A mathematical study of finite-amplitude rock-folding

The problem of the finite-amplitude folding of an isolated, linearly viscous layer under compression and imbedded in a medium of lower viscosity is treated theoretically by using a variational method to derive finite difference equations which are solved on a digital computer. The problem depends on a single physical parameter, the ratio of the fold wavelength, L, to the "dominant wavelength" of the infinitesimal-amplitude treatment, L_d. Therefore, the natural range of physical parameters is covered by the computation of three folds, with L/L_d = 0, 1, and 4.6, up to a maximum dip of 90°.

Significant differences in fold shape are found among the three folds; folds with higher L/L_d have sharper crests. Folds with L/L_d = 0 and L/L_d = 1 become fan folds at high amplitude. A description of the shape in terms of a harmonic analysis of inclination as a function of arc length shows this systematic variation with L/L_d and is relatively insensitive to the initial shape of the layer. This method of shape description is proposed as a convenient way of measuring the shape of natural folds.

The infinitesimal-amplitude treatment does not predict fold-shape development satisfactorily beyond a limb-dip of 5°. A proposed extension of the treatment continues the wavelength-selection mechanism of the infinitesimal treatment up to a limb-dip of 15°; after this stage the wavelength-selection mechanism no longer operates and fold shape is mainly determined by L/L_d and limb-dip.

Strain-rates and finite strains in the medium are calculated f or all stages of the L/L_d = 1 and L/L_d = 4.6 folds. At limb-dips greater than 45° the planes of maximum flattening and maximum flattening rat e show the characteristic orientation and fanning of axial-plane cleavage.

Interaction of aqueous inorganic orthophosphate and phosphate rock

An experimental study was made of the interaction of phosphate rock and aqueous inorganic orthophosphate, calcium, and hydroxyl ions. A model of the reaction was developed by observing electron diffraction patterns in conjunction with concentration changes of chemical components. The model was applied in explaining the performance of batch suspensions of powdered phosphate rock and packed columns of granular phosphate rock. In both cases the reaction consisted initially of a rapid nucleation phase that occurred in a time period of minutes. In the batch system the calcium phosphate nuclei then ripened into larger micro-crystals of hydroxyapatite, which eventually became indistinguishable from the original phosphate rock surface. During column operation the high supersaturation ratio that existed after the rapid nucleation phase resulted in a layer of small nuclei that covered a slowly growing hydroxyapatite crystal.

The column steady-state rate constant was found to increase with increasing temperature, pH, and fluoride concentration, and to decrease with increasing concentrations of magnesium sulfate, ammonium chloride, and bicarbonate ion.

An engineering feasibility study indicated that, based on economic considerations, nucleation of apatite on phosphate rock ore has a potential use as a wastewater phosphate removal treatment process.

Reconstructing Past Depositional and Diagenetic Processes through Quantitative Stratigraphic Analysis of the Martian Sedimentary Rock Record

High-resolution orbital and in situ observations acquired of the Martian surface during the past two decades provide the opportunity to study the rock record of Mars at an unprecedented level of detail. This dissertation consists of four studies whose common goal is to establish new standards for the quantitative analysis of visible and near-infrared data from the surface of Mars. Through the compilation of global image inventories, application of stratigraphic and sedimentologic statistical methods, and use of laboratory analogs, this dissertation provides insight into the history of past depositional and diagenetic processes on Mars. The first study presents a global inventory of stratified deposits observed in images from the High Resolution Image Science Experiment (HiRISE) camera on-board the Mars Reconnaissance Orbiter. This work uses the widespread coverage of high-resolution orbital images to make global-scale observations about the processes controlling sediment transport and deposition on Mars. The next chapter presents a study of bed thickness distributions in Martian sedimentary deposits, showing how statistical methods can be used to establish quantitative criteria for evaluating the depositional history of stratified deposits observed in orbital images. The third study tests the ability of spectral mixing models to obtain quantitative mineral abundances from near-infrared reflectance spectra of clay and sulfate mixtures in the laboratory for application to the analysis of orbital spectra of sedimentary deposits on Mars. The final study employs a statistical analysis of the size, shape, and distribution of nodules observed by the Mars Science Laboratory Curiosity rover team in the Sheepbed mudstone at Yellowknife Bay in Gale crater. This analysis is used to evaluate hypotheses for nodule formation and to gain insight into the diagenetic history of an ancient habitable environment on Mars.

Study of ion movements in isolated chicken retinas during spreading depression

Spreading depression (SD) is a phenomenon observed in several sections of vertebrate central nervous system. It can occur spontaneously or be evoked by a variety of stimuli, and consists of a wave of depression of the normal electrical activity of the nervous tissue which spreads slowly in all directions in the tissue. This wave of depression is accompanied by several concomitants including ion movements. All the concomitants of SD can be explained by an increase in the sodium permeability of the plasma membranes of cellular elements involved in this phenomenon.

In the chicken retina, SD is accompanied by a transparency change which can be detected with the naked eye. The isolated retina is a thin (0.1 mm) membrane in which the extracellular fluid quickly and completely equilibrates with the incubation solutions. This preparation was therefore used to study the ion movements during SD by measuring and comparing the ion contents and the extracellular space (ECS) of retinas incubated in various solutions of which some inhibited SD, whereas others allowed this phenomenon to occur.

The present study has shown that during SD there is a shift of extracellular sodium into the intracellular compartment of the retina, a release of intracellular K and a decrease in the magnitude of ECS. These results are in agreement with previous postulates about SD, although the in vitro experimental condition makes the ion movements appear larger and the loss of ECS smaller than observed in the intact cortical tissue. The movements of Na and K, in opposite directions, are reversible. The development and magnitudes of SD is very little affected by deprivation of the oxygen supply.

It was established that the inward sodium shift is not a consequence of an arrest of the Na-pump. It can be prevented, together with SD by the membrane stabilizers, magnesium and procaine. Spreading depression and the ion movements are incompletely inhibited by tetrodotoxin, which blocks the sodium influx into nerve fibers during the action potential. The replacement of Na in the bathing solution by Li does not prevent SD, which is accompanied by Li accumulation in the intracellular compartment. From these experiments and others it was concluded that the mechanism underlying SD and the ion shifts is an increase in the sodium permeability of cell membranes.