A compactness result for Landau state in thin-film micromagnetics

We deal with a nonconvex and nonlocal variational problem coming from thin-film micromagnetics. It consists in a free-energy functional depending on two small parameters ε and η and defined over vector fields m:Ω⊂R²→S² that are tangent at the boundary ∂Ω. We are interested in the behavior of minimizers as ε,η→0. They tend to be in-plane away from a region of length scale ε (generically, an interior vortex ball or two boundary vortex balls) and of vanishing divergence, so that S¹-transition layers of length scale η (Néel walls) are enforced by the boundary condition. We first prove an upper bound for the minimal energy that corresponds to the cost of a vortex and the configuration of Néel walls associated to the viscosity solution, so-called Landau state. Our main result concerns the compactness of vector fields {mε,η}_ε,η↓0 of energies close to the Landau state in the regime where a vortex is energetically more expensive than a Néel wall. Our method uses techniques developed for the Ginzburg-Landau type problems for the concentration of energy on vortex balls, together with an approximation argument of S²-vector fields by S¹-vector fields away from the vortex balls.     

Comparison of luminescence ADP production assay and radiometric scintillation proximity assay for Cdc7 kinase

Several assay technologies have been successfully adapted and used in HTS to screen for protein kinase inhibitors; however, emerging comparative analysis studies report very low hit overlap between the different technologies, which challenges the working assumption that hit identification is not dependent on the assay method of choice. To help address this issue, we performed two screens on the cancer target, Cdc7-Dbf4 heterodimeric protein kinase, using a direct assay detection method measuring [(33)P]-phosphate incorporation into the substrate and an indirect method measuring residual ADP production using luminescence. We conducted the two screens under similar conditions, where in one, we measured [(33)P]-phosphate incorporation using scintillation proximity assay (SPA), and in the other, we detected luminescence signal of the ATP-dependent luciferase after regenerating ATP from residual ADP (LUM). Surprisingly, little or no correlation were observed between the positives identified by the two methods; at a threshold of 30% inhibition, 25 positives were identified in the LUM screen whereas the SPA screen only identified two positives, Tannic acid and Gentian violet, with Tannic acid being common to both. We tested 20 out of the 25 positive compounds in secondary confirmatory study and confirmed 12 compounds including Tannic acid as Cdc7-Dbf4 kinase inhibitors. Gentian violet, which was only positive in the SPA screen, inhibited luminescence detection and categorized as a false positive. This report demonstrates the strong impact in detection format on the success of a screening campaign and the importance of carefully designed confirmatory assays to eliminate those compounds that target the detection part of the assay.     

Invariant Measures for Cherry Flows

We investigate the invariant probability measures for Cherry flows, i.e. flows on the two-torus which have a saddle, a source, and no other fixed points, closed orbits or homoclinic orbits. In the case when the saddle is dissipative or conservative we show that the only invariant probability measures are the Dirac measures at the two fixed points, and the Dirac measure at the saddle is the physical measure. In the other case we prove that there exists also an invariant probability measure supported on the quasi-minimal set, we discuss some situations when this other invariant measure is the physical measure, and conjecture that this is always the case. The main techniques used are the study of the integrability of the return time with respect to the invariant measure of the return map to a closed transversal to the flow, and the study of the close returns near the saddle.     

A new identity for Parseval frames

In this paper we establish a surprising new identity for Parseval frames in a Hilbert space. Several variations of this result are given, including an extension to general frames. Finally, we discuss the derived results.

     

Investigation of helium implantation induced blistering in InP

 Four-inch InP wafers were implanted with 100 keV helium ions with a dose of 5×10¹⁶ cm⁻² and subsequently annealed in air in the temperature range of 225-400°C in order to determine the blistering kinetics of these wafers. An Arrhenius plot of the blistering time as a function of reciprocal temperature revealed two different activation energies for the formation of surface blisters in InP. The activation energy was found to be 0.30 eV in the higher temperature regime of 300-400 °C and 0.74 eV in the lower temperature regime of 225-300 °C. The implantation induced damage was analyzed by cross-sectional transmission electron microscopy, which revealed a band of defects extending from 400-700 nm from the surface of InP. The damage band was found to be decorated with a large number of nanovoids having diameters between 2 and 5 nm. These nanovoids served as precursors for the formation of microcracks inside InP upon annealing, which led to the formation of surface blisters.     

Sur les décompositions directes des contractions de l'espace de Hilbert

Soit H un espace de Hilbert séparable, T ∈ $\text{B}$(H) une contraction complètement nonunitaire et H₁ ? H un sous-espace fermé, invariant à T. Le but de cette Note est de trouver une condition nécessaire et suffisante pour qu'il existe un sous-espace fermé H′ ? H, invariant à T et tel que l'espace H se décompose en somme directe $\text{H = H′ ? H}{}_1$ pas nécessairement orthogonale.     

On the shape resonances in NO− and N2−

The method used by Koike and Watanabe to describe negative molecular ion formation is generalized for multiwaves states of the extra electron. The structure of the shape resonances in NO^? and N₂^? is discussed. For the NO^?-captured electron it is found that the dπ-wave component increases with increasing resonance energy.