Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Development of physical and mathematical models for the Porous Ceramic Tube Plant Nutrification System (PCTPNS)

A physical model of the Porous Ceramic Tube Plant Nutrification System (PCTPNS) was developed through microscopic observations of the tube surface under various operational conditions. In addition, a mathematical model of this system was developed which incorporated the effects of the applied suction pressure, surface tension, and gravitational forces as well as the porosity and physical dimensions of the tubes. The flow of liquid through the PCTPNS was thus characterized for non-biological situations. One of the key factors in the verification of these models is the accurate and rapid measurement of the 'wetness' or holding capacity of the ceramic tubes. This study evaluated a thermistor based moisture sensor device and recommendations for future research on alternative sensing devices are proposed. In addition, extensions of the physical and mathematical models to include the effects of plant physiology and growth are also discussed for future research

A summary of porous tube plant nutrient delivery system investigations from 1985 to 1991

The Controlled Ecological Life Support System (CELSS) Program is a research effort to evaluate biological processes at a one person scale to provide air, water, and food for humans in closed environments for space habitation. This program focuses currently on the use of conventional crop plants and the use of hydroponic systems to grow them. Because conventional hydroponic systems are dependent on gravity to conduct solution flow, they cannot be used in the microgravity of space. Thus, there is a need for a system that will deliver water and nutrients to plant roots under microgravity conditions. The Plant Space Biology Program is interested in investigating the effect that the space environment has on the growth and development of plants. Thus, there is also a need to have a standard nutrient delivery method for growing plants in space for research into plant responses to microgravity. The Porous Tube Plant Nutrient Delivery System (PTPNDS) utilizes a hydrophilic, microporous material to control water and nutrient delivery to plant roots. It has been designed and analyzed to support plant growth independent of gravity and plans are progressing to test it in microgravity. It has been used successfully to grow food crops to maturity in an earth-bound laboratory. This document includes a bibliography and summary reports from the growth trials performed utilizing the PTPNDS

Impact of guided bone regeneration and defect dimension on wound healing at chemically modified hydrophilic titanium implant surfaces: an experimental study in dogs

OBJECTIVES: The aim of the present study was to evaluate the impact of guided bone regeneration and defect dimension on wound healing at chemically modified titanium implant surfaces (modSLA). MATERIALS AND METHODS: ModSLA implants were placed at chronic-type lateral ridge defects of different heights (H1-H4: 2, 4, 6 and 8 mm) and randomly allocated to either (a) GBR (polyethylene glycol membrane + biphasic calcium phosphate) or (b) untreated control. At 2 and 8 weeks (n=6 dogs each), dissected blocks were processed for histomorphometrical analysis [e.g., percentage linear fill (PLF), regenerated area (RA)]. RESULTS: At 8 weeks, both groups revealed comparable mean PLF (%) [Control: H1 (26.1 +/- 5.8)-H4 (60.4 +/- 11.8); GBR: H1 (8.3 +/- 5.3)-H4 (50.7 +/- 23.1)] and RA (mm(2)) [Control: H1 (2.5 +/- 0.4)-H4 (7.4 +/- 4.1); GBR: H1 (1.8 +/- 1.0)-H4 (10.8 +/- 5.9)] values. A significant difference was observed for the mean PLF values at H1 defects. CONCLUSION: It was concluded that (i) modSLA titanium implants supported bone regeneration and osseointegration at H1-H4 defects and (ii) the present GBR procedure did not seem to improve the outcome of vertical bone regeneration, but tended to increase the mean RA values

Factors affecting plant growth in membrane nutrient delivery

The development of the tubular membrane plant growth unit for the delivery of water and nutrients to roots in microgravity has recently focused on measuring the effects of changes in physical variables controlling solution availability to the plants. Significant effects of membrane pore size and the negative pressure used to contain the solution were demonstrated. Generally, wheat grew better in units with a larger pore size but equal negative pressure and in units with the same pore size but less negative pressure. Lettuce also exhibited better plant growth at less negative pressure

