Invariant distributions and scaling limits for some diffusions in time-varying random environments

We consider a family of one-dimensional diffusions, in dynamical Wiener mediums, which are random perturbations of the Ornstein–Uhlenbeck diffusion process. We prove quenched and annealed convergences in distribution and under weigh-ted total variation norms. We find two kind of stationary probability measures, which are either the standard normal distribution or a quasi-invariant measure, depending on the environment, and which is naturally connected to a random dynamical system. We apply these results to the study of a model of time-inhomogeneous Brox’s diffusions, which generalizes the diffusion studied by Brox (Ann Probab 14(4):1206–1218, 1986) and those investigated by Gradinaru and Offret (Ann Inst Henri Poincaré Probab Stat, 2011). We point out two distinct diffusive behaviours and we give the speed of convergences in the quenched situations.     

Thermal transport in the hidden-order state of URu2Si2

We present a study of thermal conductivity in the normal state of the heavy-fermion superconductor URu2Si2. Ordering at 18 K leads to a steep increase in thermal conductivity and (in contrast with all other cases of magnetic ordering in heavy-fermion compounds) to an enhancement of the Lorenz number. By linking this observation to several other previously reported features, we conclude that most of the carriers disappear in the ordered state and this leads to a drastic increase in both the phononic and electronic mean free path.     

Impulse capture basins of sets under impulse control systems

Given a target contained in a constrained set and an impulse control system governing the evolutions of runs or executions, that are hybrids of continuous and discrete evolutions, this paper studies and provides several characterizations of the capture basin of the target viable in the constrained set. It is the subset of initial runs from which start at least one run viable in the constrained set until it reaches the target in finite time. It also provides algorithms and regulation rules governing the runs that reach the targets while obeying state constraints.     

Set-valued solutions to the Cauchy problem for hyperbolic systems of partial differential inclusions

We prove the existence of global set-valued solutions to the Cauchy problem for partial differential equations and inclusions, with either single-valued or set-valued initial conditions. The method is based on the equivalence between this problem and problem of finding viability tubes of the associated characteristic system of ordinary differential equations. As an application we construct the value function of the Mayer problem arising in control theory. Received August 25, 1995     

Thermal conductivity as a probe of unconventional superconducting gap

We have carried out a comparative study of the thermal conductivity of two rectangular single crystals: a niobium sample and a detwinned YBCO. Thermal conductivity was measured as a function of the relative orientation of the crystaline axes and a magnetic field applied parallel to the sample plane. Different angular variations, two-fold for Nb and four-fold for YBCO, were observed in the two case. We discuss the microscopic effects related to the gap structure which are at the origin of this qualitative difference in the behavior of thermal conductivity in these two superconductors.     

The depth of molecular recognition: voltage-sensitive blockage of synthetic multifunctional pores with refined architecture

Voltage-sensitive blockage by ADP, ATP and phytate (IP6) demonstrates that active-site contraction toward the middle of newly synthesized rigid-rod beta-barrels provides a general strategy to rationally create and modulate the voltage sensitivity (and to increase the efficiency) of molecular recognition by synthetic multifunctional pores.     

A note about proving non-Γ under a finite non-microstates free Fisher information assumption

We prove that if X₁,…,Xn (n>1) are self-adjoints in a W^∗-probability space with finite non-microstates free Fisher information, then the von Neumann algebra W^∗(X₁,…,Xn) they generate doesn't have property Γ (especially is not amenable). This is an analog of a well-known result of Voiculescu for microstates free entropy. We also prove factoriality under finite non-microstates entropy.     

Macroscopic traffic models: Shifting from densities to “Celerities”

The advent of techniques to measure velocities of “GPS equipped vehicles” using satellite technology, replacing the density of the road traffic sensors, motivates and justifies the revision of conceptual, mathematical algorithms and software based models. This paper summarizes studies on the traffic evolutions achieving the minimum of a congestion function controlled “macroscopic traffic velocities” called “celerities” instead of founding traffic regulation on the measures of traffic densities. The flux valued function is the Fenchel transform of the fundamental diagram and is a convex decreasing function. We use the properties of capture basins investigated in viability theory, specifically a Lax-Hopf formula characterizing them and the “Max-Plus” morphism of capture basins for deriving the statements proved in this paper. Traffic conditions involve as well boundary conditions or conditions on trajectories inside the domain.     

Atomic parity non-conservation: the francium anapole project of the FrPNC collaboration at TRIUMF

We present a method for measuring the nuclear anapole in a string of francium isotopes. The anapole is a parity non-conserving electromagnetic moment that enables parity-forbidden transitions between ground state hyperfine levels of an atom. The experiment is run by the FrPNC collaboration and relies on a beam of artificially-produced francium from the ISAC facility at TRIUMF.     

Design Strategies for Diradical Boron/Nitrogen Doped Carbon-Based Materials

New heterocyclic diradicaloids based on boron and nitrogen-doped polycyclic systems with open-shell ground-states are obtained via concomitant structural and quinoidal extensions, thus allowing to merge the best of both design strategies. A combination of experimental characterization and theoretical calculations have helped disclose their electronic structure, as well as rationalize their associated magnetic and photophysical properties, spanning the chemical space of available molecular templates for cutting-edge applications in organic electronics and spintronics.