Nonlinear Instability of the Two-Dimensional Striation Model About Smooth Steady States

The two-dimensional striation model consists of a nonlinear system of PDE's which arises in the modeling of the ionospheric plasma. The local-in-time existence of strong solutions is first proved using Banach's fixed point theorem. Then, under physically relevant assumptions, the system is shown to be nonlinearly unstable as soon as it is linearly unstable. Moreover, the instability occurs before the possible blow-up time of the solution. The proof relies on an earlier work of Hwang and Guo (2003 Hwang , H. J. , Guo , Y. ( 2003 ). On the dynamical Rayleigh–Taylor instability . Arch. of Rat. Mech. Anal. 167 : 235 – 253 .[Crossref], [Web of Science ®] , [Google Scholar]). The first step of the proof is to investigate under which conditions the linearized system is unstable and to prove that its spectrum is bounded, by means of a variational formulation. The second one consists in constructing a family of solutions depending on the parameter δ measuring the smallness of the perturbation to the steady-state. Thanks to the boundedness of the linearized spectrum, this family of solutions is shown to be unstable by means of a power series expansion in δ.     

Synthesis, characterization, and metal coordinating ability of multifunctional carbohydrate-containing compounds for Alzheimer's therapy

Dysfunctional interactions of metal ions, especially Cu, Zn, and Fe, with the amyloid-beta (A beta) peptide are hypothesized to play an important role in the etiology of Alzheimer's disease (AD). In addition to direct effects on A beta aggregation, both Cu and Fe catalyze the generation of reactive oxygen species (ROS) in the brain further contributing to neurodegeneration. Disruption of these aberrant metal-peptide interactions via chelation therapy holds considerable promise as a therapeutic strategy to combat this presently incurable disease. To this end, we developed two multifunctional carbohydrate-containing compounds N,N'-bis[(5-beta-D-glucopyranosyloxy-2-hydroxy)benzyl]-N,N'-dimethyl-ethane-1,2-diamine (H2GL1) and N,N'-bis[(5-beta-D-glucopyranosyloxy-3-tert-butyl-2-hydroxy)benzyl]-N,N'-dimethyl-ethane-1,2-diamine (H2GL2) for brain-directed metal chelation and redistribution. Acidity constants were determined by potentiometry aided by UV-vis and 1H NMR measurements to identify the protonation sites of H2GL1,2. Intramolecular H bonding between the amine nitrogen atoms and the H atoms of the hydroxyl groups was determined to have an important stabilizing effect in solution for the H2GL1 and H2GL2 species. Both H2GL1 and H2GL2 were found to have significant antioxidant capacity on the basis of an in vitro antioxidant assay. The neutral metal complexes CuGL1, NiGL1, CuGL2, and NiGL2 were synthesized and fully characterized. A square-planar arrangement of the tetradentate ligand around CuGL2 and NiGL2 was determined by X-ray crystallography with the sugar moieties remaining pendant. The coordination properties of H2GL1,2 were also investigated by potentiometry, and as expected, both ligands displayed a higher affinity for Cu2+ over Zn2+ with H2GL1 displaying better coordinating ability at physiological pH. Both H2GL1 and H2GL2 were found to reduce Zn2+- and Cu2+- induced Abeta1-40 aggregation in vitro, further demonstrating the potential of these multifunctional agents as AD therapeutics.     

A Tethered Porphyrin Dimer with π Overlap of a Single Pyrrole Ring

The special pair of the bacterial photosystem has been modeled with a porphyrin dimer (the partial structure is shown). As with the natural system, only one pyrrole ring from each monomer subunit participates in π overlap.     

Modeling,Analysis, and Simulation of Biofilm Formation and Decay

In this article, we give a brief overview of our recent work on continuum mechanical modelling and simulation of microbial films. This comprises some classical tasks of applied mathematics such as computational fluid dynamics, analysis of partial differential equations, and mathematical biology.     

Subsampling effects in neuronal avalanche distributions recorded in vivo

Background  

Many systems in nature are characterized by complex behaviour where large cascades of events, or avalanches, unpredictably alternate with periods of little activity. Snow avalanches are an example. Often the size distribution f(s) of a system's avalanches follows a power law, and the branching parameter sigma, the average number of events triggered by a single preceding event, is unity. A power law for f(s), and sigma = 1, are hallmark features of self-organized critical (SOC) systems, and both have been found for neuronal activity in vitro. Therefore, and since SOC systems and neuronal activity both show large variability, long-term stability and memory capabilities, SOC has been proposed to govern neuronal dynamics in vivo. Testing this hypothesis is difficult because neuronal activity is spatially or temporally subsampled, while theories of SOC systems assume full sampling. To close this gap, we investigated how subsampling affects f(s) and sigma by imposing subsampling on three different SOC models. We then compared f(s) and sigma of the subsampled models with those of multielectrode local field potential (LFP) activity recorded in three macaque monkeys performing a short term memory task.     

Three structures containing (E)‐1,2‐bis­(benzimidazol‐2‐yl)ethene groups

Two of the title compounds, namely (E)‐1,2‐bis­(1‐methyl­benzimidazol‐2‐yl)ethene, C₁₈H₁₆N₄, (Ib), and (E)‐1,2‐bis­(1‐ethyl­benzimidazol‐2‐yl)ethene, C₂₀H₂₀N₄, (Ic), consist of centrosymmetric trans‐bis­(1‐alkyl­benzimidazol‐2‐yl)ethene mol­ecules, while 3‐eth­yl‐2‐[(E)‐2‐(1‐ethyl­benzimidazol‐2‐yl)­ethen­yl]benzimidazol‐1‐ium perchlorate, C₂₀H₂₁N₄⁺·ClO₄⁻, (II), contains the monoprotonated analogue of compound (Ic). In the three structures, the benzimidazole and benzimidazolium moieties are essentially planar; the geometric parameters for the ethene linkages and their bonds to the aromatic groups are consistent with double and single bonds, respectively, implying little, if any, conjugation of the central C=C bonds with the nitro­gen‐containing rings. The C—N bond lengths in the N=C—N part of the benzimidazole groups differ and are consistent with localized imine C=N and amine C—N linkages in (Ib) and (Ic); in contrast, the corresponding distances in the benzimidazolium cation are equal in (II), consistent with electron delocalization resulting from protonation of the amine N atom. Crystals of (Ib) and (Ic) contain columns of parallel mol­ecules, which are linked by edge‐over‐edge C—H⋯π overlap. The columns are linked to one another by C—H⋯π inter­actions and, in the case of (Ib), C—H⋯N hydrogen bonds. Crystals of (II) contain layers of monocations linked by π–π inter­actions and separated by both perchlorate anions and the protruding eth­yl groups; the cations and anions are linked by N—H⋯O hydrogen bonds.     

Über einen zusammenhang zwischen gewissen linearen differential- und differenzengleichungen

Ohne Zusammenfassung