System development and early biological tests in NASA's biomass production chamber

The Biomass Production Chamber at Kennedy Space Center was constructed to conduct large scale plant growth studies for NASA's CELSS program. Over the past four years, physical systems and computer control software have been continually upgraded and the degree of atmospheric leakage from the chamber has decreased from about 40 to 5 percent of the total volume per day. Early tests conducted with a limited degree of closure showed that total crop (wheat) growth from the best trays was within 80 percent of reported optimal yields for similar light levels. Yields from subsequent tests under more tightly closed conditions have not been as good--up to only 65 percent of optimal yields. Yields appear to have decreased with increasing closure, yet potential problems exist in cultural techniques and further studies are warranted. With the ability to tightly seal the chamber, quantitative data were gathered on CO2 and water exchange rates. Results showed that stand photosynthesis and transpiration reached a peak near 25 days after planting, soon after full vegetative ground cover was established. In the final phase of testing when atmospheric closure was the highest, ethylene gas levels in the chamber rose from about 10 to nearly 120 ppb. Evidence suggests that the ethylene originated from the wheat plants themselves and may have caused an epinastic rolling of the leaves, but no apparent detrimental effects on whole plant function

Іноземні інвестиції у контексті економічного зростання

The eruption of Mount Pinatubo in 1991 injected a large amount of SO2 into the stratosphere, which formed sulfate aerosols. Increased scattering and absorption of UV radiation by the enhanced stratospheric SO2 and aerosols decreased the amount of UV radiation reaching the troposphere, causing changes in tropospheric photochemistry. These changes affected the oxidizing capacity of the atmosphere and the removal rate of CH4 in the years following the eruption. We use the three-dimensional chemistry transport model TM5 coupled to the aerosol microphysics module M7 to simulate the evolution of SO2 and sulfate aerosols from the Pinatubo eruption. Their effect on tropospheric photolysis frequencies and concentrations of OH and CH4 is quantified for the first time. We find that UV attenuation by stratospheric sulfur decreased the photolysis frequencies of both ozone and NO2 by about 2% globally, decreasing global OH concentrations by a similar amount in the first 2 years after the eruption. SO2 absorption mainly affects OH primary production by ozone photolysis, while aerosol scattering also alters OH recycling. The effect of stratospheric sulfur on global OH and CH4 is dominated by the effect of aerosol extinction, while SO2 absorption contributes by 12.5% to the overall effect in the first year after the eruption. The reduction in OH concentrations causes an increase in the CH4 growth rate of 4 and 2 ppb/yr in the first and second years after the eruption, respectively, contributing 11 Tg to the 27 Tg observed CH4 burden change in late 1991 and early 1992. Key Points We modeled the effect of Pinatubo sulfur on tropospheric photochemistry SO2 absorption and aerosol extinction reduce tropospheric UV levels The tropospheric OH sink of CH4 decreased by 17.8 Tg during June 1991-June 199

Investigating combustion as a method of processing inedible biomass produced in NASA's biomass production chamber

The Controlled Ecological Life Support System (CELSS) Breadboard Project at the John F. Kennedy Space Center is a research program to integrate and evaluate biological processes to provide air, water, and food for humans in closed environments for space habitation. This project focuses on the use of conventional crop plants as grown in the Biomass Production Chamber (BPC) for the production and recycling of oxygen, food, and water. The inedible portion of these crops has the potential to be converted to edible biomass or directly to the elemental constituents for direct recycling. Converting inedible biomass directly, by combustion, to carbon dioxide, water, and minerals could provide a baseline for estimating partitioning of the mass balance during recycling in a CELSS. Converting the inedible biomass to carbon dioxide and water requires the same amount of oxygen that was produced by photosynthesis. The oxygen produced during crop growth is just equal to the oxygen required to oxidize all the biomass produced during growth. Thus, the amount of oxygen produced that is available for human consumption is in proportion to the amount of biomass actually utilized by humans. The remaining oxygen must be available to oxidize the rest of the biomass back to carbon dioxide and water or the system will not be a regenerative one