Kinetic Models for Chemotaxis and their Drift-Diffusion Limits

Kinetic models for chemotaxis, nonlinearly coupled to a Poisson equation for the chemo-attractant density, are considered. Under suitable assumptions on the turning kernel (including models introduced by Othmer, Dunbar and Alt), convergence in the macroscopic limit to a drift-diffusion model is proven. The drift-diffusion models derived in this way include the classical Keller-Segel model. Furthermore, sufficient conditions for kinetic models are given such that finite-time-blow-up does not occur. Examples are given satisfying these conditions, whereas the macroscopic limit problem is known to exhibit finite-time-blow-up. The main analytical tools are entropy techniques for the macroscopic limit as well as results from potential theory for the control of the chemo-attractant density.Present address: Centro de Matemática e Aplicações Fundamentais, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003, Lisboa, Portugal     

Hot electron transport in semiconductors

A recently derived model for stationary flow of energy and charge carriers in semiconductors—consisting of a coupled system of nonlinear elliptic equations—is analysed by the methods of singular perturbation theory. This analysis reveals the solution structure and justifies a modified version of the standard drift-diffusion approximation for charge carrier flow.

---

Zusammenfassung Ein kürzlich hergeleitetes Modell für stationären Energie- und Ladungsträgerfluß in Halbleitern—bestehend aus einem gekoppelten System von nichtlinearen elliptischen Gleichungen—wird mit Methoden der singulären Störungstheorie analysiert. Daraus ergeben sich Aussagen über die Lösungsstruktur und eine Rechtfertigung einer modifizierten Version der klassischen Konvektions-Diffusions-Approximation für den Ladungsträgerfluß.

---

---

The work of the second author was supported by Österreichischer Fonds zur Förderung der wissenschaftlichen Forschung.     

Small angle X-ray scattering from lamellar phase for β-3,7-dimethyloctylglucoside/water system: comparison with β-n-alkylglucosides

Small angle X-ray scattering (SAXS) is measured for the lamellar phase in aqueous systems of 1-o-β-3,7-dimethyoctyl-D-glucopyranoside (β-Glc(Ger)), which has recently been prepared by us, 1-o-β-decyl-D-glucopyranoside (β-GlcC₁₀), and 1-o-β-octyl-D-glucopyranoside (β-GlcC₈). The repeat distance d obtained from the position of the diffraction peak does not follow the swelling law d = 2δ_hc/_hc, where δ_hc and _hc are the thickness and the volume fraction of the hydrophobic layer, respectively. This may result from the fact that δ_hc increases and, equivalently, the surface area per surfactant molecule (a_s) decreases with increasing concentration. So we calculate δ_hc and a_s from the observed d value at each concentration using the above swelling law. The half-thickness δ_hc increases in the order β-GlcC₈ < β-Glc(Ger) < β-GlcC₁₀ at a fixed concentration. On the other hand, the data on a_s for β-GlcC₁₀ and β-GlcC₈ lie on the same line and the data for β-Glc(Ger) lies above this line. These results suggest that the cross-sectional area of the geranyl chain is larger than that of the glucose headgroup. Existence of water filled defects in bilayer sheets is also discussed based on the SAXS pattern and the concentration dependence of d.     

Aqueous phase behavior of a 1-O-phytanyl-beta-D-xyloside/water system. Glycolipid-based bicontinuous cubic phases of crystallographic space groups Pn3m and Ia3d

Temperature- and concentration-dependent aqueous phase diagram of a novel alkylglycoside, 1-O-phytanyl-beta-D-xyloside (beta-Xyl(Phyt)), was studied using small-angle X-ray scattering, polarizing optical microscopy, and differential scanning calorimetry. The phases found in this system include an Lc phase, an Lalpha phase, an HII phase, two inverted cubic phases of crystallographic space groups Pn3m and Ia3d, and a fluid isotropic phase, FI. The phase diagram of the beta-Xyl(Phyt)/water system is similar to that for the 1-monooleylglycerol (MO)/water system, suggesting that the phase behavior is largely determined by the overall molecular shape rather than the details of surfactant molecular structure. Moreover, the structural parameters of the beta-Xyl(Phyt) liquid crystals are also similar to those of the MO/water, due primarily to the similar molecular dimensions of two molecules. As compared to the MO/water system, however, the beta-Xyl(Phyt)/water system displays a lower value of TK ( approximately 8.(5) degrees C) and a wider temperature window for the mesophases (8.(5)-120 degrees C). Moreover, beta-Xyl(Phyt) is chemically more robust than MO, as the ether linkage is more stable against hydrolysis than the ester linkage and the phytanyl chain is fully saturated.     

The transient behaviour of multidimensional PN-diodes in low injection

An initial boundary value problem modelling the transient behaviour of a pn-junction semiconductor diode is simplified by formal asymptotics, where the scaled minimal Debye length and the scaled intrinsic number are considered as small parameters. The implicit assumption on the biasing situation is that of low injection. The simplified model is shown to be equivalent to an integral relation between the evolution of the current and of the contact voltage. A simple switching application is governed by a non-linear Volterra integral equation for the current. This equation is shown to possess a unique solution globally in time converging to the unique steady state.     

Total nucleotide analysis of Hydra DNA and RNA by MEKC with LIF detection and 32P‐postlabeling

The model organism Hydra has been used for molecular studies for more than 20 years, however, its DNA base composition has not been determined yet. We have analyzed DNA and total RNA of the freshwater polyp Hydra magnipapillata with two independent procedures of high accuracy and sensitivity – fluorescence labeling of nucleotides followed by CE‐LIF detection and ³²P‐postlabeling. DNA of Hydra was digested either to deoxyribonucleoside‐5′‐monophosphates or deoxyribonucleoside‐3′‐monophosphates selectively conjugated with the fluorescent dye 4,4‐difluoro‐5,7‐dimethyl‐4‐bora‐3a,4a‐diaza‐s‐indacene‐3‐propionyl ethylene diamine hydrochloride (BODIPY FL EDA) separated and detected using CE‐LIF. Both versions of the assay revealed a high A+T composition of 78 and 71%, whereas total DNA methylation (5‐methyldeoxycytidine) was 2.6 and 3.1%. Total Hydra RNA showed highest base levels for guanine (33%) and a level of 1.4% for pseudouracil. All values were in good agreement with those determined by the ³²P‐postlabeling method.