A formula for the determinant of a sum of matrices

We give a formula, involving circular words and symmetric functions of the eigenvalues, for the determinant of a sum of matrices. Theorem of Hamilton-Cayley is deduced from this formula.UQAM and LITPUniversité Paris 7 and LITP.     

First announcement the 20th annual international conference on infrared and millimeter waves

First announcement the 20th annual international conference on infrared and millimeter waves     

Magnetic behavior of amorphous Fe−Ni−Zr alloys and their response to radiation damage

The magnetic properties of two amorphous Fe?Ni?Zr alloys, Fe_89.7Ni_0.03Zr₁₀ and Fe₇₀Ni₂₀Zr₁₀, both in the “as cast” and neutron irradiated states were investigated by Mössbauer spectroscopy and dc magnetic susceptibility measurements. The upper magnetic ordering temperatures of Fe_89.7Ni_0.03Zr₁₀ are 232K and 246K for the “as cast” and irradiated samples, respectively. The magnetic ordering temperature for Fe₇₀Ni₂₀Zr₁₀ was about 478K for both the “as cast” and irradiated samples. Both compositions yield magnetic hyperfine spectra, which show a considerable relaxation effect that must be explicitly considered in the calculation of the average local Fe moments. When this is done, these values derived from Mössbauer spectra are in good agreement with the dc susceptibility values. The effects of neutron irradiation on the magnetic properties of these alloys are small.     

Weak localization in multiterminal networks of diffusive wires

We study the quantum transport through networks of diffusive wires connected to reservoirs in the Landauer-Büttiker formalism. The elements of the conductance matrix are computed by the diagrammatic method. We recover the combination of classical resistances and obtain the weak localization corrections. For arbitrary networks, we show how the Cooperon must be properly weighted over the different wires. Its nonlocality is clearly analyzed. We predict a new geometrical effect that may change the sign of the weak localization correction in multiterminal geometries.     

Bone matrix like assemblies of collagen: from liquid crystals to gels and biomimetic materials

Skeletal tissues associate in close interaction, a dense organic matrix and a mineral network. In bone, the major structural protein is type I collagen, associated with inorganic crystals of hydroxyapatite. The three-dimensional arrangement of collagen fibrils in compact bone forms regularly ordered networks and a parallel was evidenced between these structures and molecular assemblies described in liquid crystals. Similar structures are now obtained in vitro. Indeed, when purified type I collagen is highly concentrated in an acid soluble state, the protein spontaneously assembles into ordered liquid crystalline phases. After a sol/gel transition triggered by pH increase, biomimetic materials are formed which resemble the exact compact bone matrix architecture over distances reaching centimetres and more. The properties of these highly ordered materials will be reviewed recalling their supramolecular arrangement and the corresponding patterns when visualised in polarised light microscopy (birefringence) and transmission electron microscopy (TEM). The association of inorganic phases (amorphous silica) to form chiral hybrid materials will also be described so as the behaviour of cells (fibroblast adhesion and migration) when seeded on these dense biomimetic matrices.     

A Bayesian method to estimate the depth and the range of phonating sperm whales using a single hydrophone

Some bioacousticians have used a single hydrophone to calculate the depth/range of phonating diving animals. The standard one-hydrophone localization method uses multipath transmissions (direct path, sea surface, and seafloor reflections) of the animal phonations as a substitute for a vertical hydrophone array. The standard method requires three multipath transmissions per phonation. Bioacousticians who study foraging sperm whales usually do not have the required amount of multipath transmissions. However, they usually detect accurately (using shallow hydrophones towed by research vessels) direct path transmissions and sea surface reflections of sperm whale phonations (clicks). Sperm whales emit a few thousand clicks per foraging dive, therefore researchers have this number of direct path transmissions and this number of sea surface reflections per dive. The author describes a Bayesian method to combine the information contained in those acoustic data plus visual observations. The author's tests using synthetic data show that the accurate estimation of the depth/range of sperm whales is possible using a single hydrophone and without using any seafloor reflections. This method could be used to study the behavior of sperm whales using a single hydrophone in any location no matter what the depth, the relief, or the constitution of the seafloor might be.     

Purcell enhancement of spontaneous emission from quantum cascades inside mirror-grating metal cavities at THz frequencies

Quantum cascade devices processed into double metal cavities with subwavelength thickness and a grating on top are studied at terahertz frequencies. The power extracted from the devices as a function of the device thickness and the grating period is analyzed owing to electrodynamical modeling of dipole emission based on a modal method in multilayer systems. The experimental data thus reveal a strong Purcell enhancement, with Purcell factors up to approximately 50.