Edges and Diffractive Effects in Casimir Energies

The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single plate with a slit in it, perpendicular plates separated by a gap, and two parallel plates, one of which has a long slit of large width, related to the case of one plate being semi-infinite. We develop a general formalism for studying such problems, based on the wavefunctional for the field in the gap between the plates. This formalism leads to a lower dimensional theory defined on the open regions of the plates or boundaries. The Casimir energy is then given in terms of the determinant of the nonlocal differential operator which defines the lower dimensional theory. We develop perturbative methods for computing these determinants. Our results are in good agreement with known results based on Monte Carlo simulations. The method is well suited to isolating the diffractive contributions to the Casimir energy.Comment: 32 pages, LaTeX, 9 figures. v2: additional discussion of renormalization procedure, version to appear in PRD. v3: corrected a sign error in (70

Potential-based methodology for active sound control in three dimensional settings

This paper extends a potential-based approach to active noise shielding with preservation of wanted sound in three-dimensional settings. The approach, which was described in a previous publication [Lim et al., J. Acoust. Soc. Am. 129(2), 717–725 (2011)], provides several significant advantages over conventional noise control methods. Most significantly, the methodology does not require any information including the characterization of sources, impedance boundary conditions and surrounding medium, and that the methodology automatically differentiates between the wanted and unwanted sound components. The previous publication proved the concept in one-dimensional conditions. In this paper, the approach for more realistic conditions is studied by numerical simulation and experimental validation in three-dimensional cases. The results provide a guideline to the implementation of the active shielding method with practical three-dimensional conditions. Through numerical simulation it is demonstrated that while leaving the wanted sound unchanged, the developed approach offers selective volumetric noise cancellation within a targeted domain. In addition, the method is implemented in a three-dimensional experiment with a white noise source in a semi-anechoic chamber. The experimental study identifies practical difficulties and limitations in the use of the approach for real applications