Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Flow convergence and stability at a tidal estuarine front: Acoustic Doppler current observations

Characteristics of the flow field in an estuarine frontal zone have been investigated in a field study in the lower James River estuary. Underway sampling with an acoustic Doppler current profiler (ADCP) on repeated transects across the front provided information on the structure of the flow field near the front and its evolution in time. As this tidal intrusion front advanced up the estuary during the flooding tide, prominent and consistent features in the velocity field included a localized zone of convergent flow beneath the visible surface line and a stratified shear layer just upriver of the front. Within the shear layer between the buoyant surface water and the faster, higher-salinity undercurrent, gradient Richardson number estimates suggest that the flow was at or near the threshold for sheer instability. Another shear-type gradient in the flow field, the across-front variation of the along-front velocity component, strengthened over a sequence of transects, with intensity increasing toward the surface. Tracking of the front was then interrupted when the identifying line of foam and accumulated material on the surface, previously sharp and well defined, broke up and dispersed to such an extent that the visible signature of the front was lost temporarily. A visible frontal expression later reappeared, and propagation upriver continued. Lower bound estimates of downwelling flow in the frontal zone were determined by continuity considerations

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation

Constructing habitus: promoting an international arts trend at the Singapore Arts Festival

The Singapore Arts Festival (SAF) is Singapore’s largest government-supported international arts festival. SAF presents the best in international and local arts, in an attempt, to develop what it perceives to be a lack of cultural knowledge of the Singaporean arts-going public. Using Pierre Bourdieu’s key concept of ‘habitus’ together with an analysis of the programming of the festival, this paper will highlight how the festival seeks to create a specific cultural taste in Singaporean art-goers through privileging and promoting works that are internationally marketable to European countries. The paper will conclude that this programming style occurs at the expense of Singaporean artists and hinders the development of the city’s state cultural and artistic development

Physical Response of the York River Estuary to Hurricane Isabel

After making landfall on the North Carolina coast on the morning of 18 September 2003, Category 2 Hurricane Isabel tracked northward parallel to and slightly west of the Chesapeake Bay. At Gloucester Point, near the mouth of the York River estuary, strong onshore winds with speeds in excess of 20 m⋅s-1 persisted for over 12 hours and peak winds reached over 40 m⋅s-1, causing a sustained up-estuary wind stress. Storm surge exceeded 2 m throughout most of the lower Chesapeake Bay. A 600 kHz acoustic Doppler current profiler (ADCP), deployed at a depth of 8.5 m off Gloucester Point, provided high-quality data on waves, storm surge, currents, and acoustic backscatter throughout the water column before, during, and after the storm. Pressure and salinity sensors at three additional sites further up the estuary provided information on water surface slope and saltwater excursion up the estuary. A first-order estimate of three terms of the along-channel momentum equation (barotropic pressure gradient, acceleration, and friction) showed that the pressure gradient appeared to be balanced by the wind stress and the acceleration during the storm. The storm’s path and slow speed were the primary causes of the extremely high storm surge relative to past storms in the area.https://scholarworks.wm.edu/vimsbooks/1001/thumbnail.jp

Superconducting properties of nanocrystalline MgB2_2 thin films made by an in situ annealing process

We have studied the structural and superconducting properties of MgB$_2$ thin films made by pulsed laser deposition followed by in situ annealing. The cross-sectional transmission electron microscopy reveals a nanocrystalline mixture of textured MgO and MgB$_2$ with very small grain sizes. A zero-resistance transition temperature ($T_{c0}$) of 34 K and a zero-field critical current density ($J_c$) of $1.3 \times 10^6$ A/cm$^2$ were obtained. The irreversibility field was $\sim$ 8 T at low temperatures, although severe pinning instability was observed. These bulk-like superconducting properties show that the in situ deposition process can be a viable candidate for MgB$_2$ Josephson junction technologies

Young tableaux and crystal B(∞)B(\infty) for finite simple Lie algebras

We study the crystal base of the negative part of a quantum group. An explicit realization of the crystal is given in terms of Young tableaux for types $A_n$, $B_n$, $C_n$, $D_n$, and $G_2$. Connection between our realization and a previous realization of Cliff is also given