Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients

Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the existence of spatial inhomogeneities in various biological systems, most models have only been considered in a spatially homogeneous environment. The authors consider a two-chemical reaction-diffusion mechanism in one space dimension in which one of the diffusion coefficients depends explicitly on the spatial variable. The model is analysed in the case of a step function diffusion coefficient and the insight gained for this special case is used to discuss pattern generation for smoothly varying diffusion coefficients. The results show that spatial inhomogeneity may be an important biological pattern regulator, and possible applications of the model to chondrogenesis in the vertebrate limb are suggested

Unravelling the Turing bifurcation using spatially varying diffusion coefficients

The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors determine the structure of this bifurcation for two coupled reaction diffusion equations on a two-dimensional square spatial domain when the diffusion coefficients have a small explicit variation in space across the domain. In the case of homogeneous diffusivities, the Turing bifurcation is highly degenerate. Using a two variable perturbation method, the authors show that the small explicit spatial inhomogeneity splits the bifurcation into two separate primary and two separate secondary bifurcations, with all solution branches distinct. This splitting of the bifurcation is more effective than that given by making the domain slightly rectangular, and shows clearly the structure of the Turing bifurcation and the way in which the! var ious solution branches collapse together as the spatial variation is reduced. The authors determine the stability of the solution branches, which indicates that several new phenomena are introduced by the spatial variation, including stable subcritical striped patterns, and the possibility that stable stripes lose stability supercritically to give stable spotted patterns

Patchy He II reionization and the physical state of the IGM

We present a Monte-Carlo model of He II reionization by QSOs and its effect on the thermal state of the clumpy intergalactic medium (IGM). The model assumes that patchy reionization develops as a result of the discrete distribution of QSOs. It includes various recipes for the propagation of the ionizing photons, and treats photo-heating self-consistently. The model provides the fraction of He III, the mean temperature in the IGM, and the He II mean optical depth -- all as a function of redshift. It also predicts the evolution of the local temperature versus density relation during reionization. Our findings are as follows: The fraction of He III increases gradually until it becomes close to unity at $z\sim 2.8-3.0$. The He II mean optical depth decreases from $\tau\sim 10$ at $z\geq 3.5$ to $\tau\leq 0.5$ at $z\leq 2.5$. The mean temperature rises gradually between $z\sim 4$ and $z\sim 3$ and declines slowly at lower redshifts. The model predicts a flattening of the temperature-density relation with significant increase in the scatter during reionization at $z\sim 3$. Towards the end of reionization the scatter is reduced and a tight relation is re-established. This scatter should be incorporated in the analysis of the Ly$\alpha$ forest at $z\leq 3$. Comparison with observational results of the optical depth and the mean temperature at moderate redshifts constrains several key physical parameters.Comment: 18 pages, 9 figures; Changed content. Accepted for publication in MNRA

The Conformal Anomaly in General Rank 1 Symmetric Spaces and Associated Operator Product

We compute the one-loop effective action and the conformal anomaly associated with the product $\bigotimes_p{\cal L}_p$ of the Laplace type operators ${\cal L}_p, p=1,2$, acting in irreducible rank 1 symmetric spaces of non-compact type. The explicit form of the zeta functions and the conformal anomaly of the stress-energy momentum tensor is derived.Comment: 10 pages, LaTe

Fundamental study of transpiration cooling

Isothermal and non-isothermal pressure drop data and heat transfer data generated on porous 304L stainless steel wire forms, sintered spherical stainless steel powder, and sintered spherical OFHC copper powder are reported and correlated. Pressure drop data was collected over a temperature range from 500 R to 2000 R and heat transfer data collected over a heat flux range from 5 to 15 BTU/in2/sec. It was found that flow data could be correlated independently of transpirant temperature and type (i.e., H2, N2). It was also found that no simple relation between heat transfer coefficient and specimen porosity was obtainable

Pacifism and Emotional Arousal

Excerpt: At the age of eighteen, American youths must make an ideological decision about war. Although most probably perceive selective service registration as little more than a rite of passage, others struggle with the ethics of military service and options of conscientious objection. What can be said of youths who decide, for moral and religious reasons, that they will not be involved in warfare? To date, no descriptive studies have been reported that address this question. Previous studies on pacifism focus on the likelihood of pacifism in eliciting cooperation (Gruder & Duslak, 1973; Marwell & Schmitt, 1973) or aggression (Borden, 1975; Borden & Taylor, 1976; Fitz, Kimble, & Heidenfelder, 1979; Fitz, Marwit, & Gerstenzang, 1983; Kimble, Fitz, Onorad, 1977; Mander & Gaebelein, 1977). Moreover, these studies have typically recruited participants who were assigned pacifistic strategies rather than recruiting those with pre-existing pacifistic inclinations

Remote sensing techniques for mapping range sites and estimating range yield

Image interpretation procedures for determining range yield and for extrapolating range information were investigated for an area of the Pine Ridge Indian Reservation in southwestern South Dakota. Soil and vegetative data collected in the field utilizing a grid sampling design and digital film data from color infrared film and black and white films were analyzed statistically using correlation and regression techniques. The pattern recognition techniques used were K-class, mode seeking, and thresholding. The herbage yield equation derived for the detailed test site was used to predict yield for an adjacent similar field. The herbage yield estimate for the adjacent field was 1744 lbs. of dry matter per acre and was favorably compared to the mean yield of 1830 lbs. of dry matter per acre based upon ground observations. Also an inverse relationship was observed between vegetative cover and the ratio of MSS 5 to MSS 7 of ERTS-1 imagery

Modification of the ECAS reference steam power generating plant to comply with the EPA 1979 new source performance standards

Detailed capital cost estimates for the ECAS and modified reference plants in mid-1978 dollars for both 250 and 175 F (394 and 353 K) stack gas reheat temperatures based on the cost estimates developed for the ECAS study are presented. The scope of the work included technical assessment of sulfur dioxide scrubber system design, on site calcination versus purchased lime, reheat of stack gas, effect of sulfur dioxide scrubber on particulate emission, and control of nitrogen oxides

Controlled photon transfer between two individual nanoemitters via shared high-Q modes of a microsphere resonator

We realize controlled cavity-mediated photon transfer between two single nanoparticles over a distance of several tens of micrometers. First, we show how a single nanoscopic emitter attached to a near-field probe can be coupled to high-Q whispering-gallery modes of a silica microsphere at will. Then we demonstrate transfer of energy between this and a second nanoparticle deposited on the sphere surface. We estimate the photon transfer efficiency to be about six orders of magnitude higher than that via free space propagation at comparable separations.Comment: accepted for publication in Nano Letter