Optimal distribution of the internal null control for the one-dimensional heat equation

This paper addresses the problem of optimizing the distribution of the support of the internal null control of minimal L²-norm for the 1-D heat equation. A measure constraint is imposed on the support but no topological assumption such as the number of connected components. Therefore, the problem typically lacks of solution in the class of characteristic functions and needs of relaxation. We show that the relaxed formulation is obtained by replacing the set of characteristic functions by its convex envelope. The proof requires that the observability constant related to the control problem be uniform with respect to the support, property which is obtained by the control transmutation method. The optimality conditions of the relaxed problem as well as the case where the number of connected components is fixed a priori are also discussed. Several numerical experiments complete the study and suggest the ill-posedness of the problem in contrast to the wave situation.     

Complexity issues for the sandwich homogeneous set problem

Graph sandwich problems were introduced by Golumbic et al. (1994) in [12] for DNA physical mapping problems and can be described as follows. Given a property Π of graphs and two disjoint sets of edges E₁, E₂ with E₁⊆E₂ on a vertex set V, the problem is to find a graph G on V with edge set E_s having property Π and such that E₁⊆E_s⊆E₂.In this paper, we exhibit a quasi-linear reduction between the problem of finding an independent set of size k≥2 in a graph and the problem of finding a sandwich homogeneous set of the same size k. Using this reduction, we prove that a number of natural (decision and counting) problems related to sandwich homogeneous sets are hard in general. We then exploit a little further the reduction and show that finding efficient algorithms to compute small sandwich homogeneous sets would imply substantial improvement for computing triangles in graphs.     

Ergodic BSDEs under weak dissipative assumptions

In this paper we study ergodic backward stochastic differential equations (EBSDEs) dropping the strong dissipativity assumption needed in Fuhrman et al. (2009) [12]. In other words we do not need to require the uniform exponential decay of the difference of two solutions of the underlying forward equation, which, on the contrary, is assumed to be non-degenerate.We show the existence of solutions by the use of coupling estimates for a non-degenerate forward stochastic differential equation with bounded measurable nonlinearity. Moreover we prove the uniqueness of “Markovian” solutions by exploiting the recurrence of the same class of forward equations.Applications are then given for the optimal ergodic control of stochastic partial differential equations and to the associated ergodic Hamilton-Jacobi-Bellman equations.     

60]Fullerene-based monolayers as neuroprotective biocompatible hybrid materials

Here we report on the surface immobilization of redox-active [60]fullerene derivatives and the consequent neuroprotective effects toward l-glutamate induced excitotoxicity in human derived undifferentiated neuroblastoma cells.     

Electrochemical and spectrophotometrical investigation of the electron-accepting strength of organic superelectrophiles: X-ray structure of their charge transfer complexes with tetrathiafulvalene

Nitro Benzoxadiazoles (benzofurazans), benzoxadiazoles-N-oxide (benzofuroxans) and benzothiadiazoles are ranked amongst the strongest electrophiles known to date. In the past twenty years, their propensity to act as electron organic acceptors has been less studied. In this paper, we report on the study of their electrochemical behavior and on the structural characterization of charge transfer complexes (CTC) deriving from their interaction with tetrathiafulvalene (TTF) derivatives, both in solution and in the solid state. The first half wave reduction potentials (E(1/2)(I)) associated with a reversible monoelectronic transfer process of a large set of nitro substituted benzoxadiazoles (benzofurazans), benzoxadiazoles-N-oxide (benzofuroxans) and benzothiadiazoles have been determined through a detailed electrochemical approach in acetonitrile with a microelectrode network using the ferrocene as an internal reference potential in this electrochemical study. Determination of the electron affinity (EA(CT)) of this series of substituted electrodeficient heteroaromatics as well as their LUMO energy was performed using the Charge Transfer Spectroscopic (CTS) method in solution and by DFT calculations, respectively. The use of the correlation EA(CT) versus the reversible half wave potential (E(1/2)(I)) appears to be a useful tool to estimate readily the E(1/2)(I) or EA(CT) values when they cannot be experimentally determined. The diffusion coefficient of these electrophiles has, for the first time, been determined in acetonitrile. These air stable electrodeficient heteroaromatics have been explored as potential new organic acceptors in the formation of charge transfer (CT) complexes with TTF derivatives. Crystallographic data of two CT complexes with TTF (especially the C-C and C-S bond lengths of the TTF moieties) indicate that these complexes exhibit weak electron delocalization and that both molecules remain neutral. Their resulting levels of charge transfer were probed using UV-visible, IR spectroscopy and by DFT calculations.     

