The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Rigidity in holomorphic and quasiregular dynamics

We consider rigidity phenomena for holomorphic functions and then more generally for uniformly quasiregular maps.

     

Precise Coupling Terms in Adiabatic Quantum Evolution

It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems with real-symmetric Hamiltonian we construct such a superadiabatic representation and explicitly determine the asymptotic behavior of the exponentially small coupling term. First order perturbation theory in the superadiabatic representation then allows us to describe the time-development of exponentially small adiabatic transitions. The latter result rigorously confirms the predictions of Sir Michael Berry for our family of Hamiltonians and slightly generalizes a recent mathematical result of George Hagedorn and Alain Joye.submitted 29/06/04, accepted 14/08/04     

Stoßwellenausbreitung in Rohrverzweigungen

Summary The interaction of a shock wave with the junction of a straight duct having a side branch is considered. The paper checks the validity of three hypotheses. The first and second one calculate the shock waves after the junctions only by a geometrical consideration. A comparison with experimental values shows only an unsatisfactory result for weak shock waves. The third theory assumes that the pressure drop across the junction, in the quasi-steady flow which takes place after the incident shock wave, is the same as in steady flow tests. The pressure drops were measured for different junctions and the results of the calculation were compared with experimental values from a shock tube, both for circular and rectangular channels. A good agreement was obtained.     

Characterization of an optical multilayer hydrophone with constant frequency response in the range from 1 to 75 MHz

The performance of an optical multilayer hydrophone for ultrasound measurements is investigated both in theoretical terms and experimentally. The optical measurement system comprises a thin high-finesse dielectric interference filter structure that is deposited onto a plane glass plate. An incident acoustic pressure wave deforms the layer system, and the induced variation of the optical reflectance is determined. Applying the concept of an optical off-axis detection scheme offers good sensitivity and a simple and low-cost setup. A primary interferometric calibration technique is applied to experimentally determine the pressure-voltage transfer function in the range from 1 to 75 MHz. Within the measurement uncertainty a constant transfer factor is obtained for the whole frequency range. Measurements of broadband ultrasound pulses are influenced neither by acoustic resonances of the very thin sensing element nor by diffraction phenomena that are known to cause waveform distortions in small probe hydrophone measurements. High temporal and spatial resolution is combined with high durability of the probe, which is why the optical multilayer hydrophone is well suited for use as a reference for secondary hydrophone calibration.     

A Connes-amenable, dual Banach algebra need not have a normal, virtual diagonal

Let be a locally compact group, and let denote the space of weakly almost periodic functions on . We show that, if is a -group, but not compact, then the dual Banach algebra does not have a normal, virtual diagonal. Consequently, whenever is an amenable, non-compact -group, is an example of a Connes-amenable, dual Banach algebra without a normal, virtual diagonal. On the other hand, there are amenable, non-compact, locally compact groups such that does have a normal, virtual diagonal.

     

The N* physics program at Jefferson Lab

Recent measurements of nucleon resonance transition form factors with CLAS at Jefferson Lab are discussed. The new data confirm the assertion of the symmetric constituent quark model of the Roper as the first radial excitation of the nucleon. The data on high Q2 nπ＋ production better constrain the branching ratios liNK and [3Nn. For the first time, the longitudinal transition amplitude to the S11（1535） was extracted from the nπ＋ data. Also, new results on the transition amplitudes for the D13（1520） resonance are presented showing a rapid transition from helicity 3/2 dominance seen at the real photon point to helicty 1/2 dominance at higher Q2. I also discuss the status of the search for new excited nucleon states.     

Stability Analysis for maxwell’s Equation with a Thermal Effect in one Space Dimension

In this paper we study the asymptotic behavior of a system modeling heating of material by microwaves. Various assumptions have been made, concerning complexity (nonhomogeneous structure) and the two-phase state of the material. The mathematical model includes Maxwell’s and heat–transfer equations. Stability of solutions of the system is shown.     

Uptake mechanism of oppositely charged fluorescent nanoparticles in HeLa cells

The endocytotic mechanisms involved in the uptake of charged polystyrene nanoparticles into HeLa cells were investigated. Uptake experiments were done in the presence or absence of drugs known to inhibit various factors in endocytosis. Independent of the particle charge, endocytosis is highly dependent on dynamin, F-actin, and tyrosine-specific protein kinases, which suggests a dynamin-dependent and lipid raft-dependent mechanism. However, cholesterol depletion did not hinder particle uptake. Regarding positively charged particles, macropinocytosis, the microtubule network, and cyclooxygenases are also involved. The clathrin-dependent pathway plays a minor role.