摘要：
Collisionless damping of the geodesic acoustic mode due to electron dynamics in rotating tokamak plasmas is investigated. A dispersion relation of the geodesic acoustic mode with a non-adiabatic electron response in a rotating tokamak is derived and solved both analytically and numerically. It is found that the collisionless damping of the geodesic acoustic mode, due to electron dynamics, significantly increases with the increasing toroidal rotation, especially in the large safety factor regime. The rotation-induced frequency up-shift of the geodesic acoustic mode increases the resonant velocity, which enables a larger number of electrons to resonate with the geodesic acoustic mode. The significant increase of the number of the resonant electrons significantly enhances the collisionless damping of the geodesic acoustic mode. The result indicates that in rotating tokamak plasmas a more complete picture of the geodesic acoustic mode should include the electron dynamics.
期刊：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS,2016年26(7):1650119:1-1650119:11 ISSN：0218-1274
通讯作者：
Wang, Qi-Ru
作者机构：
[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Wang, Qi-Ru] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China.
通讯机构：
[Wang, Qi-Ru] S;Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China.
摘要：
In this paper, the dynamic properties for a Brusselator-type system with diffusion are investigated. By employing the theory of Hopf bifurcation for ordinary and partial differential equations, we mainly obtain some conditions of the stability and Hopf bifurcation for the ODE system, diffusion-driven instability of the equilibrium solution, and the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions for the PDE system. Finally, some numerical simulations are presented to verify our results.
作者：
Cao, Jinjia;Gong, Xueyu*;Xiang, Dong;Huang, Qianhong;Yu, Jun
期刊：
PHYSICS OF PLASMAS,2016年23(8):082301 ISSN：1070-664X
通讯作者：
Gong, Xueyu
作者机构：
[Xiang, Dong; Huang, Qianhong; Gong, Xueyu; Cao, Jinjia] Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.;[Yu, Jun] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Gong, Xueyu] U;Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.
关键词：
plasma interactions;plasma transport processes
摘要：
The structure of the drift-island surface of passing fast ions (PFIs) is investigated in the presence of the resonant interaction with a magnetic island. Two overlapping regions of the drift-island surface and the magnetic island surface are found, one corresponding to local overlapping region and the other to non-local one. Here, the word “nonlocal” denotes that the resonances in the core plasma can have effects on the PFIs near the plasma boundary, while the “local” represents that the PFIs just near the resonant location are influenced. The nonlocal overlapping constructs a transport path along which the PFIs can become losses. There are three kinds of drift-island surfaces to join in forming the transport paths. A pitch angle region, which is called pitch angle gap, is found near the plasma boundary, where the drift-island surface cannot be formed and few PFIs are lost. The pitch-angle selective features of PFI losses are obtained by analyzing the three kinds of drift-island surfaces. The coupling between the crowd drift island surfaces and the collision can induce the prompt losses of PFIs and rapidly slowing down of PFI energy. The time of the prompt losses and the slowing down rate are calculated. Qualitatively, the theoretical results are in well agreement with the experimental observations in ASDEX Upgrade [M. García-Muñoz et al., Nucl. Fusion 47, L10 (2007)].
摘要：
In this paper, we investigate a class of stochastic shunting inhibitory cellular neural networks with time-varying delays. Applying integral inequality, some sufficient conditions on the existence and p-exponential stability of periodic solutions for stochastic shunting inhibitory cellular neural networks with time-varying delays are established. An example is presented to illustrate our main theoretical findings. Our results are new and complementary to previously known studies.
作者机构：
[Pan, Chaohong; Liu, Zhengrong] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Pan, Chaohong] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Solitary wave;Infinitely many solitary waves;Bifurcation method;Integrable equation
摘要：
Little seems to be known about the solitary waves and their properties of the completely integrable equations with singularity. This paper addresses the solitary waves of an integrable equation based on the bifurcation method of dynamical systems. We highlight two interesting results on the solitary waves. First, for arbitrary wave speed, there do exist infinitely many solitary waves in the integrable equation, which are classified by their expressions and forms of motion. Second, we find a family of solitary waves whose profiles seem like tree stumps.
作者机构：
[Pan, Chaohong] Univ South China, Sch Math & Phys, Hengyang, Peoples R China.;[Li, Shaoyong] Shaoguan Univ, Sch Math & Stat, Shaoguan, Peoples R China.