Theoretical and experimental studies of CH3X-Y2 rotational line shapes for atmospheric spectra modelling: application to room-temperature CH3Cl-O2

The case of symmetric tops CH(3)X (X = Br, Cl, F, …) perturbed by non-polar diatoms Y(2) (Y = N(2), O(2), …) is analysed from the viewpoint of theoretical collisional broadening of their rotational lines observed in atmospheric spectra. A semi-classical approach involving an exponential representation of the scattering operator and exact trajectories governed by the isotropic potential is presented. For the first time the active molecule is strictly treated as a symmetric top and the atom-atom interactions are included in the intermolecular potential model. It is shown for the CH(3)Cl-O(2) system that these interactions contribute significantly to the line width for all values of the rotational quantum numbers J and K. Additional testing of modifications required in the semi-classical formalism for a correct application of the cumulant expansion is performed and it is shown that the use of the cumulant average on the rotational states of the perturbing molecule leads to entirely negligible effects for the not very strongly interacting CH(3)Cl-O(2) system. In order to check the theoretical predictions and to extend the scarce experimental data available in the literature to higher values of the rotational quantum numbers, new measurements of room-temperature O(2)-broadened CH(3)Cl rotational lines are carried out by a photomixing continuous-wave terahertz spectrometer. The experimental line widths extracted with a Voigt profile model demonstrate an excellent agreement with theoretical results up to very high J-values (J = 31, 37, 40, 45, 50).     

Two-mode dynamics in dispersed systems: the case of particle-stabilized foams studied by diffusing wave spectroscopy

The stabilization of aqueous foams solely by solid particles is an active field of research. Thanks to controlled particle chemistry and production devices, we are able to generate large volumes of such foams. We previously investigated some of their unique properties, especially the strongly reduced coarsening. Here we report another type of study on these foams: performing diffusing wave spectroscopy (DWS), we investigate for the first time the internal dynamics on the scales of both the particles and the bubbles. When compared to surfactant foams, unusual features are observed; in particular, two well-separated modes are found in the dynamics, both evolving with foam aging. We propose an interpretation of these specificities, taking into account both the scattering by free particles in the foam fluid (fast mode), and by the foam structure (slow mode). To validate our interpretation, we show that independent measurements of the interstitial fluid scattering length, obtained indirectly on the foam and directly on the drained liquid, are in good agreement. We have also identified the experimental conditions required to observe such two-process dynamics. Counter-intuitively, the fraction of free particles within the foam interstitial fluid has to be very low to get an optimal signature of these particles on the DWS correlation curves. This study also sheds light on the partitioning of the particles inside the foams and at the interfaces, as the foam ages. Lastly, the results shown here (obtained by analyzing the fluctuations of the transmitted light) implement the previous ones (obtained by analyzing the mean transmitted intensity), and prove that the foam structure is actually not fully frozen.     

Dynamic masking of PIV images using the Radon transform in free surface flows

Particle image velocimetry (PIV) processing of free surface flow images often requires the use of digital masks to overcome the problems caused by the interface. In cases where a large number of particle images are collected it is essential that the time-varying boundary between the two phases can be tracked automatically to produce the binary masks. The Radon transform-based technique presented in this paper allows the automatic detection of the air–water interface in a stream of particle images acquired from a single camera. It is applied to time-resolved PIV measurements in the liquid phase of a stratified multiphase flow in a circular pipe. Accuracy estimations are provided using synthetic and real wave profiles. An extension to the more complex case of an overturning wave is also discussed.