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Value-added Data Services at the Goddard Earth Sciences Data and Information Services Center

The NASA Goddard Earth Sciences Data and Information Services Center (GES DISC), in addition to serving the Earth Science community as one of the major Distributed Active Archives Centers (DAACs), provides much more than just data. Among the value-added services available to general users are subsetting data spatially and/or by parameter, online analysis (to avoid downloading unnecessarily all the data), and assistance in obtaining data from other centers. Services available to data producers and high-volume users include consulting on building new products with standard formats and metadata and construction of data management systems. A particularly useful service is data processing at the DISC (i.e., close to the input data) with the users algorithm. This can take a number of different forms: as a configuration-managed algorithm within the main processing stream; as a stand-alone program next to the on-line data storage; as build-it-yourself code within the Near-Archive Data Mining (NADM) system; or as an on-the-fly analysis with simple algorithms embedded into the web-based tools. Partnerships between the GES DISC and scientists, both producers and users, allow the scientists to concentrate on science, while the GES DISC handles the data management, e.g., formats, integration, and data processing. The existing data management infrastructure at the GES DISC supports a wide spectrum of options: from simple data support to sophisticated on-line analysis tools, producing economies of scale and rapid time-to-deploy. At the same time, such partnerships allow the GES DISC to serve the user community more efficiently and to better prioritize on-line holdings. Several examples of successful partnerships are described in the presentation.

Leptoukh, Gregory G.↗

SOHO Ultraviolet Coronagraph Spectrometer (UVCS) Mission Operations and Data Analysis

The scientific goal of UVCS is to obtain detailed empirical descriptions of the extended solar corona as it evolves over the solar cycle and to use these descriptions to identify and understand the physical processes responsible for coronal heating, solar wind acceleration, coronal mass ejections (CMEs), and the phenomena that establish the plasma properties of the solar wind as measured by "in situ" solar wind instruments. This report covers the period from 15 February 2003 to 14 April 2004. During that time, UVCS observations have consisted of three types: 1) standard synoptic observations comprising, primarily, the H I Lyalpha line profile and the 0 VI 103.2 and 103.7 nm intensity over a range of heights from 1.5 to about 3.0 solar radii and covering 360 degrees about the Sun, 2) sit and stare observations for major flare watches, and 3) special observations designed by the UVCS Lead Observer of the Week for a specific scientific purpose. The special observations are often coordinated with those of other space-based and ground-based instruments and they often are part of SOHO joint observation programs and campaigns. Lead observers have included UVCS Co-Investigators, scientists from the solar physics community and several graduate and undergraduate level students. UVCS has continued to achieve its purpose of using powerful spectroscopic diagnostic techniques to obtain a much more detailed description of coronal structures and dynamic phenomena than existed before the SOHO mission. The new descriptions of coronal mass ejections (CMEs) and coronal structures from UVCS have inspired a large number of theoretical studies aimed at identifying the physical processes responsible for CMEs and solar wind acceleration in coronal holes and streamers. UVCS has proven to be a very stable instrument. Stellar observations have demonstrated its radiometric stability. UVCS has not required any flight software modifications and all mechanisms are operational. The UVCS 0 VI Channel with its redundant optical path for wavelengths near H I Lyalpha is capable of observing the entire UVCS wavelength range. The regions of the detector currently being used require different grating angles for direct OVI observations and redundant path H I Lyalpha observations, and so those can no longer be observed simultaneously. Since December 1998, the 0 VI Channel has been used for all UVCS observations. Although the H I Lyalpha Channel and detector are still operational, increases in the dark count up to about 5x10(exp 4) counts/sec/pixel and an increase in high voltage current to within a factor of two of the maximum used in the laboratory before flight led to the decision to not use that detector after 1998. The visible light channel functioned nominally during the reporting period. UVCS data, data analysis software, calibration files and the mission log are available from the SOHO archive and SAO. All UVCS data are now available within three months of the observations to scientists and the general public via the SOHO Data Archive and SAO. UVCS has resulted in 33 scientific papers in 2003. There were numerous presentations at scientific meetings. UVCS Education and Public Outreach activities involved nine members of the UVCS team. During the reporting period, there were over a dozen events directed at students and teachers, museum audiences, and public audiences via the mass media, internet and educational literature.

