Microgravity: A Teacher's Guide with Activities in Science, Mathematics, and Technology

NASA Technical Reports Server (NTRS)

Rogers, Melissa J.B.; Vogt, Gregory L.; Wargo, Michael J.

1997-01-01

Microgravity is the subject of this teacher's guide. This publication identifies the underlying mathematics, physics, and technology principles that apply to microgravity. The topics included in this publication are: 1) Microgravity Science Primer; 2) The Microgravity Environment of Orbiting Spacecraft; 3) Biotechnology; 4) Combustion Science; 5) Fluid Physics; 6) Fundamental Physics; and 7) Materials Science; 8) Microgravity Research and Exploration; and 9) Microgravity Science Space Flights. This publication also contains a glossary of selected terms.

Dannie Heineman Prize for Mathematical Physics: Applying mathematical techniques to solve important problems in quantum theory

NASA Astrophysics Data System (ADS)

Bender, Carl

2017-01-01

The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.

Playful Physics

NASA Technical Reports Server (NTRS)

Weaver, David

2008-01-01

Effectively communicate qualitative and quantitative information orally and in writing. Explain the application of fundamental physical principles to various physical phenomena. Apply appropriate problem-solving techniques to practical and meaningful problems using graphical, mathematical, and written modeling tools. Work effectively in collaborative groups.

Gender Gap in Mathematics and Physics in Chinese Middle Schools: A Case Study of A Beijing's District

ERIC Educational Resources Information Center

Li, Manli; Zhang, Yu; Wang, Yihan

2017-01-01

This study examines the gender gaps in mathematics and physics in Chinese middle schools. The data is from the Education Bureau management database which includes all middle school students who took high school entrance exam in a district of Beijing from 2006-2013. The ordinary least square model and quantile regression model are applied. This…

Comparing the Math Anxiety of Secondary School Female Students in Groups (Science and Mathematical Physics) Public Schools

ERIC Educational Resources Information Center

Vakili, Khatoon; Pourrazavy, Zinat alsadat

2017-01-01

The aim of this study is comparing math anxiety of secondary school female students in groups (Science and Mathematical Physics) Public Schools, district 2, city of Sari. The purpose of the research is applied research, it is a development branch, and in terms of the nature and method, it is a causal-comparative research. The statistical…

How Plankton Swim: An Interdisciplinary Approach for Using Mathematics & Physics to Understand the Biology of the Natural World

ERIC Educational Resources Information Center

Clay, Tansy W.; Fox, Jennifer B.; Grunbaum, Daniel; Jumars, Peter A.

2008-01-01

The authors have developed and field-tested high school-level curricular materials that guide students to use biology, mathematics, and physics to understand plankton and how these tiny organisms move in a world where their intuition does not apply. The authors chose plankton as the focus of their materials primarily because the challenges faced…

Unified Technical Concepts. Math for Technicians.

ERIC Educational Resources Information Center

Center for Occupational Research and Development, Inc., Waco, TX.

Unified Technical Concepts (UTC) is a modular system for teaching applied physics in two-year postsecondary technician programs. This UTC classroom textbook, consisting of 10 chapters, deals with mathematical concepts as they apply to the study of physics. Addressed in the individual chapters of the text are the following topics: angles and…

Gaining Modelling and Mathematical Experience by Constructing Virtual Sensory Systems in Maze-Videogames

ERIC Educational Resources Information Center

Sacristán, Ana Isabel; Pretelín-Ricárdez, Angel

2017-01-01

This work is part of a research project that aims to enhance engineering students' learning of how to apply mathematics in modelling activities of real-world situations, through the construction (design and programming) of videogames. We want also for students to relate their mathematical knowledge with other disciplines (e.g., physics, computer…

Phil Wallace and Theoretical Physics at McGill in the 1950's: A Personal Perspective

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jackson, John David

In 1946 Philip (Phil) Russell Wallace joined the Mathematics Department of McGill University as an Associate Professor of Applied Mathematics, apparently because A. H. S. Gillson, Dean of Arts and Science, wanted theoretical physicists to be in the Mathematics Department. He came with the dream of creating a theoretical physics group at McGill. By the spring of 1949, Phil was authorized to recruit two junior faculty in Mathematics. He hired Theodore (Ted) F. Morris from U. Toronto, who joined in September 1949, and me, who came in January 1950. The group had begun. Phil Wallace was born in Toronto inmore » 1915 and grew up there. He entered the University of Toronto in 1933, earned a B.A. in mathematics in 1937, a M.A. in 1938, and a Ph.D. in applied mathematics in 1940 under Leopold Infeld. His Ph.D. thesis in general relativity was entitled 'On the relativistic equations of motion in electromagnetic theory.' In 1940 World War II had engulfed Europe and was having its effect on Canada, but the US was still at peace. L. J. Synge, Head of the Applied Mathematics Department at Toronto, told Wallace that people such as he would be needed in war work, but things were not ready quite yet. Hold yourself ready. Phil took a two-year position as lecturer in mathematics at the University of Cincinnati (1940-42); in the fall of 1942 he became a lecturer in mathematics at M.I.T. It was from there that he was recruited by Synge to join the war effort from 1943 to 1946 at N.R.C.'s Montreal Laboratory, the genesis of the Canadian Atomic Energy Project. Phil has described those heady wartime years in these pages. Much of the effort of the theoretical physicists was on nuclear reactor theory and the properties of relevant materials, such as graphite, under long and intense neutron bombardment. In late 1945 Phil was sent for four months to Bristol to learn about the properties of graphite from the esteemed N. F. Mott. This exposure led Phil to a life-long interest in graphite and in condensed matter physics in general. After the war, the group of Montreal Lab theorists dissolved - some had already left for Los Alamos; some went to Chalk River; Volkoff returned to UBC to foster theoretical physics as part of physics in the West; Wallace to do the same in the East. But the path at McGill was not smooth. As a singular anomaly in a pure math department, Phil was tucked away in the corner of some engineering building, remote from the bulk of the mathematicians. And there was no welcoming mat from Physics. As Wallace remarks, 'I took a post at McGill, not surprisingly in the department of Mathematics. Certain complications of academic politics followed, such as jurisdictional disputes over course assignments. Theoretical physicists were treated more or less as foreigners or rivals by at least a segment of the physics department.' 'Why was that?' McGill's attitude about theoretical physics was colored for fifty years by the lingering influence of Ernest Rutherford, who was a faculty member from 1898 to 1907. In his essay about the beginnings of theoretical physics in Canada, Wallace quotes examples of Rutherford's views about theoretical physics. In short, theoretical physics is applied mathematics and has no place in a department devoted to the study of natural phenomena. Because of his eminence and connection to McGill, numerous physics graduates went to the 'Mecca' of Manchester then Cambridge to do a Ph.D. with the great man. Some then returned to the McGill Physics faculty to teach and perpetuate the Rutherfordian view of theory. Although the theoretical physics group at McGill in the 1950s had no official standing and no statutory leader, Phil Wallace was that leader and builder of the group. An inspiration to students and junior colleagues alike, he protected and nurtured us in the sometimes difficult circumstances of citizens without a country.« less

Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

2013-07-01

The Mathematics and Computation Division of the American Nuclear (ANS) and the Idaho Section of the ANS hosted the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M and C 2013). This proceedings contains over 250 full papers with topics ranging from reactor physics; radiation transport; materials science; nuclear fuels; core performance and optimization; reactor systems and safety; fluid dynamics; medical applications; analytical and numerical methods; algorithms for advanced architectures; and validation verification, and uncertainty quantification.

10 CFR 35.51 - Training for an authorized medical physicist.

Code of Federal Regulations, 2013 CFR

2013-01-01

... all candidates for certification to: (1) Hold a master's or doctor's degree in physics, medical physics, other physical science, engineering, or applied mathematics from an accredited college or university; (2) Have 2 years of full-time practical training and/or supervised experience in medical physics...

10 CFR 35.51 - Training for an authorized medical physicist.

Code of Federal Regulations, 2012 CFR

2012-01-01

... all candidates for certification to: (1) Hold a master's or doctor's degree in physics, medical physics, other physical science, engineering, or applied mathematics from an accredited college or university; (2) Have 2 years of full-time practical training and/or supervised experience in medical physics...

10 CFR 35.51 - Training for an authorized medical physicist.

Code of Federal Regulations, 2014 CFR

2014-01-01

... all candidates for certification to: (1) Hold a master's or doctor's degree in physics, medical physics, other physical science, engineering, or applied mathematics from an accredited college or university; (2) Have 2 years of full-time practical training and/or supervised experience in medical physics...

10 CFR 35.51 - Training for an authorized medical physicist.

Code of Federal Regulations, 2010 CFR

2010-01-01

... all candidates for certification to: (1) Hold a master's or doctor's degree in physics, medical physics, other physical science, engineering, or applied mathematics from an accredited college or university; (2) Have 2 years of full-time practical training and/or supervised experience in medical physics...

First-Year Mathematics and Its Application to Science: Evidence of Transfer of Learning to Physics and Engineering

ERIC Educational Resources Information Center

Nakakoji, Yoshitaka; Wilson, Rachel

2018-01-01

Transfer of mathematical learning to science is seen as critical to the development of education and industrial societies, yet it is rarely interrogated in applied research. We present here research looking for evidence of transfer from university mathematics learning in semester one to second semester sciences/engineering courses (n = 1125). A…

ANNUAL REPORT ON PHYSICAL SCIENCES, ENGINEERING AND LIFE SCIENCES , JULY 1, 1961

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

1962-10-31

The research program at Brooknaven is described. Current activities in physics, high-energy accelerators, instrumentation, chemistry, nuclear engineering, applied mathematics, biology, and medical research are outlined. (D.L.C.)

A New Wave in Applied Mathematics.

ERIC Educational Resources Information Center

Cipra, Barry A.

1990-01-01

Discussed is wavelet theory, which provides ways to rearrange data to reveal features of a physical or mathematical system which might otherwise be hidden. This theory is compared to fourier analysis and the advantages of wavelet theory are stressed. Applications of this technique are suggested. (CW)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arimura, Hidetaka, E-mail: arimurah@med.kyushu-u.ac.jp; Kamezawa, Hidemi; Jin, Ze

Good relationships between computational image analysis and radiological physics have been constructed for increasing the accuracy of medical diagnostic imaging and radiation therapy in radiological physics. Computational image analysis has been established based on applied mathematics, physics, and engineering. This review paper will introduce how computational image analysis is useful in radiation therapy with respect to radiological physics.

Draw Your Physics Homework? Art as a Path to Understanding in Physics Teaching

ERIC Educational Resources Information Center

van der Veen, Jatila

2012-01-01

The persistent fear of physics by learners motivated the author to take action to increase all students' interest in the subject via a new curriculum for introductory college physics that applies Greene's model of Aesthetic Education to the study of contemporary physics, utilizing symmetry as the mathematical foundation of physics as well as the…

Viscous Flow

NASA Astrophysics Data System (ADS)

Ockendon, Hilary; Ockendon, John

1995-01-01

Viscous flow crops up in many real-life situations such as aerodynamics and lubrication, and because of its universality it is a paradigm for the application of mathematics to the real world. This book is a coherent account of the ways in which mathematics can both give insight into viscous flow and suggest analogies and implications for other branches of applied mathematics. The authors place particular emphasis on the unification brought about by the use of asymptotic analysis and scaling properties and the use of everyday observations from the real world (especially industry) to illustrate the theory. The book is aimed at final-year undergraduate and beginning graduate students in applied mathematics, physics, and engineering courses on fluid flow.

Catastrophe modelling in the biological sciences.

PubMed

Deakin, M A

1990-03-01

Catastrophe Theory was developed in an attempt to provide a form of Mathematics particularly apt for applications in the biological sciences. It was claimed that while it could be applied in the more conventional "physical" way, it could also be applied in a new "metaphysical" way, derived from the Structuralism of Saussure in Linguistics and Lévi-Strauss in Anthropology. Since those early beginnings there have been many attempts to apply Catastrophe Theory to Biology, but these hopes cannot be said to have been fully realised. This paper will document and classify the work that has been done. It will be argued that, like other applied Mathematics, applied Catastrophe Theory works best where the underlying laws are securely known and precisely quantified, requiring those same guarantees as does any other branch of Mathematics when it confronts a real-life situation.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Quantum-Like Models for Decision Making in Psychology and Cognitive Science

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei.

