Search NASA⌕ Search

SEARCH · Search NASA

Results for “Group theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

The Effects of Long-Duration Spaceflight on Training Retention and Transfer

Training our crew members for long duration, exploration-class missions will have to maximize long-term retention and transfer of the trained skills. The expected duration of the missions, our inability to predict all the possible tasks the crew will be called upon to perform, and the low training-to-mission time ratio require that the training be maximally effective such that the skills acquired during training will be retained and will be transferrable across a wide range of specific tasks that are different from the particular tasks used during training. However, to be able to design training that can achieve these ambitious goals, we must first understand the ways in which long-duration spaceflight affects training retention and transfer. Current theories of training retention and transfer are largely based on experimental studies conducted at university laboratories using undergraduate students as participants. Furthermore, all such studies have been conducted on Earth. We do not know how well the results of these studies predict the performance of crew members. More specifically, we do not know how well the results of these studies predict the performance of crew members in space and especially during long-duration missions. To address this gap in our knowledge, the current on-going study seeks to test the null hypothesis that performance of university undergraduate students on Earth on training retention and transfer tests do in fact predict accurately the performance of crew members during long-duration spaceflights. To test this hypothesis, the study employs a single 16-month long experimental protocol with 3 different participant groups: undergraduate university students, crew members on the ground, and crew members in space. Results from this study will be presented upon its completion. This poster presents results of study trials of the two tasks used in this study: a data entry task and a mapping task. By researching established training principles, by examining future needs, and by using current practices in spaceflight training as test beds, this research project is mitigating program risks and generating templates and requirements to meet future training needs.

ISS↗
NASA NTRS2018

The Effects of Long-Duration Spaceflight on Training Retention and Transfer

Training our crew members for long duration, exploration-class missions will have to maximize long-term retention and transfer of the trained skills. The expected duration of the missions, our inability to predict all the possible tasks the crew will be called upon to perform, and the low training-to-mission time ratio require that the training be maximally effective such that the skills acquired during training will be retained and will be transferrable across a wide range of specific tasks that are different from the particular tasks used during training. However, to be able to design training that can achieve these ambitious goals, we must first understand the ways in which long-duration spaceflight affects training retention and transfer. Current theories of training retention and transfer are largely based on experimental studies conducted at university laboratories using undergraduate students as participants. Furthermore, all such studies have been conducted on Earth. We do not know how well the results of these studies predict the performance of crew members. More specifically, we do not know how well the results of these studies predict the performance of crew members in space and especially during long-duration missions. To address this gap in our knowledge, the current on-going study seeks to test the null hypothesis that performance of university undergraduate students on Earth on training retention and transfer tests do in fact predict accurately the performance of crew members during long-duration spaceflights. To test this hypothesis, the study employs a single 16-month long experimental protocol with 3 different participant groups: undergraduate university students, crew members on the ground, and crew members in space. Results from this study will be presented upon its completion. This poster presents results of study trials of the two tasks used in this study: a data entry task and a mapping task. By researching established training principles, by examining future needs, and by using current practices in spaceflight training as test beds, this research project is mitigating program risks and generating templates and requirements to meet future training needs.

training↗
NASA NTRS1961

Boundary-Layer Transition on a Group of Blunt Nose Shapes at a Mach Number of 2.20

An investigation has been made to study boundary-layer transition on six axisymmetrical blunt bodies of revolution. Model shapes were selected with respect to the degree of favorable pressure gradient over the model surface. Tests were conducted at a Mach number of 2.20 and over a range of free-stream Reynolds number per foot of about 1.4 x 10(exp 6) to 6.5 x 10(exp 6). The tests were made at an angle of attack of 0 deg. with zero heat transfer. For the hemisphere, the flow remained essentially laminar over the model surface length for the entire pressure range of the tests. For a strong favorable pressure gradient followed by any weak favorable, neutral, or adverse gradient, the tendency was for transition to occur at or immediately behind the shoulder. A single strip of three-dimensional roughness in the region of strong favorable pressure gradient did not fix transition on the models at the roughness location except at the maximum test pressures, whereas a second roughness strip added in a region of neutral or adverse pressure gradient did fix transition. Experimental pressure coefficients agreed closely with modified Newtonian theory except in the shoulder region.