Gurman, Joseph↗

Joint Interdisciplinary Earth Science Information Center

The report spans the three year period beginning in June of 2001 and ending June of 2004. Joint Interdisciplinary Earth Science Information Center's (JIESIC) primary purpose has been to carry out research in support of the Global Change Data Center and other Earth science laboratories at Goddard involved in Earth science, remote sensing and applications data and information services. The purpose is to extend the usage of NASA Earth Observing System data, microwave data and other Earth observing data. JIESIC projects fall within the following categories: research and development; STW and WW prototyping; science data, information products and services; and science algorithm support. JIESIC facilitates extending the utility of NASA's Earth System Enterprise (ESE) data, information products and services to better meet the science data and information needs of a number of science and applications user communities, including domain users such as discipline Earth scientists, interdisciplinary Earth scientists, Earth science applications users and educators.

Kafatos, Menas↗

Picturing Data With Uncertainty

NASA is in the business of creating maps for scientific purposes to represent important biophysical or geophysical quantities over space and time. For example, maps of surface temperature over the globe tell scientists where and when the Earth is heating up; regional maps of the greenness of vegetation tell scientists where and when plants are photosynthesizing. There is always uncertainty associated with each value in any such map due to various factors. When uncertainty is fully modeled, instead of a single value at each map location, there is a distribution expressing a set of possible outcomes at each location. We consider such distribution data as multi-valued data since it consists of a collection of values about a single variable. Thus, a multi-valued data represents both the map and its uncertainty. We have been working on ways to visualize spatial multi-valued data sets effectively for fields with regularly spaced units or grid cells such as those in NASA's Earth science applications. A new way to display distributions at multiple grid locations is to project the distributions from an individual row, column or other user-selectable straight transect from the 2D domain. First at each grid cell in a given slice (row, column or transect), we compute a smooth density estimate from the underlying data. Such a density estimate for the probability density function (PDF) is generally more useful than a histogram, which is a classic density estimate. Then, the collection of PDFs along a given slice are presented vertically above the slice and form a wall. To minimize occlusion of intersecting slices, the corresponding walls are positioned at the far edges of the boundary. The PDF wall depicts the shapes of the distributions very dearly since peaks represent the modes (or bumps) in the PDFs. We've defined roughness as the number of peaks in the distribution. Roughness is another useful summary information for multimodal distributions. The uncertainty of the multi-valued data can also be interpreted by the number of peaks and the widths of the peaks as shown by the PDF walls.

Kao, David↗

Geomorphology and Geodynamics at Crustal Boundaries within Asia and Africa

The release of SRTM images by NASA over the past two years year has been greeted by foreign Earth scientist's as "NASA's gift to the World". The goodwill that this has engendered in parts of Africa. India, Pakistan and Bangladesh, as scientists in those countries contemplated what many of them considered an unprovoked and unjustifiable US invasion of Iraq, cannot be underestimated. We have used SRTM images from Africa and India and elsewhere to examine aspects of tectonism, geodynamics and tsunami and earthquake hazards. Highlights of this research are itemized in this final report. One difficulty that has arisen is , of course, that the funding for the science lead the availability of the data by more than a year. and as a result many of the findings are as yet unpublished.

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NASA's Earth Observing System (EOS): Observing the Atmosphere, Land, Oceans, and Ice from Space

The Earth Observing System (EOS) is a space-based observing system comprised of a series of satellite sensors by which scientists can monitor the Earth, a Data and Information System (EOSDIS) enabling researchers worldwide to access the satellite data, and an interdisciplinary science research program to interpret the satellite data. During this year, the last of the first series of EOS missions, Aura, was launched. Aura is designed exclusively to conduct research on the composition, chemistry, and dynamics of the Earth's upper and lower atmosphere, employing multiple instruments on a single spacecraft. Aura is the third in a series of major Earth observing satellites to study the environment and climate change and is part of NASA's Earth Science Enterprise. The first and second missions, Terra and Aqua, are designed to study the land, oceans, atmospheric constituents (aerosols, clouds, temperature, and water vapor), and the Earth's radiation budget. The other seven EOS spacecraft include satellites to study (i) land cover & land use change, (ii) solar irradiance and solar spectral variation, (iii) ice volume, (iv) ocean processes (vector wind and sea surface topography), and (v) vertical variations of clouds, water vapor, and aerosols up to and including the stratosphere. Aura's chemistry measurements will also follow up on measurements that began with NASA's Upper Atmosphere Research Satellite and continue the record of satellite ozone data collected from the TOMS missions. In this presentation I will describe how scientists are using EOS data to examine the health of the earth's atmosphere, including atmospheric chemistry, aerosol properties, and cloud properties, with a special but not exclusive look at the latest earth observing mission, Aura.