2009-02-01

We show that (in contrast to rather common opinion) the domain of applications of the mathematical formalism of quantum mechanics is not restricted to physics. This formalism can be applied to the description of various quantum-like (QL) information processing. In particular, the calculus of quantum (and more general QL) probabilities can be used to explain some paradoxical statistical data which was collected in psychology and cognitive science. The main lesson of our study is that one should sharply distinguish the mathematical apparatus of QM from QM as a physical theory. The domain of application of the mathematical apparatus is essentially wider than quantum physics. Quantum-like representation algorithm, formula of total probability, interference of probabilities, psychology, cognition, decision making.

Development of Contextual Mathematics teaching Material integrated related sciences and realistic for students grade xi senior high school

NASA Astrophysics Data System (ADS)

Helma, H.; Mirna, M.; Edizon, E.

2018-04-01

Mathematics is often applied in physics, chemistry, economics, engineering, and others. Besides that, mathematics is also used in everyday life. Learning mathematics in school should be associated with other sciences and everyday life. In this way, the learning of mathematics is more realstic, interesting, and meaningful. Needs analysis shows that required contextual mathematics teaching materials integrated related sciences and realistic on learning mathematics. The purpose of research is to produce a valid and practical contextual mathematics teaching material integrated related sciences and realistic. This research is development research. The result of this research is a valid and practical contextual mathematics teaching material integrated related sciences and realistic produced

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

Astronomy and Mathematics Education

NASA Astrophysics Data System (ADS)

Ros, Rosa M.

There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.

10 CFR 35.50 - Training for Radiation Safety Officer.

Code of Federal Regulations, 2010 CFR

2010-01-01

... professional experience in health physics (graduate training may be substituted for no more than 2 years of the required experience) including at least 3 years in applied health physics; and (iii) Pass an examination... physics and instrumentation, radiation protection, mathematics pertaining to the use and measurement of...

Johannes Kepler and his contribution to Applied Mathematics

NASA Astrophysics Data System (ADS)

Pichler, Franz

The worldwide renown of Johannes Kepler is based above all on his contribution to astronomy. The 3 Kepler's Laws relating to the planets are well known and will ensure that his name is remembered by future generations. Besides his astronomical work, Kepler also made important contributions in the fields of theology, physics, phylosophy and mathematics. The actual paper discusses the advances by Kepler in the application of mathematics to the solution of "real life problems". The author made a concise account of some of the disciples by Kepler: Klug, Wieleitner, Caspar, Hammer, paying particular attention to works published by Kepler while he was living in Linz (1612-1628). The Kepler's contribution to applied mathematics is an example supremely worthy of emulation, the author concludes.

David crighton, 1942-2000: a commentary on his career and his influence on aeroacoustic theory

NASA Astrophysics Data System (ADS)

Ffowcs Williams, John E.

David Crighton, a greatly admired figure in fluid mechanics, Head of the Department of Applied Mathematics and Theoretical Physics at Cambridge, and Master of Jesus College, Cambridge, died at the peak of his career. He had made important contributions to the theory of waves generated by unsteady flow. Crighton's work was always characterized by the application of rigorous mathematical approximations to fluid mechanical idealizations of practically relevant problems. At the time of his death, he was certainly the most influential British applied mathematical figure, and his former collaborators and students form a strong school that continues his special style of mathematical application. Rigorous analysis of well-posed aeroacoustical problems was transformed by David Crighton.

A Physics Show Performed by Students for Kids: "From Mechanics to Elementary Particle Physics"

ERIC Educational Resources Information Center

Dreiner, Herbi K.

2008-01-01

Physics students spend the early part of their training attending physics and mathematics lectures, solving problem sets, and experimenting in laboratory courses. The program is typically intensive and fairly rigid. They have little opportunity to follow their own curiosity or apply their knowledge. There have been many attempts to address this…

Computational Modeling and Mathematics Applied to the Physical Sciences.

ERIC Educational Resources Information Center

National Academy of Sciences - National Research Council, Washington, DC.

One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…

Brookhaven highlights, October 1979-September 1980

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1980-01-01

Highlights are given for the research areas of the Brookhaven National Laboratory. These areas include high energy physics, physics and chemistry, life sciences, applied energy science (energy and environment, and nuclear energy), and support activities (including mathematics, instrumentation, reactors, and safety). (GHT)

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

NASA Technical Reports Server (NTRS)

Tsao, D. Teh-Wei; Okos, M. R.; Sager, J. C.; Dreschel, T. W.

1992-01-01

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

Research in applied mathematics, numerical analysis, and computer science

NASA Technical Reports Server (NTRS)

1984-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

Matrix Treatment of Ray Optics.

ERIC Educational Resources Information Center

Quon, W. Steve

1996-01-01

Describes a method to combine two learning experiences--optical physics and matrix mathematics--in a straightforward laboratory experiment that allows engineering/physics students to integrate a variety of learning insights and technical skills, including using lasers, studying refraction through thin lenses, applying concepts of matrix…

Computing the Ediz eccentric connectivity index of discrete dynamic structures

NASA Astrophysics Data System (ADS)

Wu, Hualong; Kamran Siddiqui, Muhammad; Zhao, Bo; Gan, Jianhou; Gao, Wei

2017-06-01

From the earlier studies in physical and chemical sciences, it is found that the physico-chemical characteristics of chemical compounds are internally connected with their molecular structures. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. In our article, we study the physico-chemical properties of certain molecular structures via computing the Ediz eccentric connectivity index from mathematical standpoint. The results we yielded mainly apply to the techniques of distance and degree computation of mathematical derivation, and the conclusions have guiding significance in physical engineering.

A Non-Intuitionist's Approach To The Interpretation Problem Of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

2005-02-01

A philosophy of physics called "linguistic empiricism" is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language-dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.

Modulation theory, dispersive shock waves and Gerald Beresford Whitham

NASA Astrophysics Data System (ADS)

Minzoni, A. A.; Smyth, Noel F.

2016-10-01

Gerald Beresford (GB) Whitham, FRS, (13th December, 1927-26th January, 2014) was one of the leading applied mathematicians of the twentieth century whose work over forty years had a profound, formative impact on research on wave motion across a broad range of areas. Many of the ideas and techniques he developed have now become the standard tools used to analyse and understand wave motion, as the papers of this special issue of Physica D testify. Many of the techniques pioneered by GB Whitham have spread beyond wave propagation into other applied mathematics areas, such as reaction-diffusion, and even into theoretical physics and pure mathematics, in which Whitham modulation theory is an active area of research. GB Whitham's classic textbook Linear and Nonlinear Waves, published in 1974, is still the standard reference for the applied mathematics of wave motion. In honour of his scientific achievements, GB Whitham was elected a Fellow of the American Academy of Arts and Sciences in 1959 and a Fellow of the Royal Society in 1965. He was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.

34 CFR 609.4 - What definitions apply?

Code of Federal Regulations, 2011 CFR

2011-07-01

... a graduate or professional program that— (i) Provides a program of instruction in the physical or natural sciences, engineering, mathematics, or other scientific disciplines in which African Americans are...

34 CFR 609.4 - What definitions apply?

Code of Federal Regulations, 2012 CFR

2012-07-01

... a graduate or professional program that— (i) Provides a program of instruction in the physical or natural sciences, engineering, mathematics, or other scientific disciplines in which African Americans are...

34 CFR 609.4 - What definitions apply?

Code of Federal Regulations, 2013 CFR

2013-07-01

... a graduate or professional program that— (i) Provides a program of instruction in the physical or natural sciences, engineering, mathematics, or other scientific disciplines in which African Americans are...

34 CFR 609.4 - What definitions apply?

Code of Federal Regulations, 2014 CFR

2014-07-01

... a graduate or professional program that— (i) Provides a program of instruction in the physical or natural sciences, engineering, mathematics, or other scientific disciplines in which African Americans are...

LECTURES ON DECISION THEORY,

DTIC Science & Technology

These lecture notes deal with the mathematical theory of decision - making , i.e., wihematical models of situations in which there is a set of...individual and group decision - making as a quantitative science, in contrast with a field such as physics, suggests that mathematical theorizing on...phenomena of decision - making is very much an exploratory enterprise and that ex isting models have limited generality and appli cability. The purpose is to

The phenomenon of information- approaches and nature

NASA Astrophysics Data System (ADS)

Borsevici, V.; Cushnir, G.

1997-12-01

The authors discuss the phenomenon of information from a philosophical, general sistemic, cybernetic and physical-mathematical standpoints. The phenomenon of information consists in a transmission, refection, interaction and development of forms of organized matter and energy, has been shown. Questions related to contradictions and antinomies, arising when various treatments of the phenomenon apply, in communication, cybernetic, mathematical, social-economic and biologic systems has been discussed.

Associations of Physical Activity, Sports Participation and Active Commuting on Mathematic Performance and Inhibitory Control in Adolescents.

PubMed

Domazet, Sidsel L; Tarp, Jakob; Huang, Tao; Gejl, Anne Kær; Andersen, Lars Bo; Froberg, Karsten; Bugge, Anna

2016-01-01

To examine objectively measured physical activity level, organized sports participation and active commuting to school in relation to mathematic performance and inhibitory control in adolescents. The design was cross-sectional. A convenient sample of 869 sixth and seventh grade students (12-14 years) was invited to participate in the study. A total of 568 students fulfilled the inclusion criteria and comprised the final sample for this study. Mathematic performance was assessed by a customized test and inhibitory control was assessed by a modified Eriksen flanker task. Physical activity was assessed with GT3X and GT3X+ accelerometers presented in sex-specific quartiles of mean counts per minute and mean minutes per day in moderate-to-vigorous physical activity. Active commuting and sports participation was self-reported. Mixed model regression was applied. Total physical activity level was stratified by bicycling status in order to bypass measurement error subject to the accelerometer. Non-cyclists in the 2nd quartile of counts per minute displayed a higher mathematic score, so did cyclists in the 2nd and 3rd quartile of moderate-to-vigorous physical activity relative to the least active quartile. Non-cyclists in the 3rd quartile of counts per minute had an improved reaction time and cyclists in the 2nd quartile of counts per minute and moderate-to-vigorous physical activity displayed an improved accuracy, whereas non-cyclists in the 2nd quartile of counts per minute showed an inferior accuracy relative to the least active quartile. Bicycling to school and organized sports participation were positively associated with mathematic performance. Sports participation and bicycling were positively associated with mathematic performance. Results regarding objectively measured physical activity were mixed. Although, no linear nor dose-response relationship was observed there was no indication of a higher activity level impairing the scholastic or cognitive performance.

