A note on instabilities of a Kelvin-Helmholtz velocity profile in different approximations

Summary The Kelvin-Helmholtz problem deals with the stability of superposed fluids in relative motion. For a basic discontinuity in the velocity of 2U and a constant Brunt-V?is?l? frequencyN it has been found that in the Boussinesq approximation small perturbations with a horizontal wavenumberk, such thatk ²>N ²/2U ², are unstable. When the fluid is assumed to be compressible and taking into account the variation of the density in all the equations we find that there are also instabilities fork ²<N ²/2U ². However, the growth rate of these instabilities is small. The horizontal phase velocities of the instabilities are also different from those obtained in the Boussinesq approximation. But again the difference is small. On the other hand, in the hydrostatic approximation, which takes into account the compressibility too, all instabilities disappear.     

Banach space representations and Iwasawa theory

We develop a duality theory between the continuous representations of a compactp-adic Lie groupG in Banach spaces over a givenp-adic fieldK and certain compact modules over the completed group ringo _K[[G]]. We then introduce a “finiteness” condition for Banach space representations called admissibility. It will be shown that under this duality admissibility corresponds to finite generation over the ringK[[G]]: =K ⊗o _K[[G]]. Since this latter ring is noetherian it follows that the admissible representations ofG form an abelian category. We conclude by analyzing the irreducibility properties of the continuous principal series of the groupG: = GL₂(ℤ _p ).     

On the critical dynamics of spin-glasses

The dynamic scaling of the spin-glass model, proposed by Edwards and Anderson, is studied. The dynamic critical exponents are calculated at the freezing point and at the tricritical point. The coupling of the order parameter with propagating excitations is considered.     

Enhanced two-photon fluorescence excitation by resonant grating waveguide structures

Enhanced two-photon fluorescence (TPF) spectroscopy with novel high-finesse resonant polymeric grating waveguide structures (GWSs) is presented. Under resonant conditions the field enhancement at the surface of a GWS can be exploited for TPF spectroscopy without the need for highly focused laser excitation light. We compare the TPF obtained by placing a drop of tetramethylrhodamine (TMR) on top of a GWS with that obtained with TMR on top of a glass substrate. Our procedure and results indicate that the detection of TPF can be improved by a factor of 10 with resonant GWSs.     

Selenige S?ure als neues spezifisches Reagens zur Bestimmung und Trennung von Wismut und Titan

Ohne Zusammenfassung     

Preferential concentration of heavy particles in turbulence

Particle-laden flows are of relevant interest in many industrial and natural systems. When the carrier flow is turbulent, a striking feature is the phenomenon called preferential concentration: particles denser than the fluid have the tendency to inhomogeneously distribute in space, forming clusters and depleted regions. We present an investigation of clustering of small water droplets in homogeneous and isotropic active-grid-generated turbulence. We investigate the effect of Reynolds number (R_λ) and Stokes number (St) on particles clustering in the range R_λ ～ 200?400 and St ～ 2?10. Using Voronoï diagrams, we characterise clustering level and cluster properties (geometry, typical dimension and fractality). The exact same Voronoï analysis is then applied to investigate clustering properties of specific topological points of the velocity field of homogeneous isotropic turbulence obtained from direct numerical simulations at R_λ ～ 220 and 300. The goal is to compare clustering properties of actual particles with those of such points in order to explore the relevance of possible clustering mechanisms, including centrifugal effects (heavy particles sampling preferentially low-vorticity regions) and sweep-stick mechanisms (heavy particles preferentially sticking to low-acceleration points). Our study points towards a leading role of zero-acceleration points and sweep-stick effects, at least for the experimental conditions considered in this study.     

Phase transitions far from thermal equilibrium in spin systems

The nonlinear effects in the spin resonance due to the negative differential r.f. magnetic susceptibility are considered. The r.f. magnetization is shown to exhibite a kind of first order phase transition. A set of scaling relations, valid near the appropriate critical point, is obtained.     

TMA characterization of urethane elastomers,with the structure varying from chain to network

TMA has been used to investigate the thermomechanical behaviour of six series of elastomers in connection with their chemical constitution and physical structure. The elastomers, were synthesized from an NCO-terminal pre-polymer, based on oligo (ethylene adipate), 1,4-butanediol and 2,4-toluylene diisocyanate, by curing with systems of two agents: a bifunctional one (1,4-butanediol, bistethylene glycol)terephthalate, or monoethanolamine), and a trifunctional one (1,1,1-trimethylolpropane or diethanolamine). The TMA results are presented as due to the superposition of the chemical cross-linking and the physical network, formed through microphase segregation. The TMA suggests that diethanolamine unexpectedly acts as a chain extender, rather than a cross-linking agent.     

Calculation of the rate constant for state-selected recombination of H+O2(nu) as a function of temperature and pressure

Classical trajectory calculations using the MERCURY/VENUS code have been carried out on the H+O(2) reactive system using the DMBE-IV potential energy surface. The vibrational quantum number and the temperature were selected over the ranges nu=0 to 15, and T=300 to 10 000 K, respectively. All other variables were averaged. Rate constants were determined for the energy transfer process, H+O(2)(nu)-->H+O(2)(nu(")), for the bimolecular exchange process, H+O(2)(nu)-->OH(nu('))+O, and for the dissociative process, H+O(2)(nu)-->H+O+O. The dissociative process appears to be a mere extension of the process of transferring large amounts of energy. State-to-state rate constants are given for the exchange reaction, and they are in reasonable agreement with previous results, while the energy transfer and dissociative rate constants have never been reported previously. The lifetime distributions of the HO(2) complex, calculated as a function of v and temperature, were used as a basis for determining the relative contributions of various vibrational states of O(2) to the thermal rate coefficients for recombination at various pressures. This novel approach, based on the complex's ability to survive until it collides in a secondary process with an inert gas, is used here for the first time. Complete falloff curves for the recombination of H+O(2) are also calculated over a wide range of temperatures and pressures. The combination of the two separate studies results in pressure- and temperature-dependent rate constants for H+O(2)(nu)(+Ar) right arrow over left arrow HO(2)(+Ar). It is found that, unlike the exchange reaction, vibrational and rotational-translational energy are liabilities in promoting recombination.     

Bestimmung und Trennung des Titans mit Hilfe von o-Oxyehinolin

Ohne Zusammenfassung