Time-resolved investigations of singlet oxygen luminescence in water, in phosphatidylcholine, and in aqueous suspensions of phosphatidylcholine or HT29 cells

Singlet oxygen was generated by energy transfer from the photoexcited sensitizer, Photofrin or 9-acetoxy-2,7,12,17-tetrakis-(beta-methoxyethyl)-porphycene (ATMPn), to molecular oxygen. Singlet oxygen was detected time-resolved by its luminescence at 1270 nm in an environment of increasing complexity, water (H2O), pure phosphatidylcholine, phosphatidylcholine in water (lipid suspensions), and aqueous suspensions of living cells. In the case of the lipid suspensions, the sensitizers accumulated in the lipids, whereas the localizations in the cells are the membranes containing phosphatidylcholine. By use of Photofrin, the measured luminescence decay times of singlet oxygen were 3.5 +/- 0.5 micros in water, 14 +/- 2 micros in lipid, 9 +/- 2 micros in aqueous suspensions of lipid droplets, and 10 +/- 3 micros in aqueous suspensions of human colonic cancer cells (HT29). The decay time in cell suspensions was much longer than in water and was comparable to the value in suspensions of phosphatidylcholine. That luminescence signal might be attributed to singlet oxygen decaying in the lipid areas of cellular membranes. The measured luminescence decay times of singlet oxygen excited by ATMPn in pure lipid and lipid suspensions were the same within the experimental error as for Photofrin. In contrast to experiments with Photofrin, the decay time in aqueous suspension of HT29 cells was 6 +/- 2 micros when using ATMPn.     

A combined boundary value and transmission problem arising from the calculation of eddy currents: Well-posedness and numerical treatment

The problem of calculating eddy current losses is formulated as a boundary value and transmission problem for a complex Helmholtz equation and Laplace's equation. By deriving an equivalent system of integral equations, we show the existence of a unique solution depending continuously on the data. Furthermore, we propose a numerical method based on decomposing the problem into two boundary value problems, where part of the boundary values have to be determined by a system of linear equations.

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Zusammenfassung Das Problem der Berechnung von Wirbelstromverlusten wird als Randwert- und Übergangsproblem für eine komplexe Helmholtz- und die Laplacegleichung formuliert. Wir führen dieses Problem in ein äquivalentes Integralgleichungssystem über und zeigen die Existenz einer eindeutigen, stetig von den Daten abhängenden Lösung. Weiter schlagen wir eine numerische Lösungsmethode vor, die auf der Dekomposition des Problems in zwei Randwertprobleme beruht, wobei ein Teil der Randwerte durch ein lineares Gleichungssystem zu bestimmen ist.

     

Selection of two-phase flow patterns at a simple junction in microfluidic devices

We study the behavior of a confined stream made of two immiscible fluids when it reaches a T junction. Two flow patterns are witnessed: the stream is either directed in only one sidearm, yielding a preferential flow pathway for the dispersed phase, or splits between both. We show that the selection of these patterns is not triggered by the shape of the junction nor by capillary effects, but results from confinement. It can be anticipated in terms of the hydrodynamic properties of the flow. A simple model yielding universal behavior in terms of the relevant adimensional parameters of the problem is presented and discussed.     

Turning a Coin over Instead of Tossing It

Given a sequence of numbers \((p_n)_{n\ge 2}\) in [0, 1], consider the following experiment. First, we flip a fair coin and then, at step n, we turn the coin over to the other side with probability \(p_n\), \(n\ge 2\), independently of the sequence of the previous terms. What can we say about the distribution of the empirical frequency of heads as \(n\rightarrow \infty \)? We show that a number of phase transitions take place as the turning gets slower (i. e., \(p_n\) is getting smaller), leading first to the breakdown of the Central Limit Theorem and then to that of the Law of Large Numbers. It turns out that the critical regime is \(p_n=\text {const}/n\). Among the scaling limits, we obtain uniform, Gaussian, semicircle, and arcsine laws.     

Catalytic Asymmetric Synthesis of α‐Arylpyrrolidines and Benzo‐fused Nitrogen Heterocycles

Herein, we report a practical two‐step synthetic route to α‐arylpyrrolidines through Suzuki–Miyaura cross‐coupling and enantioselective copper‐catalyzed intramolecular hydroamination reactions. The excellent stereoselectivity and broad scope for the transformation of substrates with pharmaceutically relevant heteroarenes render this method a practical and versatile approach for pyrrolidine synthesis. Additionally, this intramolecular hydroamination strategy facilitates the asymmetric synthesis of tetrahydroisoquinolines and medium‐ring dibenzo‐fused nitrogen heterocycles.     

Inverse problems related to ion channels

Ion channels are proteins with a hole down theirmiddle that allow ions to move across otherwise impermeable cellmembranes, thereby controlling many important physiological functions. The transport process of the ions can be described using the Poisson-Nernst-Plank equations, a system of coupled nonlinear partial differential equations. Based on this model we derive a simplified surrogate model that captures the main features of the associated current-voltage curves of the ion channel. This surrogate model is then used to identify individual channel parameters based on current data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)