Spectral asymptotics of periodic elliptic operators

We demonstrate that the structure of complex second-order strongly elliptic operators $H$ on ${\bf R}^d$ with coefficients invariant under translation by ${\bf Z}^d$ can be analyzed through decomposition in terms of versions $H_z$, $z\in{\bf T}^d$, of $H$ with $z$-periodic boundary conditions acting on $L_2({\bf I}^d)$ where ${\bf I}=[0,1>$. If the semigroup $S$ generated by $H$ has a H\"older continuous integral kernel satisfying Gaussian bounds then the semigroups $S^z$ generated by the $H_z$ have kernels with similar properties and $z\mapsto S^z$ extends to a function on ${\bf C}^d\setminus\{0\}$ which is analytic with respect to the trace norm. The sequence of semigroups $S^{(m),z}$ obtained by rescaling the coefficients of $H_z$ by $c(x)\to c(mx)$ converges in trace norm to the semigroup $\hat{S}^z$ generated by the homogenization $\hat{H}_z$ of $H_z$. These convergence properties allow asymptotic analysis of the spectrum of $H$.Comment: 27 pages, LaTeX article styl

Propulsion Technology Lifecycle Operational Analysis

The paper presents the results of a focused effort performed by the members of the Space Propulsion Synergy Team (SPST) Functional Requirements Sub-team to develop propulsion data to support Advanced Technology Lifecycle Analysis System (ATLAS). This is a spreadsheet application to analyze the impact of technology decisions at a system-of-systems level. Results are summarized in an Excel workbook we call the Technology Tool Box (TTB). The TTB provides data for technology performance, operations, and programmatic parameters in the form of a library of technical information to support analysis tools and/or models. The lifecycle of technologies can be analyzed from this data and particularly useful for system operations involving long running missions. The propulsion technologies in this paper are listed against Chemical Rocket Engines in a Work Breakdown Structure (WBS) format. The overall effort involved establishing four elements: (1) A general purpose Functional System Breakdown Structure (FSBS). (2) Operational Requirements for Rocket Engines. (3) Technology Metric Values associated with Operating Systems (4) Work Breakdown Structure (WBS) of Chemical Rocket Engines The list of Chemical Rocket Engines identified in the WBS is by no means complete. It is planned to update the TTB with a more complete list of available Chemical Rocket Engines for United States (US) engines and add the Foreign rocket engines to the WBS which are available to NASA and the Aerospace Industry. The Operational Technology Metric Values were derived by the SPST Sub-team in the form of the TTB and establishes a database for users to help evaluate and establish the technology level of each Chemical Rocket Engine in the database. The Technology Metric Values will serve as a guide to help determine which rocket engine to invest technology money in for future development

Mitigating Cotton Revenue Risk Through Irrigation, Insurance, and Hedging

This study focuses on managing cotton production and marketing risks using combinations of irrigation levels, put options (as price insurance), and crop insurance. Stochastic cotton yields and prices are used to simulate a whole-farm financial statement for a 1,000 acre furrow irrigated cotton farm in the Texas Lower Rio Grande Valley under 16 combinations of risk management strategies. Analyses for risk-averse decision makers indicate that multiple irrigations are preferred. The benefits to purchasing put options increase with yields, as they are more beneficial when higher yields are expected from applying more irrigation applications. Crop insurance is strongly preferred at lower irrigation levels.cotton, crop insurance, irrigation, options, puts, risk, simulation, stochastic efficiency with respect to a function, Farm Management, Risk and Uncertainty, D81, Q12, Q15,

Using blubber explants to investigate adipose function in grey seals:glycolytic, lipolytic and gene expression responses to glucose and hydrocortisone

