Billiard in a barrel

Orbits in the three-dimensional billiard of the form of a truncated ellipsoid ("barrel") are studied both analytically and numerically. A special form of mapping is proposed to get the expression for Kolmogorov-Sinai entropy, and the transition from strong chaos to weak chaos is obtained.     

Intracellular localization of meso-tetraphenylporphine tetrasulphonate probed by time-resolved and microscopic fluorescence spectroscopy.

The effects of solvent pH on spectral properties and fluorescence decay kinetics were investigated in order to characterize the microenvironment of meso-tetraphenylporphine tetrasulphonate (TPPS4) taken up by cells. Steady-state absorption and fluorescence spectra of TPPS4 in buffer solutions of different pH were used to identify a ring protonated species at pH less than or equal to 4. This dictation could also be distinguished from the unprotonated form by its altered fluorescence decay time (3.5 vs. 11.4 ns). In addition, time-resolved spectroscopy gave some evidence of a monocationic species existing at pH 6-9. This was concluded from the occurrence of another component with a decay time of 5 ns. Measurements of the spectral and kinetic properties of the fluorescence emission of single epithelial cells (RR1022) incubated with TPPS4 indicated that the sensitizer was mainly localized in a microenvironment with a pH of 5, a value which occurs intracellularly only within lysosomes. Cells kept in the dark exhibited the characteristic spectra of both the dication and the neutral form. The fluorescence decay showed two components with decay times of 2.6 ns and 10.6 ns. Irradiation of the cells changed the decay times to 4.6 ns and 13.4 ns and the dication fluorescence emission peak vanished, which is in accordance with the results obtained from buffer solutions at pH greater than or equal to 6. Therefore, we deduce that the photodynamic action leads to a rupture of the lysosomes and that the sensitizer is released into the surrounding cytoplasm.     

Compact fibre-laser-pumped Ho:YLF oscillator–amplifier system

We developed a compact Ho:YLF oscillator–amplifier system in a novel setup to utilise the unpolarised pump power from a fibre laser efficiently, and produced 21.3 mJ at 1 kHz, with an M ² better than 1.1. The amplified energies agreed well with the predicted values from a two dimensional rotational symmetric amplifier model that we developed. The model considers upconversion losses and ground-state depletion, as well as the spatial distribution of the pump beam.     

Description of Unstable Systems in Relativistic Quantum Mechanics in the Lax-Phillips Theory

We discuss some of the experimental motivation for the need for semigroup decay laws and the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and, therefore, all physical properties of the resonant states can be computed. We show that the parametrized relativistic quantum theory is a natural setting for the realization of the Lax-Phillips theory.     

Direct dark matter search with CRESST and EURECA

The current status of the direct Dark Matter experiments CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) and the planned EURECA (European Underground Rare Event Calorimeter Array) is presented. Both experiments are aimed at the direct detection of WIMPs (Weakly Interacting Massive Particles), potential candidates for the Dark Matter in the universe. New design developments of the cryogenic detectors operated at mK temperatures are investigated to optimize detector performance and to simplify mass production. Thus, CRESST is also providing a basis for the EURECA project, aimed at a ton of cryogenic detectors with a multi-material target.     

Absence of shocks in an initially dilute collisionless plasma

The Cauchy Problem for the relativistic Vlasov-Maxwell equations is studied in three space dimensions. It is assumed that the initial data satisfy the required constraints and have compact support. If in addition the data have sufficiently smallC ² norm, then a uniqueC ¹ solution to this system is shown to exist on all of spacetime.Research supported in part by NSF DMS 85-20662 and NSF DMS 84-20957     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

Instability of nonlinear bound states

We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,u _tt–u+f(u)=0, and the nonlinear Schrödinger equation, –iu _t–u+f(u)=0.Supported in part by NSF Grants MCS 81-21487 and MCS 82-01599