Parallel solvers for the depletion region identification in metal semiconductor field effect transistors

In this work we are interested in a sufficiently accurate approximation of the steady-state potentials in a Metal Semiconductor Field Effect Transistor (MESFET), which can be obtained with the so-called depletion region approximation (see [5]). We propose a robust method based on the shape optimization techniques to analyze and compute the depletion boundary as a function of the applied voltage and the geometry material properties of the device. During the optimization process several intermediate direct problems are solved using the boundary element method (BEM). To accelerate the solutions of of these systems we use a strategy of subdividing the domain into a number of smaller subdomains [11,9]. The scheme is iterative and each subdomain is handled by a separate node in parallel. Test runs comparing the performance of the parallel with the serial code, and other numerical discussions are presented. AMS subject classification 65N55, 65N38, 65K10, 78A55. A. Nachaoui: Corresponding author.     

Applications of the Wold decomposition to the study of row contractions associated with directed graphs

Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the -algebra of a CKT family, and prove a universality theorem for -algebras generated by these families. In both cases, the -algebras generated by quiver algebras play the universal role.

     

Polarization Tomography of Quantum Radiation: Theoretical Aspects and Operator Approach

We present theoretical foundations for the quantum tomography of polarization states of light fields as a method for measuring their polarization density operator , which characterizes only the polarization degrees of freedom of the radiation. We mainly attend to the method in which the tomographic observables (the “measurement instruments”) are polarizable in nature. We show that the quantum nature of this method can be adequately expressed using the quasispectral tomographic decompositions of in special operator bases, which are finite sums of partially orthogonal projection operators determining the probability distributions of tomographic observables as the decomposition coefficients. We obtain the matrix versions of such “tomographic” representations of , in particular, by projecting them on semiclassical operator bases determining the polarization quasiprobability functions. We briefly discuss the information aspects of the schemes considered in the paper. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 344–357, December, 2005.     

Asymptotic Analysis for Random Walks with Nonidentically Distributed Jumps Having Finite Variance

Let ξ₁,ξ₂,... be independent random variables with distributions F₁F₂,... in a triangular array scheme (F _i may depend on some parameter). Assume that Eξ _i = 0, Eξ _i ² < ∞, and put \(S_n = \sum {_{i = 1}^n \;} \xi _i ,\;\overline S _n = \max _{k \leqslant n} S_k\). Assuming further that some regularly varying functions majorize or minorize the “averaged” distribution \(F = \frac{1}{n}\sum {_{i = 1}^n F_i }\), we find upper and lower bounds for the probabilities P(S _n > x) and \(P(\bar S_n > x)\). We also study the asymptotics of these probabilities and of the probabilities that a trajectory {S _k } crosses the remote boundary {g(k)}; that is, the asymptotics of P(max_k≤n(S _k ? g(k)) > 0). The case n = ∞ is not excluded. We also estimate the distribution of the first crossing time.     

Some multivariate inequalities with applications

Summary Let <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>{\cal {X}}_{n} =(X_1,\ldots,X_n)$ be a random vector. Suppose that the random variables $(X_i)_{1\leq i\leq n}$ are stationary and fulfill a suitable dependence criterion. Let $f$ be a real valued function defined on $\mathbbm{R}^n$ having some regular properties. Let ${\cal {Y}}_{n}$ be a random vector, independent of ${\cal {X}}_{n}$, having independent and identically distributed components. We control $\left|\mathbbm{E}(f({\cal {X}}_{n}))-\mathbbm{E} (f({\cal {Y}}_{n}))\right|$. Suitable choices of the function $f$ yield, under minimal conditions, to rates of convergence in the central limit theorem, to some moment inequalities or to bounds useful for Poisson approximation. The proofs are derived from multivariate extensions of Taylor's formula and of the Lindeberg decomposition. In the univariate case and in the mixing setting the method is due to Rio (1995).     

Regularity of Weak Solutions of Nonlinear Equations with Discontinuous Coefficients

In this paper, we prove that the weak solutions u∈Wloc^1, p （Ω） （1 〈p〈∞） of the following equation with vanishing mean oscillation coefficients A（x）： -div[（A（x）△↓u·△↓u）p-2/2 A（x）△↓u＋│F（x）│^p-2 F（x）]=B（x, u, △↓u）, belong to Wloc^1, q （Ω）（A↓q∈（p, ∞）, provided F ∈ Lloc^q（Ω） and B（x, u, h） satisfies proper growth conditions where Ω ∪→R^N（N≥2） is a bounded open set, A（x）=（A^ij（x）） N×N is a symmetric matrix function.     

Optimum design of four-bar function generators with minimum variance criterion

The closure equation of a four-bar linkage generally gives a nonzero result, which may be taken as an index of the error in the output for a given input. The actual output can be brought close to the desired value by specifying the mean error permissible in the entire range of operation and by minimizing the variance (standard deviation). The present method differs from the closed-form synthesis (i.e., precision-point synthesis), in the sense that it does not limit the number of precision points. The results show that the present method compares well with other methods.     

Kinetics of phase separation in polymer blends. Calculations based on nonlinear theory

Suzuki's scaling theory for transient phenomena is applied to the calculation of the kinetics of phase separation in the early-to-intermediate stage based on a nonlinear theory proposed by Langer, Bar-on, and Miller (LBM). Calculated results are compared with experimental data on light scattering from a polymer blend system. Deviations from predictions of Cahn's linearized theory in the early time range of phase separation can be explained well by the proposed method of calculation. Nonlinear effects are found to play an essential role in characterizing the light scattering behavior of phase separation in the intermediate stage. Time evolutions of the single-point distribution function of composition are calculated, and the results are in good agreement with those reported in digital imaging analysis experiments and computer simulations of the time-dependent Ginzburg-Landau equation. The influence of asymmetry of free-energy on the single-point distribution function is also investigated in this study. © 1993 John Wiley & Sons, Inc.     

Decomposition and interval arithmetic applied to global minimization of polynomial and rational functions

A recent global optimization algorithm using decomposition (GOP), due to Floudas and Visweswaran, when specialized to the case of polynomial functions is shown to be equivalent to an interval arithmetic global optimization algorithm which applies natural extension to the cord-slope form of Taylor's expansion. Several more efficient variants using other forms of interval arithmetic are explored. Extensions to rational functions are presented. Comparative computational experiences are reported.     

ZnO纳米棒的低温溶液法制备、光电特性研究及其在有机/无机复合电致发光中的应用

利用水热法制备了垂直于衬底的定向生长的ZnO纳米棒,利用扫描电子显微镜及光致发光的方法对其形貌及光学特性进行了表征,利用场发射性能测试装置对ZnO纳米棒的场发射性能进行了测试.结果表明:利用水热法在较低的温度(95 ℃) 下生长了具有较好形貌和结构的ZnO纳米棒,并表现出了较好的场发射特性,当电流密度为1 μA/cm²时,开启电场是2.8 V/μm,当电场为6.4 V/μm时,电流密度可以达到0.67 mA/cm²,场增强因子为3360.稳定性测试表明,在5 h内,4.5 V/μm的电场下,其波动不超过25%.将制备的ZnO纳米棒应用到有机/无机电致发光中,其中ZnO纳米棒为电子传输层,m-MTDATA(4,4',4″-tris{N,(3-methylphenyl)-N-phenylamino}-triphenylamine) 为空穴传输层,得到了ZnO的342 nm的紫外电致发光,此发光较ZnO纳米棒光致发光的紫外发射有约40 nm的蓝移. 关键词： ZnO纳米棒 场发射 水热法 有机/无机复合电致发光