King, Michael D.↗

The Center for Star Formation Studies

The Center for Star Formation Studies, a consortium of scientists from the Space Science Division at Ames and the Astronomy Departments of the University of California at Berkeley and Santa Cruz, conducts a coordinated program of theoretical research on star and planet formation. Under the directorship of D. Hollenbach (Ames), the Center supports postdoctoral fellows, senior visitors, and students; meets regularly at Ames to exchange ideas and to present informal seminars on current research; hosts visits of outside scientists; and conducts a week-long workshop on selected aspects of star and planet formation each summer.

Hollenbach, D.↗

NASA's Geospatial Interoperability Office(GIO)Program

NASA produces vast amounts of information about the Earth from satellites, supercomputer models, and other sources. These data are most useful when made easily accessible to NASA researchers and scientists, to NASA's partner Federal Agencies, and to society as a whole. A NASA goal is to apply its data for knowledge gain, decision support and understanding of Earth, and other planetary systems. The NASA Earth Science Enterprise (ESE) Geospatial Interoperability Office (GIO) Program leads the development, promotion and implementation of information technology standards that accelerate and expand the delivery of NASA's Earth system science research through integrated systems solutions. Our overarching goal is to make it easy for decision-makers, scientists and citizens to use NASA's science information. NASA's Federal partners currently participate with NASA and one another in the development and implementation of geospatial standards to ensure the most efficient and effective access to one another's data. Through the GIO, NASA participates with its Federal partners in implementing interoperability standards in support of E-Gov and the associated President's Management Agenda initiatives by collaborating on standards development. Through partnerships with government, private industry, education and communities the GIO works towards enhancing the ESE Applications Division in the area of National Applications and decision support systems. The GIO provides geospatial standards leadership within NASA, represents NASA on the Federal Geographic Data Committee (FGDC) Coordination Working Group and chairs the FGDC's Geospatial Applications and Interoperability Working Group (GAI) and supports development and implementation efforts such as Earth Science Gateway (ESG), Space Time Tool Kit and Web Map Services (WMS) Global Mosaic. The GIO supports NASA in the collection and dissemination of geospatial interoperability standards needs and progress throughout the agency including areas such as ESE Applications, the SEEDS Working Groups, the Facilities Engineering Division (Code JX) and NASA's Chief Information Offices (CIO). With these agency level requirements GIO leads, brokers and facilitates efforts to, develop, implement, influence and fully participate in standards development internationally, federally and locally. The GIO also represents NASA in the OpenGIS Consortium and ISO TC211. The OGC has made considerable progress in regards to relations with other open standards bodies; namely ISO, W3C and OASIS. ISO TC211 is the Geographic and Geomatics Information technical committee that works towards standardization in the field of digital geographic information. The GIO focuses on seamless access to data, applications of data, and enabling technologies furthering the interoperability of distributed data. Through teaming within the Applications Directorate and partnerships with government, private industry, education and communities, GIO works towards the data application goals of NASA, the ESE Applications Directorate, and our Federal partners by managing projects in four categories: Geospatial Standards and Leadership, Geospatial One Stop, Standards Development and Implementation, and National and NASA Activities.

Weir, Patricia↗

To Boldly Go. America's Next Era in Space: New Frontiers in Climate Research

Dr. France Cordova, NASA's Chief Scientist, chaired this, the fourth seminar in the NASA Administrator's Seminar Series. She introduced NASA Administrator, Daniel S. Goldin, who greeted the attendees, and in his opening remarks said that human beings have a need to understand the what and why of the forces of nature and of people, and the stresses on the planet Earth. The first speaker, Dr. Ellen Mosley-Thompson of Ohio State University discussed the many things that scientists have learned from ice cores obtained in Peru and the Antarctic. The next speaker, Dr. Michael McElroy of Harvard University, is active in environmental research. He noted that insurance companies need to know more about the physics and chemistry of weather in order to avoid bankruptcy; that the greenhouse effect, which is good because it reflects heat, is being changed, and we don't know the rules. In the discussion that followed, Goldin asked if the present technology for measuring circulation of air and water and contents of the atmosphere is worth the cost. Drs. McElroy and Mosley-Thompson noted that the historic record in an ice core is endangered by ice melts; that in the last 10 years we've learned that tropics change; that the water vapor in the tropics is critical right now; that clouds absorb short-wave radiation; and that there is a need to improve measurements of atmospheric contents, the development of models, and the understanding of basic physics. We also need to understand parameters for detecting climate change, water, water temperature, and be able to provide fundamental information. Additional information is included in the original extended abstract.

