Chemistry and Apparent Quality of Surface Water and Ground Water Associated with Coal Basins

Personnel of the Arkansas Mining and Mineral Resources Research Institute conducted preliminary investigations on the chemistry and quality of surface and ground water associated with 12 coal-bearing sub-basins in the Arkansas Valley coal field. The coal field is approximately 60 miles long and 33 miles wide but only in 12 areas coal is thick enough and has proper quality to be termed commercial. Both surface and underground sample sites were established in each of the sub-basins with some minor variations in four areas where not all types of sites could be located. Water was collected from 19 surface points and 19 underground points in the established areas. Both field and laboratory analyses were made and elemental contents are reported herein. In the main, the chemistry and water quality suggests that all water is suitable for agricultural and industrial uses. To obtain potable water, treatment must be made to reduce calcium, magnesium, sodium sulfate and iron. The mineral content of the water is due to its contact with coal-bearing zones and, as such, reflects the mineral content of the coal. However, it is recommended that additional studies on the petrography and geochemistry of the coal, overburden and underburden is in order. Also, it is recommended that at least one detailed study be made of one of the coal sub-basins where geologic parameters can be completely established with regard to hydrogeology. This report is an important first step in determining the character and quality of Arkansas coal which must be fully understood to fully utilize this important mineral resource

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

Top, Bottom Quarks and Higgs Bosons

In this talk, I will discuss possible new physics effects that modify the interaction of Higgs boson(s) with top and bottom quarks, and discuss how to detect such effects in current and future high energy colliders.Comment: LaTeX, 16 pages including 5 figure

Critical Exponents of the Four-State Potts Model

The critical exponents of the four-state Potts model are directly derived from the exact expressions for the latent heat, the spontaneous magnetization, and the correlation length at the transition temperature of the model.Comment: LaTex, 7 page

Mean Field Renormalization Group for the Boundary Magnetization of Strip Clusters

We analyze in some detail a recently proposed transfer matrix mean field approximation which yields the exact critical point for several two dimensional nearest neighbor Ising models. For the square lattice model we show explicitly that this approximation yields not only the exact critical point, but also the exact boundary magnetization of a semi--infinite Ising model, independent of the size of the strips used. Then we develop a new mean field renormalization group strategy based on this approximation and make connections with finite size scaling. Applying our strategy to the quadratic Ising and three--state Potts models we obtain results for the critical exponents which are in excellent agreement with the exact ones. In this way we also clarify some advantages and limitations of the mean field renormalization group approach.Comment: 16 pages (plain TeX) + 8 figures (PostScript, appended), POLFIS-TH.XX/9

Critical Percolation in Finite Geometries

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only under changes of scale, but also under mappings of the region which are conformal in the interior and continuous on the boundary. This is a larger invariance than that expected for generic critical systems. Specific predictions are presented for the crossing probability between opposite sides of a rectangle, and are compared with recent numerical work. The agreement is excellent.Comment: 10 page

Internal Energy of the Potts model on the Triangular Lattice with Two- and Three-body Interactions

We calculate the internal energy of the Potts model on the triangular lattice with two- and three-body interactions at the transition point satisfying certain conditions for coupling constants. The method is a duality transformation. Therefore we have to make assumptions on uniqueness of the transition point and that the transition is of second order. These assumptions have been verified to hold by numerical simulations for q=2, 3 and 4, and our results for the internal energy are expected to be exact in these cases.Comment: 9 pages, 4 figure

NONLINEAR REGRESSION FUNCTIONS FOR FORAGE NUTRIENT DISAPPEARANCE FROM BAGS INCUBATED IN THE RUMEN

Seven nonlinear regression functions are compared for fitting rumen in situ disappearance data. The standard function is based on a simple one-compartment model. In addition, we consider a time lag modification, a two-compartment model, and functions based on underlying probability models for degradation time. The empirical suitability of the seven regression functions are assessed using two in situ experiments involving forages fed to dairy cows. A function based on the loglogistic distribution is shown to have empirical and theoretical advantages

Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.Comment: 7 pages, Latex, 4 figs., J. Phys. A Lett., in pres