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

Noncommutative Common Cause Principles in Algebraic Quantum Field Theory

States in algebraic quantum field theory "typically" establish correlation between spacelike separated events. Reichenbach's Common Cause Principle, generalized to the quantum field theoretical setting, offers an apt tool to causally account for these superluminal correlations. In the paper we motivate first why commutativity between the common cause and the correlating events should be abandoned in the definition of the common cause. Then we show that the Noncommutative Weak Common Cause Principle holds in algebraic quantum field theory with locally finite degrees of freedom. Namely, for any pair of projections A, B supported in spacelike separated regions V_A and V_B, respectively, there is a local projection C not necessarily commuting with A and B such that C is supported within the union of the backward light cones of V_A and V_B and the set {C, non-C} screens off the correlation between A and B

Jesus Using Our Lives and Communion

...But this morning I want you to realize that in God\u27s goodness, a message that sort of come out throughout the week is in God\u27s goodness, He chooses to use us and to sort of frame our thinking along that. I\u27m going to talk about another meal, not this one, but a miracle meal. And if you have your Bibles, I\u27ll be reading from John\u27s Gospel chapter six. John\u27s Gospel, chapter six. Now this is the story of the feeding of the 5,000. I\u27m not going to be exegeting the passage per se, but I am going to use it as a framework to think about the fact that what really matters is not the size of your lunch, but rather whether you\u27ll give it to Jesus

Modelling tidal energy extraction in a depth-averaged coastal domain

An extension of actuator disc theory is used to describe the properties of a tidal energy device, or row of tidal energy devices, within a depth-averaged numerical model. This approach allows a direct link to be made between an actual tidal device and its equivalent momentum sink in a depth-averaged domain. Extended actuator disc theory also leads to a measure of efficiency for an energy device in a tidal stream of finite Froude number, where efficiency is defined as the ratio of power extracted by one or more tidal devices to the total power removed from the tidal stream. To demonstrate the use of actuator disc theory in a depth-averaged model, tidal flow in a simple channel is approximated using the shallow water equations and the results are compared with the published analytical solutions. © 2010 © The Institution of Engineering and Technology

Legendrian Distributions with Applications to Poincar\'e Series

Let $X$ be a compact Kahler manifold and $L\to X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $\Lambda$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences $\{ |\Lambda, k\rangle \}_{k=1}^\infty$, where $\forall k$ $|\Lambda, k\rangle$ is a holomorphic section of $L^{\otimes k}$. The terms in each sequence concentrate on $\Lambda$, and a sequence itself has a symbol which is a half-form, $\sigma$, on $\Lambda$. We prove estimates, as $k\to\infty$, of the norm squares $\langle \Lambda, k|\Lambda, k\rangle$ in terms of $\int_\Lambda \sigma\overline{\sigma}$. More generally, we show that if $\Lambda_1$ and $\Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $\langle\Lambda_1, k|\Lambda_2, k\rangle$ have an asymptotic expansion as $k\to\infty$, the leading coefficient being an integral over the intersection $\Lambda_1\cap\Lambda_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincar\'e series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.Comment: 41 pages, LaTe

Power extraction by a water turbine in inviscid free surface flow with vertical shear

Hydro-kinetic, tidal stream, and ocean current energy turbines operate in flows subject to vertical shear, which has an influence on the turbines, especially ones located near the bed. The gravity applied on a fluid is proportional to its density, thus the static pressure induced by gravity is enhanced by the higher density of water than air. Turbines are expected to be placed in fast moving, shallow flows. Hence the Froude number may be relatively high and changes to the free surface are likely, leading to additional flow confinement. In order to investigate the combined effect of vertical shear and gravity on idealized turbines, an extension of linear momentum actuator disc theory (LMADT) is used to estimate the thrust and power extracted by an idealized turbine for two types of free surface inviscid flow. It is assumed that there is fast pressure recovery and that the core flow contains self-similar velocity profiles. Results from a parameter study in which the velocity profiles and turbine settings are varied show that idealized turbines operate at higher efficiency under the effect of gravity, but operate at either higher or lower efficiency under shear flow. The proposed model can also be used to investigate energy extracted by turbines in a periodically spaced array, enabling better evaluation of array efficiency

Semiclassical almost isometry

Let M be a complex projective manifold, and L an Hermitian ample line bundle on it. A fundamental theorem of Gang Tian, reproved and strengthened by Zelditch, implies that the Khaeler form of L can be recovered from the asymptotics of the projective embeddings associated to large tensor powers of L. More precisely, with the natural choice of metrics the projective embeddings associated to the full linear series |kL| are asymptotically symplectic, in the appropriate rescaled sense. In this article, we ask whether and how this result extends to the semiclassical setting. Specifically, we relate the Weinstein symplectic structure on a given isodrastic leaf of half-weighted Bohr-Sommerfeld Lagrangian submanifolds of M to the asymptotics of the the pull-back of the Fubini-Study form under the semiclassical projective maps constructed by Borthwick, Paul and Uribe.Comment: exposition improve