New block matrix spectral problem and Hamiltonian structure of the discrete integrable coupling system

In [W.X. Ma, J. Phys. A: Math. Theor. 40 (2007) 15055], Prof. Ma gave a beautiful result (a discrete variational identity). In this Letter, based on a discrete block matrix spectral problem, a new hierarchy of Lax integrable lattice equations with four potentials is derived. By using of the discrete variational identity, we obtain Hamiltonian structure of the discrete soliton equation hierarchy. Finally, an integrable coupling system of the soliton equation hierarchy and its Hamiltonian structure are obtained through the discrete variational identity.     

From single- to multiple-soliton solutions of the perturbed KdV equation

The solution of the perturbed KdV equation (PKDVE), when the zero-order approximation is a multiple-soliton wave, is constructed as a sum of two components: elastic and inelastic. The elastic component preserves the elastic nature of soliton collisions. Its perturbation series is identical in structure to the series-solution of the PKDVE when the zero-order approximation is a single soliton. The inelastic component exists only in the multiple-soliton case, and emerges from the first order and onwards. Depending on initial data or boundary conditions, it may contain, in every order, a plethora of inelastic processes. Examples are given of sign-exchange soliton-anti-soliton scattering, soliton-anti-soliton creation or annihilation, soliton decay or merging, and inelastic soliton deflection. The analysis has been carried out through third order in the expansion parameter, exploiting the freedom in the expansion to its fullest extent. Both elastic and inelastic components do not modify soliton parameters beyond their values in the zero-order approximation. When the PKDVE is not asymptotically integrable, the new expansion scheme transforms it into a system of two equations: The Normal Form for ordinary KdV solitons, and an auxiliary equation describing the contribution of obstacles to asymptotic integrability to the inelastic component. Through the orders studied, the solution of the latter is a conserved quantity, which contains the dispersive wave that has been observed in previous works.     

Iterative approximation of limit cycles for a class of Abel equations

This article considers the analytical approximation of limit cycles that may appear in Abel equations written in the normal form. The procedure uses an iterative approach that takes advantage of the contraction mapping theorem. Thus, the obtained sequence exhibits uniform convergence to the target periodic solution. The effectiveness of the technique is illustrated through the approximation of an unstable limit cycle that appears in an Abel equation arising in a tracking control problem that affects an elementary, second-order bilinear power converter.     

Improved result on stability analysis of discrete stochastic neural networks with time delay

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.     

Canonical sequence method applied to a two-dimensional spin system

A number of years ago, Horn and Weinstein introduced a novel nonperturbative method, the t-expansion, for calculating ground-state expectation values for Hamiltonian systems. Recently Šamaj et al. have generalized the t-expansion technique and the related connected moments expansion to a more general canonical sequence. In the present work we have expounded upon this work and have applied this to the two-dimensional square anisotropic XXZ Heisenberg model.     

Two hierarchies of integrable lattice equations associated with a discrete matrix spectral problem

Two hierarchies of nonlinear integrable positive and negative lattice models are derived from a discrete spectral 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 of the positive hierarchy, then, the integrable coupling systems of the positive hierarchy are derived from enlarging Lax pair.     

Spectroscopic and lasing characterisation of a dicarbazovinylene-MEH-benzene dye

The dye 1,4-bis(9-ethyl-3-carbazovinylene)-2-methoxy-5-(2′-ethyl-hexyloxy)-benzene (abbreviated 2CzV-MEH-B) dissolved in tetrahydrofuran (THF) and as neat film is characterised by optical absorption and emission spectroscopy. The absorption and stimulated emission cross-section spectra, the fluorescence quantum distributions, fluorescence quantum yields, degrees of fluorescence polarisation, and fluorescence lifetimes are determined. A lasing characterisation is carried out by pumping with single second harmonic pulses of a mode-locked ruby laser (wavelength 347.15 nm, pulse duration 35 ps). The excited-state absorption at the pump laser wavelength is determined by saturable absorption measurements. Laser oscillation of the dye in THF in a rectangular cell is achieved by transverse pumping using the uncoated cell windows for light feedback. From the emission behaviour around threshold the excited-state absorption cross-section spectrum in the laser active spectral region is extracted. The wave-guided travelling-wave lasing behaviour of the dye as neat film is studied by analysis of the amplification of the transverse pumped spontaneous emission. Surface emitting distributed-feedback lasing was achieved with a neat film on corrugated second-order periodic gratings.     

Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends on the disease parameters, the geometry of the migrations between the patches, and the addition of infected people into a patch. We found that there are significantly longer lived transients and additional “ancillary” epidemics when the reproductive rate R is closer to 1, as would be typical of SARS (Severe Acute Respiratory Syndrome) and bird flu, than when R is closer to 10, as would be typical of measles. In addition we show, both analytical and numerical, how the time delay between the injection of infected people into a patch and the corresponding initial epidemic that it produces depends on R.     

A Variational Iteration Solving Method for a Class of Generalized Boussinesq Equations

We study a generalized nonlinear Boussinesq equation by introducing a proper functional and constructing the variational iteration sequence with suitable initial approximation. The approximate solution is obtained for the solitary wave of the Boussinesq equation with the variational iteration method.     

Stability Analysis of an Inverted Pendulum Subjected to Combined High Frequency Harmonics and Stochastic Excitations

Stability of vertical upright position of an inverted pendulum with its suspension point subjected to high frequency harmonics and stochastic excitations is investigated. Two classes of excitations, i.e., combined high frequency harmonic excitation and Gaussian white noise excitation, and high frequency bounded noise excitation, respectively, are considered. Firstly, the terms of high frequency harmonic excitations in the equation of motion of the system can be set equivalent to nonlinear stiffness terms by using the method of direct separation of motions. Then the stochastic averaging method of energy envelope is used to derive the averaged Ito stochastic differential equation for system energy. Finally, the stability with probability 1 of the system is studied by using the largest Lyapunov exponent obtained from the averaged Ito stochastic differential equation. The effects of system parameters on the stability of the system are discussed, and some examples are given to illustrate the efficiency of the proposed procedure.     

On the Stark broadening of the He I 447.1 nm spectral line

Characteristics of the Stark broadened and overlapping 447.1 nm He I spectral line and its forbidden 447.0 nm components have been measured at electron densities between 4.4×10²² m^-3 and 8.2×10²² m^-3 and electron temperatures between 18 000 K and 33 000 K in plasmas created in five various discharge conditions using the low pressure pulsed arc as an optically thin plasma source operated in helium-nitrogen-oxygen gas mixture. Good agreement was found among our measured line characteristics and their existing calculated values, based on the quasistatic approximation. Possible influence of the singly ionized oxygen impurity atoms (O II) on the intensity values of the dip between allowed and forbidden components was found that can explain the disagreement among some existing experimental and calculated line characteristics data, at higher electron temperatures and densities. On the basis of the observed asymmetry of the 447.1 nm spectral line profile we have obtained the ion contribution parameter at 10²² m^-3 electron density and 8 000 K electron temperature. Received 20 February 2001 and Received in final form 25 April 2001     

Series expansion analysis of a tetrahedral cluster spin chain

Using analytical series expansion by continuous unitary transformations we study the magnetic properties of a frustrated tetrahedral spin- chain. Starting from the limit of isolated tetrahedra we analyze the evolution of the ground state energy and the elementary triplet dispersion as a function of the inter-tetrahedral coupling. The quantum phase diagram is evaluated and is shown to incorporate a singlet product, a dimer, and a Haldane phase. Comparison of our results with those from several other techniques, such as density matrix renormalization group, exact diagonalization, bond-operator theory and other numerical series expansion are provided and convincing agreement is found.     

Longitudinal broadening of near-side jets due to parton cascade

Longitudinal broadening along the Δη direction on the near side in the two-dimensional (Δφ×Δη) di-hadron correlation distribution has been studied for central Au+Au collisions at  GeV, within a dynamical multi-phase transport model. It was found that longitudinal broadening is generated by a longitudinal flow induced by a strong parton cascade in central Au+Au collisions, to be compared with p+p collisions at  GeV. The longitudinal broadening may shed light on the strongly interacting partonic matter at RHIC.     

Spectral line broadening in quantum wells due to Coulomb interaction of current carriers

A theoretical analysis of emission line broadening due to Coulomb interaction of carriers is performed. An analytical approximation for the spectral line shape function with exponential decays is derived by using the perturbation theory for many-body electron–hole systems for both non-degenerate and degenerate conditions. An explanation of the experimentally observed spectral line asymmetry and the linewidth change as a function of the temperature and the excitation level is given.     

Synchronization of a large number of continuous one-dimensional stochastic elements with time-delayed mean-field coupling

We study synchronization as a means of control of collective behavior of an ensemble of coupled stochastic units in which oscillations are induced merely by external noise. For a large number of one-dimensional continuous stochastic elements coupled non-homogeneously through the mean field with delay we developed an approach to find a boundary of synchronization domain and the frequency of the mean-field oscillations on it. Namely, the exact location of the synchronization threshold is shown to be a solution of the boundary value problem (BVP) which was derived from the linearized Fokker-Planck equation. Here the synchronization threshold is found by solving this BVP numerically. Approximate analytics is obtained by expanding the solution of the linearized Fokker-Planck equation into a series of eigenfunctions of the stationary Fokker-Planck operator. Bistable systems with a polynomial and piece-wise linear potential are considered as examples. Multistability and hysteresis in the mean-field behavior are observed in the stochastic network at finite noise intensities. In the limit of small noise intensities the critical coupling strength is shown to remain finite, provided that the delay in the coupling function is not infinitely small. Delay in the coupling term can be used as a control parameter that manipulates the location of the synchronization threshold.     

