Imaging of tautomerism in a single molecule

Fluorescence imaging is used to visualize directly the transfer of two inner hydrogen atoms in single porphycene molecules. This reaction leads to a chemically equivalent but differently oriented structure and hence results in a rotation of the transition dipole moments. By probing single immobilized molecules with an azimuthally polarized laser beam in the focal spot of a confocal microscope we observe ring-like emission patterns, possible only for a chromophore with two nearly orthogonal transition dipole moments. Numerical simulations of the observed emission patterns yield a value of 72 degrees for the angle between the S0-S1 transition moments in the two tautomeric forms.     

Pathwise Convergence of a Rescaled Super-Brownian Catalyst Reactant Process

Consider the one-dimensional catalytic super-Brownian motion X (called the reactant) in the catalytic medium which is an autonomous classical super-Brownian motion. We characterize both in terms of a martingale problem and (in dimension one) as solution of a certain stochastic partial differential equation. The focus of this paper is for dimension one the analysis of the longtime behavior via a mass-time-space rescaling. When scaling time by a factor of K, space is scaled by K ^η and mass by K ^−η. We show that for every parameter value η ≥ 0 the rescaled processes converge as K→ ∞ in path space. While the catalyst’s limiting process exhibits a phase transition at η = 1, the reactant’s limit is always the same degenerate process.      

The role of energy density and acoustic cavitation in shock wave lithotripsy

Today a high percentage of urinary stones are successfully treated by extracorporeal shockwave lithotripsy (SWL); however, misconceptions regarding fragmentation mechanisms, as well as treatment parameters like dose, applied energy and focal area are still common. A main stone comminution mechanism during SWL is acoustic cavitation. The objective of this study was to analyze the influence of cavitation and energy density on stone fragmentation. A research lithotripter was used to expose a large set of artificial kidney stones to shock waves varying different parameters. Hundreds of pressure records were used to calculate the energy density of the lithotripter at different settings. Results indicate that energy density is a crucial parameter and that better SWL treatment outcomes could be obtained placing the calculus at a prefocal position.     

Information theory, spectral geometry, and quantum gravity

We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well-known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.