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Variable Order and Distributed Order Fractional Operators

Many physical processes appear to exhibit fractional order behavior that may vary with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. This paper develops the concept of variable and distributed order fractional operators. Definitions based on the Riemann-Liouville definitions are introduced and behavior of the operators is studied. Several time domain definitions that assign different arguments to the order q in the Riemann-Liouville definition are introduced. For each of these definitions various characteristics are determined. These include: time invariance of the operator, operator initialization, physical realization, linearity, operational transforms. and memory characteristics of the defining kernels. A measure (m2) for memory retentiveness of the order history is introduced. A generalized linear argument for the order q allows the concept of "tailored" variable order fractional operators whose a, memory may be chosen for a particular application. Memory retentiveness (m2) and order dynamic behavior are investigated and applications are shown. The concept of distributed order operators where the order of the time based operator depends on an additional independent (spatial) variable is also forwarded. Several definitions and their Laplace transforms are developed, analysis methods with these operators are demonstrated, and examples shown. Finally operators of multivariable and distributed order are defined in their various applications are outlined.

Lorenzo, Carl F.↗

A Timescale for Major Events in Early Mars Crustal Evolution

The population of visible and buried impact basins greater than 200 km diameter revealed by high resolution gridded MOLA data and the cumulative frequency curves derived for these provide a basis for a chronology of major events in early martian history. The relative chronology can be given in terms of N(200) crater retention ages; absolute ages can be assigned using the Hartmann-Neukum (H&N) model chronology. In terms of billions of H&N years, the crustal dichotomy formed by large impact basins at 4.12 +/- 0.08 BYA [N(200) = 3.0 - 3.2] and the global magnetic field died at about or slightly before the same time (4.15 +/- 0.08 BYA) [N(200) = 3.5]. In this chronology, the buried lowlands are ~120 my younger than the buried highlands), approx. 160 my younger than the highlands overall and approx. 340 my younger than the oldest crater retention surface we see, defined by the largest impact basins.

Frey, H. V.↗

A Novel Metal-Ferroelectric-Semiconductor Field-Effect Transistor Memory Cell Design

The use of a Metal-Ferroelectric-Semiconductor Field-Effect Transistor (MFSFET) in a resistive-load SRAM memory cell has been investigated A typical two-transistor resistive-load SRAM memory cell architecture is modified by replacing one of the NMOS transistors with an n-channel MFSFET. The gate of the MFSFET is connected to a polling voltage pulse instead of the other NMOS transistor drain. The polling voltage pulses are of sufficient magnitude to saturate the ferroelectric gate material and force the MFSFET into a particular logic state. The memory cell circuit is further modified by the addition of a PMOS transistor and a load resistor in order to improve the retention characteristics of the memory cell. The retention characteristics of both the "1" and "0" logic states are simulated. The simulations show that the MFSFET memory cell design can maintain both the "1" and "0" logic states for a long period of time.

Phillips, Thomas A.↗

A Time Scale for Major Events in Early Mars Crustal Evolution

The population of visible and buried impact basins > 200 km diameter revealed by high resolution gridded MOLA data and the cumulative frequency curves derived for these pvide a basis for a chronology of major events in early martian history. The relative chronology can be given in terms of N(200) crater retention ages; 'absolute ages' can be assigued using the Hartmann-Neukum (H&N) model chronology. In terms of billions of H&N years, the crustal dichotomy formed by large impact basins at 4.12 +/- 0.08 BYA (N(200) = 3.0-3.2) and the global magnetic field died at about or slightly before the same time (4.15 +/- 0.08 BYA (N(200) = 3.5). In this chronology, the buried lowlands are approx. 120 my younger than the buried highlands, approx. 160 my younger than the highlands overall and approx. 340 my younger than the oldest crater retention surface we see, defined by the largest impact basins.

Frey, Herbert V.↗

Developmental gene regulatory network architecture across 500 million years of echinoderm evolution

Evolutionary change in morphological features must depend on architectural reorganization of developmental gene regulatory networks (GRNs), just as true conservation of morphological features must imply retention of ancestral developmental GRN features. Key elements of the provisional GRN for embryonic endomesoderm development in the sea urchin are here compared with those operating in embryos of a distantly related echinoderm, a starfish. These animals diverged from their common ancestor 520-480 million years ago. Their endomesodermal fate maps are similar, except that sea urchins generate a skeletogenic cell lineage that produces a prominent skeleton lacking entirely in starfish larvae. A relevant set of regulatory genes was isolated from the starfish Asterina miniata, their expression patterns determined, and effects on the other genes of perturbing the expression of each were demonstrated. A three-gene feedback loop that is a fundamental feature of the sea urchin GRN for endoderm specification is found in almost identical form in the starfish: a detailed element of GRN architecture has been retained since the Cambrian Period in both echinoderm lineages. The significance of this retention is highlighted by the observation of numerous specific differences in the GRN connections as well. A regulatory gene used to drive skeletogenesis in the sea urchin is used entirely differently in the starfish, where it responds to endomesodermal inputs that do not affect it in the sea urchin embryo. Evolutionary changes in the GRNs since divergence are limited sharply to certain cis-regulatory elements, whereas others have persisted unaltered.