Jackson, Mary W.↗
NASA NTRS2016

Faint-Source-Star Planetary Microlensing: The Discovery of the Cold Gas-Giant Planet OGLE-2014-BLG-0676Lb

We report the discovery of a planet OGLE-2014-BLG-0676Lb via gravitational microlensing. Observations for the lensing event were made by the following groups: Microlensing Observations in Astrophysics; Optical Gravitational Lensing Experiment; Wise Observatory; RoboNETLas Cumbres Observatory Global Telescope; Microlensing Network for the Detection of Small Terrestrial Exoplanets; and -FUN. All analyses of the light-curve data favoura lens system comprising a planetary mass orbiting a host star. The most-favoured binary lens model has a mass ratio between the two lens masses of (4.78 +/- 0.13) 10(exp -3). Subject to some important assumptions, a Bayesian probability density analysis suggests the lens system comprises a 3.09(+1.02/-1.12) MJ planet orbiting a 0.62(+0.20/-0.22) solar mass host star at a deprojected orbital separation of 4.40(+2.16/-1.46) au. The distance to the lens system is 2.22(+0.96/-0.83) kpc. Planet OGLE-2014-BLG-0676Lb provides additional data to the growing number of cool planets discover redusing gravitational microlensing against which planetary formation theories may be tested. Most of the light in the baseline of this event is expected to come from the lens and thus high-resolution imaging observations could confirm our planetary model interpretation.

OGLE-2014-BLG-0676Lb↗
NASA NTRS1999

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team 1998

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available under the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results.

Hesselink, Lambertus↗
NASA NTRS1999

Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

This project focuses on the effects of weak dissipation on vibrational flows in microgravity and in particular on (a) the generation of mean flows through viscous effects and their reaction on the flows themselves, and (b) the effects of finite group velocity and dispersion on the resulting dynamics in large domains. The basic mechanism responsible for the generation of such flows is nonlinear and was identified by Schlichting [21] and Longuet-Higgins. However, only recently has it become possible to describe such flows self-consistently in terms of amplitude equations for the parametrically excited waves coupled to a mean flow equation. The derivation of these equations is nontrivial because the limit of zero viscosity is singular. This project focuses on various aspects of this singular problem (i.e., the limit C equivalent to (nu)((g)(h(exp 3)))exp -1/2 << 1,where nu is the kinematic viscosity and h is the liquid depth) in the weakly nonlinear regime. A number of distinct cases is identified depending on the values of the Bond number, the size of the nonlinear terms, distance above threshold and the length scales of interest. The theory provides a quantitative explanation of a number of experiments on the vibration modes of liquid bridges and related experiments on parametric excitation of capillary waves in containers of both small and large aspect ratio. The following is a summary of results obtained thus far.

Knobloch, E.↗
NASA NTRS1999

Summary of Work for Joint Research Interchanges with DARWIN Integrated Product Team

The intent of Stanford University's SciVis group is to develop technologies that enabled comparative analysis and visualization techniques for simulated and experimental flow fields. These techniques would then be made available un- der the Joint Research Interchange for potential injection into the DARWIN Workspace Environment (DWE). In the past, we have focused on techniques that exploited feature based comparisons such as shock and vortex extractions. Our current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching an@ vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will briefly (1) describe current technologies in the area of comparison techniques, (2) will describe the theory of our new method and finally (3) summarize a few of the results.

