Development of an electron density probe Final report, 22 Jun. 1964 - 22 Mar. 1965

Electron density probes to perform measurements in flow fields at high altitude

A multiphase model describing vascular tumour growth

In this paper we present a new model framework for studying vascular tumour growth, in which the blood vessel density is explicitly considered. Our continuum model comprises conservation of mass and momentum equations for the volume fractions of tumour cells, extracellular material and blood vessels. We include the physical mechanisms that we believe to be dominant, namely birth and death of tumour cells, supply and removal of extracellular fluid via the blood and lymph drainage vessels, angiogenesis and blood vessel occlusion. We suppose that the tumour cells move in order to relieve the increase in mechanical stress caused by their proliferation. We show how to reduce the model to a system of coupled partial differential equations for the volume fraction of tumour cells and blood vessels and the phase averaged velocity of the mixture. We consider possible parameter regimes of the resulting model. We solve the equations numerically in these cases, and discuss the resulting behaviour. The model is able to reproduce tumour structure that is found `in vivo' in certain cases. Our framework can be easily modified to incorporate the effect of other phases, or to include the effect of drugs

Wave climate model of the Mid-Atlantic shelf and shoreline (Virginian Sea): Model development, shelf geomorphology, and preliminary results

A computerized wave climate model is developed that applies linear wave theory and shelf depth information to predict wave behavior as they pass over the continental shelf as well as the resulting wave energy distributions along the coastline. Reviewed are also the geomorphology of the Mid-Atlantic Continental Shelf, wave computations resulting from 122 wave input conditions, and a preliminary analysis of these data

Modelling spatially regulated B-catenin dynamics & invasion in intestinal crypts

Experimental data (e.g., genetic lineage and cell population studies) on intestinal crypts reveal that regulatory features of crypt behavior, such as control via morphogen gradients, are remarkably well conserved among numerous organisms (e.g., from mouse and rat to human) and throughout the different regions of the small and large intestines. In this article, we construct a partial differential equation model of a single colonic crypt that describes the spatial distribution of Wnt pathway proteins along the crypt axis. The novelty of our continuum model is that it is based upon assumptions that can be directly related to processes at the cellular and subcellular scales. We use the model to predict how the distributions of Wnt pathway proteins are affected by mutations. The model is then extended to investigate how mutant cell populations can invade neighboring crypts. The model simulations suggest that cell crowding caused by increased proliferation and decreased cell loss may be sufficient for a mutant cell population to colonize a neighboring healthy crypt

Purification and Characterization of meta-Cresol Purple for Spectrophotometric Seawater pH Measurements

Spectrophotometric procedures allow rapid and precise measurements of the pH of natural waters. However, impurities in the acid–base indicators used in these analyses can significantly affect measurement accuracy. This work describes HPLC procedures for purifying one such indicator, meta-cresol purple (mCP), and reports mCP physical–chemical characteristics (thermodynamic equilibrium constants and visible-light absorbances) over a range of temperature (T) and salinity (S). Using pure mCP, seawater pH on the total hydrogen ion concentration scale (pHT) can be expressed in terms of measured mCP absorbance ratios (R = λ2A/λ1A) as follows:where −log(K2Te2) = a + (b/T) + c ln T – dT; a = −246.64209 + 0.315971S + 2.8855 × 10–4S2; b = 7229.23864 – 7.098137S – 0.057034S2; c = 44.493382 – 0.052711S; d = 0.0781344; and mCP molar absorbance ratios (ei) are expressed as e1 = −0.007762 + 4.5174 × 10–5T and e3/e2 = −0.020813 + 2.60262 × 10–4T + 1.0436 × 10–4 (S – 35). The mCP absorbances, λ1A and λ2A, used to calculate R are measured at wavelengths (λ) of 434 and 578 nm. This characterization is appropriate for 278.15 ≤ T ≤ 308.15 and 20 ≤ S ≤ 40