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

Relative amenability

We introduce a relative fixed point property for subgroups of a locally compact group, which we call relative amenability. It is a priori weaker than amenability. We establish equivalent conditions, related among others to a problem studied by Reiter in 1968. We record a solution to Reiter's problem. We study the class X of groups in which relative amenability is equivalent to amenability for all closed subgroups; we prove that X contains all familiar groups. Actually, no group is known to lie outside X. Since relative amenability is closed under Chabauty limits, it follows that any Chabauty limit of amenable subgroups remains amenable if the ambient group belongs to the vast class X.Comment: We added a solution to Reiter's problem and a discussion of L^1-equivarianc

Google QUIC performance over a public SATCOM access

Google QUIC accounts for almost 10% of the Internet traffic and the protocol is not standardized at the IETF yet. We distinguish Google QUIC (GQUIC) and IETF QUIC (IQUIC) since there may be differences between the two. Both Google and IETF versions run over UDP and cannot be split the way satellite systems usually do with TCP connections. The need for adapting any-QUIC parameters needs to be evaluated. Since GQUIC is available, we analyze its behavior over a satellite communication system. In our evaluations, GQUIC quick connection establishment does not compensate an inappropriate congestion control. The resulting page downloading time doubles when using GQUIC as opposed to the performance with optimized split TCP connections. This paper concludes that specific tuning are required when any-QUIC runs over a high BDP network.Comment: To appear in International Journal of Satellite Communications and Networking. 13 pages, 8 figure

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

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