Hesselink, Lambertus↗
NASA NTRS1998

A Radio-Jet-Galaxy Interaction in 3C441

Multi-wavelength imaging and spectroscopy of the zeta = 0.708 radio galaxy 3C441 and a red aligned optical/infrared component are used to show that the most striking aspect of the radio-optical "alignment effect" in this object is due to the interaction of the radio jet with a companion galaxy in the same group or cluster. The stellar population of the red aligned continuum component is predominately old, but with a small post-starburst population superposed, and it is surrounded by a low surface- brightness halo, possibly a face-on spiral disc. The [OIII]500.7/[OII]372.7 emission line ratio changes dramatically from one side of the component to the other, with the low-ionisation material apparently having passed through the bow shock of the radio source and been compressed. A simple model for the interaction is used to explain the velocity shifts in the emission line gas, and to predict that the ISM of the interacting galaxy is likely to escape once the radio source bow shock has passed though. We also discuss another, much fainter, aligned component, and the sub-arcsecond scale alignment of the radio source host galaxy. Finally we comment on the implications of our explanation of 3C441 for theories of the alignment effect.

Lacy, Mark↗
NASA NTRS2000

Detection of Extrasolar Planets by Transit Photometry

A knowledge of other planetary systems that includes information on the number, size, mass, and spacing of the planets around a variety of star types is needed to deepen our understanding of planetary system formation and processes that give rise to their final configurations. Recent discoveries show that many planetary systems are quite different from the solar system in that they often possess giant planets in short period orbits. The inferred evolution of these planets and their orbital characteristics imply the absence of Earth-like planets near the habitable zone. Information on the properties of the giant-inner planets is now being obtained by both the Doppler velocity and the transit photometry techniques. The combination of the two techniques provides the mass, size, and density of the planets. For the planet orbiting star HD209458, transit photometry provided the first independent confirmation and measurement of the diameter of an extrasolar planet. The observations indicate a planet 1.27 the diameter of Jupiter with 0.63 of its mass (Charbonneau et al. 1999). The results are in excellent agreement with the theory of planetary atmospheres for a planet of the indicated mass and distance from a solar-like star. The observation of the November 23, 1999 transit of that planet made by the Ames Vulcan photometer at Lick Observatory is presented. In the future, the combination of the two techniques will greatly increase the number of discoveries and the richness of the science yield. Small rocky planets at orbital distances from 0.9 to 1.2 AU are more likely to harbor life than the gas giant planets that are now being discovered. However, new technology is needed to find smaller, Earth-like planets, which are about three hundred times less massive than Jupiter-like planets. The Kepler project is a space craft mission designed to discover hundreds of Earth-size planets in and near the habitable zone around a wide variety of stars. To demonstrate that the technology exists to find such small planets, our group has conducted an end-to-end system test. The results of the laboratory tests are presented and show that we are ready to start the search for Earth-size planets.

Borucki, William↗
NASA NTRS2004

Cognitive Modeling of Social Behaviors

The driving theme of cognitive modeling for many decades has been that knowledge affects how and which goals are accomplished by an intelligent being (Newell 1991). But when one examines groups of people living and working together, one is forced to recognize that whose knowledge is called into play, at a particular time and location, directly affects what the group accomplishes. Indeed, constraints on participation, including roles, procedures, and norms, affect whether an individual is able to act at all (Lave & Wenger 1991; Jordan 1992; Scribner & Sachs 1991). To understand both individual cognition and collective activity, perhaps the greatest opportunity today is to integrate the cognitive modeling approach (which stresses how beliefs are formed and drive behavior) with social studies (which stress how relationships and informal practices drive behavior). The crucial insight is that norms are conceptualized in the individual &nd as ways of carrying out activities (Clancey 1997a, 2002b). This requires for the psychologist a shift from only modeling goals and tasks - why people do what they do - to modeling behavioral patterns-what people do-as they are engaged in purposeful activities. Instead of a model that exclusively deduces actions from goals, behaviors are also, if not primarily, driven by broader patterns of chronological and located activities (akin to scripts). This analysis is particular inspired by activity theory (Leont ev 1979). While acknowledging that knowledge (relating goals and operations) is fundamental for intelligent behavior, activity theory claims that a broader driver is the person s motives and conceptualization of activities. Such understanding of human interaction is normative (i.e., viewed with respect to social standards), affecting how knowledge is called into play and applied in practice. Put another way, how problems are discovered and framed, what methods are chosen, and indeed who even cares or has the authority to act, are all constrained by norms, which are conceived and enacted by individuals.

