Study of Bridging of the Spectral Gap in the Lower Hybrid Wave Current Drive in the HT-7 Tokamak

An additional lower hybrid wave （LHW） with a higher refractive index （N//） was investigated in the HT-7 tokamak to bridge the spectral gap. It was found that the spectral gap between the wave and the electrons in the outer region was bridged by the additional wave with a higher N// spectrum. The results showed that the sawteeth oscillation was suppressed by launching the additional wave, and that the power deposition profile was moved outwards and the current profile was broadened due to the application of the additional wave. Our study indicates that the spectral gap may be bridged by an additional wave with a higher N// spectrum in the outer region.

Estimation of Spectral Gap for Markov Chains

The study of the convergent rate (spectra gap) in the L^2-sense is motivated from several different fields: probability statistics, mathematical physics, computer science and so on and it is now an artive research topic. Based on a new approach (the coupling technique) introduced in [7] for the estimate of the convergent rate and as a continuation of [4],[5],[7-9],[23] and [24], this paper studies the estimate of the rate for time-continuous Markov chains. Two variational formulas for the rate are presented here for the first time for birth-death processes. For diffusions, similar results are presented in an accompany paper [10]. The new formulas enable us to recover or improve the main known results. The connection between the sharp estimate and the corresponding eigenfunction is explored and illustrated by various examples. A previous result on optimal Markovian couplings is also extended in the paper.

Spectral Gap and Logarithmic Sobolev Constant for Continuous Spin Systems

The aim of this paper is to study the spectral gap and the logarithmic Sobolev constant for continuous spin systems. A simple but general result for estimating the spectral gap＇of finite dimensional systems is given by Theorem 1.1, in terms of the spectral gap for one-dimensional marginals. The study of this topic provides us a chance, and it is indeed another aim of the paper, to justify the power of the results obtained previously. The exact order in dimension one （Proposition 1.4）, and then the precise leading order and the explicit positive regions of the spectral gap and the logarithmic Sobolev constant for two typical infinite-dimensional models are presented （Theorems 6.2 and 6.3）. Since we are interested in explicit estimates, the computations become quite involved. A long section （Section 4） is devoted to the study of the spectral gap in dimension one.

Spectral Gap and Convergence Rate for Discrete-time Markov Chains

Abstract Let P be a transition matrix which is symmetric with respect to a measure π. The spectral gap of P in L2（π）-space, denoted by gap（P）, is defined as the distance between 1 and the rest of the spectrum of P. In this paper, we study the relationship between gap（P） and the convergence rate of P^n. When P is transient, the convergence rate of pn is equal to 1 - gap（P）. When P is ergodic, we give the explicit upper and lower bounds for the convergence rate of pn in terms of gap（P）. These results are extended to L^∞ （π）-space.

Estimate of Exponential Convergence Rate in Total Variation by Spectral Gap

This note is devoted to study the exponential convergence rate in the total variation for reversible Markov processes by comparing it with the spectral gap. It is proved that in a quite general setup, with a suitable restriction on the initial distributions, the rate is bounded from below by the spectral gap. Furthemore, in the compact case or for birth-death processes or half-line diffosions, the rate is shown to be equal to the spectral gap.

Spectral Gap for Open Jackson Networks

We generalize the decomposition method of the finite Markov chains for Poincare inequality in Jerrum et al.（Ann.Appl.Probab.,14,1741-1765（2004）） to the reversible continuous-time Markov chains.And inductively,we give the lower bound of spectral gap for the ergodic open Jackson network by the decomposition method and the symmetrization procedure.The upper bound of the spectral gap is also presented.

Sharp lower bound of spectral gap for Schrodinger operator and related results

We give an easy proof of Andrews and Clutterbuck＇s main results [J. Amer. Math. Soc., 2011, 24（3）： 899-916], which gives both a sharp lower bound for the spectral gap of a Schr5dinger operator and a sharp modulus of concavity for the logarithm of the corresponding first eigenfunction. We arrive directly at the same estimates by the ＇double coordinate＇ approach and asymptotic behavior of parabolic flows. Although using the techniques appeared in the above paper, we partly simplify the method and argument. This maybe help to provide an easy way for estimating spectral gap. Besides, we also get a new lower bound of spectral gap for a class of SchSdinger operator.

The Spectral Gap for Quasi-birth and Death Processes

For a reversible quasi-birth and death process, we generalize and refine the decomposition method, by constructing a birth-death process and a sequence of restriction processes. The spectral gap for the quasi-birth and death process is estimated in terms of the spectral gaps for these processes, and in some special cases, the estimation is sharp. With the aid of the symmetrization procedure, the result is also applied to two queueing models： M/M/1 in random environment and MIMIc with synchronous vacation.

Spectral gap of Boltzmann measures on unit circle

We give a two sided estimate on the spectral gap for the Boltzmann measures μh on the circle. We prove that the spectral gap is greater than 1 for any h∈R and the spectral gap tends to the positive infinity as h→∞ with speed |h|.

Coupling, spectral gap and related topics (Ⅱ)

THIS is the second one of a series of three reviews. The ideas introduced in the last review are used to study the estimate of spectral gap and four classes of typical eigenvalue problems on manifolds. The comparison with the known optimal estimates is given, some new progress is reported and some open problems are proposed.

Coupling, spectral gap and related topics (Ⅲ)

THIS is the last one of a series of three papers. Here, we discuss six topics related to the spectral gap: the gradient estimate, the heat kernel and Harnack inequality, the logarithmic Sobolev inequality, the convergence in total variation, the algebraic convergence and the infinite-dimensional case. The perturbation of spectral gap and the logarithmic Sobolev constant under a linear transform is given (Theorem 5). A new proof for computing the logarithmic Sobolev constant in a basic case is also presented (Theorem 7).

