Characteristics of critical amplitude of a sinusoidal stimulus in a model neuron

The characteristics of the critical amplitude of a sinusoidal stimulus in a model neuron, Morris－Lecar model, are investigated numerically. It is important in the study of stochastic resonance to determine whether a periodic stimulus is subthreshold or not. The critical amplitude as a function of the stimulus frequency is not a constant, but a curve, which is the boundary between subthreshold and suprathreshold stimulation. It has been considered that this curve is U-shaped in the previous investigations, and this has been accepted as a universal phenomenon. Nevertheless, we think that it is only true for a type of neuron: namely, resonators. Actually, there exists another type of neuron, integrators, which can undergo a saddle-node on invariant circle bifurcation from the rest state to the firing state. For the latter we find that the critical amplitude increases monotonically as the frequency of sinusoidal stimulus is increased. This is shown by way of the Morris－Lecar model. As a consequence, the critical amplitude curve is studied further, and the dynamical mechanisms underlying the change in critical amplitude curve are uncovered. The results of this paper can provide a reference to choose the subthreshold periodic stimulus.     

A series of new double periodic solutions to a (2+1)-dimensional asymmetric Nizhnik－Novikov－Veselov equation

By means of a new general ans?tz and with the aid of symbolic computation, a new algebraic method named Jacobi elliptic function rational expansion is devised to uniformly construct a series of new double periodic solutions to (2+1)-dimensional asymmetric Nizhnik－Novikov－Veselov (ANNV) equation in terms of rational Jacobi elliptic function.     

Variable separation solutions and new solitary wave structures to the (1+1)-dimensional equations of long-wave－short-wave resonant interaction

A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave－short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.     

Bound states of two-dimensional relativistic harmonic oscillators

We give the exact normalized bound state wavefunctions and energy expressions of the Klein－Gordon and Dirac equations with equal scalar and vector harmonic oscillator potentials in the two-dimensional space.     

Analytical model of electron transport characteristics for 4H-SiC material and devices

Based on 4H-SiC material parameters, three different analytical expressions are used to characterize the electron mobility as the function of electric field. The first model is based on simple saturation of the steady-state drift velocity with electric field (conventional three-parameter model for silicon). The second GaAs-based mobility model partially reflects the peak velocity in high electric fields. The third multi-parameter model proposed in this paper is more realistic since it well reproduces the drift velocity－field characteristics obtained by Monte Carlo calculations, revealing the peak drift velocity with subsequent saturation at higher electric fields. Thus, the drift velocity model presented in this paper is much better for device simulation. In this paper, the influence of mobility model on DC characteristics of 4H-SiC MESFET is calculated and the better accordance with the experimental results is presented with multi-parameter model.     

Effect of adiabatic variation of dust charges on dust acoustic solitary waves in magnetized dusty plasmas

The effect of dust charging and the influence of its adiabatic variation on dust acoustic waves is investigated. By employing the reductive perturbation technique we derived a Zakharov－Kuznetsov (ZK) equation for small amplitude dust acoustic waves. We have analytically verified that there are only rarefactive solitary waves for this system. The instability region for one-dimensional solitary wave under transverse perturbations has also been obtained. The obliquely propagating solitary waves to the z-direction for the ZK equation are given in this paper as well.     

A SENSITIVE AND STABLE CONFOCAL FABRY－PéROT INTERFEROMETER FOR SURFACE ULTRASONIC VIBRATION DETECTION

A new confocal Fabry－Pérot interferometer (CFPI) has been constructed. By using both of the conjugate rays, the sensitivity of the system was doubled. Moreover, the negative feedback control loop of a single-chip microcomputer (MCS-51) was applied to stabilize the working point at an optimum position. The system has been used in detecting the piezoelectric ultrasonic vibration on the surface of an aluminium sample.     

Using symbolic computation to construct travelling wave solutions to nonlinear partial differential equations

Based upon the symbolic computation and the coupled projective Riccati equation, the tanh function method is further improved. As its applications, Wu－Zhang equation (which describes a (2+1)-dimensional dispersive long wave) and the (1+1)-dimensional dispersive long wave equation obtained from Wu－Zhang equation by scaling transformation and symmetry reduction are chosen to illustrate the validity of the proposed approach.     

Mapping deformation method and its application to nonlinear equations

An extended mapping deformation method is proposed for finding new exact travelling wave solutions of nonlinear partial differential equations (PDEs). The key idea of this method is to take full advantage of the simple algebraic mapping relation between the solutions of the PDEs and those of the cubic nonlinear Klein－Gordon equation. This is applied to solve a system of variant Boussinesq equations. As a result, many explicit and exact solutions are obtained, including solitary wave solutions, periodic wave solutions, Jacobian elliptic function solutions and other exact solutions.     

Directed transport of coupled systems in symmetric periodic potentials

In this paper, we discuss the damped unidirectional motions of a coupled lattice in a periodic potential. Each particle in the lattice is subject to a time-periodic ac force. Our studies reveal that a directed transport process can be observed when the ac forces acting on the coupled lattice have a phase shift (mismatch). This directed motion is a collaboration of the coupling, the substrate potential, and the periodic force, which are all symmetric. The absence of any one of these three factors will not give rise to a directed current. We discuss the complex relations between the directed current and parameters in the system. Results in this paper can be accomplished in experiments. Moreover,our results can be generalized to the studies of directed transport processes in more complicated spatially extended systems.