Clancey, William J.↗
NASA NTRS1988

Geochemical comparison of K-T boundaries from the Northern and Southern Hemispheres

Closely spaced (cm-scale) traverses through the K-T boundary at Stevns Klint (Denmark), Woodside Creek (New Zealand) and a new Southern Hemisphere site at Richards Bay (South Africa) were subjected to trace element and isotopic (C, O, Sr) investigation. Intercomparison between these data-sets, and correlation with the broad K-T database available in the literature, indicate that the chemistry of the boundary clays is not globally constant. Variations are more common than similarities, both of absolute concentrations, and interelement ratios. For example, the chondrite normalized platinum-group elements (PGE) patterns of Stevns Klint are not like those of Woodside Creek, with the Pt/Os ratios showing the biggest variation. These differences in PGE patterns are difficult to explain by secondary alteration of a layer that was originally chemically homogeneous, especially for elements of such dubious crustal mobility as Os and Ir. The data also show that enhanced PGE concentrations, with similar trends to those of the boundary layers, occur in the Cretaceous sediments below the actual boundary at Stevns Klint and all three the New Zealand localities. This confirms the observations of others that the geochemistry of the boundary layers apparently does not record a unique component. It is suggested that terrestrial processes, eg. an extended period of Late Cretaceous volcanism can offer a satisfactory explanation for the features of the K-T geochemical anomaly. Such models would probably be more consistent with the observed stepwise, or gradual, palaeontological changes across this boundary, than the instant catastrophe predicated by the impact theory.

Tredous, M.↗
NASA NTRS1994

The role of extinction in evolution

The extinction of species is not normally considered an important element of neodarwinian theory, in contrast to the opposite phenomenon, speciation. This is surprising in view of the special importance Darwin attached to extinction, and because the number of species extinctions in the history of life is almost the same as the number of originations; present-day biodiversity is the result of a trivial surplus of originations, cumulated over millions of years. For an evolutionary biologist to ignore extinction is probably as foolhardy as for a demographer to ignore mortality. The past decade has seen a resurgence of interest in extinction, yet research on the topic is still at a reconnaissance level, and our present understanding of its role in evolution is weak. Despite uncertainties, extinction probably contains three important elements. (i) For geographically widespread species, extinction is likely only if the killing stress is one so rare as to be beyond the experience of the species, and thus outside the reach of natural selection. (ii) The largest mass extinctions produce major restructuring of the biosphere wherein some successful groups are eliminated, allowing previously minor groups to expand and diversify. (iii) Except for a few cases, there is little evidence that extinction is selective in the positive sense argued by Darwin. It has generally been impossible to predict, before the fact, which species will be victims of an extinction event.

Review, Tutorial↗
NASA NTRS2005

Maunder's Butterfly Diagram in the 21st Century

E. Walter Maunder created his first "Butterfly Diagram" showing the equatorward drift of the sunspot latitudes over the course of each of two solar cycles in 1903. This diagram was constructed from data obtained through the Royal Greenwich Observatory (RGO) starting in 1874. The RGO continued to acquire data up until 1976. Fortunately, the US Air Force (USAF) and the US National Oceanic and Atmospheric Administration (NOAA) have continued to acquire similar data since that time. This combined RGO/USAF/NOAA dataset on sunspot group positions and areas now extends virtually unbroken from the 19th century to the 21st century. The data represented in the Butterfly Diagram contain a wealth of information about solar activity and the solar cycle. Solar activity (as represented by the sunspots) appears at mid-latitudes at the start of each cycle. The bands of activity spread in each hemisphere and then drift toward the equator as the cycle progresses. Although the equator itself tends to be avoided, the spread of activity reaches the equator at about the time of cycle maximum. The cycles overlap at minimum with old cycle spots appearing near the equator while new cycle spots emerge in the mid-latitudes. Large amplitude cycles tend to have activity starting at higher latitudes with the activity spreading to higher latitudes as well. Large amplitude cycles also tend to be preceded by earlier cycles with faster drift rates. These drift rates may be tied to the Sun s meridional circulation - a component in many dynamo theories for the origin of the sunspot cycle. The Butterfly Diagram must be reproduced in any successful dynamo model for the Sun.