Associations of Physical Activity, Sports Participation and Active Commuting on Mathematic Performance and Inhibitory Control in Adolescents

PubMed Central

Huang, Tao; Gejl, Anne Kær; Froberg, Karsten

2016-01-01

Objectives To examine objectively measured physical activity level, organized sports participation and active commuting to school in relation to mathematic performance and inhibitory control in adolescents. Methods The design was cross-sectional. A convenient sample of 869 sixth and seventh grade students (12–14 years) was invited to participate in the study. A total of 568 students fulfilled the inclusion criteria and comprised the final sample for this study. Mathematic performance was assessed by a customized test and inhibitory control was assessed by a modified Eriksen flanker task. Physical activity was assessed with GT3X and GT3X+ accelerometers presented in sex-specific quartiles of mean counts per minute and mean minutes per day in moderate-to-vigorous physical activity. Active commuting and sports participation was self-reported. Mixed model regression was applied. Total physical activity level was stratified by bicycling status in order to bypass measurement error subject to the accelerometer. Results Non-cyclists in the 2nd quartile of counts per minute displayed a higher mathematic score, so did cyclists in the 2nd and 3rd quartile of moderate-to-vigorous physical activity relative to the least active quartile. Non-cyclists in the 3rd quartile of counts per minute had an improved reaction time and cyclists in the 2nd quartile of counts per minute and moderate-to-vigorous physical activity displayed an improved accuracy, whereas non-cyclists in the 2nd quartile of counts per minute showed an inferior accuracy relative to the least active quartile. Bicycling to school and organized sports participation were positively associated with mathematic performance. Conclusions Sports participation and bicycling were positively associated with mathematic performance. Results regarding objectively measured physical activity were mixed. Although, no linear nor dose-response relationship was observed there was no indication of a higher activity level impairing the scholastic or cognitive performance. PMID:26727211

Statistics of Radial Ship Extent as Seen by a Seeker

DTIC Science & Technology

2014-06-01

Auckland in pure and applied mathematics and physics, and a Master of Science in physics from the same university with a thesis in applied accelerator...does not demand contributions from two angle bins to one extent bin, unlike the rectangle; this is a very big advantage of the ellipse model. However...waveform that mimics the full length of a ship. This allows more economical use to be made of available false-target generation resources. I wish to

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

Light-Emitting Diodes: Learning New Physics

ERIC Educational Resources Information Center

Planinšic, Gorazd; Etkina, Eugenia

2015-01-01

This is the third paper in our Light-Emitting Diodes series. The series aims to create a systematic library of LED-based materials and to provide the readers with the description of experiments and pedagogical treatment that would help their students construct, test, and apply physics concepts and mathematical relations. The first paper, published…

Diverse opportunities in defence

NASA Astrophysics Data System (ADS)

Brown, Gareth

2016-08-01

Working at the UK's defence laboratory gives Gareth Brown the ability to apply his physics and mathematics knowledge to real-world applications - and not necessarily in the ways you might expect. This article is Crown copyright

Identification of multiple intelligences for high school students in theoretical and applied science courses

NASA Astrophysics Data System (ADS)

Wiseman, D. Kim

Historically educators in the United States have used the Stanford-Binet intelligence test to measure a students' ability in logical/mathematical and linguistic domains. This measurement is being used by a society that has evolved from agrarian and industrial-based economies to what is presently labeled a technological society. As society has changed so have the educational needs of the students who will live in this technological society. This study assessed the multiple intelligences of high school students enrolled in theoretical and applied science (physics and applied physics) courses. Studies have verified that performance and outcomes of students enrolled in these courses are similar in standardized testing but instructional methodology and processes are dissimilar. Analysis of multiple intelligence profiles collected from this study found significant differences in logical/mathematical, bodily/kinesthetic and intrapersonal multiple intelligences of students in theoretical science courses compared to students in applied science courses. Those differences clearly illustrate why it is imperative for educators to expand the definition of intelligence for students entering the new millennium.

An Introduction to Groups. Abstract Algebra. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 461.

ERIC Educational Resources Information Center

Rosenberg, Nancy S.

A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…

Hanford Laboratories monthly activities report, March 1964

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1964-04-15

The monthly report for the Hanford Laboratories Operation, March 1964. Reactor fuels, chemistry, dosimetry, separation processes, reactor technology, financial activities, biology operation, and physics and instrumentation research, and applied mathematics operation, and programming operations are discussed.

SIAM conference on applications of dynamical systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-01-01

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

SIAM conference on applications of dynamical systems. Abstracts and author index

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-12-31

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

PREFACE: International Conference on Advancement in Science and Technology 2012 (iCAST): Contemporary Mathematics, Mathematical Physics and their Applications

NASA Astrophysics Data System (ADS)

Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin

2013-04-01

The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.

Conception and development of the Second Life® Embryo Physics Course.

PubMed

Gordon, Richard

2013-06-01

The study of embryos with the tools and mindset of physics, started by Wilhelm His in the 1880s, has resumed after a hiatus of a century. The Embryo Physics Course convenes online allowing interested researchers and students, who are scattered around the world, to gather weekly in one place, the virtual world of Second Life®. It attracts people from a wide variety of disciplines and walks of life: applied mathematics, artificial life, bioengineering, biophysics, cancer biology, cellular automata, civil engineering, computer science, embryology, electrical engineering, evolution, finite element methods, history of biology, human genetics, mathematics, molecular developmental biology, molecular biology, nanotechnology, philosophy of biology, phycology, physics, self-reproducing systems, stem cells, tensegrity structures, theoretical biology, and tissue engineering. Now in its fifth year, the Embryo Physics Course provides a focus for research on the central question of how an embryo builds itself.

Design of multiple representations e-learning resources based on a contextual approach for the basic physics course

NASA Astrophysics Data System (ADS)

Bakri, F.; Muliyati, D.

2018-05-01

This research aims to design e-learning resources with multiple representations based on a contextual approach for the Basic Physics Course. The research uses the research and development methods accordance Dick & Carey strategy. The development carried out in the digital laboratory of Physics Education Department, Mathematics and Science Faculty, Universitas Negeri Jakarta. The result of the process of product development with Dick & Carey strategy, have produced e-learning design of the Basic Physics Course is presented in multiple representations in contextual learning syntax. The appropriate of representation used in the design of learning basic physics include: concept map, video, figures, data tables of experiment results, charts of data tables, the verbal explanations, mathematical equations, problem and solutions example, and exercise. Multiple representations are presented in the form of contextual learning by stages: relating, experiencing, applying, transferring, and cooperating.

A Qualitative Study Comparing the Instruction on Vectors between a Physics Course and a Trigonometry Course

ERIC Educational Resources Information Center

James, Wendy Michelle

2013-01-01

Science and engineering instructors often observe that students have difficulty using or applying prerequisite mathematics knowledge in their courses. This qualitative project uses a case-study method to investigate the instruction in a trigonometry course and a physics course based on a different methodology and set of assumptions about student…

Physics of Non-Newtonian Fluids and Interdisciplinary Relations (Biology and Criminology)

ERIC Educational Resources Information Center

Holubova, R.

2018-01-01

The aim of the paper is the presentation of an interdisciplinary topic that allows applying content knowledge in physics, mathematics and biology in real life environment. Students use to play games and view crime scenes but in common they have little knowledge about the science used during crime scene investigation. In this paper the science…

Workshop on Harmonic Oscillators

NASA Technical Reports Server (NTRS)

Han, D. (Editor); Kim, Y. S. (Editor); Zachary, W. W. (Editor)

1993-01-01

Proceedings of a workshop on Harmonic Oscillators held at the College Park Campus of the University of Maryland on March 25 - 28, 1992 are presented. The harmonic oscillator formalism is playing an important role in many branches of physics. This is the simplest mathematical device which can connect the basic principle of physics with what is observed in the real world. The harmonic oscillator is the bridge between pure and applied physics.

Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations

PubMed Central

Liao, David; Tlsty, Thea D.

2014-01-01

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

Hanford Laboratories monthly activities report, February 1964

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1964-03-16

This is the monthly report for the Hanford Laboratories Operation, February, 1964. Reactor fuels, chemistry, dosimetry, separation process, reactor technology financial activities, biology operation, physics and instrumentation research, employee relations, applied mathematics, programming, and radiation protection are discussed.

The Goddard Profiling Algorithm (GPROF): Description and Current Applications

NASA Technical Reports Server (NTRS)

Olson, William S.; Yang, Song; Stout, John E.; Grecu, Mircea

2004-01-01

Atmospheric scientists use different methods for interpreting satellite data. In the early days of satellite meteorology, the analysis of cloud pictures from satellites was primarily subjective. As computer technology improved, satellite pictures could be processed digitally, and mathematical algorithms were developed and applied to the digital images in different wavelength bands to extract information about the atmosphere in an objective way. The kind of mathematical algorithm one applies to satellite data may depend on the complexity of the physical processes that lead to the observed image, and how much information is contained in the satellite images both spatially and at different wavelengths. Imagery from satellite-borne passive microwave radiometers has limited horizontal resolution, and the observed microwave radiances are the result of complex physical processes that are not easily modeled. For this reason, a type of algorithm called a Bayesian estimation method is utilized to interpret passive microwave imagery in an objective, yet computationally efficient manner.

Applying physical science techniques and CERN technology to an unsolved problem in radiation treatment for cancer: the multidisciplinary ‘VoxTox’ research programme

PubMed Central

Burnet, Neil G; Scaife, Jessica E; Romanchikova, Marina; Thomas, Simon J; Bates, Amy M; Wong, Emma; Noble, David J; Shelley, Leila EA; Bond, Simon J; Forman, Julia R; Hoole, Andrew CF; Barnett, Gillian C; Brochu, Frederic M; Simmons, Michael PD; Jena, Raj; Harrison, Karl; Yeap, Ping Lin; Drew, Amelia; Silvester, Emma; Elwood, Patrick; Pullen, Hannah; Sultana, Andrew; Seah, Shannon YK; Wilson, Megan Z; Russell, Simon G; Benson, Richard J; Rimmer, Yvonne L; Jefferies, Sarah J; Taku, Nicolette; Gurnell, Mark; Powlson, Andrew S; Schönlieb, Carola-Bibiane; Cai, Xiaohao; Sutcliffe, Michael PF; Parker, Michael A

2017-01-01

The VoxTox research programme has applied expertise from the physical sciences to the problem of radiotherapy toxicity, bringing together expertise from engineering, mathematics, high energy physics (including the Large Hadron Collider), medical physics and radiation oncology. In our initial cohort of 109 men treated with curative radiotherapy for prostate cancer, daily image guidance computed tomography (CT) scans have been used to calculate delivered dose to the rectum, as distinct from planned dose, using an automated approach. Clinical toxicity data have been collected, allowing us to address the hypothesis that delivered dose provides a better predictor of toxicity than planned dose. PMID:29177202

Applying physical science techniques and CERN technology to an unsolved problem in radiation treatment for cancer: the multidisciplinary 'VoxTox' research programme.

PubMed

Burnet, Neil G; Scaife, Jessica E; Romanchikova, Marina; Thomas, Simon J; Bates, Amy M; Wong, Emma; Noble, David J; Shelley, Leila Ea; Bond, Simon J; Forman, Julia R; Hoole, Andrew Cf; Barnett, Gillian C; Brochu, Frederic M; Simmons, Michael Pd; Jena, Raj; Harrison, Karl; Yeap, Ping Lin; Drew, Amelia; Silvester, Emma; Elwood, Patrick; Pullen, Hannah; Sultana, Andrew; Seah, Shannon Yk; Wilson, Megan Z; Russell, Simon G; Benson, Richard J; Rimmer, Yvonne L; Jefferies, Sarah J; Taku, Nicolette; Gurnell, Mark; Powlson, Andrew S; Schönlieb, Carola-Bibiane; Cai, Xiaohao; Sutcliffe, Michael Pf; Parker, Michael A

2017-06-01

The VoxTox research programme has applied expertise from the physical sciences to the problem of radiotherapy toxicity, bringing together expertise from engineering, mathematics, high energy physics (including the Large Hadron Collider), medical physics and radiation oncology. In our initial cohort of 109 men treated with curative radiotherapy for prostate cancer, daily image guidance computed tomography (CT) scans have been used to calculate delivered dose to the rectum, as distinct from planned dose, using an automated approach. Clinical toxicity data have been collected, allowing us to address the hypothesis that delivered dose provides a better predictor of toxicity than planned dose.

Dispersive shock waves and modulation theory

NASA Astrophysics Data System (ADS)

El, G. A.; Hoefer, M. A.

2016-10-01

There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent experimental, theoretical, and numerical investigations of problems in applied mechanics are discussed in reviews and reports. The fields covered include vibration and stability; the mechanics of elastic and plastic materials; fluid mechanics; the numerical treatment of differential equations; finite and boundary elements; optimization, decision theory, stochastics, and actuarial analysis; applied analysis and mathematical physics; and numerical analysis. Reviews are presented on mathematical applications of geometric-optics methods, biomechanics and implant technology, vibration theory in engineering, the stiffness and strength of damaged materials, and the existence of slow steady flows of viscoelastic fluids of integral type.

Science modelling in pre-calculus: how to make mathematics problems contextually meaningful

NASA Astrophysics Data System (ADS)

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-04-01

'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization of computer-based science simulations. Although there are several exceptional computer-based science simulations designed for mathematics classes (see, e.g. Kinetic Book (http://www.kineticbooks.com/) or Gizmos (http://www.explorelearning.com/)), we concentrate mainly on the PhET Interactive Simulations developed at the University of Colorado at Boulder (http://phet.colorado.edu/) in generating our argument that computer simulations more accurately represent the contextual characteristics of scientific phenomena than their textual descriptions.

