Stability and Perturbations of the Domain for the First Eigenvalue of the 1-Laplacian

We discuss stability of the first eigenvalue of the 1-Laplacian under perturbations of the domain.Comment: 10 page

Active control of sound inside a sphere via control of the acoustic pressure at the boundary surface

Here we investigate the practical feasibility of performing soundfield reproduction throughout a three-dimensional area by controlling the acoustic pressure measured at the boundary surface of the volume in question. The main aim is to obtain quantitative data showing what performances a practical implementation of this strategy is likely to yield. In particular, the influence of two main limitations is studied, namely the spatial aliasing and the resonance problems occurring at the eigenfrequencies associated with the internal Dirichlet problem. The strategy studied is first approached by performing numerical simulations, and then in experiments involving active noise cancellation inside a sphere in an anechoic environment. The results show that noise can be efficiently cancelled everywhere inside the sphere in a wide frequency range, in the case of both pure tones and broadband noise, including cases where the wavelength is similar to the diameter of the sphere. Excellent agreement was observed between the results of the simulations and the measurements. This method can be expected to yield similar performances when it is used to reproduce soundfields.Comment: 28 pages de text

Almost sure optimal hedging strategy

In this work, we study the optimal discretization error of stochastic integrals, in the context of the hedging error in a multidimensional It\^{o} model when the discrete rebalancing dates are stopping times. We investigate the convergence, in an almost sure sense, of the renormalized quadratic variation of the hedging error, for which we exhibit an asymptotic lower bound for a large class of stopping time strategies. Moreover, we make explicit a strategy which asymptotically attains this lower bound a.s. Remarkably, the results hold under great generality on the payoff and the model. Our analysis relies on new results enabling us to control a.s. processes, stochastic integrals and related increments.Comment: Published in at http://dx.doi.org/10.1214/13-AAP959 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Contribution of studies of sub-seismic fracture populations to paleo-hydrological reconstructions (Bighorn Basin, USA)

This work reports on the reconstruction of the paleo-hydrological history of the Bighorn Basin (Wyoming, USA) and illustrates the advantages and drawbacks of using sub-seismic diffuse fracture populations (i.e., micrometric to metric joints and veins forming heterogeneous networks), rather than fault zones, to characterize paleo-fluid systems at both fold and basin scales. Because sub-seismic fractures reliably record the successive steps of deformation of folded rocks, the analysis of the geochemical signatures of fluids that precipitated in these fractures reveals the paleo-fluid history not only during, but also before and after, folding. The present study also points out the need for considering pre-existing fluid systems and basin-scale fluid migrations to reliably constrain the evolution of fluid systems in individual folds

Quantum Measurements, Energy Conservation and Quantum Clocks

We consider a spin chain extending from Alice to Bob with next neighbors interactions, initially in its ground state. Assuming that Bob measures the last spin of the chain, the energy of the spin chain has to increase, at least on average, due to the measurement disturbance. Presumably, the energy is provided by Bob's measurement apparatus. Assuming now that, simultaneously to Bob's measurement, Alice measures the first spin, we show that either energy is not conserved, - implausible - or the projection postulate doesn't apply, and that there is signalling. An explicit measurement model shows that energy is conserved (as expected), but that the spin chain energy increase is not provided by the measurement apparatus(es), that the projection postulate is not always valid - illustrating the Wigner-Araki-Yanase (WAY) theorem - and that there is signalling, indeed. The signalling is due to the non-local interaction Hamiltonian. This raises the question of a suitable quantum information inspired model of such non-local Hamiltonians.Comment: 7 pages + appendices, 6 figure