Hathaway, David H.↗
NASA NTRS1993

Oxygen abundances in low surface-brightness galaxies

Recent theories predict that some protogalaxies, in low-density environments of the field, are contracting and interacting so slowly that global star formation can be delayed until today. These systems should be gas rich and have low surface-brightness. Blue compact galaxies (BCG's) and other compact HII region galaxies currently experiencing a burst of star formation are good candidates of truly young galaxies (in the sense that global star formation recently has been initiated). If they really are young, they ought to have a recent phase when their brightness was much lower than in the bursting phase. No claims of observations of such proto-BCG's exist. Observations of galaxies in their juvenile phases would undoubtedly be of great interest, e.g. the determination of the primordial helium abundance would improve. A proper place to search for young nearby galaxies could be among blue low surface-brightness galaxies (BLSBG's) in the local field. The study of low surface-brightness galaxies (LSBG's) as a group began relatively recently. They are galaxies with extraordinary properties both as individuals and as a group. A few years ago we started an optical study of a sample of BLSBG's selected from the ESO/Uppsala catalogue. Results of spectroscopic observations obtained on a subsample - 8 galaxies - of our selection are reported. The HII region oxygen chemical abundances and its relation to the blue absolute magnitude and surface-brightness is investigated.

Roennback, Jari↗
NASA NTRS1999

Three-Dimensional Gear Crack Propagation Studied

Gears used in current helicopters and turboprops are designed for light weight, high margins of safety, and high reliability. However, unexpected gear failures may occur even with adequate tooth design. To design an extremely safe system, the designer must ask and address the question, "What happens when a failure occurs?" With gear-tooth bending fatigue, tooth or rim fractures may occur. A crack that propagates through a rim will be catastrophic, leading to disengagement of the rotor or propeller, loss of an aircraft, and possible fatalities. This failure mode should be avoided. A crack that propagates through a tooth may or may not be catastrophic, depending on the design and operating conditions. Also, early warning of this failure mode may be possible because of advances in modern diagnostic systems. One concept proposed to address bending fatigue fracture from a safety aspect is a splittooth gear design. The prime objective of this design would be to control crack propagation in a desired direction such that at least half of the tooth would remain operational should a bending failure occur. A study at the NASA Lewis Research Center analytically validated the crack-propagation failsafe characteristics of a split-tooth gear. It used a specially developed three-dimensional crack analysis program that was based on boundary element modeling and principles of linear elastic fracture mechanics. Crack shapes as well as the crack-propagation life were predicted on the basis of the calculated stress intensity factors, mixed-mode crack-propagation trajectory theories, and fatigue crack-growth theories. The preceding figures show the effect of the location of initial cracks on crack propagation. Initial cracks in the fillet of the teeth produced stress intensity factors of greater magnitude (and thus, greater crack growth rates) than those in the root or groove areas of the teeth. Crack growth was simulated in a case study to evaluate crack-propagation paths. Tooth fracture was predicted from the crackgrowth simulation for an initial crack in the tooth fillet region. This was the desired failure mode for an ultrasafe design. Lastly, tooth loads on the uncracked mesh of the split-tooth design were up to five times greater than those on the cracked mesh if equal deflections of the cracked and uncracked teeth were considered. This effect needs to be considered in the design of a split-tooth configuration. This work was done in-house at Lewis in support of the National Rotorcraft Technology Center project, Ultra-Safe Gear Design, with the Boeing Defense and Space Group. The crack-propagation package was developed by the Cornell Fracture Group at Cornell University. The reported results, which are the initial findings of Lewis gear-crackpropagation research for the Rotorcraft Base Program, will be further investigated to develop generalized gear design guidelines.

