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

Thermal and structural modeling of superinsulation

Model permits direct physical measurement of the thermal response of critical components of space telescopes, thus providing flexibility for systems studies and design changes

Mechanochemical models for generating biological pattern and form in development

The central issue in development is the formation of spatial patterns of cells in the early embryo. The mechanisms which generate these patterns are unknown. Here we describe the new Oster-Murray mechanochemical approach to the problem, the elements of which are experimentally well documented. By way of illustration we derive one of the basic models from first principles and apply it to a variety of problems of current interest and research. We specifically discuss the formation of skin organ patterns, such as feather and scale germs, cartilage condensations in the developing vertebrate limb and finally wound healing

Two dimensional pattern formation in a chemotactic system

Chemotaxis is known to be important in cell aggregation in a variety of contexts. We propose a simple partial differential equation model for a chemotactic system of two species, a population of cells and a chemoattractant to which cells respond. Linear analysis shows that there exists the possibility of spatially inhomogeneous solutions to the model equations for suitable choices of parameters. We solve the full nonlinear steady state equations numerically on a two dimensional rectangular domain. By using mode selection from the linear analysis we produce simple pattern elements such as stripes and regular spots. More complex patterns evolve from these simple solutions as parameter values or domain shape change continuously. An example bifurcation diagram is calculated using the chemotactic response of the cells as the bifurcation parameter. These numerical solutions suggest that a chemotactic mechanism can produce a rich variety of complex patterns

Thermal and structural modeling of a large aperture space telescope Technical summary report, 22 Jun. - 22 Sep. 1968

Thermal and structural modeling for large aperture space telescop

Hydrodynamic modelling of accretion flows

In the proceedings of this, and of several recent close binary conferences, there have been several contributions describing smoothed particle hydrodynamics simulations of accretion disks. It is apposite therefore to review the numerical scheme itself with emphasis on its advantages for disk modelling, and the methods used for modelling viscous processes.Comment: 3 pages, to appear in proceedings of IAU Colloquium 194: Compact binaries in the galaxy and beyon

Reduction of Algebraic Parametric Systems by Rectification of their Affine Expanded Lie Symmetries

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equations. We apply this principle by finding some \emph{affine derivations} that induces \emph{expanded} Lie point symmetries of considered system. By rewriting original problem in an invariant coordinates set for these symmetries, we \emph{reduce} the number of involved parameters. We present an algorithm based on this standpoint whose arithmetic complexity is \emph{quasi-polynomial} in input's size.Comment: Before analysing an algebraic system (differential or not), one can generally reduce the number of parameters defining the system behavior by studying the system's Lie symmetrie

Angular Momentum Transfer in the Binary X-ray Pulsar GX 1+4

We describe three presentations relating to the X-ray pulsar GX 1+4 at a workshop on magnetic fields and accretion at the Astrophysical Theory Centre, Australian National University on 1998, November 12-13. Optical and X-ray spectroscopy indicate that GX 1+4 is seen through a cloud of gravitationaly bound matter. We discuss an unstable negative feedback mechanism (originally proposed by Kotani et al, 1999), based on X-ray heating of this matter which controls the accretion rate when the source is in a low X-ray luminosity state. A deep minimum lasting ~6 hours occurred during observations with the RXTE satellite over 1996, July 19-21. The shape of the X-ray pulses changed remarkably from before to after the minimum. These changes may be related to the transition from neutron star spin-down to spin-up which occurred at about the same time. Smoothed particle hydrodynamic simulations of the effect of adding matter with opposite angular momentum to an existing disc, show that it is possible for a number of concentric rings with alternating senses of rotation to co-exist in a disc. This could provide an explanation for the step-like changes in Pdot which are observed in GX 1+4. Changes at the inner boundary of the disc occur at the same timescale as that imposed at the outer boundary. Reversals of material torque on the neutron star occur at a minimum in L_X.Comment: 10 pages, 5 figures; accepted for publication by PAS

Spin wave dispersion softening in the ferromagnetic Kondo lattice model for manganites

Spin dynamics is calculated in the ferromagnetic (FM) state of the generalized Kondo lattice model taking into account strong on-site correlations between e_g electrons and antiferromagnetic (AFM) exchange among t_{2g} spins. Our study suggests that competing FM double-exchange and AFM super-exchange interaction lead to a rather nontrivial spin-wave spectrum. While spin excitations have a conventional Dq^2 spectrum in the long-wavelength limit, there is a strong deviation from the spin-wave spectrum of the isotropic Heisenberg model close to the zone boundary. The relevance of our results to the experimental data are discussed.Comment: 6 RevTex pages, 3 embedded PostScript figure

A hydrogen energy carrier. Volume 2: Systems analysis

A systems analysis of hydrogen as an energy carrier in the United States indicated that it is feasible to use hydrogen in all energy use areas, except some types of transportation. These use areas are industrial, residential and commercial, and electric power generation. Saturation concept and conservation concept forecasts of future total energy demands were made. Projected costs of producing hydrogen from coal or from nuclear heat combined with thermochemical decomposition of water are in the range $1.00 to$1.50 per million Btu of hydrogen produced. Other methods are estimated to be more costly. The use of hydrogen as a fuel will require the development of large-scale transmission and storage systems. A pipeline system similar to the existing natural gas pipeline system appears practical, if design factors are included to avoid hydrogen environment embrittlement of pipeline metals. Conclusions from the examination of the safety, legal, environmental, economic, political and societal aspects of hydrogen fuel are that a hydrogen energy carrier system would be compatible with American values and the existing energy system