Dynamical Bounds for Sturmian Schr\"{o}dinger Operators

The Fibonacci Hamiltonian, that is a Schr\"{o}dinger operator associated to a quasiperiodical sturmian potential with respect to the golden mean has been investigated intensively in recent years. Damanik and Tcheremchantsev developed a method and find a non trivial dynamical upper bound for this model. In this paper, we use this method to generalize to a large family of Sturmian operators dynamical upper bounds and show at sufficently large coupling anomalous transport for operators associated to irrational number with a generic diophantine condition. As a counter example, we exhibit a pathological irrational number which do not verify this condition and show its associated dynamic exponent only has ballistic bound. Moreover, we establish a global lower bound for the lower box counting dimension of the spectrum that is used to obtain a dynamical lower bound for bounded density irrational numbers

Spatially resolving the thermally inhomogeneous outer atmosphere of the red giant Arcturus in the 2.3 micron CO lines

The outer atmosphere of K giants shows thermally inhomogeneous structures consisting of the hot chromospheric gas and the cool molecular gas. We present spectro-interferometric observations of the multicomponent outer atmosphere of the well-studied K1.5 giant Arcturus (alpha Boo) in the CO first overtone lines near 2.3 micron. We observed Arcturus with the AMBER instrument at the Very Large Telescope Interferometer (VLTI) at 2.28--2.31 micron with a spectral resolution of 12000 and at projected baselines of 7.3, 14.6, and 21.8 m. The high spectral resolution of the VLTI/AMBER instrument allowed us to spatially resolve Arcturus in the individual CO lines. Comparison of the observed interferometric data with the MARCS photospheric model shows that the star appears to be significantly larger than predicted by the model. It indicates the presence of an extended component that is not accounted for by the current photospheric models for this well-studied star. We found out that the observed AMBER data can be explained by a model with two additional CO layers above the photosphere. The inner CO layer is located just above the photosphere, at 1.04 +/- 0.02 stellar radii, with a temperature of 1600 +/- 400 K and a CO column density of 10^{20 +/- 0.3} cm^-2. On the other hand, the outer CO layer is found to be as extended as to 2.6 +/- 0.2 stellar radii with a temperature of 1800 +/- 100 K and a CO column density of 10^{19 +/- 0.15} cm^-2. The properties of the inner CO layer are in broad agreement with those previously inferred from the spatially unresolved spectroscopic analyses. However, our AMBER observations have revealed that the quasi-static cool molecular component extends out to 2--3 stellar radii, within which region the chromospheric wind steeply accelerates.Comment: 10 pages, 9 figures, accepted for publication in Astronomy and Astrophysic

Kinetic research on heterogeneously catalysed processes: a questionnaire on the state-of-the-art in industry

On the initiative of the Working Party `Chemical Engineering in the Applications of Catalysis¿ of the European Federation of Chemical Engineering an assessment of the issues in the determination and application of kinetic data within the European industry was performed. The basis of the analysis consisted of a questionnaire put together by researchers from Dow, DSM, Shell and Eindhoven University of Technology. The 24 companies, which have responded to the questionnaire, can be classified into four groups: chemical, oil, engineering contractors and catalyst manufacturers. From the overall input it appears that there are three, equally important, utilisation areas for kinetic data: process development, process optimisation and catalyst development. There is a wide variety of kinetic data sources. Most of the respondents make use of test units which were primarily designed for development and optimisation. Avoiding transport limitation is, certainly in the case of short range projects or for complex feedstocks, not always taken care of. With respect to the modelling approaches, a common philosophy is `as simple as possible¿. Most of the respondents state that `in principle¿ one should strive for intrinsic kinetics, but the majority nevertheless does for various reasons not separate all transport phenomena from reaction kinetics. Kinetic models are mostly simple first or nth order or Langmuir-Hinshelwood type expressions. More complex kinetic models are scarcely used. Three areas were frequently identified to offer opportunities for improvement. Gathering of kinetic data is too costly and time consuming. There is no systematic approach at all for determination and application of kinetics in case of unstable catalytic performance. Furthermore, the software available for the regression of kinetic data to rate equations based on mechanistic schemes as well as software to model reactors are insufficiently user friendly. The majority of the respondents state that the problems indicated should be solved by cooperation, e.g., between companies, between industry and academia and between the catalysis and the chemical engineering community. A workshop on the above topics was held in December 1996 with 15 companies and 6 academics attending. More information can be obtained from the secretariat of the Working Party

Wave equation and dispersion relations for a compressible rotating fluid

A fundamental non-classical fourth-order partial differential equation to describe small amplitude linear oscillations in a rotating compressible fluid, is obtained. The dispersion relations for such a fluid, and the different regions of the group and phase velocity are analyzed.Comment: 9 page

3D discrete element modeling of concrete: study of the rolling resistance effects on the macroscopic constitutive behavior

The Discrete Element Method (DEM) is appropriate for modeling granular materials [14] but also cohesive materials as concrete when submitted to a severe loading such an impact leading to fractures or fragmentation in the continuum [1, 5, 6, 8]. Contrarily to granular materials, the macroscopic constitutive behavior of a cohesive material is not directly linked to contact interactions between the rigid Discrete Elements (DE) and interaction laws are then defined between DE surrounding each DE. Spherical DE are used because the contact detection is easy to implement and the computation time is reduced in comparison with the use of 3D DE with a more complex shape. The element size is variable and the assembly is disordered to prevent preferential cleavage planes. The purpose of this paper is to highlight the influence of DE rotations on the macroscopic non-linear quasi-static behavior of concrete. Classically, the interactions between DE are modeled by spring-like interactions based on displacements and rotation velocities of DE are only controlled by tangential forces perpendicular to the line linking the two sphere centroids. The disadvantage of this modeling with only spring-like interactions based on displacements is that excessive rolling occurs under shear, therefore the macroscopic behavior of concrete is too brittle. To overcome this problem a non linear Moment Transfer Law (MTL) is introduced to add a rolling resistance to elements. This solution has no influence on the calculation cost and allows a more accurate macroscopic representation of concrete behavior. The identification process of material parameters is given and simulations of tests performed on concrete samples are shown

Power in the Multinational Corporation in Industry Equilibrium

Recent theories of the multinational corporation introduce the property rights model of the firm and examine whether to integrate our outsource firm activities locally or to a foreign country. This paper focus instead on the internal organization of the multinational corporation by examining the power allocation between headquarters and subsidiaries. We provide a framework to analyse the interaction between the decision to serve the local market by exporting or FDI, market acces and the optimal mode of organization of the multinational corporation. We find that subsidiary managers are given most autonomy in their decision how to run the firm at intermediate levels of local competition. We then provide comparative statics for changes in fixed FDI entry costs and trade costs, information technology, the number of local competitors, and in the size of the local market