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Physics and Mathematics as Interwoven Disciplines in Science Education

NASA Astrophysics Data System (ADS)

Galili, Igal

2018-03-01

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

Session Overview

NASA Astrophysics Data System (ADS)

Spencer, Cherrill

2010-02-01

High-school teachers are amongst the most important contributors to the development of the science and technology workforce of the future. Many of the more than 23,000 US high-school physics teachers are not adequately prepared to teach the subject. Only one-third of them, for example, majored in physics or physics education. Can inadequate teacher preparation be a factor in the poor performance of US students on international assessments of their achievements in science and physics? Since 1995 the Trends in International Mathematics and Science Study (TIMSS) has been administered four times to many hundreds of thousands of students in over 60 countries. TIMSS is used to measure trends in the mathematics and science knowledge and skills of fourth- and eighth-graders. The Program for International Student Assessment (PISA) has been administered three times since 2000, it focuses on 15-year-olds' capabilities in reading literacy, mathematics literacy, and science literacy. TIMSS Advanced (1995) assessed school-leaving students who have had special preparation in advanced mathematics and physics. In all these studies the US students, including the Advanced Placement physics students, scored below the international average, sometimes in the bottom third of countries! Three speakers have been invited to talk about the physics K-12 education systems in other countries, one that consistently scores at the top of the PISA (Finland) or score much higher than the USA on TIMSS ( various Northern European countries) and significantly better on recent bi-lateral comparisons (China). What can we learn from the physics teaching systems in these high-scoring countries that might be applied in the USA? There will be a panel discussion following the 3 invited talks, audience participation will be encouraged. )

Some remarks on quantum physics, stochastic processes, and nonlinear filtering theory

NASA Astrophysics Data System (ADS)

Balaji, Bhashyam

2016-05-01

The mathematical similarities between quantum mechanics and stochastic processes has been studied in the literature. Some of the major results are reviewed, such as the relationship between the Fokker-Planck equation and the Schrödinger equation. Also reviewed are more recent results that show the mathematical similarities between quantum many particle systems and concepts in other areas of applied science, such as stochastic Petri nets. Some connections to filtering theory are discussed.

ANNUAL REPORT, JULY 1, 1960

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

1961-10-31

Research facilities, general construction progress, research activities, and administration are discussed and a financial statement is given. Fairly detailed accounts are given of research programs in the fields of physics, accelerator development, instrumentation, applied mathematics, chemistry, nuclear engineering, biology, and medicine. (M.C.G.)

Publisher's Announcement

NASA Astrophysics Data System (ADS)

Scriven, Neil

2003-12-01

We are delighted to announce that the new Editor-in-Chief of Journal of Physics A: Mathematical and General for 2004 will be Professor Carl M Bender of Washington University, St. Louis. Carl will, with the help of his world class editorial board, maintain standards of scientific rigour whilst ensuring that research published is of the highest importance. Carl attained his first degree in physics at Cornell University before studying for his PhD at Harvard. He later worked at The Institute for Advanced Study in Princeton and at MIT before assuming his current position at Washington University, St Louis. He has been a visiting professor at Technion, Haifa, and Imperial College, London and a scientific consultant for Los Alamos National Laboratory. His main expertise is in using classical applied mathematics to solve a broad range of problems in high-energy theoretical physics and mathematical physics. Since the publication of his book Advanced Mathematical Methods for Scientists and Engineers, written with Steven Orszag, he has been regarded as an expert on the subject of asymptotic analysis and perturbative methods. `Carl publishes his own internationally-important research in the journal and has been an invaluable, energetic member of the Editorial Board for some time' said Professor Ed Corrigan, Carl's predecessor as Editor, `he will be an excellent Editor-in-Chief'. Our grateful thanks and best wishes go to Professor Corrigan who has done a magnificent job for the journal during his five-year tenure.

Joint the Center for Applied Scientific Computing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamblin, Todd; Bremer, Timo; Van Essen, Brian

The Center for Applied Scientific Computing serves as Livermore Lab’s window to the broader computer science, computational physics, applied mathematics, and data science research communities. In collaboration with academic, industrial, and other government laboratory partners, we conduct world-class scientific research and development on problems critical to national security. CASC applies the power of high-performance computing and the efficiency of modern computational methods to the realms of stockpile stewardship, cyber and energy security, and knowledge discovery for intelligence applications.

Pre-Service Physics Teachers’ Problem-solving Skills in Projectile Motion Concept

NASA Astrophysics Data System (ADS)

Sutarno, S.; Setiawan, A.; Kaniawati, I.; Suhandi, A.

2017-09-01

This study is a preliminary research aiming at exploring pre-service physics teachers’ skills in applying the stage of problem-solving strategies. A total of 76 students of physics education study program at a college in Bengkulu Indonesia participated in the study. The skills on solving physics problems are being explored through exercises that demand the use of problem-solving strategies with several stages such as useful description, physics approach, specific application of physics, physics equation, mathematical procedures, and logical progression. Based on the results of data analysis, it is found that the pre-service physics teachers’ skills are in the moderate category for physics approach and mathematical procedural, and low category for the others. It was concluded that the pre-service physics teachers’ problem-solving skills are categorized low. It is caused by the learning of physics that has done less to practice problem-solving skills. The problems provided are only routine and poorly trained in the implementation of problem-solving strategies.The results of the research can be used as a reference for the importance of the development of physics learning based on higher order thinking skills.

Modelling Mathematical Reasoning in Physics Education

NASA Astrophysics Data System (ADS)

Uhden, Olaf; Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche

2012-04-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a tool for calculation which hinders a conceptual understanding of physical principles. However, the role of mathematics cannot be reduced to this technical aspect. Hence, instead of putting mathematics away we delve into the nature of physical science to reveal the strong conceptual relationship between mathematics and physics. Moreover, we suggest that, for both prospective teaching and further research, a focus on deeply exploring such interdependency can significantly improve the understanding of physics. To provide a suitable basis, we develop a new model which can be used for analysing different levels of mathematical reasoning within physics. It is also a guideline for shifting the attention from technical to structural mathematical skills while teaching physics. We demonstrate its applicability for analysing physical-mathematical reasoning processes with an example.

Dimensional analysis, similarity, analogy, and the simulation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Davis, A.A.

1978-01-01

Dimensional analysis, similarity, analogy, and cybernetics are shown to be four consecutive steps in application of the simulation theory. This paper introduces the classes of phenomena which follow the same formal mathematical equations as models of the natural laws and the interior sphere of restraints groups of phenomena in which one can introduce simplfied nondimensional mathematical equations. The simulation by similarity in a specific field of physics, by analogy in two or more different fields of physics, and by cybernetics in nature in two or more fields of mathematics, physics, biology, economics, politics, sociology, etc., appears as a unique theorymore » which permits one to transport the results of experiments from the models, convenably selected to meet the conditions of researches, constructions, and measurements in the laboratories to the originals which are the primary objectives of the researches. Some interesting conclusions which cannot be avoided in the use of simplified nondimensional mathematical equations as models of natural laws are presented. Interesting limitations on the use of simulation theory based on assumed simplifications are recognized. This paper shows as necessary, in scientific research, that one write mathematical models of general laws which will be applied to nature in its entirety. The paper proposes the extent of the second law of thermodynamics as the generalized law of entropy to model life and its activities. This paper shows that the physical studies and philosophical interpretations of phenomena and natural laws cannot be separated in scientific work; they are interconnected and one cannot be put above the others.« less

New extended (G'/G)-expansion method to solve nonlinear evolution equation: the (3 + 1)-dimensional potential-YTSF equation.

PubMed

Roshid, Harun-Or-; Akbar, M Ali; Alam, Md Nur; Hoque, Md Fazlul; Rahman, Nizhum

2014-01-01

In this article, a new extended (G'/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution equations with the aid of symbolic computation. In order to illustrate the validity and effectiveness of the method, we pick the (3 + 1)-dimensional potential-YTSF equation. As a result, abundant new and more general exact solutions have been achieved of this equation. It has been shown that the proposed method provides a powerful mathematical tool for solving nonlinear wave equations in applied mathematics, engineering and mathematical physics.

Knot theory in modern chemistry.

PubMed

Horner, Kate E; Miller, Mark A; Steed, Jonathan W; Sutcliffe, Paul M

2016-11-21

Knot theory is a branch of pure mathematics, but it is increasingly being applied in a variety of sciences. Knots appear in chemistry, not only in synthetic molecular design, but also in an array of materials and media, including some not traditionally associated with knots. Mathematics and chemistry can now be used synergistically to identify, characterise and create knots, as well as to understand and predict their physical properties. This tutorial review provides a brief introduction to the mathematics of knots and related topological concepts in the context of the chemical sciences. We then survey the broad range of applications of the theory to contemporary research in the field.

Engineering Problem-Solving Knowledge: The Impact of Context

ERIC Educational Resources Information Center

Wolff, Karin

2017-01-01

Employer complaints of engineering graduate inability to "apply knowledge" suggests a need to interrogate the complex theory-practice relationship in twenty-first century real world contexts. Focussing specifically on the application of mathematics, physics and logic-based disciplinary knowledge, the research examines engineering…

New tools for investigating student learning in upper-division electrostatics

NASA Astrophysics Data System (ADS)

Wilcox, Bethany R.

Student learning in upper-division physics courses is a growing area of research in the field of Physics Education. Developing effective new curricular materials and pedagogical techniques to improve student learning in upper-division courses requires knowledge of both what material students struggle with and what curricular approaches help to overcome these struggles. To facilitate the course transformation process for one specific content area --- upper-division electrostatics --- this thesis presents two new methodological tools: (1) an analytical framework designed to investigate students' struggles with the advanced physics content and mathematically sophisticated tools/techniques required at the junior and senior level, and (2) a new multiple-response conceptual assessment designed to measure student learning and assess the effectiveness of different curricular approaches. We first describe the development and theoretical grounding of a new analytical framework designed to characterize how students use mathematical tools and techniques during physics problem solving. We apply this framework to investigate student difficulties with three specific mathematical tools used in upper-division electrostatics: multivariable integration in the context of Coulomb's law, the Dirac delta function in the context of expressing volume charge densities, and separation of variables as a technique to solve Laplace's equation. We find a number of common themes in students' difficulties around these mathematical tools including: recognizing when a particular mathematical tool is appropriate for a given physics problem, mapping between the specific physical context and the formal mathematical structures, and reflecting spontaneously on the solution to a physics problem to gain physical insight or ensure consistency with expected results. We then describe the development of a novel, multiple-response version of an existing conceptual assessment in upper-division electrostatics courses. The goal of this new version is to provide an easily-graded electrostatics assessment that can potentially be implemented to investigate student learning on a large scale. We show that student performance on the new multiple-response version exhibits a significant degree of consistency with performance on the free-response version, and that it continues to provide significant insight into student reasoning and student difficulties. Moreover, we demonstrate that the new assessment is both valid and reliable using data from upper-division physics students at multiple institutions. Overall, the work described in this thesis represents a significant contribution to the methodological tools available to researchers and instructors interested in improving student learning at the upper-division level.

Dispersive hydrodynamics: Preface

NASA Astrophysics Data System (ADS)

Biondini, G.; El, G. A.; Hoefer, M. A.; Miller, P. D.

2016-10-01

This Special Issue on Dispersive Hydrodynamics is dedicated to the memory and work of G.B. Whitham who was one of the pioneers in this field of physical applied mathematics. Some of the papers appearing here are related to work reported on at the workshop "Dispersive Hydrodynamics: The Mathematics of Dispersive Shock Waves and Applications" held in May 2015 at the Banff International Research Station. This Preface provides a broad overview of the field and summaries of the various contributions to the Special Issue, placing them in a unified context.

Elementary metallography

NASA Technical Reports Server (NTRS)

Kazem, Sayyed M.

1992-01-01

Materials and Processes 1 (MET 141) is offered to freshmen by the Mechanical Engineering Department at Purdue University. The goal of MET 141 is to broaden the technical background of students who have not had any college science courses. Hence, applied physics, chemistry, and mathematics are included and quantitative problem solving is involved. In the elementary metallography experiment of this course, the objectives are: (1) introduce the vocabulary and establish outlook; (2) make qualitative observations and quantitative measurements; (3) demonstrate the proper use of equipment; and (4) review basic mathematics and science.

The role of gender on academic performance in STEM-related disciplines: Data from a tertiary institution.