Lewicki, David G.↗
NASA NTRS2005

Influence of Nucleation Mechanisms on the Radiative Properties of Deep Convective Clouds and Subvisible Cirrus in CRYSTAL/FACE

During the past few years we have conducted work on several different topics, as reflected by our publications. As one of the Co-Project scientists for The Cirrus Regional Study of Tropical Anvils and Cirrus Layers - Florida Area Cirrus Experiment (CRYSTAL FACE) we worked to help design the mission and then conduct it in the field. Another major activity during the past two years has been to pull together various groups to formulate plans for follow on missions to CRYSTAL FACE. We organized a workshop at the University of Colorado during the summer of 2003 to assess the best locations for future missions. Working with a group of about 10 scientists from around the country we prepared a science-planning document (Tropical Composition, Cloud and Climate Coupling Experiment (TC(sup 4)) that outlined the rationale, locations, strategy to accomplish the goals, and possible payloads for a set of three tropical missions. We also prepared background materials for various NRAs being prepared at NASA Headquarters for missions in Costa Rica, Darwin and Guam. In conjunction with the group at NASA Ames we have helped build a new numerical model for deep convection and have applied that model to simulate the CRYSTAL data. Our goal in particular has been to better understand how convection distributes water vapor isotopes. CRYSTAL observations of water isotopes are very different from those suggested by previous workers who assumed the isotopes would obey Rayleigh fractionation. The water isotope study has several implications. First it is a check on the realism of the deep convection model. Second, the isotopes are a measure of the precipitation removal in the atmosphere. Hence they provide a constraint on a parameter that is difficult to otherwise measure. Finally it has been suggested that isotopes may be the key to unraveling the water transport into the stratosphere and upper troposphere. Such transport is critical both for the radiation balance and for stratospheric chemistry. Ours is the first model that is able to treat this transport. Our initial results have just been submitted to Geophys. Res. Lett (Smith et al., 2005). Essentially we are able to explain the vertical profiles of isotopes in the tropical tropopause transition layer. We are also able to account for stratospheric humidity and isotope abundances with this model. We have also been heavily involved in trying to improve our understanding of nitric acid condensation on ice. Gao et al (2004) have shown that water supersaturations above ice occur when the atmosphere is supersaturated with respect to nitric acid trihydrate. As one of the co-authors of that work, we suggested the mechanism that may explain why this is occurring. Essentially, ice does not like to grow near unit supersaturation, but does so because the water molecules can find sites on the ice surface to attach themselves to before they fly off the ice surface. This phenomena was well known in the 1960s when it was a source of debate about whether condensation and evaporation coefficients for ice would be the same. Evaporation does not require any molecular orientation, while condensation does, so it was possible that the coefficients would differ. They don't differ because the water molecules rapidly move across the surface and find places to attach. Nitric acid may be occupying these preferred sites and therefore the water molecules can't find a desirable place to attach. We anticipate that this research will be the subject of laboratory work during the coming few years. Another possibility that has been suggested is that cubic ice is forming in clouds. We have measured the vapor pressure of cubic ice, and plan to publish that result in the next few months. We have also been working on additional aspects of the condensation of nitric acid on ice. With Y. Kondo we studied the condensation of NOy on ice using the SOLVE data. Gamblin et al. have continued this work. The CRYSTAL NOy and HNO, groups have shown th their data can be fit using standard Langmuir isotherms as suggested in some, but not all, laboratory studies. We have found in the SOLVE data set that this is not the case. Moreover some laboratory studies show there are important kinetic effects that may be occurring in the atmosphere limiting the transfer of nitric acid to the ice. The SOLVE data seem consistent with these studies. We are currently re-analyzing the CRYSTAL data to look for these kinetic effects. There are a number of implications of these studies. One of the more interesting is that the nitric acid coating on ice can be used as a cloud clock to determine how long the cloud parcel has been in existence. We have also been involved with several laboratory studies. We have worked to improve the database on ice optical constants, which are critical for remote sensing. We have also studied the ways in which ice nucleates on clays. We suspect now that the standard theories used for depositional ice nucleation are completely incorrect. Further work will be needed to develop a new theory.