NASA Program Fundamental Space Biology↗

Computer simulation of the effect of dDAVP with saline loading on fluid balance after 24-hour head-down tilt

Fluid loading (FL) before Shuttle reentry is a countermeasure currently in use by NASA to improve the orthostatic tolerance of astronauts during reentry and postflight. The fluid load consists of water and salt tablets equivalent to 32 oz (946 ml) of isotonic saline. However, the effectiveness of this countermeasure has been observed to decrease with the duration of spaceflight. The countermeasure's effectiveness may be improved by enhancing fluid retention using analogs of vasopressin such as lypressin (LVP) and desmopressin (dDAVP). In a computer simulation study reported previously, we attempted to assess the improvement in fluid retention obtained by the use of LVP administered before FL. The present study is concerned with the use of dDAVP. In a recent 24-hour, 6 degree head-down tilt (HDT) study involving seven men, dDAVP was found to improve orthostatic tolerance as assessed by both lower body negative pressure (LBNP) and stand tests. The treatment restored Luft's cumulative stress index (cumulative product of magnitude and duration of LBNP) to nearly pre-bedrest level. The heart rate was lower and stroke volume was marginally higher at the same LBNP levels with administration of dDAVP compared to placebo. Lower heart rates were also observed with dDAVP during stand test, despite the lower level of cardiovascular stress. These improvements were seen with only a small but significant increase in plasma volume of approximately 3 percent. This paper presents a computer simulation analysis of some of the results of this HDT study.

NASA Discipline Cardiopulmonary↗

Analysis of strontium metabolism in humans on the basis of the Techa river data

Age and sex features of strontium metabolism have been analyzed on studies of the population residing on the banks of the Techa river which was contaminated by fission products during the years 1949-1956. Measurements of 90Sr body burden have been performed since 1974 using a whole-body counter, and these have made it possible to estimate age-specific long-term retention and elimination rates for men and women. Regarding the retention that correlated with the respective maturation ages, distinct sex differences have been observed for adolescents, whereas only postmenopausal women showed a sharp increase of their elimination rates. There were no differences concerning the reproductive ages. Our experimental findings have a clear physiological interpretation and can be used to develop metabolic models for bone-seeking radionuclides.

NASA Discipline Radiation Health↗

Regulation of body fluid volume and electrolyte concentrations in spaceflight

Despite a number of difficulties in performing experiments during weightlessness, a great deal of information has been obtained concerning the effects of spaceflight on the regulation of body fluid and electrolytes. Many paradoxes and questions remain, however. Although body mass, extracellular fluid volume, and plasma volume are reduced during spaceflight and remain so at landing, the changes in total body water are comparatively small. Serum or plasma sodium and osmolality have generally been unchanged or reduced during the spaceflight, and fluid intake is substantially reduced, especially during the first of flight. The diuresis that was predicted to be caused by weightlessness, has only rarely been observed as an increased urine volume. What has been well established by now, is the occurrence of a relative diuresis, where fluid intake decreases more than urine volume does. Urinary excretion of electrolytes has been variable during spaceflight, but retention of fluid and electrolytes at landing has been consistently observed. The glomerular filtration rate was significantly elevated during the SLS missions, and water and electrolyte loading tests have indicated that renal function is altered during readaptation to Earth's gravity. Endocrine control of fluid volumes and electrolyte concentrations may be altered during weightlessness, but levels of hormones in body fluids do not conform to predictions based on early hypotheses. Antidiuretic hormone is not suppressed, though its level is highly variable and its secretion may be affected by space motion sickness and environmental factors. Plasma renin activity and aldosterone are generally elevated at landing, consistent with sodium retention, but inflight levels have been variable. Salt intake may be an important factor influencing the levels of these hormones. The circadian rhythm of cortisol has undoubtedly contributed to its variability, and little is known yet about the influence of spaceflight on circadian rhythms. Atrial natriuretic peptide does not seem to play an important role in the control of natriuresis during spaceflight. Inflight activity of the sympathetic nervous system, assessed by measuring catecholamines and their metabolites and precursors in body fluids, generally seems to be no greater than on Earth, but this system is usually activated at landing. Collaborative experiments on the Mir and the International Space Station should provide more of the data needed from long-term flights, and perhaps help to resolve some of the discrepancies between U.S. and Russian data. The use of alternative methods that are easier to execute during spaceflight, such as collection of saliva instead of blood and urine, should permit more thorough study of circadian rhythms and rapid hormone changes in weightlessness. More investigations of dietary intake of fluid and electrolytes must be performed to understand regulatory processes. Additional hormones that may participate in these processes, such as other natriuretic hormones, should be determined during and after spaceflight. Alterations in body fluid volume and blood electrolyte concentrations during spaceflight have important consequences for readaptation to the 1-G environment. The current assessment of fluid and electrolyte status during weightlessness and at landing and our still incomplete understanding of the processes of adaptation to weightlessness and readaptation to Earth's gravity have resulted in the development of countermeasures that are only partly successful in reducing the postflight orthostatic intolerance experienced by astronauts and cosmonauts. More complete knowledge of these processes can be expected to produce countermeasures that are even more successful, as well as expand our comprehension of the range of adaptability of human physiologic processes.

