8,219 research outputs found
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
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