Inverse-scattering theory and the density perturbations from inflation

We show how to use inverse-scattering theory as the basis for the inflationary reconstruction program, the goal of which is to gain information about the physics which drives inflation. Inverse-scattering theory provides an effective and well-motivated procedure, having a sound mathematical basis and being of sufficient generality that it can be considered the foundation for a nonparametric reconstruction program. We show how simple properties of the power spectrum translate directly into statements about the evolution of the background geometry during inflation.     

Polarization tensors and effective properties of anisotropic composite materials

In this paper, we present a systematic scheme for derivations of asymptotic expansions including higher-order terms, with estimates, of the effective electrical conductivity of periodic dilute composites in terms of the volume fraction occupied by the inclusions. The conductivities of the inclusion and the matrix may be anisotropic. Our derivations are based on layer potential techniques, and valid for high contrast mixtures and inclusions with Lipschitz boundaries. The asymptotic expansion is given in terms of the polarization tensor and the volume fraction of the inclusions. Important properties, such as symmetry and positivity, of the anisotropic polarization tensors are derived.     

Partitive hypergraphs

We define a new class of hypergraphs (partitive hypergraphs) which generalizes both, the set of all externally related subsets of a graph and the set of all committees of an hypergraph.We give a characterization of the partitive hypergraphs and moreover of those which are associated with hypergraphs or graphs.     

Application of a palladium hexacyanoferrate film-modified aluminum electrode to electrocatalytic oxidation of hydrazine.

A palladium hexacyanoferrate (PdHCF) film as an electrocatalytic material was obtained at an aluminum (Al) electrode by a simple electroless dipping method. The modified Al electrode demonstrated a well-behaved redox couple due to the redox reaction of the PdHCF film. The PdHCF film showed an excellent electrocatalytic activity toward the oxidation of hydrazine. The electrocatalytic oxidation of hydrazine was studied by cyclic voltammetry and rotating disk electrode voltammetry techniques. A calibration graph obtained for the hydrazine consisted of two segments (localized at concentration ranges 0.39-10 and 20-75 mM). The rate constant k and transfer coefficient alpha for the catalytic reaction and the diffusion coefficient of hydrazine in the solution D, were found to be 3.11 x 10(3) M(-1) s(-1), 0.52 and 8.03 x 10(-6) cm2 s(-1) respectively. The modified electrode was used to amperometric determination of hydrazine in photographic developer. The interference of ascorbic acid and thiosulfate were investigated and greatly reduced using a thin film of Nafion on the modified electrode. The modified electrode indicated reproducible behavior and a high level of stability during electrochemical experiments, making it particularly suitable for analytical purposes.     

Key fragmentation patterns of aporphine alkaloids by electrospray ionization with multistage mass spectrometry

This work reports a detailed study of the fragmentations of aporphine alkaloids by electrospray ionization with multistage mass spectrometry (ESI-MS(n)) in positive mode. In a first step the loss of the amino group and its substituent is observed. Further steps display the loss of the peripheral groups. Losses of methanol and CO are observed if an OH is vicinal to an OCH(3) on the aromatic ring. Otherwise the spectra show radical losses of CH(3)* or CH(3)O* as the main fragmentations. If a methylenedioxy group is present losses of formaldehyde followed by CO are observed. These fragmentations yield important information on the structures of aporphines.     

Nonlinear and nonequilibrium dynamics in geomaterials

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a simple macroscopic dynamical model. At even higher strains, effects due to a driven nonequilibrium state, and relaxation from it, complicate the characterization of the nonlinear behavior.     

Quantum feedback control of atomic motion in an optical cavity

We study quantum feedback cooling of atomic motion in an optical cavity. We design a feedback algorithm that can cool the atom to the ground state of the optical potential with high efficiency despite the nonlinear nature of this problem. An important ingredient is a simplified state-estimation algorithm, necessary for a real-time implementation of the feedback loop. We also describe the critical role of parity dynamics in the cooling process and present a simple theory that predicts the achievable steady-state atomic energies.