NASA Discipline Number 18-10↗

Shelf Life of PMR Polyimide Monomer Solutions and Prepregs Extended

PMR (Polymerization of Monomeric Reactants) technology was developed in the mid-1970's at the NASA Glenn Research Center at Lewis Field for fabricating high-temperature stable polyimide composites. This technology allowed a solution of polyimide monomers or prepreg (a fiber, such as glass or graphite, impregnated with PMR polyimide monomers) to be thermally cured without the release of volatiles that cause the formation of voids unlike the non-PMR technology used for polyimide condensation type resins. The initial PMR resin introduced as PMR 15 is still commercially available and is used worldwide by aerospace industries as the state-of-the-art resin for high-temperature polyimide composite applications. PMR 15 offers easy composite processing, excellent composite mechanical property retention, a long lifetime at use temperatures of 500 to 550 F, and relatively low cost. Later, second-generation PMR resin versions, such as PMR II 50 and VCAP 75, offer improvements in the upper-use temperature (to 700 F) and in the useful life at temperature without major compromises in processing and property retention but with significant increases in resin cost. Newer versions of nontoxic (non-methylene dianiline) PMR resins, such as BAX PMR 15, offer similar advantages as originally found for PMR 15 but also with significant increases in resin cost. Thus, the current scope of the entire PMR technology available meets a wide range of aeronautical requirements for polymer composite applications.

Alston, William B.↗

Tensile Strength and Microstructure of Al2O3-ZrO2 Hypo-Eutectic Fibers Studied

Oxide eutectics offer high-temperature strength retention and creep resistance in oxidizing environments. Al2O3-ZrO2 eutectic strengths have been studied since the 1970's. Directionally solidified oxide eutectics exhibit improved resistance to slow crack growth and excellent strength retention at high temperatures up to 1400 C. Materials studied typically contain Y2O3 to metastably retain the high-temperature cubic and tetragonal polymorphs at room temperature. Al2O3-ZrO2 is of fundamental interest for creep studies because it combines a creep-resistant material, Al2O3, with a very low creep resistance material, ZrO2. Results on mechanical properties and microstructures of these materials will be used to define compositions for creep testing in future work. Substantial variations from the eutectic alumina to zirconia ratio can be tolerated without a loss in room-temperature strength. The effect of increasing Y2O3 addition on the room-temperature tensile strength of an Al2O3-ZrO2 material containing excess Al2O3 was examined at the NASA Glenn Research Center, where the materials were grown using Glenn's world-class laser growth facilities.

Farmer, Serene C.↗

Radiation Evaluation of an Advanced 64Mb 3.3V DRAM and Insights into the Effects of Scaling on Radiation Hardness

In this paper, total ionizing dose radiation evaluations of the Micron 64 Mb 3.3 V, fast page mode DRAM and the IBM LUNA-ES 16 Mb DRAM are presented. The effects of scaling on total ionizing dose radiation hardness are studied utilizing test structures and a series of 16 Mb DRAMs with different feature sizes from the same manufacturing line. General agreement was found between the threshold voltage shifts of 16 Mb DRAM test structures and the threshold voltage measured on complete circuits using retention time measurements. Retention time measurement data from early radiation doses are shown that allow internal failure modes to be distinguished.

Radiation Hardness↗

Increased Water Storage at Ice-stream Onsets: A Critical Mechanism?