PubMed

John, Temitope M; Badejo, Joke A; Popoola, Segun I; Omole, David O; Odukoya, Jonathan A; Ajayi, Priscilla O; Aboyade, Mary; Atayero, Aderemi A

2018-06-01

This data article presents data of academic performances of undergraduate students in Science, Technology, Engineering and Mathematics (STEM) disciplines in Covenant University, Nigeria. The data shows academic performances of Male and Female students who graduated from 2010 to 2014. The total population of samples in the observation is 3046 undergraduates mined from Biochemistry (BCH), Building technology (BLD), Computer Engineering (CEN), Chemical Engineering (CHE), Industrial Chemistry (CHM), Computer Science (CIS), Civil Engineering (CVE), Electrical and Electronics Engineering (EEE), Information and Communication Engineering (ICE), Mathematics (MAT), Microbiology (MCB), Mechanical Engineering (MCE), Management and Information System (MIS), Petroleum Engineering (PET), Industrial Physics-Electronics and IT Applications (PHYE), Industrial Physics-Applied Geophysics (PHYG) and Industrial Physics-Renewable Energy (PHYR). The detailed dataset is made available in form of a Microsoft Excel spreadsheet in the supplementary material of this article.

Theoretical Explanations in Mathematical Physics

NASA Astrophysics Data System (ADS)

Rivadulla, Andrés

Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

Can Youthful Students be Encouraged to Self-repair Damaged Vision Using Elementary Mathematics and Physics Principles?

NASA Astrophysics Data System (ADS)

Ferreira, Nadja; McLeod, Roger

2006-03-01

Safe and easy self-repair of damaged vision in youth, detected from squinted eyes, motivated by simple applied math and physics, and over-stretched elastics. Parental permission and participation, with math skills of numerical cancellation, bring physics understanding to students. They recognize pupil diameter changes with light intensity. Ideas of focal surfaces and wavelength dependence can be achieved by burning paper with a magnifying glass, and dispersing light with a prism. Safeness of eye and head movements required are like those of the mother in applying makeup, or of a father in shaving. Easily defined, performed and monitored visual tasks can complete the repair(s).

Resolving phase ambiguities in the calibration of redundant interferometric arrays: implications for array design

DTIC Science & Technology

2016-05-18

course of this paper, we will first iden- tify this ambiguity from a mathematical perspective, relate it to a particular physical structure (i.e. the...invariance to a physical condition on aperture place- ment is more intuitive when considering the raw phase mea- surements as opposed to their closures. For...to wrapping of the phase measure- ments. We have hence arrived at a a physical definition of a wrap-invariant pattern. We now apply Algorithm 1 to the

Science on Wheels

ERIC Educational Resources Information Center

Savitz, Maxine L.

1973-01-01

A science program was developed which is based on a mobile laboratory containing scientific experiments in biology, chemistry, physics, applied science, and mathematics. Discussion and experiments differ from the normal classroom setting as they utilize small groups and center around the relationship of modern science and technology of the urban…

77 FR 17102 - Advisory Committee for Mathematical and Physical Sciences

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-23

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences Correction... meeting information is as follows: Name: Directorate for Mathematical and Physical Sciences Advisory... Person: Dr. Morris L. Aizenman, Senior Science Associate, Directorate for Mathematical and Physical...

Introduction to the focus issue: fifty years of chaos: applied and theoretical.

PubMed

Hikihara, Takashi; Holmes, Philip; Kambe, Tsutomu; Rega, Giuseppe

2012-12-01

The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011. The symposium, sponsored by the International Union of Theoretical and Applied Mechanics, was called 50 Years of Chaos: Applied and Theoretical. Following some historical remarks to provide a background for the last 50 years, and for chaos, this Introduction surveys the papers and identifies some common themes that appear in them and in the theory of dynamical systems.

A Verification-Driven Approach to Traceability and Documentation for Auto-Generated Mathematical Software

NASA Technical Reports Server (NTRS)

Denney, Ewen W.; Fischer, Bernd

2009-01-01

Model-based development and automated code generation are increasingly used for production code in safety-critical applications, but since code generators are typically not qualified, the generated code must still be fully tested, reviewed, and certified. This is particularly arduous for mathematical and control engineering software which requires reviewers to trace subtle details of textbook formulas and algorithms to the code, and to match requirements (e.g., physical units or coordinate frames) not represented explicitly in models or code. Both tasks are complicated by the often opaque nature of auto-generated code. We address these problems by developing a verification-driven approach to traceability and documentation. We apply the AUTOCERT verification system to identify and then verify mathematical concepts in the code, based on a mathematical domain theory, and then use these verified traceability links between concepts, code, and verification conditions to construct a natural language report that provides a high-level structured argument explaining why and how the code uses the assumptions and complies with the requirements. We have applied our approach to generate review documents for several sub-systems of NASA s Project Constellation.

Higher-order automatic differentiation of mathematical functions

NASA Astrophysics Data System (ADS)

Charpentier, Isabelle; Dal Cappello, Claude

2015-04-01

Functions of mathematical physics such as the Bessel functions, the Chebyshev polynomials, the Gauss hypergeometric function and so forth, have practical applications in many scientific domains. On the one hand, differentiation formulas provided in reference books apply to real or complex variables. These do not account for the chain rule. On the other hand, based on the chain rule, the automatic differentiation has become a natural tool in numerical modeling. Nevertheless automatic differentiation tools do not deal with the numerous mathematical functions. This paper describes formulas and provides codes for the higher-order automatic differentiation of mathematical functions. The first method is based on Faà di Bruno's formula that generalizes the chain rule. The second one makes use of the second order differential equation they satisfy. Both methods are exemplified with the aforementioned functions.

Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

ERIC Educational Resources Information Center

Michelsen, Claus

2015-01-01

Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

Brookhaven highlights, October 1978-September 1979. [October 1978 to September 1979

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1979-01-01

These highlights present an overview of the major research and development achievements at Brookhaven National Laboratory from October 1978 to September 1979. Specific areas covered include: accelerator and high energy physics programs; high energy physics research; the AGS and improvements to the AGS; neutral beam development; heavy ion fusion; superconducting power cables; ISABELLE storage rings; the BNL Tandem accelerator; heavy ion experiments at the Tandem; the High Flux Beam Reactor; medium energy physics; nuclear theory; atomic and applied physics; solid state physics; neutron scattering studies; x-ray scattering studies; solid state theory; defects and disorder in solids; surface physics; the Nationalmore » Synchrotron Light Source ; Chemistry Department; Biology Department; Medical Department; energy sciences; environmental sciences; energy technology programs; National Center for Analysis of Energy Systems; advanced reactor systems; nuclear safety; National Nuclear Data Center; nuclear materials safeguards; Applied Mathematics Department; and support activities. (GHT)« less

77 FR 42768 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2012-07-20

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences; Notice of... Science Foundation announces the following meeting: Name: Directorate for Mathematical and Physical... Person: Dr. Morris L. Aizenman, Senior Science Associate, Directorate for Mathematical and Physical...

75 FR 62891 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2010-10-13

... science and education activities within the Directorate for Mathematical and Physical Sciences. Agenda... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences; Notice of... Science Foundation announces the following meeting: Name: Directorate for Mathematical and Physical...

77 FR 64831 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2012-10-23

... education activities within the Directorate for Mathematical and Physical Sciences. Agenda: Update on... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences; Notice of... Science Foundation announces the following meeting: Name: Mathematical and Physical Sciences Advisory...

77 FR 16076 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-19

... education activities within the Directorate for Mathematical and Physical Sciences. Agenda Update on current... National Science Foundation Advisory Committee for Mathematical and Physical Sciences; Notice of... Science Foundation announces the following meeting: Name: Directorate for Mathematical and Physical...

76 FR 64123 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2011-10-17

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences; Notice of... Science Foundation announces the following meeting: Name: Directorate for Mathematical and Physical.... Morris L. Aizenman, Senior Science Associate, Directorate for Mathematical and Physical Sciences, Room...

Applied Mathematics for agronomical engineers in Spain at UPM

NASA Astrophysics Data System (ADS)

Anton, J. M.; Grau, J. B.; Tarquis, A. M.; Fabregat, J.; Sanchez, M. E.

2009-04-01

Mathematics, created or discovered, are a global human conceptual endowment, containing large systems of knowledge, and varied skills to use definite parts of them, in creation or discovery, or for applications, e.g. in Physics, or notably in engineering behaviour. When getting upper intellectual levels in the 19th century, the agronomical science and praxis was noticeably or mainly organised in Spain in agronomical engineering schools and also in institutes, together with technician schools, also with different lower lever centres, and they have evolved with progress and they are much changing at present to a EEES schema (Bolonia process). They work in different lines that need some basis or skills from mathematics. The vocation to start such careers, that have varied curriculums, contains only some mathematics, and the number of credits for mathematics is restrained because time is necessary for other initial sciences such as applied chemistry, biology, ecology and soil sciences, but some basis and skill of maths are needed, also with Physics, at least for electricity, machines, construction, economics at initial ground levels, and also for Statistics that are here considered part of Applied Mathematics. The ways of teaching mathematical basis and skills are especial, and are different from the practical ways needed e. g. for Soil Sciences, and they involve especial efforts from students, and especial controls or exams that guide much learning. The mathematics have a very large accepted content that uses mostly a standard logic, and that is remarkably stable and international, rather similar notation and expressions being used with different main languages. For engineering the logical basis is really often not taught, but the use of it is transferred, especially for calculus that requires both adapted somehow simplified schemas and the learning of a specific skill to use it, and also for linear algebra. The basic forms of differential calculus in several variables are an example, maybe since Leibnitz, of the difficulty of balance rigor and usefulness in limited hours of teaching. In part engineers use of mathematics with manuals and now with computers that use packages, general (MAPLE, MATLAB, may be MATHCAD, et. C. ) or specific, such as for Statistics, Topography, Structural design, Hydraulics, specific Machines,…, and mostly the details of the algorithms are hidden, but the engineer must have in mind the basic mathematical schemas justifying what he is constructing with these tools, the PC being also used for organisation and drawing. The engineers must adapt to the evolution of these packages and computers that get much changed and improved in five or ten years, quicker than the specific engineering environment, and a clear idea of the much more stable mathematical structures behind gives a solid mental ground for that. An initiation to using computers also with a mathematical structure behind is necessary, to be followed in professional life. A specific actualisation of mathematical knowledge is often necessary for some new applications.

Modeling hazardous mass flows Geoflows09: Mathematical and computational aspects of modeling hazardous geophysical mass flows; Seattle, Washington, 9–11 March 2009

USGS Publications Warehouse

Iverson, Richard M.; LeVeque, Randall J.

2009-01-01

A recent workshop at the University of Washington focused on mathematical and computational aspects of modeling the dynamics of dense, gravity-driven mass movements such as rock avalanches and debris flows. About 30 participants came from seven countries and brought diverse backgrounds in geophysics; geology; physics; applied and computational mathematics; and civil, mechanical, and geotechnical engineering. The workshop was cosponsored by the U.S. Geological Survey Volcano Hazards Program, by the U.S. National Science Foundation through a Vertical Integration of Research and Education (VIGRE) in the Mathematical Sciences grant to the University of Washington, and by the Pacific Institute for the Mathematical Sciences. It began with a day of lectures open to the academic community at large and concluded with 2 days of focused discussions and collaborative work among the participants.

What's in a Symbol?

ERIC Educational Resources Information Center

Leadstone, Stuart

2013-01-01

This "Science Note" explores the new adaptation of Newton's Second Law of Motion, "F = ma." In older physics and applied mathematics textbooks this expression appears as "P = mf." The author examines why "f" is now favored over "a" and why practitioners write "P = mf" rather than…

ANNUAL REPORT

DOE Office of Scientific and Technical Information (OSTI.GOV)

None

1959-07-01

The national laboratory concept, laboratory objectives, the staff, research facilities. research activities, and administration are discussed in general terms and a financial statement is given. Fairly detailed accounts are given for the research programs in the fields of physics, accelerator development, instrumentation, applied mathematics, chemistry, nuclear engineering, biology, and medicine. (W.D.M.)

Pollution Police: How to Determine Spectroscopic Selection Rules

ERIC Educational Resources Information Center

Selco, Jodye I.; Beery, Janet

2004-01-01

Students employ mathematics and physical chemistry in a project called Pollution Police to establish spectroscopic selection rules, and apply them to detect environmental contaminants from infrared spectra. This interdisciplinary project enables students to gain multiple information on molecular symmetry, and its role in the development of…

Computational oncology.

