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We report progress in three areas of investigation related to dendritic crystal growth. Those items include: 1. Selection of tip features dendritic crystal growth; 2) Investigation of nonlinear evolution for two-sided model; and 3) Rigorous mathematical justification.
A physicist with an engineering background, the author presents a mathematical dictionary containing material encountered over many years of study and professional work at NASA. This work is a compilation of the author's experience and progress in the field of study represented and consists of personal notes and observations that can be used by students in physics and engineering.
Different mathematical models of varying complexity have been proposed in recent years to study the cardiovascular (CV) system. However, only a few of them specifically address the response to lower body negative pressure (LBNP), a stress that can be applied in weightlessness to predict changes in orthostatic tolerance. Also, the simulated results produced by these models agree only partially with experimental observations. In contrast, the model proposed by Melchior et al., and modified by Karam et al. is a simple representation of the CV system capable of accurately reproducing observed LBNP responses up to presyncopal levels. There are significant changes in LBNP response due to a loss of blood volume and other alterations that occur in weightlessness and related one-g conditions such as bedrest. A few days of bedrest can cause up to 15% blood volume loss (BVL), with consequent decreases in both stroke volume and cardiac output, and increases in heart rate, mean arterial pressure, and total peripheral resistance. These changes are more pronounced at higher levels of LBNP. This paper presents the results of a simulation study using our CV model to examine the effect of BVL on LBNP response.
Microbial activity in the Antarctic cryptoendolithic habitat is regulated primarily by temperature. Previous field studies have provided some information on the thermal regime in this habitat, but this type of information is limited by the remoteness of the site and the harsh climatic conditions. Therefore, a mathematical model of the endolithic thermal regime was constructed to augment the field data. This model enabled the parameters affecting the horizontal and altitudinal distribution of the community to be examined. The model predicts that colonization should be possible on surfaces with zenith angle less than 15 degrees. At greater zenith angles, colonization should be restricted to surfaces with azimuth angles less than 135 degrees or greater than 225 degrees. The upper elevational limit of the community should be less than 2,500 m. The thermal regime probably does not influence the zonation of the community within a rock.
BACKGROUND/AIMS: Astronauts exposed to microgravity during the course of spaceflight undergo physiologic changes that alter the urinary environment so as to increase the risk of renal stone formation. This study was undertaken to identify a simple method with which to evaluate the potential risk of renal stone development during spaceflight. METHOD: We used a large database of urinary risk factors obtained from 323 astronauts before and after spaceflight to generate a mathematical model with which to predict the urinary supersaturation of calcium stone forming salts. RESULT: This model, which involves the fewest possible analytical variables (urinary calcium, citrate, oxalate, phosphorus, and total volume), reliably and accurately predicted the urinary supersaturation of the calcium stone forming salts when compared to results obtained from a group of 6 astronauts who collected urine during flight. CONCLUSIONS: The use of this model will simplify both routine medical monitoring during spaceflight as well as the evaluation of countermeasures designed to minimize renal stone development. This model also can be used for Earth-based applications in which access to analytical resources is limited.
This study describes a two-compartment model of pulmonary gas exchange in which alveolar ventilation to perfusion (VA/Q) heterogeneity and impairment of pulmonary diffusing capacity (D) are simultaneously taken into account. The mathematical model uses as input data measurements usually obtained in the lung function laboratory. It consists of two compartments and an anatomical shunt. Each compartment receives fractions of alveolar ventilation and blood flow. Mass balance equations and integration of Fick's law of diffusion are used to compute alveolar and blood O2 and CO2 values compatible with input O2 uptake and CO2 elimination. Two applications are presented. The first is a method to partition O2 and CO2 alveolar-arterial gradients into VA/Q and D components. The technique is evaluated in data of patients with chronic obstructive pulmonary disease (COPD). The second is a theoretical analysis of the effects of blood flow variation in alveolar and blood O2 partial pressures. The results show the importance of simultaneous consideration of D to estimate VA/Q heterogeneity in patients with diffusion impairment. This factor plays an increasing role in gas alveolar-arterial gradients as severity of COPD increases. Association of VA/Q heterogeneity and D may produce an increase of O2 arterial pressure with decreasing QT which would not be observed if only D were considered. We conclude that the presented computer model is a useful tool for description and interpretation of data from COPD patients and for performing theoretical analysis of variables involved in the gas exchange process.
The emergence of early metabolism - a network of catalyzed chemical reactions that supported self-maintenance, growth, reproduction and evolution of the ancestors of contemporary cells (protocells) was a critical, but still very poorly understood step on the path from inanimate to animate matter. Here, it is proposed and tested through mathematical modeling of biochemically plausible systems that the emergence of metabolism and its initial evolution towards higher complexity preceded the emergence of a genome. Even though the formation of protocellular metabolism was driven by non-genomic, highly stochastic processes the outcome was largely deterministic, strongly constrained by laws of chemistry. It is shown that such concepts as speciation and fitness to the environment, developed in the context of genomic evolution, also held in the absence of a genome.
Economic forces and technology development have made low-earth-orbit satellite constellations extremely attractive to the emergent personal communications industry. These constellations range from 2 to nearly 1000 satellites. Even though none of the constellations are as yet completely deployed, design on second generation constellations have already begun. The satellite coverage and network links provide some interesting mathematical problems. We examine some of the geometric and combinatorial problems associated with these networks.
