Differential impulse response of unipolar space-charge-limited current

Zusammenfassung Die Zeitabhängigkeit des Stromstossesi(t) wird berechnet, den eine kleine Ladung beeinflusst, wenn sie sich durch das elektrische FeldE(r) bewegt, das ein stationärer, raumladungsbegrenzter Strom in drei verschiedenen Medien und in Strukturen von ebener, zylindrischer und sphärischer Geometrie erzeugt. Die drei betrachteten Medien sind das Vakuum, und zwei Festkörper, in denen entweder die Beweglichkeit oder die Bahngeschwindigkeit der Ladungsträger von der Feldstärke unabhängig ist. Man findet, dass für die beiden Festkörperi(t) undE(r) zwei eng verwandte Funktionen sind, deren Zusammenhang beschrieben wird. Eine experimentelle Bestimmung der Feldverteilung nach diesem Verfahren erscheint knapp durchführbar und würde direkte Einsicht in den Vorgang des Stromflusses vermitteln.     

The Variational Principle and Effective Action for a Spherical Dust Shell

The variational principle for a spherical configuration consisting of a thin spherical dust shell in a gravitational field is constructed. The principle is consistent with the boundary-value problem of the corresponding Euler-Lagrange equations, and leads to natural boundary conditions. These conditions and the field equations following from the variational principle are used for performing of the reduction of this system. The equations of motion for the shell follow from the obtained reduced action. The transformation of the variational formula for the reduced action leads to two natural variants of the effective action. One of them describes the shell from a stationary interior observer's point of view, another from the exterior one. The conditions of isometry of the exterior and interior faces of the shell lead to the momentum and Hamiltonian constraints.     

Surface structure of TiO2(011)-(2x1)

A combined experimental and first principles study of the (2x1)-reconstructed rutile TiO2(011) surface is presented. Our results provide evidence that the surface structure is described by a model that includes onefold coordinated (titanyl) oxygen atoms giving rise to double bonded Ti=O species. These species should play a special role in the enhanced photocatalytic activity of the TiO2(011) surface.     

Dynamical motifs: building blocks of complex dynamics in sparsely connected random networks

Spatiotemporal network dynamics is an emergent property of many complex systems that remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs-small subnetworks with periodic and chaotic dynamics. We simulate randomly connected neural networks and, with increasing density of connections, observe the transition from quiescence to periodic and chaotic dynamics. This transition is explained by the appearance of dynamical motifs in the structure of these networks. We also observe domination of periodic dynamics in simulations of spatially distributed networks with local connectivity and explain it by the absence of chaotic and the presence of periodic motifs in their structure.     

Fourier Multipliers and Integro-Differential Equations in Banach Spaces

Operator-valued Fourier multiplier theorems are used to establishmaximal regularity results for an integro-differential equationwith infinite delay in Banach spaces. Results are obtained undergeneral conditions for periodic solutions in the vector-valuedLebesgue and Besov spaces. The latter scale includes in particularthe Hölder spaces C, 0 < < 1 .     

Trotter-Kato product formula and fractional powers of self-adjoint generators

Let A and B be non-negative self-adjoint operators in a Hilbert space such that their densely defined form sum obeys dom(H^α)⊆dom(A^α)∩dom(B^α) for some α∈(1/2,1). It is proved that if, in addition, A and B satisfy dom(A^1/2)⊆dom(B^1/2), then the symmetric and non-symmetric Trotter-Kato product formula converges in the operator norm:

||(e−tB/2ne−tA/ne−tB/2n)n−e−tH||=O(n−(2α−1))||(e−tA/ne−tB/n)n−e−tH||=O(n−(2α−1))     

Superparamagnetism of magnetite nanoparticles: dependence on surface modification

Superparamagnetic iron oxide nanoparticles (SPION) with an average particle diameter of 6 nm are prepared by controlled chemical coprecipitations. Colloidal suspensions of noninteracting SPION, where the surface has been modified with three different types of biocompatible substances, namely, starch, gold (Au), and methoxypoly(ethylene glycol) (MPEG) have been fabricated via three different techniques. Starch-coated SPION are prepared by coprecipitation in a polymeric matrix, Au-coated SPION are fabricated by the microemulsion method, and MPEG-coated SPION are prepared using the self-assembly approach. The magnetic nanoparticles form a core-shell structure, and the magnetic dipole-dipole interactions are screened by a layer of coating agents. The amounts of coating agents and SPION are indirectly calculated from the thermogravimetric analysis and superconducting quantum interference device measurements by assuming passive oxidation on the surface of the SPION, and the other conditions do not influence the measurements. The dependency of the spectral characteristics of M?ssbauer spectroscopy as a function of an external magnetic field Hext is measured to investigate the effect of dipole-dipole screening of the different coating layers on the SPION. Uncoated SPION show a stable magnetic moment under Hext, and the superparamagnetic (SPM) fraction transforms to a ferrimagnetic state. Starch and Au-coated SPION retain the SPM fraction according to M?ssbauer spectroscopy and magnetization measurements. MPEG-coated SPION show hyperfine magnetic structure without the quadrupole effect with increasing the value of the blocking temperature.     

Catalytic reaction mechanism of homogentisate dioxygenase: a hybrid DFT study

Human homogentisate dioxygenase is an Fe(II)-dependent enzyme responsible for aromatic ring cleavage. The mechanism of its catalytic reaction has been investigated with the hybrid density functional method B3LYP. A relatively big model of the active site was first used to determine the substrate binding mode. It was found that binding of the substrate dianion with a vacant position trans to Glu341 is most favorable. The model was then truncated to include only the most relevant parts of the active-site residues involved in iron coordination and substrate binding. Thus, methylimidazole was used to model His292, His335, His365, and His371, while propionate modeled Glu341. The computational results suggest that the catalytic reaction of homogentisate dioxygenases involves three major chemical steps: formation of the peroxo intermediate, homolytic cleavage of the O-O bond leading to an arene oxide radical, and finally, cleavage of the six-membered ring. Calculated barriers for alternative reaction paths are markedly higher than for the proposed mechanism, and thus the computational results successfully explain the product specificity of the enzyme. Interestingly, the results indicate that the type of ring scission, intra or extra with respect to the substituents coordinating to iron, is controlled by the barrier heights for the decay of the arene oxide radical intermediate.     

Relationship between multiscale enrichment and stabilized finite element methods for the generalized Stokes problem

We derive a new stabilized finite element method for the generalized Stokes problem starting from the non-stable continuous ${\mathbb{P}}_1/{\mathbb{P}}_1$ finite element space enriched with multiscale functions. The stabilization parameter is related with the enrichment functions which are analytically computed from a boundary value problem at the element level leading to a method which is free of constants. Optimal error estimates are obtained in natural norms and numerical tests validate the method. To cite this article: G.R. Barrenechea, F. Valentin, C. R. Acad. Sci. Paris, Ser. I 341 (2005).