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To Boldly Go: America's Next Era in Space. Probing the Primordial Constituents of Our Solar System

Dr. France Cordova, NASA's Chief Scientist, chaired this, another seminar in the Administrator's Seminar Series. She introduced NASA Administrator, Daniel S. Goldin, who greeted the attendees, and noted that, from the day people first looked into the sky, they've wondered what was up there, who or what created it, is Earth unique, what shaped the solar system, what is the Kuiper Belt and why is it there, and what are the solar system's building blocks. NASA's missions may discover some of the answers. Dr. Cordova then introduced Dr. Anita Cochran, research scientist at the University of Texas. Dr. Cochran has been searching for some of this information. She is especially interested in finding out when various planets and asteroids were discovered, what their orbits are, when the solar system was formed, and more about the comets in the Kuiper Belt. Are they icy planetisimals that helped form our solar system? Dr. Toby Owen of the University of Hawaii faculty spoke next. He believes that life on Earth exists because comets brought water and a variety of light elements to Earth from the outer parts of the solar system. Without them, we couldn't exist. He noted that noble gases don't mix with other gases. Gases come to Earth via rocks and by bombardment. Ice can trap argon and carbon, but not neon. Dr. Owens concluded with comments that we need 'better numbers for the Martian atmosphere', and it would be good to get samples of material from a comet. The third speaker was Dr. Eugene Shoemaker of the Lowell Observatory and the U.S. Geological Survey. He is credited with discovering more than 800 asteroids and learning about the Oort Cloud, which is believed to be a cloud of rocks and dust that may surround our solar system and be where comets originate. Comet storms reoccur about every 30 million years. Dr. Shoemaker suggested that since we are presently in a period of comet showers, it would be good to get a comet sample. It might provide insight regarding the origin of life. Additional information is included in the original extended abstract.

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To Boldly Go: America's Next Era in Space. Living Places in Other Solar Systems

Dr. Sargent noted that evidence of other solar systems that might sustain life, particularly human life, is being sought. Protoplanetary (or debris) disks have been observed and are considered evidence that other solar systems exist or are being formed. Also observed is a wobble which is seen as evidence of circulation around a celestial body and gaps that are created by the potential planet. One indicator of life may be these rings or disks of debris around stars. Interferometers, which are telescopic devices that consist of multiple lenses, are being developed in order to better see celestial objects and what may be found around them. Other methods for improving celestial viewing capabilities are also under development. She spoke of particularly looking for wobble and gaps and debris disks where new planets are being formed in an effort to discover another planet that might sustain life as we know it. The next speaker, Dr. Chris McKay, is a planetary scientist at NASA Ames. He talked about the possibility of life on Mars or in some other solar system. He commented on the sameness of the origin of all life, and of the origin of, and the need for, oxygen and water. He believes that water originally came to Earth from comets. At least that is a viable possible source. Water might also have come to Earth via asteroids. Dr. McKay also postulates that there can be no water on Mars because Mars has no plate tectonic system, which he believes is an essential for recycling water. . Dr. Wes Huntress, NASA s Associate Administrator for Space Science, and Dr. Barbara Stone, also from NASA Headquarters, joined Drs. Cordova, Sargent and McKay in the question and answer period following the presentations. (Mr. Goldin was excused to keep an appointment with the President.) The discussion included the following statements and questions: The more missions that there are, the more technology is developed. We need to study our solar system to have something to which we can compare other systems. Before we send people to distant places or to other planets, we need to study the psychological and biological problems that are created by going away from Earth for a long period of time. Pulsars appear to have planets rotating around them. This is of interest and should be studied further. Looking back in time, is there any thought to seeing the development of life? How long did it take for oxygen to rise on the Earth? Do debris disks around the stars provide velocity patterns? To detect life scientists are listening for radio signals, looking for oxygen or ozone, and looking for liquid water. On Earth liquid water is the defining ecological parameter for life. This means that operationally the search for life elsewhere is primarily a search for liquid water.