A whole-body mathematical model (10) for simulating intracranial pressure dynamics. In one embodiment, model (10) includes 17 interacting compartments, of which nine lie entirely outside of intracranial vault (14). Compartments (F) and (T) are defined to distinguish ventricular from extraventricular CSF. The vasculature of the intracranial system within cranial vault (14) is also subdivided into five compartments (A, C, P, V, and S, respectively) representing the intracranial arteries, capillaries, choroid plexus, veins, and venous sinus. The body's extracranial systemic vasculature is divided into six compartments (I, J, O, Z, D, and X, respectively) representing the arteries, capillaries, and veins of the central body and the lower body. Compartments (G) and (B) include tissue and the associated interstitial fluid in the intracranial and lower regions. Compartment (Y) is a composite involving the tissues, organs, and pulmonary circulation of the central body and compartment (M) represents the external environment.
A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.
In air traffic management, conflict prevention information refers to the guidance maneuvers, which if taken, ensure that an aircraft's path is conflict-free. These guidance maneuvers take the form of changes to track angle or ground speed. Conflict prevention information may be assembled into prevention bands that advise the crew on maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for any maneuver, giving the pilot confidence that if a maneuver is made, then no near-term conflicts will result. Because near-term conflicts can lead to safety concerns, strong verification of information correctness is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information incorporating an arbitrary number of traffic aircraft and with both a near-term and intermediate-term lookahead times. The framework is illustrated with a formally verified algorithm for 2-dimensional track angle prevention bands.
Two innovative mathematical models of nonlinear vibrations, and methods of applying them, have been conceived as byproducts of an effort to develop a Kalman filter for highly precise estimation of bending motions of a large truss structure deployed in outer space from a space-shuttle payload bay. These models are also applicable to modeling and analysis of vibrations in other engineering disciplines, on Earth as well as in outer space.
The United States ranking among the world in science, technology, engineering, and mathematics (STEM) education is decreasing. To counteract this problem NASA has made it part of its mission to promote STEM education among the nation s youth. Mockups can serve as a great tool when promoting STEM education in America. The Orion Cockpit Working Group has created a new program called Students Shaping America s Next Space Craft (SSANS) to outfit the Medium Fidelity Orion Mockup. SSANS will challenge the students to come up with unique designs to represent the flight design hardware. There are two main types of project packages created by SSANS, those for high school students and those for university students. The high school projects will challenge wood shop, metal shop and pre-engineering classes. The university projects are created mainly for senior design projects and will require the students to perform finite element analysis. These projects will also challenge the undergraduate students in material selection and safety requirements. The SSANS program will help NASA in its mission to promote STEM education, and will help to shape our nations youth into the next generation of STEM leaders.
This is a teacher's guide to assist teachers in developing modules on windows for use in both earth and space and astronaut photographs. Activities incorporating mathematical exercises are suggested for grades five through ten.
We describe a mathematical formalism for determining the mirror shell nodal positions and detector tilts that optimize the spatial resolution averaged over a field-of-view for a nested x-ray telescope, assuming known mirror segment surface prescriptions and known detector focal surface. The results are expressed in terms of ensemble averages over variable combinations of the ray positions and wave vectors in the flat focal plane intersecting the optical axis at the nominal on-axis focus, which can be determined by Monte-Carlo ray traces of the individual mirror shells. This work is part of our continuing efforts to provide analytical tools to aid in the design process for wide-field survey x-ray astronomy missions.
We describe a mathematical formalism for determining the mirror shell nodal positions and detector tilts that optimize the spatial resolution averaged over a field-of-view for a nested x-ray telescope, assuming known mirror segment surface prescriptions and known detector focal surface. The results are expressed in terms of ensemble averages over variable combinations of the ray positions and wavevectors in the flat focal plane intersecting the optical axis at the nominal on-axis focus, which can be determined by Monte-Carlo ray traces of the individual mirror shells. This work is part of our continuing efforts to provide analytical tools to aid in the design process for wide-field survey x-ray astronomy missions.
We provide a mathematical formalism for optimizing the mirror nodal positions along the optical axis and the tilt of a commonly employed detector configuration at the focus of a x-ray telescope consisting of nested mirror shells with known mirror surface prescriptions. We adopt the spatial resolution averaged over the field-of-view as the figure of merit M. A more complete description appears in our paper in these proceedings.
In response to the White House Educate to Innovate campaign, NASA developed a new science, technology, engineering, and mathematics (STEM) education program for non-traditional audiences that also focused on public-private partnerships and nationwide participation. NASA recognized that summer break is an often overlooked but opportune time to engage youth in STEM experiences, and elevated its ongoing commitment to the cultivation of diversity. The Summer of Innovation (SoI) is the resulting initiative that uses NASA's unique missions and resources to boost summer learning, particularly for students who are underrepresented, underserved and underperforming in STEM. The SoI pilot, launched in June 2010, is a multi-faceted effort designed to improve STEM teaching and learning through partnership, multi-week summer learning programs, special events, a national concluding event, and teacher development. The SoI pilot features strategic infusion of NASA content and educational resource materials, sustainability through STEM Learning Communities, and assessments of effectiveness of SoI interventions with other pilot efforts. This paper examines the inception and development of the Summer of Innovation pilot project, including achievements and effectiveness, as well as lessons learned for future efforts.