Lattice sub-tilings and frames in LCA groups

Given a lattice Λ in a locally compact Abelian group G and a measurable subset Ω with finite and positive measure, then the set of characters associated with the dual lattice form a frame for $L^2(\mathrm{\Omega })$ if and only if the distinct translates by Λ of Ω have almost empty intersections. Some consequences of this results are the well-known Fuglede theorem for lattices, as well as a simple characterization for frames of modulates.     

Étude expérimentale de la dispersion active d'un polluant hydrocarboné en milieu poreux hétérogèneActive dispersion of a hydrocarbon pollutant in heterogeneous porous media: experimental study

This study deals with Non Aqueous Phase Liquid (NAPL) dissolution in subsurface water in order to predict the pollutant plume development and to optimize remediation processes. An experimental study of NAPL dissolution in porous media is presented. Local water saturation and effluent pollutant concentration measurements are presented for several kinds of porous media. Experimental results show clearly the influence of microscopic and/or macroscopic heterogeneities of the porous media and the distribution of the pollutant on the active dispersion of the NAPL. The NAPL dissolution occurs in several steps which highlights the existence of non-local equilibrium related to the heterogeneity of the porous media. To cite this article: A. Yra et al., C. R. Mecanique 334 (2006).     

Absence of biological damage from prolonged exposure to intravascular ultrasound: a swine model

Ultrasound (US) has been used in IMS II (intravascular US) and CLOTBUST (transcranial US) clinical trials for thrombolysis. During the treatment, in addition to the targeted thrombus, other biological components, such as blood and vessel walls are subjected to long durations of US exposure. In this study we explored evidence of biological damage due to mechanical forces or thermal effects of US exposure at the frequency, intensity and duration employed for thrombolysis treatment. Biological effects were investigated by exposing swine ilio-femoral arteries bilaterally to an intravascular US generating catheter and a conventional catheter. A total of 12 animals each underwent 8h of exposure to intravascular pulsed US with a frequency of 2.2MHz and spatial peak time average intensity (I(SPTA)) of 6W/cm(2) per transducer (a total of six transducers per catheter) while the ultrasonic device surface temperature was maintained at 43 degrees C. The animals were euthanized either 24+/-3h or 28+/-3 days post treatment. A range of physiological and hematological parameters were evaluated pre-, post-, and during US exposure. The vascular diameter was determined pre- and post-US exposure using angiograms. Following euthanasia, each animal underwent a gross pathological examination, and the treated vessels and an unexposed vessel were excised for comparative histopathological evaluation. No evidence of biological damage was found at the end of 8h exposure to intravascular US.     

Application of Non-toxic Yield Stress Fluids Porosimetry Method and Pore-Network Modelling to Characterize the Pore Size Distribution of Packs of Spherical Beads

Transport in Porous Media - With X-ray computed tomography still being flawed as a result of limitations in terms of spatial resolution and cost, toxic mercury intrusion porosimetry (MIP) is...     

Homogenization of Solute Transport in Unsaturated Double-Porosity Media: Model and Numerical Validation

Transport in Porous Media - The development of a macroscopic model for solute transport coupled with unsaturated water flow in double-porosity media is presented in this work, by using the...     

On the Inertial Single Phase Flow in 2D Model Porous Media: Role of Microscopic Structural Disorder

Transport in Porous Media - In this work, single-phase incompressible laminar flow in 2D model porous media is studied and the influence of microscopic structural disorder on the flow is thoroughly...     

Empirical Flow Rate/Pressure Drop Relationships for Capillaries of Triangular and Rectangular Cross-Sections to be Used in Yield Stress Fluid Porosimetry

Transport in Porous Media - The aim of the present work is to investigate the flow rate/pressure gradient relationship for the flow of yield stress fluids through rectilinear capillaries of...     

Thermal Spin Squeezing as a Signature of Thermal Global Entanglement in Heisenberg Models

We study thermal spin squeezing (TSS) and thermal global entanglement (TGE) in a general Heisenberg spin chain, in the presence of Dzyaloshinskii-Moriya interaction and an external magnetic field. We derive an inequality associating the squeezing parameter and the global concurrence, which establishes (TSS) as a signature of (TGE). The inequality reduces to equality for particular symmetric chains which also associates TSS with bipartite entanglement in such systems. We also check the results by presenting two numerical examples.     

On the metal–insulator transition in vanadium dioxide

The conductivity σ of vanadium dioxide (VO₂) drops at a metal–insulator transition by four orders of magnitude due to the structural change between tetragonal and monoclinic crystals. In order to elucidate this conductivity drop, we introduce the semiclassical equation of motion to describe the dynamics of the conduction electron (wave packet), where the existence of a k-vector k is prerequisite for the conduction. We showed that the periodicity using the non-orthogonal bases does not legitimize the electron dynamics in solids. The theory suggests that the decrease in the dimensionality of the k-vectors due to the structural change is the cause of the conductivity drop.     

Tight wavelet frame sets in finite vector spaces

Let $q\ge 2$ be an integer, and ${\mathbb{F}}_q^d$, $d\ge 1$, be the vector space over the cyclic space ${\mathbb{F}}_q$. The purpose of this paper is two-fold. First, we obtain sufficient conditions on $E?{\mathbb{F}}_q^d$ such that the inverse Fourier transform of $1_E$ generates a tight wavelet frame in $L^2({\mathbb{F}}_q^d)$. We call these sets (tight) wavelet frame sets. The conditions are given in terms of multiplicative and translational tilings, which is analogous with Theorem 1.1 ([20]) by Wang in the setting of finite fields. In the second part of the paper, we exhibit a constructive method for obtaining tight wavelet frame sets in ${\mathbb{F}}_q^d$, $d\ge 2$, q an odd prime and $q\equiv 3$ (mod 4).