Correcting mean-field approximations for spatially-dependent advection-diffusion-reaction processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description

Models of collective cell motion for cell populations with different aspect ratio: diffusion, proliferation & travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealisations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population-level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two-dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data with varying cell shape

Thermal control for mobile packages in the dusty lunar environment

Dual surface configurations illustrating thermal protection concepts to improve performance of simple radiative surfaces in mobile, dusty, lunar environment

Effect of Correlation on Multi-Engine Rocket Propulsion Systems

A matter of great concern in the design and operation of multi-engine rocket propulsion systems is the effect of the premature shutdown of one engine on the vehicle. This probability that a premature shutdown will cause a vehicle loss is termed correlation. Based on airbreathing experiences as well as rocket engine data the best estimate of this correlation is made and then applied to the overall multi-engine reliability problem to demonstrate its potential effect. At this point, follow-on analyses are pointed out that illustrate how any potential failures that may cause a correlatable event can be eliminated; thus bringing this correlation to almost 0

Bidirectional step torque filter with zero backlash characteristic Patent

Gearing system for eliminating backlash and filtering input torque fluctuations from high inertia loa

"Oxide-free" tip for scanning tunneling microscopy

We report a new tip for scanning tunneling microscopy and a tip repair procedure that allows one to reproducibly obtain atomic images of highly oriented pyrolytic graphite with previously inoperable tips. The tips are shown to be relatively oxide-free and highly resistant to oxidation. The tips are fabricated with graphite by two distinct methods

Exciton-polaron complexes in pulsed electrically-detected magnetic resonance

Several microscopic pathways have been proposed to explain the large magnetic effects observed in organic semiconductors, but identifying and characterising which microscopic process actually influences the overall magnetic field response is challenging. Pulsed electrically-detected magnetic resonance provides an ideal platform for this task as it intrinsically monitors the charge carriers of interest and provides dynamical information which is inaccessible through conventional magnetoconductance measurements. Here we develop a general time domain theory to describe the spin-dependent reaction of exciton-charge complexes following the coherent manipulation of paramagnetic centers through electron spin resonance. A general Hamiltonian is treated, and it is shown that the transition frequencies and resonance positions of the exciton-polaron complex can be used to estimate inter-species coupling. This work also provides a general formalism for analysing multi-pulse experiments which can be used to extract relaxation and transport rates

Modelling delta-notch perturbations during zebrafish somitogenesis

The discovery over the last 15 years of molecular clocks and gradients in the pre-somitic mesoderm of numerous vertebrate species has added significant weight to Cooke and Zeeman's ‘clock and wavefront’ model of somitogenesis, in which a travelling wavefront determines the spatial position of somite formation and the somitogenesis clock controls periodicity (Cooke and Zeeman, 1976). However, recent high-throughput measurements of spatiotemporal patterns of gene expression in different zebrafish mutant backgrounds allow further quantitative evaluation of the clock and wavefront hypothesis. In this study we describe how our recently proposed model, in which oscillator coupling drives the propagation of an emergent wavefront, can be used to provide mechanistic and testable explanations for the following observed phenomena in zebrafish embryos: (a) the variation in somite measurements across a number of zebrafish mutants; (b) the delayed formation of somites and the formation of ‘salt and pepper’ patterns of gene expression upon disruption of oscillator coupling; and (c) spatial correlations in the ‘salt and pepper’ patterns in Delta-Notch mutants. In light of our results, we propose a number of plausible experiments that could be used to further test the model