Coupling, spectral gap and related topics (Ⅰ)

THIS is the first of a series of three reviews. They are partially surveys on three aspects: (ⅰ) explaining the main ideas of our recent application of the coupling method to the estimation of spectral gap, (ⅱ) introducing some more recent progress on the study on some related topics,(ⅲ) collecting some open problems for the further study.

Spectral gap for diffusion processes on noncompact manifolds

Let （M, g） be a complete Riemannian manifold of dimension d and Ricci curvaturebounded below by-K for some K∈. Let dx and p（x,y） be respectively the Riemannianvolum element and Riemannian distance. Consider L=△+V with V∈C2（M） satisfyingZ=∫mexp[V]dx 【 ∞. Then the L-diffusion process is reversible with respect to μ（dx）=Z-lexp[V]dx. It is well known that the exponentially L2-convergence of the L-diffusion pro-cess equivalent to a spectral gap

Spectral gap on path spaces with infinite time-interval

Under certain curvature condition, the existence of spectral gap is proved on path spaces with infinite time-interval.

Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap

The Cheeger’s inequalities and some existence criteria for spectral gap and for general symmetric forms are established. The criteria are also extended to general reversible Markov processes but not reported here. Even though in the past several decades, the topics have been widely studied, as far as we know the first problem in the unbounded case and the second one in the general case remain open.

绝缘隔板对空气间隙放电光谱特性的影响及电荷演变机理

在空间有限的开关柜等电力设备中,开展棒-板间隙放电的放电规律以及检测方法的研究具有重要意义。实验探讨了“棒电极-绝缘隔板-接地电极”系统中不同隔板材料、隔板位置时放电光谱的分布规律;采用表面电位计,计算分析了放电后绝缘隔板表面陷阱能级分布特征;通过建立等尺寸绝缘系统仿真模型,分析绝缘隔板的引入对电子密度、电场分布的影响,揭示放电机理。实验研究表明,绝缘隔板的引入,可以显著提高系统的击穿电压,最高可提升1.6倍。不同隔板材料对应的放电光谱特征信息有所不同,环氧树脂隔板的放电光谱强度整体较大,但在波段309.25 nm、589.05 nm处聚酯板的光谱强度略大于环氧树脂。此外,电极间距对放电光谱具有较大的影响。隔板材料表面存在明显的残余电荷,环氧树脂的电荷积聚高于聚酯板,对击穿电压的影响较大。仿真结果显示,隔板材料的改变会影响击穿电压的幅值,同时会改变微观粒子的物理运动,从而改变放电光谱。研究成果可为电力设备光谱放电监测和绝缘状态评估提供理论和实验指导。

Au对GaP接触界面形成及其特性

借助Ｘ射线衍射和扫描电子显微镜研究了Ａｎ和ＧａＰ接触体系界面特性的温度依赖性．测量表明，既使在低于４００℃温度下界面反应也会生成少量的Ａｎ－ＧａＰ金属间化合物，它的主要成份是（ＧａＡｕ）Ｈ，Ｇａ２Ａｕ．在较高温度５５０℃合金条件下，ＧａＰ化合物表面发生分解，界面反应增强并伴随着快速的原子间互扩散．大量Ｇａ原子向外迁移进人Ａｎ膜复盖层．同时，Ａｎ原子也内扩散进入ＧａＰ表面，Ａｎ－Ｇａ之间界面反应生成（ＧａＡｕ）Ｈ，Ｇａ２Ａｎ和（ＧａＡｕ）８Ｏ．实验结果指出，Ａｎ和ＧａＰ接触界面是一个金属一半导体界面反应层和合金再生长层．它含有Ａｎ、Ｇａ、Ｐ原子．Ａｎ－Ｇａ金属间化合物的形成有助改善Ａｎ膜机械强度和粘附性．扫描电子显微镜观察发现，当合金温度超过ＡｕＧａ共熔温度４７０℃，表面形貌变得粗糙和不均匀．随着温度上升，Ｍ－Ｓ接触界面层微结晶颗粒变大．在６００℃下，微结晶效应显著．事实上，这种合金条件无助于欧姆接触制备．

基于层次密度聚类和谱间隙的雷达信号分选

雷达信号分选是现代电子战中的重要环节.为了解决传统算法鲁棒性较差的问题,提出一种基于层次密度聚类和谱间隙的雷达信号分选算法.使用载频和脉宽参数进行层次密度聚类,根据重新定义的簇间距得到赋权邻接矩阵,计算赋权邻接矩阵的拉普拉斯谱间隙,通过k-means聚类的超参数k对信号进行分选.仿真实验结果表明:该文算法的平均分选准确率达0.9960、平均召回率达0.9560;相对于密度聚类(density-based spatial clustering of applications with noise,简称DBSCAN)和Meanshift算法,该文算法对杂乱脉冲、漏脉冲及超参数的干扰均有最强的鲁棒性.

TID隔振器浮置板轨道低频减振特性研究

为了实现对地铁低频环境振动的控制,提出了一种基于TID(Tuned inerter damper,调谐惯容阻尼器)的浮置板板下隔振器,并以此形成新型浮置板轨道结构。分别探究了TID隔振器浮置板轨道的低频弹性波传播特性、简谐点荷载作用下振动特性以及列车荷载作用下减振效果;结合多目标遗传算法,开展了TID参数优化分析。结果表明:TID的引入使得传统钢弹簧浮置板新增弯曲波带隙,实现了对板内弹性波的调控;浮置板低频共振所致的振动放大问题得到较大改善。TID隔振器浮置板轨道在4 Hz~16 Hz频率范围内的减振效果得以提升,浮置板振动响应也得到减弱。