网格上及四边形与三角形混合网格上求解二维非线性抛物型方程,并在不规则四边形网格上求解二维三温辐射热传导方程,均获得了较为理想的数值结果.     

Meson-baryon s-wave resonances with strangeness -3

Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian ( Phys. Rev. D 74, 034025 (2006)), we study the s-wave meson-baryon resonances in the strangeness S = - 3 and negative-parity sectors. Those resonances are generated by solving the Bethe-Salpeter equation with the WT interaction used as kernel. The considered mesons are those of the 35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the vector (V) nonet of the rho-meson. For baryons we consider the 56-SU(6)-plet, made of the 1/2⁺ octet of the nucleon and the 3/2⁺ decuplet of the Delta. Quantum numbers I(J ^P) = 0(3/2^-) are suggested for the experimental resonances Ω ^*(2250)^- and Ω ^*(2380)^-. Among other, resonances with I = 1 are found, which minimal quark content is sssˉl', being s the strange quark and l, l' any of the the light up or down quarks. A clear signal for such a pentaquark would be a baryonic resonance with strangeness -3 and electric charge -2 or 0, in proton charge units. We suggest looking for K ^- Ξ ^- resonances with masses around 2100 and 2240MeV in the sector 1(1/2^-), and for π ^± Ω ^- and K ^- Ξ ^*- resonances with masses around 2260MeV in the sector 1(3/2^-).     

A data-analysis method for identifying differential effects of time-delayed feedback forces and periodic driving forces in stochastic systems

In this work a method is developed for analyzing time series of periodically driven stochastic systems involving time-delayed feedback. The proposed data-analysis method yields dynamical models in terms of stochastic delay differential equations. On the basis of these dynamical models differential effects of driving forces and time-delayed feedback forces can be identified.     

Role of polarization and alignment in photoactuation of nematic elastomers

Changing the orientational order in liquid-crystal elastomers leads to internal stresses and changes of the sample shape. When this effect is induced by light, due to photoisomerization of constituent molecular moieties, the photomechanical actuation results. We investigate quantitatively how the intensity and the polarization of light affect photoactuation. By studying dissolved, as well as covalently bonded azo-dyes, we determine the changes in absorption and the response kinetics. For the first time we compare the response of aligned monodomain, and randomly disordered polydomain nematic elastomers, and demonstrate that both have a comparable photoresponse, strongly dependent on the polarization of light. Polarization-dependent photoactuation in polydomain elastomers gives an unambiguous proof of its mechanism since it is the only experiment that distinguishes from the associated thermal effects.     

Small amplitude ion-acoustic double layers with cold electron beam and q-nonextensive electrons

Small amplitude ion-acoustic double layers in an unmagnetized and collisionless plasma consisting of cold positive ions, q-nonextensive electrons, and a cold electron beam are investigated. Small amplitude double layer solution is obtained by expanding the Sagdeev potential truncated method. The effects of entropic index q, speed and density of cold electron beam on double layer structures are discussed.     

Propagation and collision of soliton rings in quantum semiconductor plasmas

The intrinsic localization of electrostatic wave energies in quantum semiconductor plasmas can be described by solitary pulses. The collision properties of these pulses are investigated. In the present study, the fundamental model includes the quantum term, degenerate pressure of the plasma species, and the electron/hole exchange–correlation effects. In cylindrical geometry, using the extended Poincaré–Lighthill–Kuo (PLK) method, the Korteweg–de Vries (KdV) equations and the analytical phase shifts after the collision of two soliton rings are derived. Typical values for GaSb and GaN semiconductors are used to estimate the basic features of soliton rings. It is found that the pulses of GaSb semiconductor carry more energies than the pulses of GaN semiconductor. In addition, the degenerate pressure terms of electrons and holes have strong impact on the phase shift. The present theory may be useful to analyze the collision of localized coherent electrostatic waves in quantum semiconductor plasmas.     

Effect of magnetic fields on the linear and nonlinear intersubband optical absorption coefficients and refractive index changes in square and graded quantum wells

In this study, both the intersubband optical absorption coefficients and the refractive index changes as dependent on the magnetic field are calculated in square and graded quantum wells. Our results show that the position and the magnitude of the linear and total absorption coefficients and refractive index changes depend on the magnetic field strength and the shape of potential. The incident optical intensity has a great effect on the total absorption and refractive index changes.