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Following Up: Huygens Data, Questions Will Guide Cassini on Its Future Titan Passes

Planetary scientists plan to use the instruments on NASA's Cassini Saturn orbiter in future flybys of Titan to answer questions raised by Europe's Huygens probe. In particular, they hope to discover whether the dark, flat areas on the moon's surface are liquid or quasi-liquid methane seas. As the scientists plotted their next moves, European Space Agency (ESA) officials continued their investigation into how a critical command in the Huygens descent sequence was omitted costing the imaging team half of its data and rendering another Huygens instrument useless. There were suggestions that U.S. export-control rules may have hampered the sort of close international cooperation that might have caught the error.

Morring, Frank, Jr.↗

The Status of Lunar Simulants: Conclusions and Recommendations from the 2005 Lunar Regolith Simulant Materials Workshop

No coordinated program currently exists in the U.S.A to define reference materials to be used as analogs of lunar materials. While such efforts have existed at different times in the past (Apollo Landing Module and Lunar Rover programs and NASA's Space Initiative in the early 1990's), the need for mineral materials chosen to simulate the characteristics of lunar regoliths is a pressing issue that must be addressed today through the collaboration of scientists, engineers and program managers. The 2005 Lunar Regolith Materials Workshop was held at Marshall Space Flight Center in Huntsville, AL on January 24-26,2005 to launch a focused effort of defining the requirements of lunar >simulant materials and make specific recommendations to NASA Headquarters for their production. Nearly 100 scientists and engineers worked during 3 days to accomplish these goals. Their conclusions and recommendations will be presented.

Sibille, L.↗

Harnessing: Technologies for Sustainable Reindeer Husbandry in the Arctic

To accelerate the development of sustainable reindeer husbandry under the lead of indigenous reindeer herders, it is critical to empower reindeer herders with the best available technologies and to promote a new kind of science where traditional knowledge is fully integrated into the scientific management of the natural environment in the Arctic. This is particularly true given the dramatic environmental, climatic, economic, social and industrial changes, which have taken place across the Arctic in recent years, all of which have had serious impacts on the reindeer herding communities of the North. The Anar Declaration, adopted by the 2d World Reindeer Herders Congress (WRHC), in Inari, Finland, June 2001drew guidelines for the development of a sustainable reindeer husbandry based on reindeer peoples values and goals. The declaration calls for the reindeer herding peoples to be given the possibilities to develop and influence the management of the reindeer industry and its natural environment because of their knowledge and traditional practices. At the same time, Arctic scientists from many institutions and governments are carrying out increasingly highly technical reindeer related research activities. It is important that the technologies and results of these activities be more commonly co-produced with the reindeer herder community and/or made more readily available to the reindeer peoples for comparison with traditional knowledge for improved herd management. This paper describes a project in which reindeer herders and scientists are utilizing technologies to create a system for collecting and sharing knowledge. The project, Reindeer Mapper, is creating an information management and knowledge sharing system, which will help make technologies more readily available to the herder community for observing, data collection and analysis, monitoring, sharing, communications, and dissemination of information - to be integrated with traditional, local knowledge. The paper describes some of the technologies which comprise the system including an intranet system to enable the team members to work together and share information electronically, remote sensing data for monitoring environmental parameters important to reindeer husbandry (e.g. SAR, Landsat), acquisition of ground-based measurements, and the GIS-based information management and knowledge sharing system.

Maynard, Nancy G.↗

The NASA Astrobiology Institute: early history and organization

The NASA Astrobiology Institute (NAI) was established as a means to advance the field of astrobiology by providing a multidisciplinary, multi-institution, science-directed program, executed by universities, research institutes, and NASA and other government laboratories. The scientific community and NASA defined the science content at several workshops as summarized in the NASA Astrobiology Roadmap. Teams were chosen nationwide, following the recommendations of external review groups, and the research program began in 1998. There are now 16 national Teams and five international affiliated and associated astrobiology institutions. The NAI has attracted an outstanding group of scientific groups and individuals. The Institute facilitates the involvement of the scientists in its scientific and management vision. Its goal is to support basic research and allow the scientists the freedom to select their projects and alter them as indicated by new research. Additional missions include the education of the public, the involvement of students who will be the astrobiologists of future generations, and the development of a culture of collaboration in NAI, a "virtual institute," spread across many sites nationally and internationally.