The interdependence of rapid ice flow, surface topography and the spatial distribution of subglacial water are examined by linking existing theories. The motivation is to investigate whether the acceleration of an ice-stream tributary contains a positive feedback that encourages the retention of subglacial water that leads to faster flow. Periodically varying surface and bed topographies are related through a linear ice-flow perturbation theory for various values of mean surface slope, perturbation amplitude and basal sliding speeds. The topographic variations lead to a periodic variation in hydraulic potential that is used to infer the tendency for subglacial water to be retained in local hydraulic potential minima. If water retention leads to enhanced basal sliding, a positive feedback loop is closed that could explain the transition from slower tributary flow to faster-streaming flow and the sustained downstream acceleration along the tributary-ice-stream system. A sensitivity study illustrates that the same range of topographic wavelengths most effectively transmitted from the bed to the surface also strongly influences the behavior of subglacial water. A lubrication index is defined to qualitatively measure the heterogeneity of the subglacial hydrologic system. Application of this index to field data shows that the transition from tributary to ice stream closely agrees with the location where subglacial water may be first stored.

Bindschadler, Robert↗

Device Acquires and Retains Rock or Ice Samples

The Rock Baller is a sample acquisition tool that improves sample retention. The basic elements of the Rock Baller are the tool rotation axis, the hub, the two jaws, and the cutting blades, which are located on each of the jaws. The entire device rotates about the tool rotation axis, which is aligned parallel to the nominal normal direction of the parent rock surface. Both jaws also rotate about the jaw axis, which is perpendicular to the tool rotation axis, at a rate much slower than the rotation about the tool rotation axis. This movement gradually closes the jaws into a nearly continuous hemispherical shell that encloses the sample as it is cut from the parent rock. When required the jaws are opened to release the sample. The hemispherical cutting method eliminates the sample retention problems associated with existing sample acquisition methods that employ conventional cylindrical cutting. The resulting samples are hemispherical, or nearly hemispherical, and as a result the aspect ratio (sample depth relative to sample radius) is essentially fixed. This fixed sample aspect ratio may be considered a drawback of the Rock Baller method, as samples with a higher aspect ratio (more depth, less width) may be considered more scientifically valuable because such samples would allow for a broader inspection of the geological record. This aspect ratio issue can be ameliorated if the Rock Baller is paired with a device similar to the Rock Abrasion Tool (RAT) used on the Mars Exploration Rovers. The RAT could be used to first grind into the surface of the parent rock, after which the Rock Baller would extract a sample from a depth inside the rock that would not have been possible without first using the RAT. Other potential applications for this technology include medical applications such as the removal of tissue samples or tumors from the body, particularly during endoscopic, laparoscopic, or thoracoscopic surgeries.

Giersch, Louis R.↗

High-Altitude Hydration System

Three methods are being developed for keeping water from freezing during high-altitude climbs so that mountaineers can remain hydrated. Three strategies have been developed. At the time of this reporting two needed to be tested in the field and one was conceptual. The first method is Passive Thermal Control Using Aerogels. This involves mounting the fluid reservoir of the climber s canteen to an inner layer of clothing for better heat retention. For the field test, bottles were mounted to the inner fleece layer of clothing, and then aerogel insulation was placed on the outside of the bottle, and circumferentially around the drink straw. When climbers need to drink, they can pull up the insulated straw from underneath the down suit, take a sip, and then put it back into the relative warmth of the suit. For the field test, a data logger assessed the temperatures of the water reservoir, as well as near the tip of the drink straw. The second method is Passive Thermal Control with Copper-Shielded Drink Straw and Aerogels, also mounted to inner layers of clothing for better heat retention. Braided wire emanates from the inside of the fleece jacket layer, and continues up and around the drink straw in order to use body heat to keep the system-critical drink straw warm enough to keep water in the liquid state. For the field test, a data logger will be used to compare this with the above concept. The third, and still conceptual, method is Active Thermal Control with Microcontroller. If the above methods do not work, microcontrollers and tape heaters have been identified that could keep the drink straw warm even under extremely cold conditions. Power requirements are not yet determined because the thermal environment inside the down suit relative to the external environment has not been established. A data logger will be used to track both the external and internal temperatures of the suit on a summit day.

