The outbreak of plague (so-called) in South Australia

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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

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

Geometric Quantization on the Super-Disc

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a certain super-homogeneous space. First, we define an example of a super-homogeneous manifold: a super-disc. We show that it has a natural symplectic form, it can be used to introduce classical dynamics once a Hamiltonian is chosen. Existence of moment maps provide a Poisson realization of the underlying symmetry super-group. These are the natural operators to quantize via methods of geometric quantization, and we show that this can be done.Comment: 17 pages, Latex file. Subject: Mathematical physics, geometric quantizatio

Large N limit of SO(N) gauge theory of fermions and bosons

In this paper we study the large N_c limit of SO(N_c) gauge theory coupled to a Majorana field and a real scalar field in 1+1 dimensions extending ideas of Rajeev. We show that the phase space of the resulting classical theory of bilinears, which are the mesonic operators of this theory, is OSp_1(H|H )/U(H_+|H_+), where H|H refers to the underlying complex graded space of combined one-particle states of fermions and bosons and H_+|H_+ corresponds to the positive frequency subspace. In the begining to simplify our presentation we discuss in detail the case with Majorana fermions only (the purely bosonic case is treated in our earlier work). In the Majorana fermion case the phase space is given by O_1(H)/U(H_+), where H refers to the complex one-particle states and H_+ to its positive frequency subspace. The meson spectrum in the linear approximation again obeys a variant of the 't Hooft equation. The linear approximation to the boson/fermion coupled case brings an additonal bound state equation for mesons, which consists of one fermion and one boson, again of the same form as the well-known 't Hooft equation.Comment: 27 pages, no figure

Probabilistic Weyl laws for quantized tori

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.Comment: 33 pages, 3 figures, v2 corrected listed titl

Remarks on the naturality of quantization

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's constant, the Hilbert spaces of the quantization form a bundle over U with a natural connection. In this paper we examine the dependence of the Hilbert spaces on the choice of J, by computing the semi-classical limit of the curvature of this connection. We also show that parallel transport provides a link between the action of the group Symp(M) of symplectomorphisms of M and the Schrodinger equation.Comment: 20 page