Travelling waves in hyperbolic chemotaxis equations

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically

Cyclical tests of selected space shuttle TPS metallic materials in a plasma arc tunnel Volume 1: Description of tests and program summary

Work, concerned with cyclical thermal evaluation of selected space shuttle thermal protection system (TPS) metallic materials in a hypervelocity oxidizing atmosphere that approximated an actual entry environment, is presented. A total of 325 sample test hours were conducted on 21 super-alloy metallic samples at temperatures from 1800 to 2200 F (1256 to 1478 K) without any failures. The 4 x 4 in. (10.2 x 10.2 cm) samples were fabricated from five nickel base alloys and one cobalt base alloy. Eighteen of the samples were cycled 100 times each and the other three samples 50 times each in a test stream emanating from an 8 in. (20.3 cm) diam exit, Mach 4.6, conical nozzle. The test cycle consisted of a 10 min heat pulse to a controlled temperature followed by a 10 min cooldown period. The TD-NiCrAl and TD-NiAlY materials showed the least change in weight, thickness, and physical appearance even though they were subjected to the highest temperature environment

Cyclical Tests of Selected Space Shuttle TPS Metallic Materials in a Plasma Arc Tunnel. Volume 2: Appendices - Data Tabulation

Calibration data are presented for heat flux and pressure profiles, model temperature histories, and model weight and thickness changes

Adaption of the ex vivo mycobacterial growth inhibition assay for use with murine lung cells.

In the absence of a correlate(s) of protection against human tuberculosis and a validated animal model of the disease, tools to facilitate vaccine development must be identified. We present an optimised ex vivo mycobacterial growth inhibition assay (MGIA) to assess the ability of host cells within the lung to inhibit mycobacterial growth, including Bacille Calmette-Guérin (BCG) and Mycobacterium tuberculosis (MTB) Erdman. Growth of BCG was reduced by 0.39, 0.96 and 0.73 log10 CFU following subcutaneous (s.c.) BCG, intranasal (i.n.) BCG, or BCG s.c. + mucosal boost, respectively, versus naïve mice. Comparatively, a 0.49 (s.c.), 0.60 (i.n.) and 0.81 (s.c. + mucosal boost) log10 reduction in MTB CFU was found. A BCG growth inhibitor, 2-thiophenecarboxylic acid hydrazide (TCH), was used to prevent quantification of residual BCG from i.n. immunisation and allow accurate MTB quantification. Using TCH, a further 0.58 log10 reduction in MTB CFU was revealed in the i.n. group. In combination with existing methods, the ex vivo lung MGIA may represent an important tool for analysis of vaccine efficacy and the immune mechanisms associated with vaccination in the organ primarily affected by MTB disease

Self-optimization of optical confinement in ultraviolet photonic crystal slab laser

We studied numerically and experimentally the effects of structural disorder on the performance of ultraviolet photonic crystal slab lasers. Optical gain selectively amplifies the high-quality modes of the passive system. For these modes, the in-plane and out-of-plane leakage rates may be automatically balanced in the presence of disorder. The spontaneous optimization of in-plane and out-of-plane confinement of light in a photonic crystal slab may lead to a reduction of the lasing threshold.Comment: 5 pages, 5 figure

Climatic, edaphic, and biotic controls over storage and turnover of carbon in soils

Soil carbon, a major component of the global carbon inventory, has significant potential for change with changing climate and human land use. We applied the Century ecosystem model to a series of forest and grassland sites distributed globally to examine large-scale controls over soil carbon. Key site-specific parameters influencing soil carbon dynamics are soil texture and foliar lignin content; accordingly, we perturbed these variables at each site to establish a range of carbon concentrations and turnover times. We examined the simulated soil carbon stores, turnover times, and C:N ratios for correlations with patterns of independent variables. Results showed that soil carbon is related linearly to soil texture, increasing as clay content increases, that soil carbon stores and turnover time are related to mean annual temperature by negative exponential functions, and that heterotrophic respiration originates from recent detritus (∼50%), microbial turnover (∼30%), and soil organic matter (∼20%) with modest variations between forest and grassland ecosystems. The effect of changing temperature on soil organic carbon (SOC) estimated by Century is dSOC/dT= 183e−0.034T. Global extrapolation of this relationship leads to an estimated sensitivity of soil C storage to a temperature of −11.1 Pg° C−1, excluding extreme arid and organic soils. In Century, net primary production (NPP) and soil carbon are closely coupled through the N cycle, so that as temperatures increase, accelerated N release first results in fertilization responses, increasing C inputs. The Century-predicted effect of temperature on carbon storage is modified by as much as 100% by the N cycle feedback. Century-estimated soil C sensitivity (−11.1 Pg° C−1) is similar to losses predicted with a simple data-based calculation (−14.1 Pg° C−1). Inclusion of the N cycle is important for even first-order predictions of terrestrial carbon balance. If the NPP-SOC feedback is disrupted by land use or other disturbances, then SOC sensitivity can greatly exceed that estimated in our simulations. Century results further suggest that if climate change results in drying of organic soils (peats), soil carbon loss rates can be high

Travelling Waves in Hyperbolic Chemotaxis Equations

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s (Keller and Segel, J. Theor. Biol. 30:235-248, 1971). The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically. © 2010 Society for Mathematical Biology

Growth, processing, and optical properties of epitaxial Er_2O_3 on silicon

Erbium-doped materials have been investigated for generating and amplifying light in low-power chip-scale optical networks on silicon, but several effects limit their performance in dense microphotonic applications. Stoichiometric ionic crystals are a potential alternative that achieve an Er^(3+) density 100× greater. We report the growth, processing, material characterization, and optical properties of single-crystal Er_2O_3 epitaxially grown on silicon. A peak Er^(3+) resonant absorption of 364 dB/cm at 1535nm with minimal background loss places a high limit on potential gain. Using high-quality microdisk resonators, we conduct thorough C/L-band radiative efficiency and lifetime measurements and observe strong upconverted luminescence near 550 and 670 nm

Feasibility of detecting single atoms using photonic bandgap cavities

We propose an atom-cavity chip that combines laser cooling and trapping of neutral atoms with magnetic microtraps and waveguides to deliver a cold atom to the mode of a fiber taper coupled photonic bandgap (PBG) cavity. The feasibility of this device for detecting single atoms is analyzed using both a semi-classical treatment and an unconditional master equation approach. Single-atom detection seems achievable in an initial experiment involving the non-deterministic delivery of weakly trapped atoms into the mode of the PBG cavity.Comment: 11 pages, 5 figure

Mutator Dynamics on a Smooth Evolutionary Landscape

We investigate a model of evolutionary dynamics on a smooth landscape which features a ``mutator'' allele whose effect is to increase the mutation rate. We show that the expected proportion of mutators far from equilibrium, when the fitness is steadily increasing in time, is governed solely by the transition rates into and out of the mutator state. This results is a much faster rate of fitness increase than would be the case without the mutator allele. Near the fitness equilibrium, however, the mutators are severely suppressed, due to the detrimental effects of a large mutation rate near the fitness maximum. We discuss the results of a recent experiment on natural selection of E. coli in the light of our model.Comment: 4 pages, 3 figure