A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.     

Turbulence-induced changes in degree of polarization, degree of coherence and spectrum of partially coherent electromagnetic beams

Based on a recently formulated unified theory of coherence and polarization, a method is described to study turbulence-induced changes in the polarization, the coherence and the spectrum of partially coherent electromagnetic beams on propagation. The electromagnetic Gaussian Schell-model beam is taken as a typical example of partially coherent electromagnetic beams, and the closed-form expressions for the degree of polarization, the degree of coherence and the spectrum of electromagnetic Gaussian Schell-model beams propagating through atmospheric turbulence are derived in the quadratic approximation of Rytov’s phase structure function. Some interesting results are obtained, which are illustrated by numerical examples and are explained in physics.     

Upper bound for the time derivative of entropy for a stochastic dynamical system with double singularities driven by non-Gaussian noise

A stochastic dynamical system with double singularities driven by non-Gaussian noise is investigated.The Fokker-Plank equation of the system is obtained through the path-integral approach and the method of transformation.Based on the definition of Shannon’s information entropy and the Schwartz inequality principle,the upper bound for the time derivative of entropy is calculated both in the absence and in the presence of non-equilibrium constraint.The present calculations can be used to interpret the effects of the system dissipative parameter,the system singularity strength parameter,the noise correlation time and the noise deviation parameter on the upper bound.     

Two mutually conjugated tripartite entangled states and their fractional Fourier transformation kernel

We newly construct two mutually-conjugate tripartite entangled state representations,based on which we propose the formulation of three-mode entangled fractional Fourier transformation(EFFT) and derive the transformation kernel.The EFFT’s additivity property is proved and the eigenmode of EFFT is derived.As an application,we calculate the EFFT of the three-mode squeezed vacuum state.     

An algorithm for computed tomography image reconstruction from limited-view projections

<正>With the development of the compressive sensing theory,the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology.This paper develops an iterative algorithm for image reconstruction,which can fit most cases.This method gives an image reconstruction flow with the difference image vector,which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough.Then the l_2-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles.The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data.Moreover,all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.     

Tolman length of simple droplet: Theoretical study and molecular dynamics simulation

In 1949, Tolman found the relation between the surface tension and Tolman length, which determines the dimensional effect of the surface tension. Tolman length is the difference between the equimolar surface and the surface of tension. In recent years, the magnitude, expression, and sign of the Tolman length remain an open question. An incompressible and homogeneous liquid droplet model is proposed and the approximate expression and sign for Tolman length are derived in this paper. We obtain the relation between Tolman length and the radius of the surface of tension(R_s) and found that they increase with the Rs decreasing. The Tolman length of plane surface tends to zero. Taking argon for example, molecular dynamics simulation is carried out by using the Lennard–Jones(LJ) potential between atoms at a temperature of 90 K. Five simulated systems are used, with numbers of argon atoms being 10140, 10935, 11760, 13500, and 15360, respectively. By methods of theoretical study and molecular dynamics simulation, we find that the calculated value of Tolman length is more than zero, and it decreases as the size is increased among the whole size range. The value of surface tension increases with the radius of the surface of tension increasing, which is consistent with Tolman’s theory. These conclusions are significant for studying the size dependence of the surface tension.     

Second harmonic magnetoacoustic responses of magnetic nanoparticles in magnetoacoustic tomography with magnetic induction

Due to the unique magnetic, mechanical and thermal properties, magnetic nanoparticles(MNPs) have comprehensive applications as the contrast and therapeutic agents in biomedical imaging and magnetic hyperthermia. The linear and nonlinear magnetoacoustic responses determined by the magnetic properties of MNPs have attracted more and more attention in biomedical engineering. By considering the relaxation time of MNPs, we derive the formulae of second harmonic magnetoacoustic responses(2H-MARs) for a cylindrical MNP solution model based on the mechanical oscillations of MNPs in magnetoacoustic tomography with magnetic induction(MAT-MI). It is proved that only the second harmonic magnetoacoustic oscillations can be generated by MNPs under an alternating magnetic excitation. The acoustic pressure of the 2H-MAR is proportional to the square of the magnetic field intensity and exhibits a linear increase with the concentration of MNPs. Numerical simulations of the 2H-MAR are confirmed by the experimental measurements for various magnetic field intensities and solution concentrations using a laser vibrometer. The favorable results demonstrate the feasibility of the harmonic measurements without the fundamental interference of the electromagnetic excitation, and suggest a new harmonic imaging strategy of MAT-MI for MNPs with enhanced spatial resolution and improved signal-to-noise ratio in biomedical applications.     

Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order

In this paper,the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied.By using the first integral method,which is based on the divisor theorem,some exact explicit travelling solitary wave solutions for the above equation are obtained.As a result,some minor errors and some known results in the previousl literature are clarified and improved.     

An improved boundary element-free method （IBEFM） for two-dimensional potential problems

The interpolating moving least-squares (IMLS) method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method (BEFM), combining the boundary integral equation (BIE) method with the IMLS method, the improved boundary element-free method (IBEFM) for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker δ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker δ function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.     

Robust stability analysis for Markovian jumping stochastic neural networks with mode-dependent time-varying interval delay and multiplicative noise

This paper is concerned with the problem of robust stability for a class of Markovian jumping stochastic neural networks (MJSNNs) subject to mode-dependent time-varying interval delay and state-multiplicative noise.Based on the Lyapunov-Krasovskii functional and a stochastic analysis approach,some new delay-dependent sufficient conditions are obtained in the linear matrix inequality (LMI) format such that delayed MJSNNs are globally asymptotically stable in the mean-square sense for all admissible uncertainties.An important feature of the results is that the stability criteria are dependent on not only the lower bound and upper bound of delay for all modes but also the covariance matrix consisting of the correlation coefficient.Numerical examples are given to illustrate the effectiveness.