PubMed

Lefor, Alan T

2011-08-01

Oncology research has traditionally been conducted using techniques from the biological sciences. The new field of computational oncology has forged a new relationship between the physical sciences and oncology to further advance research. By applying physics and mathematics to oncologic problems, new insights will emerge into the pathogenesis and treatment of malignancies. One major area of investigation in computational oncology centers around the acquisition and analysis of data, using improved computing hardware and software. Large databases of cellular pathways are being analyzed to understand the interrelationship among complex biological processes. Computer-aided detection is being applied to the analysis of routine imaging data including mammography and chest imaging to improve the accuracy and detection rate for population screening. The second major area of investigation uses computers to construct sophisticated mathematical models of individual cancer cells as well as larger systems using partial differential equations. These models are further refined with clinically available information to more accurately reflect living systems. One of the major obstacles in the partnership between physical scientists and the oncology community is communications. Standard ways to convey information must be developed. Future progress in computational oncology will depend on close collaboration between clinicians and investigators to further the understanding of cancer using these new approaches.

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

The problem of the Grand Unification Theory

NASA Astrophysics Data System (ADS)

Treder, H.-J.

The evolution and fundamental questions of physical theories unifying the gravitational, electromagnetic, and quantum-mechanical interactions are explored, taking Pauli's aphorism as a motto: 'Let no man join what God has cast asunder.' The contributions of Faraday and Riemann, Lorentz, Einstein, and others are discussed, and the criterion of Pauli is applied to Grand Unification Theories (GUT) in general and to those seeking to link gravitation and electromagnetism in particular. Formal mathematical symmetry principles must be shown to have real physical relevance by predicting measurable phenomena not explainable without a GUT; these phenomena must be macroscopic because gravitational effects are to weak to be measured on the microscopic level. It is shown that empirical and theoretical studies of 'gravomagnetism', 'gravoelectricity', or possible links between gravoelectrity and the cosmic baryon assymmetry eventually lead back to basic questions which appear philosophical or purely mathematical but actually challenge physics to seek verifiable answers.

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

The Six Core Theories of Modern Physics

NASA Astrophysics Data System (ADS)

Stevens, Charles F.

1996-09-01

Charles Stevens, a prominent neurobiologist who originally trained as a biophysicist (with George Uhlenbeck and Mark Kac), wrote this book almost by accident. Each summer he found himself reviewing key areas of physics that he had once known and understood well, for use in his present biological research. Since there was no book, he created his own set of notes, which formed the basis for this brief, clear, and self-contained summary of the basic theoretical structures of classical mechanics, electricity and magnetism, quantum mechanics, statistical physics, special relativity, and quantum field theory. The Six Core Theories of Modern Physics can be used by advanced undergraduates or beginning graduate students as a supplement to the standard texts or for an uncluttered, succinct review of the key areas. Professionals in such quantitative sciences as chemistry, engineering, computer science, applied mathematics, and biophysics who need to brush up on the essentials of a particular area will find most of the required background material, including the mathematics.

PT quantum mechanics.

PubMed

Bender, Carl M; DeKieviet, Maarten; Klevansky, S P

2013-04-28

PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.

78 FR 42111 - Advisory Committee for Mathematical and Physical Sciences #66; Notice of Meeting; Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2013-07-15

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences 66; Notice... July 18 Advisory Committee for Mathematical and Physical Sciences in the Federal Register on June 21..., Directorate for Mathematical and Physical Sciences, National Science Foundation, 4201 Wilson Blvd., Arlington...

Should I Take Further Mathematics? Physics Undergraduates' Experiences of Post-Compulsory Mathematics

ERIC Educational Resources Information Center

Bowyer, Jessica; Darlington, Ellie

2017-01-01

It is essential that physics undergraduates are appropriately prepared for the mathematical demands of their course. This study investigated physics students' perceptions of post-compulsory mathematics as preparation for their degree course. 494 physics undergraduates responded to an online questionnaire about their experiences of A-level…

On laminar and turbulent friction

NASA Technical Reports Server (NTRS)

Von Karman, TH

1946-01-01

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

An Introductory Calculus-Based Mechanics Investigation

ERIC Educational Resources Information Center

Allen, Bradley

2017-01-01

One challenge for the introductory physics teacher is incorporating calculus techniques into the laboratory setting. It can be difficult to strike a balance between presenting an experimental task for which calculus is essential and making the mathematics accessible to learners who may be apprehensive about applying it. One-dimensional kinematics…

Developing the New Infostructure

DTIC Science & Technology

2003-12-01

Engineering Physics and Applied Mathematics from Cornell, and a post-doc in neurophysiology from University of Mississippi Medical School. Dr. Jens G...transport you about 6,000 miles here to England, I’ve been doing some work with, I found it, this is kind of enlightening , in England, they don’t, this

Computer Programs in Marine Science: Key to Oceanographic Records Documentation No. 5.

ERIC Educational Resources Information Center

Firestone, Mary A.

Presented are abstracts of 700 computer programs in marine science. The programs listed are categorized under a wide range of headings which include physical oceanography, chemistry, coastal and estuarine processes, biology, pollution, air-sea interaction and heat budget, navigation and charting, curve fitting, and applied mathematics. The…

Framing the Structural Role of Mathematics in Physics Lectures: A Case Study on Electromagnetism

ERIC Educational Resources Information Center

Karam, Ricardo

2014-01-01

Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction.…

Teaching thermal physics in the paradigms project

NASA Astrophysics Data System (ADS)

Roundy, David

2011-10-01

Thermal physics is probably the most disliked course in the physics major curriculum, with students feeling that they are being led through a mathematical maze, leading to an unsatisfactory conclusion. Classical thermodynamics involves scary derivatives, while statistical mechanics leads to lengthy summations and is difficult to apply to interacting systems. It is unsurprising that students find themselves failing to see the physics for the math. In this talk, I will discuss my experiences teaching the Energy and Entropy paradigm, and will introduce materials we have developed to aide student understanding of partial derivatives and their relationship to experimental observables.

Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

NASA Astrophysics Data System (ADS)

Tweney, Ryan D.

2011-07-01

James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

Engineering physics and mathematics division

NASA Astrophysics Data System (ADS)

Sincovec, R. F.

1995-07-01

This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period 1 Jan. 1993 - 31 Dec. 1994. This report is the final archival record of the EPM Division. On 1 Oct. 1994, ORELA was transferred to Physics Division and on 1 Jan. 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division.

[Development of New Mathematical Methodology in Air Traffic Control for the Analysis of Hybrid Systems

NASA Technical Reports Server (NTRS)

Hermann, Robert

1997-01-01

The aim of this research is to develop new mathematical methodology for the analysis of hybrid systems of the type involved in Air Traffic Control (ATC) problems. Two directions of investigation were initiated. The first used the methodology of nonlinear generalized functions, whose mathematical foundations were initiated by Colombeau and developed further by Oberguggenberger; it has been extended to apply to ordinary differential. Systems of the type encountered in control in joint work with the PI and M. Oberguggenberger. This involved a 'mixture' of 'continuous' and 'discrete' methodology. ATC clearly involves mixtures of two sorts of mathematical problems: (1) The 'continuous' dynamics of a standard control type described by ordinary differential equations (ODE) of the form: {dx/dt = f(x, u)} and (2) the discrete lattice dynamics involved of cellular automata. Most of the CA literature involves a discretization of a partial differential equation system of the type encountered in physics problems (e.g. fluid and gas problems). Both of these directions requires much thinking and new development of mathematical fundamentals before they may be utilized in the ATC work. Rather than consider CA as 'discretization' of PDE systems, I believe that the ATC applications will require a completely different and new mathematical methodology, a sort of discrete analogue of jet bundles and/or the sheaf-theoretic techniques to topologists. Here too, I have begun work on virtually 'virgin' mathematical ground (at least from an 'applied' point of view) which will require considerable preliminary work.

Framing the structural role of mathematics in physics lectures: A case study on electromagnetism

NASA Astrophysics Data System (ADS)

Karam, Ricardo

2014-06-01

Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like) use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.

Turbulent Flow Simulation at the Exascale: Opportunities and Challenges Workshop: August 4-5, 2015, Washington, D.C.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sprague, Michael A.; Boldyrev, Stanislav; Fischer, Paul

This report details the impact exascale will bring to turbulent-flow simulations in applied science and technology. The need for accurate simulation of turbulent flows is evident across the DOE applied-science and engineering portfolios, including combustion, plasma physics, nuclear-reactor physics, wind energy, and atmospheric science. The workshop brought together experts in turbulent-flow simulation, computational mathematics, and high-performance computing. Building upon previous ASCR workshops on exascale computing, participants defined a research agenda and path forward that will enable scientists and engineers to continually leverage, engage, and direct advances in computational systems on the path to exascale computing.

Teachers' Beliefs about Improving Transfer of Algebraic Skills from Mathematics into Physics in Senior Pre-University Education

ERIC Educational Resources Information Center

Tursucu, Süleyman; Spandaw, Jeroen; Flipse, Steven; de Vries, Marc J.

2017-01-01

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers' beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using a…

Reality-Theoretical Models-Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School

ERIC Educational Resources Information Center

Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas

2015-01-01

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

The Emergence of Mathematical Physics at the University of Leipzig

NASA Astrophysics Data System (ADS)

Schlote, Karl-Heinz

Except for the well-known blossoming of theoretical physics with the group around Werner Heisenberg at the University of Leipzig at the end of the 1920s, the tradition of mathematical physics had been analyzed in only a few aspects, in particular the work of Carl Neumann and his contributions to the shaping of mathematical physics in general and the theory of electrodynamics in particular. However, the establishment of mathematical physics and its strong position at the University of Leipzig, with Neumann as its leading figure in the last third of the nineteenth century, formed important preconditions for the later upswing. That process is analyzed in this article, focusing on the work of Neumann. It includes a discussion of his ideas on the structure of a physical theory and the role of mathematics in physics as well as his impact on the interaction of mathematics and physics.

Actuality of transcendental æsthetics for modern physics

NASA Astrophysics Data System (ADS)

Petitot, Jean

1. The more mathematics and physics unify themselves in the physico-mathematical modern theories, the more an objective epistemology becomes necessary. Only such a transcendental epistemology is able to thematize correctly the status of the mathematical determination of physical reality. 2. There exists a transcendental history of the synthetic a priori and of the construction of physical categories. 3. The transcendental approach allows to supersed Wittgenstein's and Carnap's antiplatonist thesis according to which pure mathematics are physically applicable only if they lack any descriptive, cognitive or objective, content and reduce to mere prescriptive and normative devices. In fact, pure mathematics are prescriptive-normative in physics because: (i) the categories of physical objectivity are prescriptive-normative, and (ii) their categorial content is mathematically “constructed” through a Transcendental Aesthetics. Only a transcendental approach make compatible, in the one hand, a grammatical conventionalism of Wittgensteinian or Carnapian type and, on the other hand, a platonist realism of Gödelian type. Mathematics are not a grammar of the world but a mathematical hermeneutics of the intuitive forms and of the categorial grammar of the world.

Wavelets and their applications past and future

NASA Astrophysics Data System (ADS)

Coifman, Ronald R.

2009-04-01

As this is a conference on mathematical tools for defense, I would like to dedicate this talk to the memory of Louis Auslander, who through his insights and visionary leadership, brought powerful new mathematics into DARPA, he has provided the main impetus to the development and insertion of wavelet based processing in defense. My goal here is to describe the evolution of a stream of ideas in Harmonic Analysis, ideas which in the past have been mostly applied for the analysis and extraction of information from physical data, and which now are increasingly applied to organize and extract information and knowledge from any set of digital documents, from text to music to questionnaires. This form of signal processing on digital data, is part of the future of wavelet analysis.

An Introduction to Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Davidson, P. A.

2001-03-01

Magnetic fields are routinely used in industry to heat, pump, stir and levitate liquid metals. There is the terrestrial magnetic field that is maintained by fluid motion in the earth's core, the solar magnetic field, which generates sunspots and solar flares, and the galactic field that influences the formation of stars. This introductory text on magnetohydrodynamics (MHD) (the study of the interaction of magnetic fields and conducting fluids) is intended to serve as an introductory text for advanced undergraduates and graduate students in physics, applied mathematics and engineering. The material in the text is heavily weighted toward incompressible flows and to terrestrial (as distinct from astrophysical) applications. The final sections of the text, which outline the latest advances in the metallurgical applications of MHD, make the book of interest to professional researchers in applied mathematics, engineering and metallurgy.

