1,705 research outputs found
Inverse scattering results for manifolds hyperbolic near infinity
We study the inverse resonance problem for conformally compact manifolds
which are hyperbolic outside a compact set. Our results include compactness of
isoresonant metrics in dimension two and of isophasal negatively curved metrics
in dimension three. In dimensions four or higher we prove topological
finiteness theorems under the negative curvature assumption.Comment: 25 pages. v3: Minor corrections, references adde
Matrix Cartan superdomains, super Toeplitz operators, and quantization
We present a general theory of non-perturbative quantization of a class of
hermitian symmetric supermanifolds. The quantization scheme is based on the
notion of a super Toeplitz operator on a suitable Z_2 -graded Hilbert space of
superholomorphic functions. The quantized supermanifold arises as the C^*
-algebra generated by all such operators. We prove that our quantization
framework reproduces the invariant super Poisson structure on the classical
supermanifold as Planck's constant tends to zero.Comment: 52
Supersymmetry and Fredholm modules over quantized spaces
The purpose of this paper is to apply the framework of non- commutative
differential geometry to quantum deformations of a class of Kahler manifolds.
For the examples of the Cartan domains of type I and flat space, we construct
Fredholm modules over the quantized manifolds using the supercharges which
arise in the quantization of supersymmetric generalizations of the manifolds.
We compute the explicit formula for the Chern character on generators of the
Toeplitz C^* -algebra.Comment: 24
Energy potential of a tidal fence deployed near a coastal headland
Enhanced tidal streams close to coastal headlands appear to present ideal locations for the deployment of tidal energy devices. In this paper, the power potential of tidal streams near an idealized coastal headland with a sloping seabed is investigated using a near-field approximation to represent a tidal fence, i.e. a row of tidal devices, in a two-dimensional depth-averaged numerical model. Simulations indicate that the power extracted by the tidal fence is limited because the flow will bypass the fence, predominantly on the ocean side, as the thrust applied by the devices increases. For the dynamic conditions, fence placements and headland aspect ratios considered, the maximum power extracted at the fence is not related in any obvious way to the local undisturbed kinetic flux or the natural rate of energy dissipation due to bed friction (although both of these have been used in the past to predict the amount of power that may be extracted). The available power (equal to the extracted power net of vertical mixing losses in the immediate wake of devices) is optimized for devices with large area and small centre-to-centre spacing within the fence. The influence of energy extraction on the natural flow field is assessed relative to changes in the M2 component of elevation and velocity, and residual bed shear stress and tidal dispersion
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