Suppression of complex fingerlike patterns at the interface between air and a viscous fluid by elastic membranes

Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluid-structure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyze the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behavior.     

First measurements with the neutron decay spectrometer a SPECT

The neutron decay spectrometera SPECT has been built to perform a precise measurement of the proton spectrum shape in the decay of free neutrons. Such a measurement allows a determination of the neutrino electron angular-correlation coefficienta . The present best experiments have an uncertainty of Δa/a = 5% and since the seventies there is no substantial improvement. Witha SPECT, we aim for an uncertainty which is lower by more than an order of magnitude, thus enabling us to perform several precise tests of the Standard Model. In our first beam time at the particle physics beam MEPHISTO at the Forschungsneutronenquelle Heinz Maier-Leibnitz, we studied the properties of the spectrometer. The most serious problem turned out to be the situation- and time-dependent behavior of the background. From the data sets from this beam time in which a background problem was not obvious, we could extract a value ofa = - 0.1151±0.0040^stat , but we could not quantify the background uncertainty. We show ways to deal with the background and other problems for future beam times.     

Kinetic two-dimensional modeling of inductively coupled plasmasbased on a hybrid kinetic approach

In this paper, we present a two-dimensional (2-D) kinetic model for low-pressure inductively coupled discharges. The kinetic treatment of the plasma electrons is based on a hybrid kinetic scheme in which the range of electron energies is divided into two subdomains. In the low energy range the electron distribution function is determined from the traditional nonlocal approximation. In the high energy part the complete spatially dependent Boltzmann equation is solved. The scheme provides computational efficiency and enables inclusion of electron-electron collisions which are important in low-pressure high-density plasmas. The self-consistent scheme is complemented by a 2-D fluid model for the ions and the solution of the complex wave equation for the RF electric field. Results of this model are compared to experimental results. Good agreement in terms of plasma density and potential profiles is observed. In particular, the model is capable of reproducing the transition from on-axis to off-axis peaked density profiles as observed in experiments which underlines the significant improvements compared to models purely based on the traditional nonlocal approximation     

Determination of the neutron electric form factor in the D(e,e′n)p reaction and the influence of nuclear binding

The electric form factor of the neutron G _E,n has been determined at the Mainz Microtron MAMI at the low momentum transfer Q ²= 0.15 (GeV/c)² in a measurement of the recoil polarisation ratio P _x/P_z in the quasifree reaction D(e,e′n)p. At this Q ² the influence of the nuclear binding is strong. A purely kinematical model is used to get some insight into the effect of the initial Fermi momentum distribution of the neutron. The influence of the final state interaction is determined quantitatively by a model of Arenh?vel et al.. After the corresponding corrections a value of G _E,n(0.15 (GeV/c)²) = 0.0481±0.0065_stat±0.0053_syst is obtained. Received: 12 April 1999     

Structure of the space of reducible connections for Yang-Mills theories

The geometrical structure of the gauge equivalence classes of reducible connections are investigated. The general procedure to determine the set of orbit types (strata) generated by the action of the gauge group on the space of gauge potentials is given. In the so obtained classification, a stratum, containing generically certain reducible connections, corresponds to a class of isomorphic subbundles given by an orbit of the structure and gauge group. The structure of every stratum is completely clarified. A nonmain stratum can be understood in terms of the main stratum corresponding to a stratification at the level of a subbundle.     

Existenz eines 6-Normalenpunktes in einem konvexen Körper

Ohne Zusammenfassung     

Differentiation and the Balian-Low Theorem

The Balian-Low theorem (BLT) is a key result in time-frequency analysis, originally stated by Balian and, independently, by Low, as: If a Gabor system $\{e^{2\pi imbt} \, g(t-na)\}_{m,n \in \mbox{\bf Z}}$ with $ab=1$ forms an orthonormal basis for $L^2({\bf R}),$ then $\left(\int_{-\infty}^\infty |t \, g(t)|^2 \, dt\right) \, \left(\int_{-\infty}^\infty |\gamma \, \hat g(\gamma)|^2 \, d\gamma\right) = +\infty.$ The BLT was later extended from orthonormal bases to exact frames. This paper presents a tutorial on Gabor systems, the BLT, and related topics, such as the Zak transform and Wilson bases. Because of the fact that $(g')^{\wedge}(\gamma) = 2 \pi i \gamma \, \hat g(\gamma)$ , the role of differentiation in the proof of the BLT is examined carefully. The major new contributions of this paper are the construction of a complete Gabor system of the form $\{e^{2\pi ib_mt\} \, g(t-a_n)}$ such that $\{(a_n,b_m)\}$ has density strictly less than 1, an Amalgam BLT that provides distinct restrictions on Gabor systems $\{e^{2\pi imbt} \, g(t-na)\}$ that form exact frames, and a new proof of the BLT for exact frames that does not require differentiation and relies only on classical real variable methods from harmonic analysis.     

1,4:3,6-dianhydro-2,5-dideoxy-2,5-bis(diphenylphosphino)-l-iditol. A new chiral ligand for asymmetric hydrogenation with rhodium complexes as catalysts

A new chiral 1,4-diphosphine, 1,4:3,6-dianhydro-2,5-dideoxy-2,5-bis(diphenylphosphino)-l-iditol, has been prepared from d-mannitol. Rhodium complexes of this ligand are asymmetric homogeneous hydrogenation catalysts for dehydroamino acids, giving (S)-amino acids in 21–58% optical yields.