An instrument to measure atmospheric pressure fluctuations above surface gravity waves

This paper describes an instrument which has been used successfully at a field site in the Bight of Abaco, Bahamas, to monitor the atmospheric pressure field above surface gravity waves in the frequency range .5 to 5. rad/s. The atmospheric pressure is sampled at fixed elevations with a cone-shaped probe having a pressure coefficient of less than .02 magnitude for angles of attack less than 15°; the probe is mounted on a vane to minimize horizontal angles of attack. The pressure signal is conducted to a subsurface transducer through a mercury-sealed bearing. Overall system noise is estimated to be of order .5 µbars and is largely wave-incoherent

Toeplitz operators on symplectic manifolds

We study the Berezin-Toeplitz quantization on symplectic manifolds making use of the full off-diagonal asymptotic expansion of the Bergman kernel. We give also a characterization of Toeplitz operators in terms of their asymptotic expansion. The semi-classical limit properties of the Berezin-Toeplitz quantization for non-compact manifolds and orbifolds are also established.Comment: 40 page

On the algebraic index for riemannian \'etale groupoids

In this paper we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a riemannian \'etale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for riemannian \'etale groupoids. We discuss solutions to that index problem when the groupoid is proper or defined by a constant Dirac structure on a 3-dim torus.Comment: 19 page

Symmetry Reduction by Lifting for Maps

We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies existence of an invariant. Conversely, a map with an invariant need not have a symmetry. We show that when a symmetry flow has a global Poincar\'{e} section there are coordinates in which the map takes a reduced, skew-product form, and hence allows for reduction of dimensionality. We show that the reduction of a volume-preserving map again is volume preserving. Finally we sharpen the Noether theorem for symplectic maps. A number of illustrative examples are discussed and the method is compared with traditional reduction techniques.Comment: laTeX, 31 pages, 5 figure

All bicovariant differential calculi on Glq(3,C) and SLq(3,C)

All bicovariant first order differential calculi on the quantum group GLq(3,C) are determined. There are two distinct one-parameter families of calculi. In terms of a suitable basis of 1-forms the commutation relations can be expressed with the help of the R-matrix of GLq(3,C). Some calculi induce bicovariant differential calculi on SLq(3,C) and on real forms of GLq(3,C). For generic deformation parameter q there are six calculi on SLq(3,C), on SUq(3) there are only two. The classical limit q-->1 of bicovariant calculi on SLq(3,C) is not the ordinary calculus on SL(3,C). One obtains a deformation of it which involves the Cartan-Killing metric.Comment: 24 pages, LaTe

A variant of the Mukai pairing via deformation quantization

We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler, Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped that our method is useful for generalization to settings involving certain singular varieties.Comment: 8 pages. Comments and suggestions welcom

Gauge Orbit Types for Theories with Classical Compact Gauge Group

We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or $Sp(n)$ over a closed, simply connected manifold of dimension 4. Complemented with earlier results on U(n) and SU(n) this completes the classification of the orbit types for all classical compact gauge groups over such space-time manifolds. On the way we derive the classification of principal bundles with structure group SO(n) over these manifolds and the Howe subgroups of SO(n).Comment: 57 page

Structural Transitions and Global Minima of Sodium Chloride Clusters

In recent experiments on sodium chloride clusters structural transitions between nanocrystals with different cuboidal shapes were detected. Here we determine reaction pathways between the low energy isomers of one of these clusters, (NaCl)35Cl-. The key process in these structural transitions is a highly cooperative rearrangement in which two parts of the nanocrystal slip past one another on a {110} plane in a direction. In this way the nanocrystals can plastically deform, in contrast to the brittle behaviour of bulk sodium chloride crystals at the same temperatures; the nanocrystals have mechanical properties which are a unique feature of their finite size. We also report and compare the global potential energy minima for (NaCl)NCl- using two empirical potentials, and comment on the effect of polarization.Comment: extended version, 13 pages, 8 figures, revte

The Inverse Ocean Modeling System. Part I: Implementation

The Inverse Ocean Modeling (IOM) system constructs and runs weak-constraint, four-dimensional variational data assimilation (W4DVAR) for any dynamical model and any observing array. The dynamics and the observing algorithms may be nonlinear but must be functionally smooth. The user need only provide the model and the observing algorithms, together with an interpolation scheme that relates the model numerics to the observer’s coordinates. All other model-dependent elements of the Inverse Ocean Modeling assimilation algorithm (see both Chua and Bennett), including adjoint generators and Monte Carlo estimates of posteriors, have been derived and coded as templates in Parametric FORTRAN (Erwig et al.). This language has been developed for the IOM but has wider application in scientific programming. Guided by the Parametric FORTRAN templates, and by model information entered via a graphical user interface (GUI), the IOM generates conventional FORTRAN code for each of the many algorithm elements, customized to the user’s model. The IOM also runs the various W4DVAR assimilations, which are monitored by the GUI. The system is supported by a Web site that includes interactive tutorials for the assimilation algorithm.Keywords: Data assimilation, Ocean models, Variational analysi