Using Fast Fourier Transform to compute the line shape of frequency-modulated spectral profiles

An expression for the shape of spectral lines recorded by sinusoidal frequency modulation and harmonic detection is derived. It can be fast computed by means of the Fast Fourier Transform method and it holds for any modulation depth and modulation frequency. Different line shape functions, such as Voigt, Galatry, and speed-dependent Voigt, may be included in the model. In this work, the performance of the computing method is tested with experimental second harmonic rotational profiles, but it can be applied to higher harmonic spectra as well.     

Quantitative analysis of multi-element oxide thin films by angle-resolved XPS: Application to ultra-thin oxide films on MgAl substrates

An original procedure has been developed for the quantitative analysis and microstructural interpretation of angle-resolved X-ray photoelectron spectra (AR-XPS) of very thin (<6 nm), multi-element oxide films as grown on metallic binary alloy substrates by, e.g., thermal or plasma oxidation. To this end, first an approach has been given to retrieve the different metallic, oxidic and oxygen primary zero-loss (PZL) intensities from the measured AR-XPS spectra of the bare and oxidized alloy. The principal equations for the determination of the oxide-film thickness, composition and constitution from the resolved PZL intensities have been presented. On this basis, various corresponding calculation routes have been distinguished. The procedure has been applied to the case of very thin (<6 nm), mixed (Mg, Al)-oxide films on bare Mg-based MgAl substrates as grown by dry, thermal oxidation at room temperature. The results obtained on the thickness, composition, defect structure and constitution of the oxide-film have been discussed as function of the bulk Al alloying content and the applied partial pressure of oxygen.     

Experimental observation of lattice distortions due to a flux line lattice in niobium

A polarized neutron scattering investigation of the flux line lattice in the type-II superconductor niobium is reported. A modulation of the nuclear lattice has been detected, and the magnitude of the first Fourier component of the lattice distortion established relative to the magnitude of the magnetic scattering. This constitutes the first experimental observation of lattice distortions due to the presence of magnetic flux lines within the bulk of a type-II superconductor. Using a simple microscopic model the lattice distortion in niobium is estimated. A new mechanism is suggested for the coupling of the flux line lattice to the crystallographic lattice. The experimental technique opens up the possibility of investigating the microscopic mechanism of flux line - nuclear lattice interactions, in particular the pinning of flux lines within the bulk of a type-II superconductor. Received: 8 August 1997 / Accepted: 16 October 1997     

Asymmetrical spectral broadening of SRS and its temperature dependence in a phenylethanol liquid-core wave-guide optical fiber

Spectral broadening of stimulated Raman scattering has been studied in a phenylethanol liquid-core wave-guide optical fiber by using a frequency-doubled Q-switched Nd: YAG laser. Four orders of Stokes lines were observed. All the Stokes lines were asymmetrically broadened favoring the lower frequencies. Both the red-shifted broadening and the blue-shifted broadening increased with the rise of the temperature of the Raman medium. The asymmetric broadening was discussed to be mainly due to the effect of the cascaded stimulated Rayleigh-wing scattering.     

Photoacoustic detection of phase transitions with a resonant piezoelectric scheme with extreme sensitivity to small volume changes

Resonant piezoelectric photoacoustic detection is demonstrated to be a sensitive tool for the determination of phase transitions. A model is presented that describes the changes in the signal expected during phase transitions when resonant detection is used. The technique is applied to the study of first-order martensitic diffusionless transformations in copper-based shape-memory alloys. The model takes into account the signal changes arising from two sources. One behaves like an effective change in the heat capacity, and arises due to the enthalpy of the reaction, and the other can be described as an effective change in the thermal expansion coefficient, and arises from the volume change during the transformation. Due to the relative high frequency used (around 20 kHz), the transformation lags behind the temperature oscillations, yielding a phase shift in the acoustic signal as the transformation temperature is passed. The relative sign of the phase angle and amplitude as the transformation proceeds is an indication as to whether the signal arises from volume changes or heat exchange (enthalpy). Huge signals from very small volume changes (smaller than 0.5%) were observed.