Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

Measurement of the K α to L α and K β to L β intensity ratios of seven elements in the atomic number range 52≤ Z ≤62 using photoionization at 59.5 keV1

The Kα to Lα and Kβ to Lβ intensity ratios of seven elements have been measured following photoionization at 59.5 keV by using a Si (Li) detector (FWHM=155 eV at 5.96 keV). The intensity ratios were determined by measuring K and L x-rays emitted from a standard target of a given element. The theoretical values of the Kα to Lα and Kβ to Lβ intensity ratios were calculated using theoretically tabulated values of shell/subshell photoionization cross sections, fluorescence yields, Coster-Kronig transition probabilities, and radiative decay rates for ηKLi≠ and ηKLi=0. The measured values are in good agreement with theoretical results. From Optika i Spektroskopiya, Vol. 97, No. 2, 2004, pp. 186–189. Original English Text Copyright ? 2004 by A. Kü?ük?nder, S?ğüt, E. Kü?ük?nder, Büyükkasap. This article was submitted by the authors in English.     

Rotational temperature and density measurements in a hypersonic flow by dual-line CARS

Rotational temperature and nitrogen number density are measured in the shock wave/boundary layer interaction region in the vicinity of a two-dimensional compression corner disposed in a low pressure, 55 K, Mach 10 hypersonic air flow. Spatially-resolved data are recorded using a nonlinear optical technique named dual-line coherent anti-Stokes Raman scattering (DLCARS). Averaged temperature and density profiles are compared with those predicted by a Navier-Stokes solver. Good agreement is found.     

Fejér means of functions on noncommutative Vilenkin groups with respect to the character system

Summary It is known that the Fejér means - with respect to the character system of the Walsh, and bounded Vilenkin groups - of an integrable function converge to the function a.e. In this work we discuss analogous problems on the complete product of finite, not necessarily Abelian groups with respect to the character system for functions that are constant on the conjugacy classes. We find that the nonabelian case differs from the commutative case. We prove the a.e. convergence of the (C,1) means of the Fourier series of square integrable functions. We also prove the existence of a function f∊L^q for some q >1 such that sup |σ_n f | = + ∞ a.e. This is a sharp contrast between the Abelian and the nonabelian cases.     

A high-current electron beam ion trap as an on-line charge breeder for the high precision mass measurement TITAN experiment

The precision of atomic mass measurements in a Penning trap is directly proportional to the charge state q of the ion and, hence, can be increased by using highly charged ions (HCI). For this reason, charge breeding with an electron beam ion trap (EBIT) is employed at TRIUMF’s Ion Trap for Atomic and Nuclear science (TITAN) on-line facility in Vancouver, Canada. By bombarding the injected and trapped singly charged ions with an intense beam of electrons, the charge state of the ions is rapidly increased inside the EBIT. To be compatible with the on-line requirements of short-lived isotopes, very high electron beam current densities are needed. The TITAN EBIT includes a 6 Tesla superconducting magnet and is designed to have electron beam currents and energies of up to 5 A and 60 keV, respectively. Once operational at full capacity, most species can be bred into a He-like configuration within tens of ms. Subsequently, the HCI are extracted, pass a Wien filter to reduce isobaric contamination, are cooled, and injected into a precision Penning trap for mass measurement. We will present the first results and current status of the TITAN EBIT, which has recently been moved to TRIUMF after assembly and commissioning at the Max-Planck-Institute (MPI) for Nuclear Physics in Heidelberg, Germany.     

Closure laws for a two-fluid two-pressure modelLois de fermeture pour un modèle à deux pressions d'écoulement diphasique

Closure laws for interfacial pressure and interfacial velocity are proposed within the frame work of two-pressure two-phase flow models. These enable us to ensure positivity of void fractions, mass fractions and internal energies when investigating field by field waves in the Riemann problem. To cite this article: F. Coquel et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 927–932.     

On a class of elliptic operators with nonpolynomial degeneracy on a boundary

Rostov-on-Don. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 33, No. 5, pp. 91–99, September–October, 1992.     

Analysis of some combination-overtone infrared bands of SO3

Several new infrared absorption bands for ³²S¹⁶O₃ have been measured and analyzed. The principal bands observed were ν₁+ν₂ (at 1561 cm⁻¹), ν₁+ν₄ (at 1594 cm⁻¹), ν₃+ν₄ (at 1918 cm⁻¹), and 3ν₃ (at 4136 cm⁻¹). Except for 3ν₃, these bands are very complicated because of (a) the Coriolis coupling between ν₂ and ν₄, (b) the Fermi resonance between ν₁ and 2ν₄, (c) the Fermi resonance between ν₁ and 2ν₂, (d) ordinary l-type resonance that couples levels that differ by 2 in both the k and l quantum numbers, and (e) the vibrational l-type resonance between the A₁^′ and A₂^′ levels of ν₃+ν₄. The unraveling of the complex pattern of these bands was facilitated by a systematic approach to the understanding of the various interactions. Fortunately, previous work on the fundamentals permitted good estimates of many constants necessary to begin the assignments and the fit of the measurements. In addition, the use of hot band transitions accompanying the ν₃ band was an essential aid in fitting the ν₃+ν₄ transitions since these could be directly observed for only one of four interacting states. From the hot band analysis we find that the A₁^′ vibrational level is 3.50 cm⁻¹ above the A₂^′ level, i.e., r₃₄=1.75236(7) cm⁻¹. In the case of the 3ν₃ band, the spectral analysis is straightforward and a weak Δk=±2, Δl₃=±2 interaction between the l₃=1 and l₃=3 substates locates the latter A₁^′ and A₂^′ “ghost” states 22.55(4) cm⁻¹ higher than the infrared accessible l₃=1 E^′ state.