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

Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation

Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent) formal power series which follow from the perturbative evaluation of arbitrary "$N$-point" functions for the simple case of zero-dimensional $\phi^4$ field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.Comment: v2: one reference added, one paragraph added in the conclusions, small changes in the text, corrected typos; v3: published versio

Asymptotic expansions of Feynman diagrams and the Mellin-Barnes representation

In this talk, we describe part of our recent work \cite{FGdeR05} (see also \cite{F05,G05}) that gives new results in the context of asymptotic expansions of Feynman diagrams using the Mellin-Barnes representation.Comment: Talk given at the $12^{th}$ High-Energy Physics International Conference on Quantum Chromodynamics, 4-8 July (2005), Montpellier (France

Anomalous GPDs in the photon

We consider deeply virtual Compton scattering (DVCS) on a photon target, in the generalized Bjorken limit, at the Born order and in the leading logarithmic approximation. This leads us to the extraction of the photon anomalous generalized parton distributions (GPDs) \cite{url, DVCSphoton}.Comment: To appear in the proceedings of Photon 2007: International Conference on the Structure and Interactions of the Photon and the 17th International Workshop on Photon-Photon Collisions and International Workshop on High Energy Photon Linear Colliders, Paris, France, 9-13 Jul 200

Time-domain versus frequency-domain effort weighting in active noise control

Although Active Noise Control aims at reducing the noise at a set of error sensors, it is often designed by minimizing an error index that includes a weightedpenalty on the actuator inputs. In this way, the control tends to be more robust and the effort-weighting parameter allows the maximum voltages applied to the control sources to be monitored. Two similar effort-weighting techniques have been widely implemented in active control studies: optimal control can be computed using Tikhonov regularization in frequency-domain simulations, whereas the leaky Filtered-reference least mean squares algorithm can be implemented for real-time feedforward control. This paper makes explicit the relationship between the two effort-weighting parameters which lead, in the case of a single-tone noise, to exactly the same error index in both the time and frequency domains. The best real-time leakage factor can then be computed from frequency-domain optimization. This paper also discusses numerical simulations of a single-channel set-up, showing that with these two related parameters, the control performances are indeed very similar. One exception occurs in the case of a control flter with a very short impulse response, when the control is more conservative in the time-domain simulations than in those of the frequency-domain

Chaotic iterations versus Spread-spectrum: chaos and stego security

A new framework for information hiding security, called chaos-security, has been proposed in a previous study. It is based on the evaluation of unpredictability of the scheme, whereas existing notions of security, as stego-security, are more linked to information leaks. It has been proven that spread-spectrum techniques, a well-known stego-secure scheme, are chaos-secure too. In this paper, the links between the two notions of security is deepened and the usability of chaos-security is clarified, by presenting a novel data hiding scheme that is twice stego and chaos-secure. This last scheme has better scores than spread-spectrum when evaluating qualitative and quantitative chaos-security properties. Incidentally, this result shows that the new framework for security tends to improve the ability to compare data hiding scheme

Lyapunov exponent evaluation of a digital watermarking scheme proven to be secure

In our previous researches, a new digital watermarking scheme based on chaotic iterations has been introduced. This scheme was both stego-secure and topologically secure. The stego-security is to face an attacker in the "watermark only attack" category, whereas the topological security concerns other categories of attacks. Its Lyapunov exponent is evaluated here, to quantify the chaos generated by this scheme. Keywords : Lyapunov exponent; Information hiding; Security; Chaotic iterations; Digital Watermarking.Comment: 10 page