通讯机构：
[Pan, Chaohong] U;Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
关键词：
The Novikov equation;Soliton solutions;Hamiltonian function;Bifurcation method
摘要：
This paper is concerned with the smooth and nonsmooth soliton solutions of the Novikov equation based on the bifurcation method of dynamical systems. Two interesting results are highlighted. First, the new Hamiltonian function is established in the case of
$$\varphi ^2<c$$
while
$$\varphi ^2>c$$
is discussed in Li (Int J Bifurcat Chaos 24(3):1450037 2014). Second, we prove that the corresponding traveling wave system of the Novikov equation exists new smooth and nonsmooth soliton solutions.
作者机构：
[饶益花] School of Mathematics and Physics, University of South China, Hengyang, 421001, China;[冯鲲; 饶军; 康自华] Southwestern Institute of Physics, Chengdu, 610041, China;[陈文光; 胡波] School of Electrical Engineering, University of South China, Hengyang, 421001, China
通讯机构：
School of Electrical Engineering, University of South China, Hengyang, China
关键词：
回旋管;电子回旋共振加热;脉冲步进调制;高压电源;控制系统
摘要：
电子回旋共振管是产生高功率毫米微波的真空电子器件，在可控热核聚变研究、雷达等领域中有重要的应用。针对可控热核聚变研究中1 M W／105 G Hz回旋管加热系统阳极电源幅度可调且调制的要求，使用高频开关电源技术和脉冲步进调制技术（PSM ）研制了全固态阳极高压电源。重点阐述了阳极高压电源实现稳压、调制、前沿时间可调功能的软件控制算法，并通过实验对设计进行了验证。该阳极高压电源具有单脉冲、多脉冲调制和六电平预置波形等3种模式输出功能；输出参数达到35 kV／200 mA ，波形前沿3 ms内可调，最大调制频率为1 kHz ，调节精度在100 V以内。设计的控制方法也可应用于其他大功率微波源。
作者机构：
[Li, Zhenbo] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Tang, Jiashi] Hunan Univ, Coll Mech & Vehicle Engn, Changsha 410082, Hunan, Peoples R China.
通讯机构：
[Li, Zhenbo] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Generalized Pade approximation;Homoclinic bifurcation;Heteroclinic bifurcation;Helmholtz-Duffing oscillator;Phi(6)-Van der Pol oscillator
摘要：
By combining the generalized Pad, approximation method and the well-known Lindstedt-Poincar, method, a novel technique, referred to as the generalized Pad,-Lindstedt-Poincar, method, is proposed for determining homo-/heteroclinic orbits of nonlinear autonomous oscillators. First, the classical Pad, approximation method is generalized. According to this generalization, the numerator and denominator of the Pad, approximant are extended from polynomial functions to a series composed of any kind of continuous function, which means that the generalized Pad, approximant is not limited to some certain forms, but can be constructed variously in solving different matters. Next, the generalized Pad, approximation method is introduced into the Lindstedt-Poincar, method's procedure for solving the perturbation equations. Via the proposed generalized Pad,aEuro"Lindstedt-Poincar, method, the homo-/heteroclinic bifurcations of the generalized Helmholtz-Duffing-Van der Pol oscillator and -Van der Pol oscillator are predicted. Meanwhile, the analytical solutions to these oscillators are also calculated. To illustrate the accuracy of the present method, the solutions obtained in this paper are compared with those of the Runge-Kutta method, which shows the method proposed in this paper is both effective and feasible. Furthermore, the proposed method can be also utilized to solve many other oscillators.
摘要：
With the dispersion relation derived for the geodesic acoustic mode in toroidally rotating tokamak plasmas using the fluid model, the effect of the toroidal rotation on the collisional viscous damping of the geodesic acoustic mode is investigated. It is found that the collisional viscous damping of the geodesic acoustic mode has weak increase with respect to the toroidal Mach number.
作者机构：
[Chen, You; Gong, Xueyu; Yu, Jun] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.;[Gong, Xueyu] Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Yu, Jun] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
tokamak plasma;zonal flow;turbulence
摘要：
With the nonlinear dispersion relation derived, excitation of low frequency zonal flow by drift waves is examined in tokamak plasmas with toroidal rotation. It is shown that the growth rate of the low frequency zonal flow is decreased by the frequency shift of the geodesic acoustic mode and is increased by the additional nonlinear terms with toroidal rotation velocity. If the amplitude of the pump drift wave is greater than the threshold value, which is the function of the Mach number of the toroidal rotation, the toroidal rotation increases the nonlinear growth rate, otherwise, it decreases the nonlinear growth rate. There is always a finite nonlinear growth rate of the low frequency zonal flow if only there is a finite amplitude of the pump wave in tokamak plasmas with a finite velocity of the toroidal rotation.