Parazynski, Scott E.↗

Copoly(imide siloxane) Abhesive Materials with Varied Siloxane Oligomer Length

In this work, low surface energy copoly(imide siloxane)s were synthesized with various siloxane segment lengths. Characterization of these materials revealed that domain formation of the low surface energy component within the matrix was more prevalent for longer siloxane segments as indicated by increased opacity, decreased mechanical properties, and variation of the Tg. Incorporation of siloxanes lowered the polymer s surface energy as indicated by water contact angle values. Topographical modification of these materials by laser ablation patterning further reduced the surface energy, even generating superhydrophobic surfaces. Combined, the contact angle data and particle adhesion testing indicated that copoly(imide siloxane) materials may provide greater mitigation to particulate adhesion than polyimide materials alone. These enhanced surface properties for abhesive applications did result in a reduction of the tensile moduli of the copolymers. It is possible that lower siloxane loading levels would result in retention of the mechanical properties of the polyimide while still affording abhesive surface properties. This hypothesis is currently being investigated. Laser ablation patterning offers further reduction in particle retention as the available surface area for particle adhesion is reduced. Pattern variation and size dependencies are currently being evaluated. For the purposes of lunar dust adhesion mitigation, it is likely that this approach, termed passive due to the lack of input from an external energy source, would not be sufficient to mitigate surface contamination or clean contaminated surfaces for some lunar applications. It is feasible to combine these materials with active mitigation strategies - methods that utilize input from external energy sources - would broaden the applicability of such materials for abhesive purposes. Collaborative efforts along these lines have been initiated with researchers at NASA Kennedy Space Center where experiments are being conducted involving a series of embedded electrodes within polymeric matrices.

Wohl, Christoper J.↗

The Evolution of Remnant Ice at the Lunar South Pole from Diviner Surface Temperature Results

The Diviner lunar radiometer instrument aboard the Lunar Reconnaissance Orbiter mission has revealed large areas of lunar polar terrain with surface temperatures well below 100K. At these temperatures, the sublimation rate of water ice is well below 1 mm per billion years. In contrast, the loss rate at 120K is more than 1 meter of ice in that time consequently volatiles delivered to the coldest locations can be trapped for over 1 Ga, but will be quickly lost from warmer locales. Here we investigate the loss or retention of a layer of ice-bearing regolith at the lunar south poe, assuming contemporary surface temperature conditions and no other loss processes. We use an analytic solution for the one-dimensional diffusion equation of water ice, assuming an isothermal regolith with pore space comparable to mean grain size, 75 micrometers. Only the top meter of soil is assumed to be ice-bearing. We can then calculate the history of ice content with time based on local temperature, and predict what the epithermal neutron output would be in the presence of such a concentration of hydrogen. We compare the present, observed distribution of hydrogen with what one would expect from the temperature-dependent loss or retention of ice for various times since emplacement.

Elphic, Richard C.↗

Characteristics of a Nonvolatile SRAM Memory Cell Utilizing a Ferroelectric Transistor

The SRAM cell circuit is a standard for volatile data storage. When utilizing one or more ferroelectric transistors, the hysteresis characteristics give unique properties to the SRAM circuit, providing for investigation into the development of a nonvolatile memory cell. This paper discusses various formations of the SRAM circuit, using ferroelectric transistors, n-channel and p-channel MOSFETs, and resistive loads. With varied source and supply voltages, the effects on the timing and retention characteristics are investigated, including retention times of up to 24 hours.

Mitchell, Cody↗

Aluminum-Alloy-Matrix/Alumina-Reinforcement Composites

Isotropic composites of aluminum-alloy matrices reinforced with particulate alumina have been developed as lightweight, high-specific-strength, less-expensive alternatives to nickel-base and ferrous superalloys. These composites feature a specific gravity of about 3.45 grams per cubic centimeter and specific strengths of about 200 MPa/(grams per cubic centimeter). The room-temperature tensile strength is 100 ksi (689 MPa) and stiffness is 30 Msi (206 GPa). At 500 F (260 C), these composites have shown 80 percent retention in strength and 95 percent retention in stiffness. These materials also have excellent fatigue tolerance and tribological properties. They can be fabricated in net (or nearly net) sizes and shapes to make housings, pistons, valves, and ducts in turbomachinery, and to make structural components of such diverse systems as diesel engines, automotive brake systems, and power-generation, mining, and oil-drilling equipment. Separately, incorporation of these metal matrix composites within aluminum gravity castings for localized reinforcement has been demonstrated. A composite part of this type can be fabricated in a pressure infiltration casting process. The process begins with the placement of a mold with alumina particulate preform of net or nearly net size and shape in a crucible in a vacuum furnace. A charge of the alloy is placed in the crucible with the preform. The interior of the furnace is evacuated, then the furnace heaters are turned on to heat the alloy above its liquidus temperature. Next, the interior of the furnace is filled with argon gas at a pressure about 900 psi (approximately equal to 6.2 MPa) to force the molten alloy to infiltrate the preform. Once infiltrated, the entire contents of the crucible can be allowed to cool in place, and the composite part recovered from the mold.

Kashalikar, Uday↗