Symmetry-breaking in local Lyapunov exponents

Integrable dynamical systems, namely those having as many independent conserved quantities as freedoms, have all Lyapunov exponents equal to zero. Locally, the instantaneous or finite time Lyapunov exponents are nonzero, but owing to a symmetry, their global averages vanish. When the system becomes nonintegrable, this symmetry is broken. A parallel to this phenomenon occurs in mappings which derive from quasiperiodic Schr?dinger problems in 1-dimension. For values of the energy such that the eigenstate is extended, the Lyapunov exponent is zero, while if the eigenstate is localized, the Lyapunov exponent becomes negative. This occurs by a breaking of the quasiperiodic symmetry of local Lyapunov exponents, and corresponds to a breaking of a symmetry of the wavefunction in extended and critical states. Received 25 October 2001 / Received in final form 8 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: r.ramaswamy@mail.jnu.ac.in     

3H‐1,2‐Dithiole‐3‐thione derivatives as novel solvatochromic dyes

The UV–Vis spectrum of 5‐(1‐butylthio)‐3H‐1,2‐dithiole‐3‐thione (1a) and that of the chromium pentacarbonyl complex of 5‐methyl‐3H‐1,2‐dithiole‐3‐thione (3) present significant changes with the solvent polarity. The two absorption bands shown by the compounds in the region above 300 nm were identified by theoretical calculations. For Compound 1a these are n→π^* and →π^* transitions and for Compound 3 the longest wavelength absorption corresponds to a charge transfer band and shows a remarkably negative solvatochromism. Not only has the wavelength of maximum absorption changed with the solvent but also the ratio of the absorbances at the two wavelengths. The effect of solvents was correlated with solvatochromic parameters such as π^* and α. The spectrum of 5‐(1‐butylthio)‐3H‐1,2‐dithiole‐3‐one ( 2 ) was also measured in different solvents but in this case the changes observed are less significant than for the other two compounds. The spectra of 1a and 3 were also determined in the presence of anionic (SDS), cationic (CTAB), and neutral surfactants (Brig‐35) and it is shown that these compounds can be used as probes for the polarity of the binding sites of organized assemblies. Copyright © 2008 John Wiley & Sons, Ltd.     

A combination of accreditation and certification in an evolving process at EMPA: A management system to meet ISO 9001, ISO 14001 and EN 45001

 The Swiss Federal Laboratories for Materials Testing and Research (EMPA) have established a quality assurance system based on EN 45001 which meets the requirements for accreditation of all EMPA's testing activities. As testing is only a part of EMPA's range of activities, and is performed in decentralised departments, the system does not satisfy the management needs. The fundamental reorganisation of EMPA's St. Gallen site was used as an opportunity to implement an overall process-oriented management system which also included quality and the needs for accreditation. Later, an environmental management system was added and then certified for ISO 9001 and 14001. The system consists of a "Management Manual" for the St. Gallen site and a customised "Quality Manual" for each department. One of the key elements is a comprehensive review and planning procedure covering all business aspects.     

Dynamical Localization II with an Application to the Almost Mathieu Operator

Several recent works have established dynamical localization for Schrödinger operators, starting from control on the localization length of their eigenfunctions, in terms of their centers of localization. We provide an alternative way to obtain dynamical localization, without resorting to such a strong condition on the exponential decay of the eigenfunctions. Furthermore, we illustrate our purpose with the almost Mathieu operator, H _{, ,} =–+ cos(2(+x)), 15 and with good Diophantine properties. More precisely, for almost all , for all q>0, and for all functions ²( ) of compact support, we show that The proof applies equally well to discrete and continuous random Hamiltonians. In all cases, it uses as input a repulsion principle of singular boxes, supplied in the random case by the multi-scale analysis.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

Biased Diffusion with Correlated Noise

The diffusion of hard-core particles subject to a global bias is described by a nonlinear, anisotropic generalization of the diffusion equation with conserved, local noise. Using renormalization group techniques, we analyze the effect of an additional noise term, with spatially long-ranged correlations, on the long-time, long-wavelength behavior of this model. Above an upper critical dimension d _LR, the long-ranged noise is always relevant. In contrast, for d<d _LR, we find a weak noise regime dominated by short-range noise. As the range of the noise correlations increases, an intricate sequence of stability exchanges between different fixed points of the renormalization group occurs. Both smooth and discontinuous crossovers between the associated universality classes are observed, reflected in the scaling exponents. We discuss the necessary techniques in some detail since they are applicable to a much wider range of problems.     

基于时序逻辑和SCR方法的需求分析方法

以定义事件驱动型系统需求的ＳＣＲ（Ｓｏｆｔｗａｒｅ ＣｏｓｔＲｅｄｕｃｅ）方法和时序逻辑为基础,提出了一种能够根据ＳＣＲ方法与时序逻辑之间的语义联系和时序逻辑的推理能力有效地检查用ＳＣＲ方法定义的事件驱动型系统的需求分析方法．为便于理解,还给出了一个简单的例子来介绍如何分析和检查用ＳＣＲ方法定义的需求的有效性．     

Low Rank Approximation of a Hankel Matrix by Structured Total Least Norm

The structure preserving rank reduction problem arises in many important applications. The singular value decomposition (SVD), while giving the closest low rank approximation to a given matrix in matrix L ₂ norm and Frobenius norm, may not be appropriate for these applications since it does not preserve the given structure. We present a new method for structure preserving low rank approximation of a matrix, which is based on Structured Total Least Norm (STLN). The STLN is an efficient method for obtaining an approximate solution to an overdetermined linear system AX B, preserving the given linear structure in the perturbation [E F] such that (A + E)X = B + F. The approximate solution can be obtained to minimize the perturbation [E F] in the L _p norm, where p = 1, 2, or . An algorithm is described for Hankel structure preserving low rank approximation using STLN with L _p norm. Computational results are presented, which show performances of the STLN based method for L ₁ and L ₂ norms for reduced rank approximation for Hankel matrices.     

Extraction of subsystems “Majorized” by the rademacher system

In this paper it is proved that from any uniformly bounded orthonormal system {f _n} _n=1 ^∞ of random variables defined on the probability space (Ω, ε, P), one can extract a subsystem {fni} _i ^{Emphasis>=1/∞} majorized in distribution by the Rademacher system on [0, 1]. This means that {

Indexes and Special Discretization Methods for Linear partial Differential Algebraic Equations

Linear partial differential algebraic equations (PDAEs) of the form Au _t(t, x) + Bu _xx(t, x) + Cu(t, x) = f(t, x) are studied where at least one of the matrices A, B R ^n×n is singular. For these systems we introduce a uniform differential time index and a differential space index. We show that in contrast to problems with regular matrices A and B the initial conditions and/or boundary conditions for problems with singular matrices A and B have to fulfill certain consistency conditions. Furthermore, two numerical methods for solving PDAEs are considered. In two theorems it is shown that there is a strong dependence of the order of convergence on these indexes. We present examples for the calculation of the order of convergence and give results of numerical calculations for several aspects encountered in the numerical solution of PDAEs.