A posteriori error estimators for the Stokes equations

Summary We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.This work was accomplished at the Universität Heidelberg with the support of the Deutsche Forschungsgemeinschaft     

Synchronization of a class of chaotic dynamic systems with controller gain variations

In this paper, the nonfragile control problem for synchronization of a class of chaotic dynamical systems with controller gain variations is studied. Using the Lyapunov method and LMI (linear matrix inequality) technique, a criterion for the existence of the nonfragile controller for synchronization is derived in terms of LMI. To show the effectiveness of the proposed method, the control problem is applied to Genesio chaotic system.     

Integer quantum Hall effect in graphite

We present Hall effect measurements on highly oriented pyrolytic graphite that indicate the occurrence of the integer quantum-Hall-effect. The evidence is given by the observation of regular plateau-like structures in the field dependence of the transverse conductivity obtained in van der Pauw configuration. Measurements with the Corbino-disk configuration support this result and indicate that the quasi-linear and non-saturating longitudinal magnetoresistance in graphite is governed by the Hall effect in agreement with a recent theoretical model for disordered semiconductors.     

Preliminary results of a non-spherical aerosol method for the retrieval of the atmospheric aerosol optical properties

There is experimental evidence that the non-sphericity of certain atmospheric particles can cause scattering properties different from those predicted by standard Mie theory. Numerous studies indicate the need to consider the presence of non-spherical particles in modeling the optical properties of atmospheric aerosols. On the other hand, natural aerosols show a great variety of shapes, making difficult a realistic choice of a particle shape (or shape mixture) model. In this paper, we test a parameterization of the particle shape in the retrieval of size distribution, phase function, single scattering albedo and asymmetry parameter from direct and sky-radiance measurements. For this purpose we have substituted the Kernel based on the Mie theory included in the model SKYRAD.PACK by one derived for non-spherical particles. The method is applied under different atmospheric conditions, including Saharan dust outbreak, polluted and local mineral episodes. We compare the results with those obtained by the well known spheroids algorithm used in the AERONET network.     

Speech deterioration in postlingually deafened adults

Postlinngually deafened adults reading the Rainbow Passage differed from hearing-control subjects in producing greater pitch variability and mean pitch on stressed and unstressed vowels, greater fluctuations in pitch within sentences, less correlation of intrinsic pitch with vowel height and slower temporal parameters. When reading the Phonetic Inventory Sentences, they revealed less differentiation of place of articulation in fricative and plosive consonants. The present findings, taken together with those of longitudinal and implant studies, are applied to constraining models of the role of self hearing in the elaboration of speech.     

Spectral hole burning of photosynthetic antenna of blue-green algae

Photosystem II core antenna of blue-green algae Synechococcus isolated in gel was studied by optical hole burning spectroscopy at 4·2 K. Persistent holes were burned into fluorescence spectra throughout the region 680–696 nm. The hole width extrapolated to zero burning fluence yielded a value 1·0±0·2 cm^–1. A theoretical interpretation of the hole profile in fluorescence is presented. The dependence of saturated hole depth on burning wavelength is related to inhomogeneous site distribution function.Authors would like to thank F. Vácha from the Dept. of Biochemistry, Faculty of Nature Sciences, Charles University, for the preparation of the samples.     

Asymptotic expansions for Markov processes with lévy generators

This paper considers a deterministic flow inn-dimensional space, perturbed by a Markov jump process with small variance. Asymptotic expansions are obtained for certain functionals of Feynman—Kac type, in powers of a small parameter representing a noise intensity. The methods are analytical rather than probabilistic.The research of the first author was partly supported by AFOSR under Contract No. 91-0116-0, by ONR under Contract No. N0014-83-K-0542, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR. The second author's research was partly supported by NSF under Contract No. DMS-8702537, and by the Institute for Mathematics and Its Applications with funds provided by the NSF and ONR.     

Generating functions for a class ofq-polynomials

Summary Some simple ideas are used here to prove a theorem on generating functions for a certain class of q-polynomials. This general theorem is then applied to derive a fairly large number of known as well as new generating functions for the familiar q-analogues of various polynomial systems including, for example, the classical orthogonal polynomials of Hermite, Jacobi, and Laguerre. A number of other interesting consequences of the theorem are also discussed.     

The six-vertex model eigenvectors as critical limit of the eight-vertex model bethe ansatz

The critical limit of the eight-vertex model eigenvectors obtained by means of the generalized Bethe Ansatz is shown to give the six-vertex eigenvectors as constructed in a previous paper by two of the authors. Furthermore, an explicit mapping is established between these eigenvectors and the usual Bethe Ansatz eigenvectors of the six-vertex model. This allows one to show that the indexv labeling the eight-vertex eigenstates becomes exactly the third component of the total spin in the critical limit.