Rotation covariant image processing for biomedical applications.

PubMed

Skibbe, Henrik; Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences.

Flight Physics for Beginners: Simple Examples of Applying Newton's Laws

ERIC Educational Resources Information Center

Spathopoulos, Vassilis

2011-01-01

Educators are constantly trying to find new ways of motivating their students. In subjects such as mechanics with a strong mathematical component, it is particularly important to devise real-life examples that can increase interest and student excitement. Aircraft flight is a topic that most young people find exciting. It therefore would seem…

Light-Emitting Diodes: Solving Complex Problems

ERIC Educational Resources Information Center

Planinšic, Gorazd; Etkina, Eugenia

2015-01-01

This is the fourth paper in our Light-Emitting Diodes series. The series aims to create a systematic library of LED-based materials and to provide readers with the description of experiments and the pedagogical treatment that would help their students construct, test, and apply physics concepts and mathematical relations. The first paper provided…

Dressed photons from the viewpoint of photon localization: the entrance to the off-shell science

NASA Astrophysics Data System (ADS)

Saigo, Hayato; Ojima, Izumi; Ohtsu, Motoichi

2017-12-01

In the present paper, a new aspect of the interplay is examined between mathematical-physical arguments and light-matter fusion technologies in terms of the concept of "effective mass", starting from a question: Who has seen a free photon? Owing to the general results due to Newton-Wigner and to Wightman, a position operator is absent for massless free particles with non-zero finite spins, and hence, we cannot observe free photons in any local space regions. To solve this paradox of "photon localization", the effective mass of a photon needs to be generated through the couplings of photons with matter. Here "polaritons" picture as a basic notion in optical and solid physics is shown to verify this viewpoint, which is seen to apply also to more general settings . Focusing on the role played by nanoparticles, we reach a new look at the notion of "dressed photons" as off-shell particles. The perspective above shows that essential mathematical structure of quantum field theory for the so-called elementary particles in subatomic scale can also be applied to certain phenomena in the nano-scale.

Mathematical Reasoning Requirements in Swedish National Physics Tests

ERIC Educational Resources Information Center

Johansson, Helena

2016-01-01

This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students' knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to…

Attitude Towards Physics and Additional Mathematics Achievement Towards Physics Achievement

ERIC Educational Resources Information Center

Veloo, Arsaythamby; Nor, Rahimah; Khalid, Rozalina

2015-01-01

The purpose of this research is to identify the difference in students' attitude towards Physics and Additional Mathematics achievement based on gender and relationship between attitudinal variables towards Physics and Additional Mathematics achievement with achievement in Physics. This research focused on six variables, which is attitude towards…

Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

ERIC Educational Resources Information Center

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-01-01

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…

75 FR 29369 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-25

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences; Notice of... Science Foundation announces the following meeting: Name: Directorate for Mathematical and Physical... Physical Sciences, Room 1005, National Science Foundation, 4201 Wilson Boulevard, Arlington, VA 22230. (703...

Mathematical interpretation of Brownian motor model: Limit cycles and directed transport phenomena

NASA Astrophysics Data System (ADS)

Yang, Jianqiang; Ma, Hong; Zhong, Suchuang

2018-03-01

In this article, we first suggest that the attractor of Brownian motor model is one of the reasons for the directed transport phenomenon of Brownian particle. We take the classical Smoluchowski-Feynman (SF) ratchet model as an example to investigate the relationship between limit cycles and directed transport phenomenon of the Brownian particle. We study the existence and variation rule of limit cycles of SF ratchet model at changing parameters through mathematical methods. The influences of these parameters on the directed transport phenomenon of a Brownian particle are then analyzed through numerical simulations. Reasonable mathematical explanations for the directed transport phenomenon of Brownian particle in SF ratchet model are also formulated on the basis of the existence and variation rule of the limit cycles and numerical simulations. These mathematical explanations provide a theoretical basis for applying these theories in physics, biology, chemistry, and engineering.

2014 International Conference on Science & Engineering in Mathematics, Chemistry and Physics (ScieTech 2014)

NASA Astrophysics Data System (ADS)

2014-04-01

2014 International Conference on Science & Engineering in Mathematics, Chemistry and Physics (ScieTech 2014), was held at the Media Hotel, Jakarta, Indonesia, on 13-14 January 2014. The ScieTech 2014 conference is aimed to bring together researchers, engineers and scientists in the domain of interest from around the world. ScieTech 2014 is placed on promoting interaction between the theoretical, experimental, and applied communities, so that a high level exchange is achieved in new and emerging areas within Mathematics, Chemistry and Physics. We would like to express our sincere gratitude to all in the Technical Program Committee who have reviewed the papers and developed a very interesting Conference Program as well as the invited and plenary speakers. This year, we received 187 papers and after rigorous review, 50 papers were accepted. The participants come from 16 countries. There are 5 (Five) Paralell Sessions and Four Keynote Speakers. It is an honour to present this volume of Journal of Physics: Conference Series (JPCS) and we deeply thank the authors for their enthusiastic and high-grade contributions. Finally, we would like to thank the conference chairmen, the members of the steering committee, the organizing committee, the organizing secretariat and the financial support from the conference sponsors that allowed the success of ScieTech 2014. The Editors of the Scietech 2014 Proceedings: Dr. Ford Lumban Gaol Dr. Benfano Soewito Dr. P.N. Gajjar

Topics in geophysical fluid dynamics: Atmospheric dynamics, dynamo theory, and climate dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghil, M.; Childress, S.

1987-01-01

This text is the first study to apply systematically the successive bifurcations approach to complex time-dependent processes in large scale atmospheric dynamics, geomagnetism, and theoretical climate dynamics. The presentation of recent results on planetary-scale phenomena in the earth's atmosphere, ocean, cryosphere, mantle and core provides an integral account of mathematical theory and methods together with physical phenomena and processes. The authors address a number of problems in rapidly developing areas of geophysics, bringing into closer contact the modern tools of nonlinear mathematics and the novel problems of global change in the environment.

Infrared band absorptance correlations and applications to nongray radiation. [mathematical models of absorption spectra for nongray atmospheres in order to study air pollution

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Manian, S. V. S.

1976-01-01

Various mathematical models for infrared radiation absorption spectra for atmospheric gases are reviewed, and continuous correlations for the total absorptance of a wide band are presented. Different band absorptance correlations were employed in two physically realistic problems (radiative transfer in gases with internal heat source, and heat transfer in laminar flow of absorbing-emitting gases between parallel plates) to study their influence on final radiative transfer results. This information will be applied to the study of atmospheric pollutants by infrared radiation measurement.

Applied Mathematics Should Be Taught Mixed.

ERIC Educational Resources Information Center

Brown, Gary I.

1994-01-01

Discusses the differences between applied and pure mathematics and provides extensive history of mixed mathematics. Argues that applied mathematics should be taught allowing for speculative mathematics, which involves breaking down a given problem into simpler parts until one arrives at first principles. (ASK)

A useful demonstration of calculus in a physics high school laboratory

NASA Astrophysics Data System (ADS)

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an experiment of a falling magnet in a column of self-induced eddy currents. The presented method combines multiple physics concepts such as 1D kinematics, classical mechanics, electromagnetism and non-trivial mathematics. It offers the opportunity for lateral as well as project-based learning.

Shifting College Students' Epistemological Framing Using Hypothetical Debate Problems

ERIC Educational Resources Information Center

Hu, Dehui; Rebello, N. Sanjay

2014-01-01

Developing expertise in physics problem solving requires the ability to use mathematics effectively in physical scenarios. Novices and experts often perceive the use of mathematics in physics differently. Students' perceptions and how they frame the use of mathematics in physics play an important role in their physics problem solving. In this…

Topological soliton solutions for three shallow water waves models

NASA Astrophysics Data System (ADS)

Liu, Jiangen; Zhang, Yufeng; Wang, Yan

2018-07-01

In this article, we investigate three distinct physical structures for shallow water waves models by the improved ansatz method. The method was improved and can be used to obtain more generalized form topological soliton solutions than the original method. As a result, some new exact solutions of the shallow water equations are successfully established and the obtained results are exhibited graphically. The results showed that the improved ansatz method can be applied to solve other nonlinear differential equations arising from mathematical physics.

From quantum foundations to applications and back.

PubMed

Gisin, Nicolas; Fröwis, Florian

2018-07-13

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Problemi e di Fisica e Astronomia ed il metodo di Gerberto docente

NASA Astrophysics Data System (ADS)

Sigismondi, Costantino

2015-04-01

Teaching Physics and Astronomy to pupils of 14-19 years old requires nowadays a continuous upgrade of knowledge as well as a capacity of selecting topics. The art of presenting arguments made Gerbert the teacher Rogatus a Pluribus in the end of X century and it is still actual; the proposed series of problems wants to link everyday experiences with the mathematical models of the phenomena, to allow the prediction and explanation of the experimental data. These problems of Physics and Astronomy are “observation oriented”, as the method of Gerbert was to start from the experience to get the theory, and not viceversa. Physics is much more than an “applied Algebra”. In the dispute of Ravenna (980) between Gerbert and Otric from Magdeburg, the primacy of Physics with respect to Mathematics was discussed. In the Italian secondary technical schools there are laboratory activities, while there is nothing similar for Lyceums and for the Astronomy teaching which is limited to a series of notions to be learned without any kind of observation; considered too difficult in polluted skyes.

Collisional breakup in a quantum system of three charged particles

PubMed

Rescigno; Baertschy; Isaacs; McCurdy

1999-12-24

Since the invention of quantum mechanics, even the simplest example of the collisional breakup of a system of charged particles, e(-) + H --> H(+) + e(-) + e(-) (where e(-) is an electron and H is hydrogen), has resisted solution and is now one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculation of the energies and directions for a final state in which all three particles are moving away from each other. Even with supercomputers, the correct mathematical description of this state has proved difficult to apply. A framework for solving ionization problems in many areas of chemistry and physics is finally provided by a mathematical transformation of the Schrodinger equation that makes the final state tractable, providing the key to a numerical solution of this problem that reveals its full dynamics.

Experimental Demonstration of Observability and Operability of Robustness of Coherence

NASA Astrophysics Data System (ADS)

Zheng, Wenqiang; Ma, Zhihao; Wang, Hengyan; Fei, Shao-Ming; Peng, Xinhua

2018-06-01

Quantum coherence is an invaluable physical resource for various quantum technologies. As a bona fide measure in quantifying coherence, the robustness of coherence (ROC) is not only mathematically rigorous, but also physically meaningful. We experimentally demonstrate the witness-observable and operational feature of the ROC in a multiqubit nuclear magnetic resonance system. We realize witness measurements by detecting the populations of quantum systems in one trial. The approach may also apply to physical systems compatible with ensemble or nondemolition measurements. Moreover, we experimentally show that the ROC quantifies the advantage enabled by a quantum state in a phase discrimination task.

Climate Science Program at California State University, Northridge

NASA Astrophysics Data System (ADS)

Steele Cox, H.; Klein, D.; Cadavid, A. C.; Foley, B.

2012-12-01

Due to its interdisciplinary nature, climate science poses wide-ranging challenges for science and mathematics students seeking careers in this field. There is a compelling need for universities to provide coherent programs in climate science in order to train future climate scientists. With funding from NASA Innovations in Climate Education (NICE), California State University, Northridge (CSUN), is creating the CSUN Climate Science Program. An interdisciplinary team of faculty members is working in collaboration with UCLA, Santa Monica College and NASA/JPL partners to create a new curriculum in climate science. The resulting sequence of climate science courses, or Pathway for studying the Mathematics of Climate Change (PMCC), is integrated into a Bachelor of Science degree program in the Applied Mathematical Sciences offered by the Mathematics Department at CSUN. The PMCC consists of courses offered by the departments of Mathematics, Physics, and Geography and is designed to prepare students for Ph.D. programs in technical fields relevant to global climate change and related careers. The students who choose to follow this program will be guided to enroll in the following sequence of courses for their 12 units of upper division electives: 1) A newly created course junior level course, Math 396CL, in applied mathematics which will introduce students to applications of vector calculus and differential equations to the study of thermodynamics and atmospheric dynamics. 2) An already existing course, Math 483, with new content on mathematical modeling specialized for this program; 3) An improved version of Phys 595CL on the mathematics and physics of climate change with emphasis on Radiative Transfer; 4) A choice of Geog 407 on Remote Sensing or Geog 416 on Climate Change with updated content to train the students in the analysis of satellite data obtained with the NASA Earth Observing System and instruction in the analysis of data obtained within a Geographical Information System (GIS). In addition the Geography department will similarly update the corresponding graduate courses on Remote Sensing, Geog 690D, and Climate Change Geog 620F, and there will be a reciprocal curriculum and data sharing collaboration with the Earth and Environmental Sciences program at Santa Monica College. Throughout the academic year a seminar series offers the students the opportunity to learn about ongoing work on Atmospheric Sciences and Climate and during the summer they have access to research experiences at NASA's Jet Propulsion Laboratory.