Toon, Owen B.↗
NASA NTRS1996

Artificial Boundary Conditions Based on the Difference Potentials Method

While numerically solving a problem initially formulated on an unbounded domain, one typically truncates this domain, which necessitates setting the artificial boundary conditions (ABC's) at the newly formed external boundary. The issue of setting the ABC's appears to be most significant in many areas of scientific computing, for example, in problems originating from acoustics, electrodynamics, solid mechanics, and fluid dynamics. In particular, in computational fluid dynamics (where external problems present a wide class of practically important formulations) the proper treatment of external boundaries may have a profound impact on the overall quality and performance of numerical algorithms. Most of the currently used techniques for setting the ABC's can basically be classified into two groups. The methods from the first group (global ABC's) usually provide high accuracy and robustness of the numerical procedure but often appear to be fairly cumbersome and (computationally) expensive. The methods from the second group (local ABC's) are, as a rule, algorithmically simple, numerically cheap, and geometrically universal; however, they usually lack accuracy of computations. In this paper we first present a survey and provide a comparative assessment of different existing methods for constructing the ABC's. Then, we describe a relatively new ABC's technique of ours and review the corresponding results. This new technique, in our opinion, is currently one of the most promising in the field. It enables one to construct such ABC's that combine the advantages relevant to the two aforementioned classes of existing methods. Our approach is based on application of the difference potentials method attributable to V. S. Ryaben'kii. This approach allows us to obtain highly accurate ABC's in the form of certain (nonlocal) boundary operator equations. The operators involved are analogous to the pseudodifferential boundary projections first introduced by A. P. Calderon and then also studied by R. T. Seeley. The apparatus of the boundary pseudodifferential equations, which has formerly been used mostly in the qualitative theory of integral equations and PDE'S, is now effectively employed for developing numerical methods in the different fields of scientific computing.

Tsynkov, Semyon V.↗
NASA NTRS1999

Development of Fuzzy Logic and Soft Computing Methodologies

Our earlier research on computing with words (CW) has led to a new direction in fuzzy logic which points to a major enlargement of the role of natural languages in information processing, decision analysis and control. This direction is based on the methodology of computing with words and embodies a new theory which is referred to as the computational theory of perceptions (CTP). An important feature of this theory is that it can be added to any existing theory - especially to probability theory, decision analysis, and control - and enhance the ability of the theory to deal with real-world problems in which the decision-relevant information is a mixture of measurements and perceptions. The new direction is centered on an old concept - the concept of a perception - a concept which plays a central role in human cognition. The ability to reason with perceptions perceptions of time, distance, force, direction, shape, intent, likelihood, truth and other attributes of physical and mental objects - underlies the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Everyday examples of such tasks are parking a car, driving in city traffic, cooking a meal, playing golf and summarizing a story. Perceptions are intrinsically imprecise. Imprecision of perceptions reflects the finite ability of sensory organs and ultimately, the brain, to resolve detail and store information. More concretely, perceptions are both fuzzy and granular, or, for short, f-granular. Perceptions are f-granular in the sense that: (a) the boundaries of perceived classes are not sharply defined; and (b) the elements of classes are grouped into granules, with a granule being a clump of elements drawn together by indistinguishability, similarity. proximity or functionality. F-granularity of perceptions may be viewed as a human way of achieving data compression. In large measure, scientific progress has been, and continues to be, driven by a quest to progress from perceptions to measurements. Pursuit of this aim has led to brilliant successes. But alongside the successes stand problems whose solutions are not in sight. Representative of such problems is the problem of automation of driving in city traffic. In this case, as in many others, what can be done with ease by humans - without any measurements and a computations - is an intractable task for machines.

Zadeh, L. A.↗