Adipose tissue is fundamental to energy balance, which underpins fitness and survival. Knowledge of adipose regulation in animals that undergo rapid fat deposition and mobilisation aids understanding of their energetic responses to rapid environmental change. Tissue explants can be used to investigate adipose regulation in wildlife species with large fat reserves, when opportunities for organismal experimental work are limited. We investigated glucose removal, lactate, glycerol and NEFA accumulation in media, and metabolic gene expression in blubber explants from wild grey seals. Glycolysis was higher in explants incubated in 25 mM glucose (HG) for 24 h compared to controls (C: 5.5 mM glucose). Adipose-derived lactate likely contributes to high endogenous glucose production in seals. Lipolysis was not stimulated by HG or high hydrocortisone (HC: 500 nM hydrocortisone) and was lower in heavier animals. HC caused NEFA accumulation in media to decrease by ~30% relative to C in females, indicative of increased lipogenesis. Lipolysis was higher in males than females in C and HG conditions. Lower relative abundance of 11-β-hydroxysteroid dehydrogenase 1 mRNA in HG explants suggests glucose involvement in blubber cortisol sensitivity. Our findings can help predict energy balance responses to stress and nutritional state in seals, and highlight the use of explants to study fat tissue function in wildlife

Diode laser 87Rb optical pumping in an evacuated wall-coated cell

The evacuated wall coated sealed cell coupled with diode laser optical pumping offers a number of attractive potential advantages for use in Rb or Cs atomic frequency standards. An investigation of systematic effects is required to explore possible limitations of the technique. The use of diode laser optical pumping of 87 Rb in an evacuated wall coated sealed cell is presented. Experimental results/discussion to be presented include the signal strength and line broadening of the 0 - 0 hyperfine resonance as a function of light intensity for the D1 optical transitions (F - F prime) - (2 1 prime) and (2 - 2 prime), shift of the 0 - 0 hyperfine frequency as a function of laser intensity and de-tuning from optical resonance, and diode laser frequency stabilization techniques

Development and application of the GIM code for the Cyber 203 computer

The GIM computer code for fluid dynamics research was developed. Enhancement of the computer code, implicit algorithm development, turbulence model implementation, chemistry model development, interactive input module coding and wing/body flowfield computation are described. The GIM quasi-parabolic code development was completed, and the code used to compute a number of example cases. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and implicit finite difference scheme were also added. Development was completed on the interactive module for generating the input data for GIM. Solutions for inviscid hypersonic flow over a wing/body configuration are also presented

The star-formation history of the universe - an infrared perspective

A simple and versatile parameterized approach to the star formation history allows a quantitative investigation of the constraints from far infrared and submillimetre counts and background intensity measurements. The models include four spectral components: infrared cirrus (emission from interstellar dust), an M82-like starburst, an Arp220-like starburst and an AGN dust torus. The 60 $\mu$m luminosity function is determined for each chosen rate of evolution using the PSCz redshift data for 15000 galaxies. The proportions of each spectral type as a function of 60 $\mu$m luminosity are chosen for consistency with IRAS and SCUBA colour-luminosity relations, and with the fraction of AGN as a function of luminosity found in 12 $\mu$m samples. The luminosity function for each component at any wavelength can then be calculated from the assumed spectral energy distributions. With assumptions about the optical seds corresponding to each component and, for the AGN component, the optical and near infrared counts can be accurately modelled. A good fit to the observed counts at 0.44, 2.2, 15, 60, 90, 175 and 850 $\mu$m can be found with pure luminosity evolution in all 3 cosmological models investigated: $\Omega_o$ = 1, $\Omega_o$ = 0.3 ($\Lambda$ = 0), and $\Omega_o$ = 0.3, $\Lambda$ = 0.7. All 3 models also give an acceptable fit to the integrated background spectrum. Selected predictions of the models, for example redshift distributions for each component at selected wavelengths and fluxes, are shown. The total mass-density of stars generated is consistent with that observed, in all 3 cosmological models.Comment: 20 pages, 25 figures. Accepted for publication in ApJ. Full details of models can be found at http://astro.ic.ac.uk/~mrr/countmodel