Properties of the conjugate gradient and Davidon methods, part 5 Final report

Quadratically convergent gradient methods for minimizing unconstrained function of several variable

Grosse Ile and the Irish Memorial National Historic Site, Parks Canada: A Case Study

Focuses on values and their protection by examining the place of values in management. Grosse Ile's management is still evolving, and the eventful first phases of planning are still fresh in the minds of staff

The Stefan problem with variable thermophysical properties and phase change temperature

In this paper we formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent. Thermophysical properties invariably take different values in different material phases but this is often ignored for mathematical simplicity. Size and velocity dependent phase change temperatures are often found at very short length scales, such as nanoparticle melting or dendrite formation; velocity dependence occurs in the solidification of supercooled melts. To illustrate the method we show how the governing equations may be applied to a standard one-dimensional problem and also the melting of a spherically symmetric nanoparticle. Errors which have propagated through the literature are highlighted. By writing the system in non-dimensional form we are able to study the large Stefan number formulation and an energy-conserving one-phase reduction. The results from the various simplifications and assumptions are compared with those from a finite difference numerical scheme. Finally, we briefly discuss the failure of Fourier's law at very small length and time-scales and provide an alternative formulation which takes into account the finite time of travel of heat carriers (phonons) and the mean free distance between collisions.Comment: 39 pages, 5 figure

The one-dimensional Stefan problem with non-Fourier heat conduction

We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.Comment: 29 pages, 6 figures, 2 tables + Supplementary Materia

Coefficients and terms of the liquid drop model and mass formula

The coefficients of different combinations of terms of the liquid drop model have been determined by a least square fitting procedure to the experimental atomic masses. The nuclear masses can also be reproduced using a Coulomb radius taking into account the increase of the ratio $R\_0/A^{1/3}$ with increasing mass, the fitted surface energy coefficient remaining around 18 MeV

Towards an Improved Test of the Standard Model's Most Precise Prediction

The electron and positron magnetic moments are the most precise prediction of the standard model of particle physics. The most accurate measurement of a property of an elementary particle has been made to test this result. A new experimental method is now being employed in an attempt to improve the measurement accuracy by an order of magnitude. Positrons from a "student source" now suffice for the experiment. Progress toward a new measurement is summarized

Monitoring the dispersion of ocean waste disposal plumes from ERTS-1 and Skylab

The author has identified the following significant results. About forty miles off the Delaware coast is located the disposal site for waste discharged from a plant processing titanium dioxide. The discharge is a greenish-brown; 15-20% acid liquid which consists primarily of iron chlorides and sulfates. The barge which transports this waste has a 1,000,000 gallon capacity and makes approximately three trips to the disposal site per week. ERTS-1 MSS digital tapes are being used to study the dispersion patterns and drift velocities of the iron-acid plume. Careful examination of ERTS-1 imagery disclosed a fishhook-shaped plume about 40 miles east of Cape Henlopen caused by a barge disposing acid wastes. The plume shows up more strongly in the green band than in the red band. Since some acids have a strong green component during dumping and turn slowly more brownish-reddish with age, the ratio of radiance signatures between the green and red bands may give an indication of how long before the satellite overpass the acid was dumped. Enlarged enhancements of the acid waste plumes, prepared from the ERTS-1 MSS digital tapes aided considerably in studies of the dispersion of the waste plume. Currently acid dumps are being coordinated with ERTS-1 overpasses

Dilution jet mixing program, phase 3

The objectives of the program were: (1) to extend the data base on mixing of a single-sided row of jets with a confined crossflow, (2) to collect a data base on mixing of multiple rows of jets with confined crossflow, (3) to develop empirical jet mixing correlations, and (4) to perform limited three-dimensional calculations for some of these test configurations. The tests were performed with uniform mainstream conditions for several orifice plate configurations. Schematics of the test section and the orifice configurations are given. Temperature and pressure measurements were made in the test section at 4 axial and 11 transverse stations, using a 60-element rake probe. The measured temperature distributions for these tests are reported