期刊：
Journal of Computational and Theoretical Nanoscience,2015年12(11):4383-4391 ISSN：1546-1955
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, 550004, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, Hengyang, 421001, China
通讯机构：
Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, China
摘要：
This paper is concerned with the existence and exponential stability of anti-periodic solutions of two-neural networks with variable and unbounded delays. Using some analysis skills and Lyapunov method, a series of sufficient conditions for the existence and exponential stability of anti-periodic solutions to two-neural networks with variable and unbounded delays are presented. Our results are new and complement of some previously known ones.
作者机构：
[Yin Lan; Du Dan] Univ South China, Dept Math & Phys, Hengyang 421001, Peoples R China.;[Gong Xueyu; Xiang Dong; Li Jingchun] Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.
通讯机构：
[Gong Xueyu] U;Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.
关键词：
ICRH antenna;impedance matching;transmission line theory
摘要：
The impedance matching is crucial for continuous wave operation of ion cyclotron resonance heating (ICRH) antennae with high power injection into plasmas. A sudden increase in the reflected radio frequency power due to an impedance mismatch of the ICRH system is an issue which must be solved for present-day and future fusion reactors. This paper presents a method for theoretical analysis of ICRH system impedance matching for a triple liquid stub tuner under plasma operational conditions. The relationship of the antenna input impedance with the plasma parameters and operating frequency is first obtained using a global solution. Then, the relations of the plasma parameters and operating frequency with the matching liquid heights are indirectly obtained through numerical simulation according to transmission line theory and matching conditions. The method provides an alternative theoretical method, rather than measurements, to study triple liquid stub tuner impedance matching for ICRH, which may be beneficial for the design of ICRH systems on tokamaks.
期刊：
Italian Journal of Pure and Applied Mathematics,2015年(35):705-716 ISSN：2239-0227
作者机构：
[Xu, Changjin] Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, Hengyang, China
关键词：
Competition and cooperation model;Enterprise;Global stability;Stochastic perturbation
摘要：
This paper deals with a stochastic competition and cooperation model of two enterprises. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.
期刊：
International Journal of Innovative Computing, Information and Control,2015年11(1):247-256 ISSN：1349-4198
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Key Laboratory of Economics System, Simulation Guizhou University of Finance and Economics, Huaxi District, Guiyang, China;[Zhang, Qiming] College of Science, Hunan University of Technology, Wenhua Road, Zhuzhou, China;[Liao, Maoxin] School of Mathematics and Physics, University of South China, No. 28, West Xianning Road, Hengyang, China
通讯机构：
Guizhou Key Laboratory of Economics System, Simulation Guizhou University of Finance and Economics, Huaxi District, Guiyang, China
期刊：
Metallurgical and Mining Industry,2015年7(8):78-85 ISSN：2076-0507
通讯作者：
Zou, Shuliang(3467593@qq.com)
作者机构：
[Zhang, Min] School of Nuclear Science and Technology, University of South China, Hengyang, China;[Zhang, Min; Zou, Shuliang] Hunan Provincial Key Laboratory of Emergency Safety Technology, Equipment for Nuclear Facilities, Hengyang, China;[Zhang, Min; Zou, Shuliang] School of Math and Physics, University of South China, Hengyang, China
通讯机构：
School of Math and Physics, University of South China, Hengyang, China
关键词：
Concentration dominance of adiacent point;Cubic spline interpolation;Inversion;MCNP program simulation;Radiation concentration field;Structure
摘要：
In this paper, the inversion of the particle field is put forward by a function constructed for solid radioactive sources. Based on the inverse proportion between concentration and the square of the distance from the radioactive source, the concentrations surface near the radioactive source is sharp, steep and concave. The concentration surface may be convex where the nuclear radiation field is restored with sparse data by interpolation or fitting. Hence we make use of mathematical construction techniques to construct concentration function tactfully. An inversion model is established which is based on the concentration of nodes in the grid. The concentration value of the grid lines is restored by the cubic spline interpolation. According to an idea of concentration dominance of adjacent point, the function of interior point of grid is structured, which is consistent with the characteristics of the radiation field. During the simulation experiment, concentration value of node is obtained by MCNP program based on the Monte Carlo method. It is verified that the concentration function is close to the real concentration field. Therefore inversion method is feasible, which provides theoretical basis for radioactive sources search and safe evacuation.
