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

Pattern formation in a generalised chemotactic model

Many models have been proposed for spatial pattern formation in embryology and analyzed for the standard case of zero-flux boundary conditions. However, relatively little attention has been paid to the role of boundary conditions on the form of the final pattern. Here we investigate, numerically, the effect of nonstandard boundary conditions on a model pattern generator, which we choose to be of a cell-chemotactic type. We specifically focus on the role of boundary conditions and the effects of scale and aspect ratio, and study the spatiotemporal dynamics of pattern formation. We illustrate the properties of the model by application to the spatiotemporal sequence of skeletal development

Bifurcating spatial patterns in a cell-chemotaxis model

Spatial pattern formation is a key issue in early embroynic development. Embroynic cells divide, migrate, and differentiate to form the various structures, markings and organs of the body. Perhaps the most spectacular manifestation of this process is animal coat markings. These patterns are formed by melanin-secreting cells which migrate from the neural crest to the epidermal and dermal layers of the skin

Sport in the city: measuring economic significance at the local level

In many cities throughout Europe, sport is increasingly being used as a tool for economic revitalisation. While there has been a growth in literature relating to the specific economic impacts of sports-led development, including professional sport facilities, teams, and sport events, limited research has been undertaken on the contribution of the whole sport sector to output and employment. In the United Kingdom (UK), studies have focused on evaluating sport-related economic activity at the national level, yet despite the increasing use of sport for local economic development little research has been undertaken at the city level. To address this situation, this article uses the National Income Accounting framework to measure the economic importance of sport in Sheffield, UK. It shows that the value-added in 1996/97 was 165.61m or 4.11% of Gross Domestic Product (GDP), approximately twice the amount predicted from current national estimates. It is argued that this can primarily be explained by previous studies under-estimating the economic importance of sport, largely due to methodological differences. It goes on to suggest that future research on the significance of sport should be undertaken at the local level to provide policymakers with information at the spatial level where regeneration programmes are being implemented.</p

Modeling the spectrum of V4334 Sgr (Sakurai's Object)

Theoretical spectral energy distributions were computed for a grid of hydrogen-deficient and carbon-rich model atmospheres of T(eff) in the range of 5000-6250 K and log g = 1.0 - 0.0 by the technique of opacity sampling, taking into account continuous, molecular band and atomic line absorption. These energy distributions were compared with the spectrum of V4334 Sgr (Sakurai's object) of April, 1997 in the wavelength interval 300-1000 nm. We show that (1) the shape of the theoretical spectra depends strongly on T(eff) but only very weakly on the hydrogen abundance; (2) the comparison of the observed and computed spectra permits to estimate T(eff) approximately 5500 K for V4334 Sgr in April, 1997, and its interstellar reddening (plus a possible circumstellar contribution) E(B-V) approximately 0.70.Comment: 7 pages, 8 figures, LaTeX, accepted by Astronomy and Astrophysic

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

Low Temperature Opacities

Previous computations of low temperature Rosseland and Planck mean opacities from Alexander & Ferguson (1994) are updated and expanded. The new computations include a more complete equation of state with more grain species and updated optical constants. Grains are now explicitly included in thermal equilibrium in the equation of state calculation, which allows for a much wider range of grain compositions to be accurately included than was previously the case. The inclusion of high temperature condensates such as Al$_2$O$_3$ and CaTiO$_3$ significantly affects the total opacity over a narrow range of temperatures before the appearance of the first silicate grains. The new opacity tables are tabulated for temperatures ranging from 30000 K to 500 K with gas densities from 10$^{-4}$ g cm$^{-3}$ to 10$^{-19}$ g cm$^{-3}$. Comparisons with previous Rosseland mean opacity calculations are discussed. At high temperatures, the agreement with OPAL and Opacity Project is quite good. Comparisons at lower temperatures are more divergent as a result of differences in molecular and grain physics included in different calculations. The computation of Planck mean opacities performed with the opacity sampling method are shown to require a very large number of opacity sampling wavelength points; previously published results obtained with fewer wavelength points are shown to be significantly in error. Methods for requesting or obtaining the new tables are provided.Comment: 39 pages with 12 figures. To be published in ApJ, April 200

Gross solids from combined sewers in dry weather and storms, elucidating production, storage and social factors

Variation in rates of sanitary hygiene products, toilet tissue and faeces occurring in sewers are presented for dry and wet weather from three steep upstream urban catchments with different economic, age and ethnic profiles. Results show, for example, that total daily solids per capita from the low income and ageing populations are almost twice that from high income or ethnic populations. Relative differences are verified through independent questionnaires. The relationship between solids stored in sewers prior to storms, antecedent dry weather period and the proportion of roof to total catchment area is quantified. A full solids' flush occurs when storm flows exceed three times the peak dry weather flow. The data presented will assist urban drainage designers in managing pollution caused by the discharge of sewage solids

The identification of HCN and HNC in Carbon Stars: Model Atmospheres, Synthetic Spectra and Fits to Observations in the 2.7-4.0 micron Region

Model carbon star atmospheres and synthetic spectra have been calculated using the recent HCN/HNC vibration rotation linelist of Harris et al. (2002) ApJ, 578, 657. The calculations are repeated using only HCN lines and show that HNC has a significant effect upon the temperature, density and optical depth of a stellar atmosphere. We fit synthetic spectra in the 2.7-4.0 micron region to observed ISO spectra of the carbon stars WZ Cas and TX Psc obtained by Aoki et al. (1998), A&A, 340, 222. These fits allow us to identify absorption by HNC in the spectrum of WZ Cas at 2.8-2.9 microns, and to determine new independent estimates of effective temperature and log(Nc)/log(No). The findings reported here indicate that absorption by both HCN and HNC is needed to fully explain the observed stellar spectra and represent the first identification of HNC in a star. Q branch absorption by the HCN $\Delta v_2=1$, $\Delta v_3=1$ and $\Delta v_1=1$, $\Delta v_2=-1$ bands at 3.55 and 3.86 microns respectively, are identified in the spectrum of WZ Cas.Comment: 13 pages, 9 figure