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.     

A caged lanthanide complex as a paramagnetic shift agent for protein NMR

A lanthanide complex, named CLaNP (caged lanthanide NMR probe) has been developed for the characterisation of proteins by paramagnetic NMR spectroscopy. The probe consists of a lanthanide chelated by a derivative of DTPA (diethylenetriaminepentaacetic acid) with two thiol reactive functional groups. The CLaNP molecule is attached to a protein by two engineered, surface-exposed, Cys residues in a bidentate manner. This drastically limits the dynamics of the metal relative to the protein and enables measurements of pseudocontact shifts. NMR spectroscopy experiments on a diamagnetic control and the crystal structure of the probe-protein complex demonstrate that the protein structure is not affected by probe attachment. The probe is able to induce pseudocontact shifts to at least 40 A from the metal and causes residual dipolar couplings due to alignment at a high magnetic field. The molecule exists in several isomeric forms with different paramagnetic tensors; this provides a fast way to obtain long-range distance restraints.     

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.     

Travelling Waves for Adaptive Grid Discretizations of Reaction Diffusion Systems I: Well-Posedness

Journal of Dynamics and Differential Equations - In this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE. In particular, we consider a commonly used time...     

Über einen zusammenhang zwischen gewissen linearen differential- und differenzengleichungen

Ohne Zusammenfassung     

Center projections for smooth difference equations of mixed type

We study a class of mixed type difference equations that enjoy a special smoothening property, in the sense that solutions automatically satisfy an associated functional differential equation of mixed type. Using this connection, a finite dimensional center manifold is constructed that captures all solutions that remain sufficiently close to an equilibrium. The results enable a rigorous analysis of a recently developed model in economic theory, that exhibits periodic oscillations in the interest rates of a simple economy of overlapping generations.     

Carrier dynamics in conducting polymers: case of PF6 doped polypyrrole

The carrier dynamics in PF6 doped polypyrrole has been probed by dielectric spectroscopy (from 10(-4) to 4 eV), down to 4.2 K. The phase-sensitive sub-THz data have assisted to resolve the discrepancies in Kramers-Kronig analysis in earlier studies. Even in metallic samples, just 1% of the carriers are delocalized, at 300 K; the fraction drops down considerably as a function of disorder, carrier density, and temperature. This subtle metallic feature and the anomalies in carrier dynamics are attributed to coherent and incoherent transport between short conjugated segments.     

Physicochemical characterization of the endotoxins from Coxiella burnetii strain Priscilla in relation to their bioactivities

Background  

Coxiella burnetiiis the etiological agent of Q fever found worldwide. The microorganism has like other Gram-negative bacteria a lipopolysaccharide (LPS, endotoxin) in its outer membrane, which is important for the pathogenicity of the bacteria. In order to understand the biological activity of LPS, a detailed physico-chemical analysis of LPS is of utmost importace.