Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion

In the Laser-Induced Breakdown Spectroscopy (LIBS) technique, the existence of Local Thermodynamic Equilibrium (LTE) is the essential requisite for meaningful application of theoretical Boltzmann–Maxwell and Saha–Eggert expressions that relate fundamental plasma parameters and concentration of analyte species. The most popular criterion reported in the literature dealing with plasma diagnostics, and usually invoked as a proof of the existence of LTE in the plasma, is the McWhirter criterion [R.W.P. McWhirter, in: Eds. R.H. Huddlestone, S.L. Leonard, Plasma Diagnostic Techniques, Academic Press, New York, 1965, pp. 201–264]. However, as pointed out in several papers, this criterion is known to be a necessary but not a sufficient condition to insure LTE. The considerations reported here are meant to briefly review the theoretical analysis underlying the concept of thermodynamic equilibrium and the derivation of the McWhirter criterion, and to critically discuss its application to a transient and non-homogeneous plasma, like that created by a laser pulse on solid targets. Specific examples are given of theoretical expressions involving relaxation times and diffusion coefficients, as well as a discussion of different experimental approaches involving space and time-resolved measurements that could be used to complement a positive result of the calculation of the minimum electron number density required for LTE using the McWhirter formula. It is argued that these approaches will allow a more complete assessment of the existence of LTE and therefore permit a better quantitative result. It is suggested that the mere use of the McWhirter criterion to assess the existence of LTE in laser-induced plasmas should be discontinued.     

一类无限群中局部幂零性的判定准则

设G是任意群,群G的Frattini子群nat(G)定义为G的所有极大子群的交.类似地,群G的另外两个特征子群nFrat(G)及R(G)分别定义为群G的所有极大正规子群及群G的所有正规的极大子群的交.本文通过对nat(G),nnat(G)及R(G)的相互包含关系的研究,得到CF-群或中心由多重循环群的扩张群中局部幂零性的一个判定准则.同时也讨论了在某些群类中若干种广义幂零性的等价性.     

Active constraints,indefinite quadratic test problems,and complexity

The observation that at leasts constraints are active when the Hessian of the Lagrangian hass negative eigenvalues at a local minimizer is used to obtain two results: (i) a class of nearly concave quadratic minimization problem can be solved in polynomial time; (ii) a class of indefinite quadratic test problems can be constructed with a specified number of positive and negative eigenvalues and with a known global minimizer.The authors thank the reviewers for their constructive comments. The first author was supported by the National Science Foundation Grant DMS-85-20926 and by the Air Force Office of Scientific Research Grant AFOSR-ISSA-86-0091.     

Simultaneous observation of the triangular and honeycomb structures on highly oriented pyrolytic graphite at room temperature: An STM study

Scanning tunneling microscopy (STM) was used to study the surface structures of dry-prepared and di-chloroethane-treated HOPG samples. Both triangular and honeycomb structures were simultaneously observed with the same tip at room temperature around a strand (grain boundary) on the HOPG surface. This observation did not support the tip effect in STM imaging explanation for HOPG in literature. A general layer-sliding model was utilized to explain the experimental results: sliding of the HOPG topmost layer was used to explain the origins of the triangular and honeycomb structures, and molecule intercalation into inter-layer spacing between the first and second layers of HOPG induced inhomogeneous deformation of the HOPG topmost layer that accordingly generated the Moiré patterns of the HOPG sample in di-chloroethane.     

Edge-splittings preserving local edge-connectivity of graphs

Let G=(V+s,E) be a 2-edge-connected graph with a designated vertex s. A pair of edges rs,st is called admissible if splitting off these edges (replacing rs and st by rt) preserves the local edge-connectivity (the maximum number of pairwise edge disjoint paths) between each pair of vertices in V. The operation splitting off is very useful in graph theory, it is especially powerful in the solution of edge-connectivity augmentation problems as it was shown by Frank [Augmenting graphs to meet edge-connectivity requirements, SIAM J. Discrete Math. 5(1) (1992) 22-53]. Mader [A reduction method for edge-connectivity in graphs, Ann. Discrete Math. 3 (1978) 145-164] proved that if d(s)≠3 then there exists an admissible pair incident to s. We generalize this result by showing that if d(s)?4 then there exists an edge incident to s that belongs to at least ⌊d(s)/3⌋ admissible pairs. An infinite family of graphs shows that this bound is best possible. We also refine a result of Frank [On a theorem of Mader, Discrete Math. 101 (1992) 49-57] by describing the structure of the graph if an edge incident to s belongs to no admissible pairs. This provides a new proof for Mader's theorem.     

Aromaticity of corazulenic fullerenes

A novel class of non-classical fullerenes, having pentagon–heptagon pairs, as in azulene, is modeled. The various coverings, sometimes alternating azulenic and benzenic units, are designed by some new sequences of map operations or generalized operations. The hypothetical azulenic fullerenes are characterized by PM3 semiempirical data and POAV1 strain energy SE. Their aromaticity is discussed in the light of several criteria. The HOMA index of aromaticity enabled evaluation of global and local aromaticity of the designed fullerenes.     

Level Sets of Multiparameter Stable Processes

We establish the correct Hausdorff measure function for the level sets of additive strictly stable processes derived from strictly stable processes satisfying Taylor’s condition (A). This leads naturally to a characterization of local time in terms of the corresponding Hausdorff measure function of the level set.      

带跳的时滞随机微分方程近似解的收敛性

本文研究了一类具有Possion跳的时滞随机微分方程（SDDEwJPs）．在一般情况下SDDEwJPs没有解析解．因此合适的数值逼近法，例如欧拉法，就是在研究它们性质时所采用的重要工具．本文在局部李普希兹条件下证明了欧拉近似解强收敛于SDDEwJPs的精确解（分析解）．     

扩散过程在Hlder范数下的局部Strassen重对数律

在该文中,作者应用扩散过程在Holder范数下的大偏差得到了扩散过程在Holder范数下的局部Strassen重对数律．并且还得到了重It■积分的泛函重对数律．     

Electrical characterization of Schottky diodes based on boron doped homoepitaxial diamond films by conducting probe atomic force microscopy

A large planar tungsten carbide (WC) Schottky diode on p-type homoepitaxial diamond was mainly investigated on a microscopic level by atomic force microscopy (AFM) and conducting probe atomic force microscopy (CP-AFM), allowing simultaneous topographic and local electrical resistance imaging measurements. These techniques revealed the existence of a specific microstructure on the WC Schottky contact consisting of electrically insulating islands surrounded by conductive paths. The islands are found to be insulating in the whole range of explored bias [−5 V, +5 V], whereas the current flowing between the islands is 1000 times lower at a reverse bias of −5 V than at a forward bias of +5 V, in agreement with the rectifying ratio found from macroscopic current–voltage (I–V) measurements. CP-AFM provides a prospective imaging tool which is well suited for analyzing the local electrical properties and instabilities of Schottky junctions.