Equine Review

This article contains a quiz pertaining to topics of equine medicine for the benefit of students of the College of Veterinary Medicine

Basic linear algebra subprograms for FORTRAN usage

A package of 38 low level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of components of largest magnitude. The subprograms and a test driver are available in portable FORTRAN. Versions of the subprograms are also provided in assembly language for the IBM 360/67, the CDC 6600 and CDC 7600, and the Univac 1108

A Mathematical Hydrodynamic Circulation Model of Great Salt Lake for Resource Management

In the Great Basin region of this country, the resource which has always been of great importance is water. In Utah, the proper management of the resources of Great Salt Lake and the watersheds tributary to it, has become a topic of increasing concern. Recently, much emphasis has been placed on developing the recreational and industrial resources of Great Salt Lake. For optimum economic and social benefits from future development plans, the lake and its tributary watersheds need to be considered in terms of a single entity. In this regard, the Utah Water Research Laboratory (UWRL) has conducted several studies which involve hydrologic basins tributary to Great Salt Lake. Significantly lacking, however, was a comprehensive study of Great Salt Lake itself. The reserach reported herein is directed towards the development of a comprehensive predictive hydrodynamic model of Great Salt Lake (see Figure 1). This model provides two general types of information. First, it provides circulation patterns within the lake for configurations and conditions imposed by the planner. This information is necessary to predict movement of pollutants, paths of freshwater inflows, and other phenomena which depend on currents. Second, the model provides information on the distribution of salinity throughout the lake. This informatino is vital to the industries around the lake which extract minerals from the brines of the lake. These capabilities of the model will also be valuable in providing data to be used by quality models. It could be argued that because of a lack of field data for model verification, the development of a mathematical model was premature. Some field data on salinity are being collected regularly and the data base is steadily growing. Hopefully, the Utah Separtment of Natural Resources will implement a program of measuring velocities and circulation patterns to provide a data base for calibrating the hydraulic model. In any case, the initial development of a mathematical model is appropriate so that over the next few years, it can be improved and adjusted as more data become available. It seemed unwise to wait for a complete data base before launching a lengthy program of development of a mathematical model. The objectives of the research were as follows: 1. To develop new mathematical models or incorporate existing models of the flow through the Southern Pacific causeway embankment and culverts to act as boundary conditions in mathementical circulation models of the southern and northern arms of the Great Salt Lake. 2. To develop an upper-layer hydrodynamic circulation model of Great Salt Lake. As a first step toward developing a more comprehensive two-layer model, it was recognized that the main function of the lower layer within the lake may be to act as a reservoir for passing salinity from the north arm to the surface layer in the south arm. If this is indeed the case, then an upper-layer model could be constucted based on the assumption that the interface is a horizontal boundary which feeds salinity itno the upper layer in some reasonable fashion to maintain continuity. 3. To attempt to develop a coupled two-layer model of Great Salt Lake. It was proposed to use the finite element technique to generate a hydrodynamic model of the circulation patterns in both the upper and lower layers. The finite element representation incorporates cubic velocity variations in the two layers to more accurately simulate the recircualtion flow patterns caused by wind action on the surface and fresh water flow from the contributing streams. 4. To perform a laboratory experiment devised to evaluate the rate of salinity exchange from the lower high-density layer through the interfacial shear zone into the upper layer. It was believed that the exchange of salinity between the two layers is a direct function of the intensity of the interfacial shear and the resulting turbulent mixing at the interface. 5. To attempt to adjust the model to Great Salt Lake. All available velocity and salinity concentration data collected by the United States Geological Survey (USGS) and the Utah Geological and Mineral Survey (UGMS) during recent years was used. 6. To cooperate with researchers who are studying other aspects of the lake by making the mathematical model available to them. A modeling appraoch utilizing equations based on the fundamental laws of physics, coupled with the application of the versatile finite element method gives the hydrodynamic and convetion-dispersion models of Great Salt Lake the versatility required to examine the spectrum of management alternatives. The predictive capability is greatly enhanced in this approach by minimizing the number of empirical constants to be evlatued. It seems clear that the development of these comprehensive models of the lake is a necessary step in the subsequent development and use of both water quality and management models of this important natural resource

The Application of Finite Element Method Analysis to Eddy Current NDE

The Finite Element Method for the computation of eddy current fields is presented. The method is described for geometries with a one component eddy current field. The use of the method for the calculation of the impedance of eddy current sensors in the vicinity of defects is shown. An example is given of the method applied to a C-magnet type sensor positioned over a crack in a plane conducting material

Progress in Solving the 3-Dimensional Inversion Problem for Eddy Current NDE

The eddy current NDE inversion problem is to determine the parameters of a flaw from the measured eddy current sensor impedance changes. Mathematically, this requires finding the transformation which gives the sensor impedance changes in terms of the flaw parameters, and then inverting this transformation. Finding the transformation is called the forward problem, and finding the inverse of the transformation is equivalent to the inversion problem. The principal difficulty in solving the forward problem is finding solutions to Maxwell\u27s equations in the complex geometries involved. This paper describes a solution to the forward problem which is valid for ellipsoidal shaped void flaws in a non-magnetic conductor, and for flaw dimensions such that the incident field variations are at most linear over the region occupied by the flaw

Theorem on the Distribution of Short-Time Particle Displacements with Physical Applications

The distribution of the initial short-time displacements of particles is considered for a class of classical systems under rather general conditions on the dynamics and with Gaussian initial velocity distributions, while the positions could have an arbitrary distribution. This class of systems contains canonical equilibrium of a Hamiltonian system as a special case. We prove that for this class of systems the nth order cumulants of the initial short-time displacements behave as the 2n-th power of time for all n>2, rather than exhibiting an nth power scaling. This has direct applications to the initial short-time behavior of the Van Hove self-correlation function, to its non-equilibrium generalizations the Green's functions for mass transport, and to the non-Gaussian parameters used in supercooled liquids and glasses.Comment: A less ambiguous mathematical notation for cumulants was adopted and several passages were reformulated and clarified. 40 pages, 1 figure. Accepted by J. Stat. Phy

Phase behavior of a system of particles with core collapse

The pressure-temperature phase diagram of a one-component system, with particles interacting through a spherically symmetric pair potential in two dimensions is studied. The interaction consists of a hard core plus an additional repulsion at low energies. It is shown that at zero temperature, instead of the expected isostructural transition due to core collapse occurring when increasing pressure, the system passes through a series of ground states that are not triangular lattices. In particular, and depending on parameters, structures with squares, chains, hexagons and even quasicrystalline ground states are found. At finite temperatures the solid-fluid coexistence line presents a zone with negative slope (which implies melting with decreasing in volume) and the fluid phase has a temperature of maximum density, similar to that in water.Comment: 11 pages, 15 figures included. To appear in PRE. Some figures in low quality format. Better ones available upon request from [email protected]