Partial differential equations from integrable vertex models

In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the $U_q[\widehat{\mathfrak{sl}}(2)]$ invariant six-vertex model and the resulting partial differential equation is studied for particular values of the lattice length.Comment: 19 pages. v2: affiliation and references updated, minor changes, accepted for publication in J. Math. Phy

Refined functional relations for the elliptic SOS model

In this work we refine the method of [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation is originated from the dynamical Yang-Baxter algebra and its solution is given in terms of multiple contour integrals.Comment: v2: details of derivations and reference added, typos fixed, accepted for publication in NP

Multiple integral representation for the trigonometric SOS model with domain wall boundaries

Using the dynamical Yang-Baxter algebra we derive a functional equation for the partition function of the trigonometric SOS model with domain wall boundary conditions. The solution of the equation is given in terms of a multiple contour integral.Comment: 28 pages, v2: comments and references added, typos fixed, to appear in NP

Water quality monitor

The preprototype water quality monitor (WQM) subsystem was designed based on a breadboard monitor for pH, specific conductance, and total organic carbon (TOC). The breadboard equipment demonstrated the feasibility of continuous on-line analysis of potable water for a spacecraft. The WQM subsystem incorporated these breadboard features and, in addition, measures ammonia and includes a failure detection system. The sample, reagent, and standard solutions are delivered to the WQM sensing manifold where chemical operations and measurements are performed using flow through sensors for conductance, pH, TOC, and NH3. Fault monitoring flow detection is also accomplished in this manifold assembly. The WQM is designed to operate automatically using a hardwired electronic controller. In addition, automatic shutdown is incorporated which is keyed to four flow sensors strategically located within the fluid system

Sphenopteris sellardsii, a problematical pteridosperm from the Permian of Kansas

8 p., 4 fig.http://paleo.ku.edu/contributions.htm

Fungi at the Field Station

The UWM Field Station now has a mycological reference collection, for use in identifying fungi of the area. Botanists and zoologists doing research at the Field Station will find the collection useful. It can also be used by visiting groups who have some interest in identifying the more conspicuous fungi that are likely to be seen during a tour of the area

New critical frontiers for the Potts and percolation models

We obtain the critical threshold for a host of Potts and percolation models on lattices having a structure which permits a duality consideration. The consideration generalizes the recently obtained thresholds of Scullard and Ziff for bond and site percolation on the martini and related lattices to the Potts model and to other lattices.Comment: 9 pages, 5 figure

Critical and Tricritical Hard Objects on Bicolorable Random Lattices: Exact Solutions

We address the general problem of hard objects on random lattices, and emphasize the crucial role played by the colorability of the lattices to ensure the existence of a crystallization transition. We first solve explicitly the naive (colorless) random-lattice version of the hard-square model and find that the only matter critical point is the non-unitary Lee-Yang edge singularity. We then show how to restore the crystallization transition of the hard-square model by considering the same model on bicolored random lattices. Solving this model exactly, we show moreover that the crystallization transition point lies in the universality class of the Ising model coupled to 2D quantum gravity. We finally extend our analysis to a new two-particle exclusion model, whose regular lattice version involves hard squares of two different sizes. The exact solution of this model on bicolorable random lattices displays a phase diagram with two (continuous and discontinuous) crystallization transition lines meeting at a higher order critical point, in the universality class of the tricritical Ising model coupled to 2D quantum gravity.Comment: 48 pages, 13 figures, tex, harvmac, eps