Modeling,Mathematical and Numerical Analysis of Electrorheological Fluids

Many electrorheological fluids are suspensions consisting of solid particles and a carrier oil. If such a suspension is exposed to a strong electric field the effective viscosity increases dramatically. In this paper we first derive a model which captures this behaviour. For the resulting system of equations we then prove local in time existence of strong solutions for large data. For these solutions we finally derive error estimates for a fully implicit time-discretization.     

Kinetic approximation of a boundary value problem for conservation laws

Summary. We design numerical schemes for systems of conservation laws with boundary conditions. These schemes are based on relaxation approximations taking the form of discrete BGK models with kinetic boundary conditions. The resulting schemes are Riemann solver free and easily extendable to higher order in time or in space. For scalar equations convergence is proved. We show numerical examples, including solutions of Euler equations.Mathematics Subject Classification (2000): 65M06, 65M12, 76M20Correspondence to: D. Aregba-Driollet     

The Thermal Stability of Ciprofloxacin Complexes with Magnesium(II), Zinc(II) and Cobalt(II)

The thermal behaviour of Mg(II), Zn(II) and Co(II) compounds of ciprofloxacin was studied by thermogravimetry (TG) and differential thermal analysis (DTA) in order to determine or to confirm some structural characteristics of substances. The complexes decompose in two steps: dehydration and pyrolytic decomposition of the anhydrous complexes to form metal oxide or metal fluoride. The dehydration process of one magnesium(II) compound takes place in two steps suggesting a marked difference in the bonding of water molecules. The different bonding mode of the ciprofloxacin molecules in both magnesium compounds leads to different residues of the thermal decompositions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Non-linear Sagnac interferometry for pump-probe dispersion spectroscopy

We explore pump-probe non-linear Sagnac interferometry as a tool to measure the dispersive properties of a medium. We introduce the background theory, and show experimental spectra obtained on the D₂ transition with ⁸⁵Rb and ⁸⁷Rb. The measured dispersion spectra are in excellent agreement with the Kramers-Kronig relations. In addition, as both beams traverse identical optical paths, Sagnac interferometry is very robust against mechanical vibrationReceived: 5 June 2003, Published online: 16 September 2003PACS: 39.30. + w Spectroscopic techniques - 33.55.Ad Optical activity, optical rotation; circular dichroismG. Jundt: Present address: Institute of Quantum Electronics, Department of Physics, ETH Zürich, Hönggerberg 8093, Switzerland.     

1-Homogeneous Graphs with Cocktail Party μ-Graphs

Let be a graph with diameter d 2. Recall is 1-homogeneous (in the sense of Nomura) whenever for every edge xy of the distance partition{{z V() | (z, y) = i, (x, z) = j} | 0 i, j d}is equitable and its parameters do not depend on the edge xy. Let be 1-homogeneous. Then is distance-regular and also locally strongly regular with parameters (v,k,,), where v = k, k = a ₁, (v – k – 1) = k(k – 1 – ) and c ₂ + 1, since a -graph is a regular graph with valency . If c ₂ = + 1 and c ₂ 1, then is a Terwilliger graph, i.e., all the -graphs of are complete. In [11] we classified the Terwilliger 1-homogeneous graphs with c ₂ 2 and obtained that there are only three such examples. In this article we consider the case c ₂ = + 2 3, i.e., the case when the -graphs of are the Cocktail Party graphs, and obtain that either = 0, = 2 or is one of the following graphs: (i) a Johnson graph J(2m, m) with m 2, (ii) a folded Johnson graph J¯(4m, 2m) with m 3, (iii) a halved m-cube with m 4, (iv) a folded halved (2m)-cube with m 5, (v) a Cocktail Party graph K _{m × 2} with m 3, (vi) the Schläfli graph, (vii) the Gosset graph.     

nvolutorial Płonka sums

The construction of the sum of a direct (semilattice ordered) system of algebras introduced by J. Plonka – later known as the Plonka sum – is one of the most important methods of composition in universal algebra, having a number of applications in different algebraic theories, such as semigroup theory, semiring theory, etc. In this paper we present a more general way for constructing algebras with involution, that is, algebraic systems equipped with a unary involutorial operation which is at the same time an antiautomorphism of the underlying algebra. It is the sum – involutorial Plonka sum, as we call it – of an involution semilattice ordered system of algebras. We investigate its basic properties, as well as the problem of its subdirect decomposition.     

Spectral Theory of Pauli–Fierz Operators

We study spectral properties of Pauli–Fierz operators which are commonly used to describe the interaction of a small quantum system with a bosonic free field. We give precise estimates of the location and multiplicity of the singular spectrum of such operators. Applications of these estimates, which will be discussed elsewhere, concern spectral and ergodic theory of non-relativistic QED. Our proof has two ingredients: the Feshbach method, which is developed in an abstract framework, and Mourre theory applied to the operator restricted to the sector orthogonal to the vacuum.     

First measurement of the ratio B(t --> Wb)/B(t --> Wq) and associated limit on the Cabibbo-Kobayashi-Maskawa element /V(tb)/

We present the first measurement of the ratio of branching fractions R identical withB(t-->Wb)/B(t-->Wq) from p_p collisions at sqrt[s] = 1.8 TeV. The data set corresponds to 109 pb(-1) of data recorded by the Collider Detector at Fermilab during the 1992-95 Tevatron run. We measure R = 0.94(+0.31)(-0.24)(stat+syst) or R>0.61 (0.56) at 90% (95)% C.L., in agreement with the standard model predictions. This measurement yields a limit on the Cabibbo-Kobayashi-Maskawa quark mixing matrix element /V(tb)/ under the assumption of three generations and unitarity.     

Observation of large CP violation in the neutral B meson system

We present a measurement of the standard model CP violation parameter sin2 phi(1) based on a 29.1 fb(-1) data sample collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. One neutral B meson is fully reconstructed as a J/psi K(S), psi(2S)K(S), chi(c1)K(S), eta(c)K(S), J/psi K(L), or J/psi K(*0) decay and the flavor of the accompanying B meson is identified from its decay products. From the asymmetry in the distribution of the time intervals between the two B meson decay points, we determine sin2 phi(1) = 0.99+/-0.14(stat)+/-0.06(syst). We conclude that we have observed CP violation in the neutral B meson system.     

Nonexistence of some Antipodal Distance-regular Graphs of Diameter Four

We find an inequality involving the eigenvalues of a regular graph; equality holds if and only if the graph is strongly regular. We apply this inequality to the first subconstituents of a distance-regular graph and obtain a simple proof of the fundamental bound for distance-regular graphs, discovered by Juri i , Koolen and Terwilliger. Using this we show that for distance-regular graphs with certain intersection arrays, the first subconstituent graphs are strongly regular. From these results we prove the nonexistence of distance-regular graphs associated to 20 feasible intersection arrays from the book Distance-Regular Graphs by Brouwer, Cohen and Neumaier .