Field-induced suppression of the heavy-fermion state in YbRh2Si2

We report dc-magnetization measurements on YbRh2Si2 at temperatures down to 0.04 K, magnetic fields B< or =11.5 T, and under hydrostatic pressure P< or =1.3 GPa. At ambient pressure a kink at B* =9.9 T indicates a new type of field-induced transition from an itinerant to a localized 4f state. This transition is different from the metamagnetic transition observed in other heavy-fermion compounds, as here ferromagnetic rather than antiferromagnetic correlations dominate below B*. Hydrostatic pressure experiments reveal a clear correspondence of B* to the characteristic spin fluctuation temperature determined from specific heat.     

Isomerization of a peptidic fragment studied theoretically in vacuum and in explicit water solvent at finite temperature

The cis-trans isomerization of N-methylacetamide, a molecular model of the polypeptide chain, is examined via umbrella sampling Car-Parrinello MD and classical MD, in both gas and solution phases at 300 K. A new analysis of the C(O)-N bond interconversion and a full examination of the solvent shell structure are presented.     

A priori error estimates for a mixed finite element discretization of the Richards’ equation

Summary. A mixed finite element discretization is applied to Richards equation, a nonlinear, possibly degenerate parabolic partial differential equation modeling water flow through porous medium. The equation is considered in its pressure formulation and includes both variably and fully saturated flow regime. Characteristic for such problems is the lack in regularity of the solution. To handle this we use a time-integrated scheme. We analyze the scheme and present error estimates showing its convergence.Mathematics Subject Classification (2000): 65M12, 65M60, 76S05, 35K65Acknowledgments. We would like to thank Markus Bause for very useful discussions and suggestions.     

Sequential optical coherence tomography and confocal imaging

We report a system capable of sequentially acquiring two en-face images of different depth resolutions. The two images are generated by use of different principles, optical coherence tomography (OCT) and confocal microscopy, and have depth resolutions, at present, of better than 20 microm and over 0.12 mm, respectively. The lower-depth-resolution image is ideal for target positioning before collection of stacks of en-face OCT images. Switching between the two types of image by flipping an opaque screen in the reference arm, coupled with self-adjusting gain operation of avalanche photodiodes in the receiver. We illustrate the usefulness of the system by imaging a leaf and an optic nerve in vivo.     

The Statistics of the Trajectory of a Certain Billiard in a Flat Two-Torus

We consider a billiard in the punctured torus obtained by removing a small disk of radius >0 from the flat torus ², with trajectory starting from the center of the puncture. In this case the phase space is given by the range of the velocity only. Let (), and respectively R(), denote the first exit time (length of the trajectory), and respectively the number of collisions with the side cushions when ² is being identified with [0,1)². We prove that the probability measures on [0, ) associated with the random variables and R are weakly convergent as 0⁺ and explicitly compute the densities of the limits. Research partially supported by ANSTI grant C6189/2000.     

Stability of the vortex defect in the Landau–de Gennes theory for nematic liquid crystals

We analyze the radially symmetric solution corresponding to the vortex defect (the so-called melting hedgehog) in the Landau–de Gennes theory for nematic liquid crystals. We prove the existence, uniqueness and stability results of the melting hedgehog.     

Endpoint Fragmentation Index: A Method for Monitoring the Evolution of Microbial Degradation of Polysaccharide Feedstocks

We describe a simple method for tracking the course of microbial degradation of polysaccharide-rich feedstocks. The method involves determining total polysaccharides present in the feedstock, measured in glucose equivalents, relative to the fractional component of polysaccharides exhibiting 2,3-dinitrosalycylic acid aldehyde activity. The ratio of total polysaccharide to aldehyde activity, defined as the end-point fragmentation (EPF) index, is then calculated and tracked as it shifts as microbial degradation of polysaccharide-rich feedstock progresses. While degradation occurs, the EPF index falls. It bottoms out at an asymptotic limit marking the point in time where further degradation of the polysaccharide-rich feedstock has ceased. The EPF index can be used to follow the progressive breakdown of composting polysaccharide-rich waste. It may also have applicability as a means of tracking the turnover of polysaccharides in other complex environments including soil, sediments, wetlands, and peat bogs.     

Convergence of MPFA on triangulations and for Richards' equation

Spatial discretization of transport and transformation processes in porous media requires techniques that handle general geometry, discontinuous coefficients and are locally mass conservative. Multi‐point flux approximation (MPFA) methods are such techniques, and we will here discuss some formulations on triangular grids with further application to the nonlinear Richards equation. The MPFA methods will be rewritten to mixed form to derive stability conditions and error estimates. Several MPFA versions will be shown, and the versions will be discussed with respect to convergence, symmetry and robustness when the grids are rough. It will be shown that the behavior may be quite different for challenging cases of skewness and roughness of the simulation grids. Further, we apply the MPFA discretization approach for the Richards equation and derive new error estimates without extra regularity requirements. The analysis will be accompanied by numerical results for grids that are relevant for practical simulation. Copyright © 2008 John Wiley & Sons, Ltd.