United States National Aeronautics and Space Admin↗

The Living Universe: NASA and the Development of Astrobiology

In the opening weeks of 1998 a news article in the British journal Nature reported that NASA was about to enter biology in a big way. A "virtual" Astrobiology Institute was gearing up for business, and NASA administrator Dan Goldin told his external advisory council that he would like to see spending on the new institute eventually reach $100 million per year. "You just wait for the screaming from the physical scientists (when that happens)," Goldin was quoted as saying. Nevertheless, by the time of the second Astrobiology Science Conference in 2002, attended by seven hundred scientists from many disciplines, NASA spending on astrobiology had reached nearly half that amount and was growing at a steady pace. Under NASA leadership numerous institutions around the world applied the latest scientific techniques in the service of astrobiology's ambitious goal: the study of what NASA's 1996 Strategic Plan termed the "living universe." This goal embraced nothing less than an understanding of the origin, history, and distribution of life in the universe, including Earth. Astrobiology, conceived as a broad interdisciplinary research program, held the prospect of being the science for the twenty-first century which would unlock the secrets to some of the great questions of humanity. It is no surprise that these age-old questions should continue into the twenty-first century. But that the effort should be spearheaded by NASA was not at all obvious to those - inside and outside the agency - who thought NASA's mission was human spaceflight, rather than science, especially biological science. NASA had, in fact, been involved for four decades in "exobiology," a field that embraced many of the same questions but which had stagnated after the 1976 Viking missions to Mars. In this volume we tell the colorful story of the rise of the discipline of exobiology, how and why it morphed into astrobiology at the end of the twentieth century, and why NASA was the engine for both the discipline's founding and for its transformation.

Dick, Steven J.↗

The Explorer's Guide to Impact Craters

Impact cratering is a fundamental geologic process of our solar system. It competes with other processes, such as plate tectonics, volcanism, fluvial, glacial and eolian activity, in shaping the surfaces of planetary bodies. In some cases, like the Moon and Mercury, impact craters are the dominant landform. On other planetary bodies impact craters are being continuously erased by the action of other geological processes, like volcanism on Io, erosion and plate tectonics on the Earth, tectonic and volcanic resurfacing on Venus, or ancient erosion periods on Mars. The study of crater populations is one of the principal tools for understanding the geologic history of a planetary surface. Among the general public, impact cratering has drawn wide attention through its portrayal in several Hollywood movies. Questions that are raised after watching these movies include: How do scientists learn about impact cratering? , and What information do impact craters provide in understanding the evolution of a planetary surface? Fundamental approaches used by scientists to learn about impact cratering include field work at known terrestrial craters, remote sensing studies of craters on various solid surfaces of solar system bodies, and theoretical and laboratory studies using the known physics of impact cratering.

Chuang, F.↗

Micromechanics Analysis Code (MAC) Developed

The ability to accurately predict the thermomechanical deformation response of advanced composite materials continues to play an important role in the development of these strategic materials. Analytical models that predict the effective behavior of composites are used not only by engineers in performing structural analysis of large-scale composite components but also by material scientists in developing new material systems. For an analytical model to fulfill these two distinct functions, it must be based on a micromechanics approach that uses physically based deformation and life constitutive models, and it must allow one to generate the average (macro) response of a composite material given the properties of the individual constituents and their geometric arrangement. Only then can such a model be used by a material scientist to investigate the effect of different deformation mechanisms on the overall response of the composite and, thereby, identify the appropriate constituents for a given application. However, if a micromechanical model is to be used in a large-scale structural analysis it must be (1) computationally efficient, (2) able to generate accurate displacement and stress fields at both the macro and micro level, and (3) compatible with the finite element method. In addition, new advancements in processing and fabrication techniques now make it possible to engineer the architectures of these advanced composite systems. Full utilization of these emerging manufacturing capabilities require the development of a computationally efficient micromechanics analysis tool that can accurately predict the effect of microstructural details on the internal and macroscopic behavior of composites. Computational efficiency is required because (1) a large number of parameters must be varied in the course of engineering (or designing) composite materials and (2) the optimization of a material's microstructure requires that the micromechanics model be integrated with optimization algorithms. From this perspective, analytical approaches that produce closed-form expressions which describe the effect of a material's internal architecture on the overall material behavior are preferable to numerical methods such as the finite element or finite difference schemes.

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