Astrophysical Flows

NASA Astrophysics Data System (ADS)

Pringle, James E.; King, Andrew

2003-07-01

Almost all conventional matter in the Universe is fluid, and fluid dynamics plays a crucial role in astrophysics. This new graduate textbook provides a basic understanding of the fluid dynamical processes relevant to astrophysics. The mathematics used to describe these processes is simplified to bring out the underlying physics. The authors cover many topics, including wave propagation, shocks, spherical flows, stellar oscillations, the instabilities caused by effects such as magnetic fields, thermal driving, gravity, shear flows, and the basic concepts of compressible fluid dynamics and magnetohydrodynamics. The authors are Directors of the UK Astrophysical Fluids Facility (UKAFF) at the University of Leicester, and editors of the Cambridge Astrophysics Series. This book has been developed from a course in astrophysical fluid dynamics taught at the University of Cambridge. It is suitable for graduate students in astrophysics, physics and applied mathematics, and requires only a basic familiarity with fluid dynamics.• Provides coverage of the fundamental fluid dynamical processes an astrophysical theorist needs to know • Introduces new mathematical theory and techniques in a straightforward manner • Includes end-of-chapter problems to illustrate the course and introduce additional ideas

78 FR 37590 - Advisory Committee for Mathematical and Physical Sciences #66; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2013-06-21

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences 66; Notice... Physical Sciences ( 66). Dates/Time: July 18, 2013 1:00 p.m.-5:15 p.m. Place: National Science Foundation... Federal Officer, Directorate for Mathematical and Physical Sciences, National Science Foundation, 4201...

NASA Tech Briefs, Winter 1977. Volume 2, No. 4

NASA Technical Reports Server (NTRS)

1977-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

A Martingale Characterization of Mixed Poisson Processes.

DTIC Science & Technology

1985-10-01

03LA A 11. TITLE (Inciuae Security Clanafication, ",A martingale characterization of mixed Poisson processes " ________________ 12. PERSONAL AUTHOR... POISSON PROCESSES Jostification .......... . ... . . Di.;t ib,,jtion by Availability Codes Dietmar Pfeifer* Technical University Aachen Dist Special and...Mixed Poisson processes play an important role in many branches of applied probability, for instance in insurance mathematics and physics (see Albrecht

NASA Tech Briefs, Summer 1979. Volume 4, No. 2

NASA Technical Reports Server (NTRS)

1979-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of neW products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hules, John

This 1998 annual report from the National Scientific Energy Research Computing Center (NERSC) presents the year in review of the following categories: Computational Science; Computer Science and Applied Mathematics; and Systems and Services. Also presented are science highlights in the following categories: Basic Energy Sciences; Biological and Environmental Research; Fusion Energy Sciences; High Energy and Nuclear Physics; and Advanced Scientific Computing Research and Other Projects.

NASA Tech Briefs, Summer 1981. Volume 6, No. 2

NASA Technical Reports Server (NTRS)

1981-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Winter 1980. Volume 5, No. 4

NASA Technical Reports Server (NTRS)

1980-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you In learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Fall 1980. Volume 5, No. 3

NASA Technical Reports Server (NTRS)

1980-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovatio.ns of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Fall 1978. Volume 3, No. 3

NASA Technical Reports Server (NTRS)

1978-01-01

Topics covered: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

JPL basic research review. [research and advanced development

NASA Technical Reports Server (NTRS)

1977-01-01

Current status, projected goals, and results of 49 research and advanced development programs at the Jet Propulsion Laboratory are reported in abstract form. Areas of investigation include: aerodynamics and fluid mechanics, applied mathematics and computer sciences, environment protection, materials science, propulsion, electric and solar power, guidance and navigation, communication and information sciences, general physics, and chemistry.

NASA Tech Briefs, Summer 1984. Volume 8, No. 4

NASA Technical Reports Server (NTRS)

1984-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Science.

NASA Tech Briefs, Fall/Winter 1981. Vol. 6, No. 3

NASA Technical Reports Server (NTRS)

1981-01-01

Topics covered: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Spring 1978. Volume 3, No. 1

NASA Technical Reports Server (NTRS)

1978-01-01

Topics covered include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Winter 1978. Volume 3, No. 4

NASA Technical Reports Server (NTRS)

1978-01-01

Topics covered include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Winter 1983. Volume 8, No. 2

NASA Technical Reports Server (NTRS)

1983-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences;

NASA Tech Briefs, Winter 1982. Volume 7, No. 2

NASA Technical Reports Server (NTRS)

1982-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Spring 1981. Volume 6, No. 1

NASA Technical Reports Server (NTRS)

1981-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you In learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Spring 1984. Volume 8, No. 3

NASA Technical Reports Server (NTRS)

1984-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Fall 1976. Volume 1, No. 3

NASA Technical Reports Server (NTRS)

1976-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of seloc.ted Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Summer 1978

NASA Technical Reports Server (NTRS)

1978-01-01

Topics covered include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Solar Energy; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Winter 1979. Volume 4, No. 4

NASA Technical Reports Server (NTRS)

1979-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you In learning about and applying NASA technology; New Product Ideas: A summary of selected Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Fall 1977. Volume 2, No. 3

NASA Technical Reports Server (NTRS)

1977-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Summer 1980. Volume 5, No. 2

NASA Technical Reports Server (NTRS)

1980-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Spring 1977. Volume 2, No. 1

NASA Technical Reports Server (NTRS)

1977-01-01

Topics: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selted innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Fall 1982. Volume 7, No. 1

NASA Technical Reports Server (NTRS)

1982-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected innovations of value to manufacturers for the develop ment of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Spring 1979. Volume 4, No. 1

NASA Technical Reports Server (NTRS)

1979-01-01

Topics covered include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences;

NASA Tech Briefs, Fall 1983. Volume 8, No. 1

NASA Technical Reports Server (NTRS)

1983-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Winter 1976. Volume 1, No. 4

NASA Technical Reports Server (NTRS)

1976-01-01

Topics covered include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of val ue to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Summer 1977. Volume 2, No. 2

NASA Technical Reports Server (NTRS)

1977-01-01

Topics: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected Innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Spring 1983. Volume 7, No. 3

NASA Technical Reports Server (NTRS)

1983-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences;

NASA Tech Briefs, Spring 1980. Volume 5, No. 1

NASA Technical Reports Server (NTRS)

1980-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Fall 1979. Volume 4, No. 3

NASA Technical Reports Server (NTRS)

1979-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences.

NASA Tech Briefs, Summer 1983. Volume 7, No. 4

NASA Technical Reports Server (NTRS)

1983-01-01

Topics include: NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology. New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and information Sciences.

Engineering Education in K-12 Schools

NASA Astrophysics Data System (ADS)

Spence, Anne

2013-03-01

Engineers rely on physicists as well as other scientists and mathematicians to explain the world in which we live. Engineers take this knowledge of the world and use it to create the world that never was. The teaching of physics and other sciences as well as mathematics is critical to maintaining our national workforce. Science and mathematics education are inherently different, however, from engineering education. Engineering educators seek to enable students to develop the habits of mind critical for innovation. Through understanding of the engineering design process and how it differs from the scientific method, students can apply problem and project based learning to solve the challenges facing society today. In this talk, I will discuss the elements critical to a solid K-12 engineering education that integrates science and mathematics to solve challenges throughout the world.

Obtaining Laws through Quantifying Experiments: Justifications of Pre-Service Physics Teachers in the Case of Electric Current, Voltage and Resistance

ERIC Educational Resources Information Center

Mäntylä, Terhi; Hämäläinen, Ari

2015-01-01

The language of physics is mathematics, and physics ideas, laws and models describing phenomena are usually represented in mathematical form. Therefore, an understanding of how to navigate between phenomena and the models representing them in mathematical form is important for a physics teacher so that the teacher can make physics understandable…

Student Perceptions about Applied Mathematics.

ERIC Educational Resources Information Center

Keif, Malcolm G.; Stewart, Bob R.

Background information on the history and rationale for Tech Prep introduces the description of a study that examines the perceptions of students enrolled in Applied Mathematics 1 and Applied Mathematics 2 courses which are based on the Center for Occupational Research and Development's (CORD) applied mathematics curriculum. The primary goal is to…

Some applications of mathematics in theoretical physics - A review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bora, Kalpana

2016-06-21

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical toolsmore » are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.« less

Some applications of mathematics in theoretical physics - A review

NASA Astrophysics Data System (ADS)

Bora, Kalpana

2016-06-01

Mathematics is a very beautiful subject-very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like-differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

Building a Program of University Physics and Mathematics Education

NASA Astrophysics Data System (ADS)

Tanaka, Tadayoshi; Nakamura, Akira; Kagiyama, Shigenori; Namiki, Masatoshi; Ejiri, Arisato; Ohshima, Kazunari; Mishima, Akiomi; Aoki, Katsuhiko

Authors built physics learning modules which consist of lectures, experiments and practices, introducing physics experiments of elementary and secondary education. In addition, we are operating "KIT Mathematics Navigation" in order to complement mathematical basics to engineering education. Based on these results, we are building studies and development of an education program in order to support the learning paradigm shift and to help students learn physics and mathematics complimentarily for liberal arts education course in universities.

Mathematical sense-making in quantum mechanics: An initial peek

NASA Astrophysics Data System (ADS)

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-12-01

Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

Zimbabwean Female Participation in Physics: The Influence of Identity Formation on Perception and Participation

ERIC Educational Resources Information Center

Gudyanga, Anna; Kurup, Raj

2017-01-01

The study investigated the influence of identity formation on the perceptions and participation of Zimbabwean Advanced Level (A' Level) female adolescent students in physics. Nine female adolescent students eighteen years and above: three doing mathematics and physics, one doing physics without mathematics and five doing mathematics without…

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

NASA Astrophysics Data System (ADS)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.

2016-09-01

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J.N., E-mail: jnshadi@sandia.gov; Department of Mathematics and Statistics, University of New Mexico; Smith, T.M.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts tomore » apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE PAGES

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; ...

2016-05-20

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

A Multifaceted Mathematical Approach for Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Alexander, F.; Anitescu, M.; Bell, J.

2012-03-07

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significantmore » impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.« less

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

The role of a posteriori mathematics in physics

NASA Astrophysics Data System (ADS)

MacKinnon, Edward

2018-05-01

The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.

Rotation Covariant Image Processing for Biomedical Applications

PubMed Central

Reisert, Marco

2013-01-01

With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences. PMID:23710255

The Challenge of Learning Physics before Mathematics: A Case Study of Curriculum Change in Taiwan

ERIC Educational Resources Information Center

Chiu, Mei-Shiu

2016-01-01

The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without…

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

PubMed

Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

2017-01-01

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

The effect of studying A-level mathematics on performance in A-level physics

NASA Astrophysics Data System (ADS)

Rutter, Pam

1994-01-01

Mathematics plays an important part in physics at all levels. At A-level, physics candidates who do not study A-level mathematics would seem to be at a disadvantage. This article presents statistical evidence to support this widely held belief.

Electromagnetic Concepts in Mathematical Representation of Physics.

ERIC Educational Resources Information Center

Albe, Virginie; Venturini, Patrice; Lascours, Jean

2001-01-01

Addresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…

pp ii Brain, behaviour and mathematics: Are we using the right approaches? [review article

NASA Astrophysics Data System (ADS)

Perez Velazquez, Jose Luis

2005-12-01

Mathematics are used in biological sciences mostly as a quantifying tool, for it is the science of numbers after all. There is a long-standing interest in the application of mathematical methods and concepts to neuroscience in attempts to decipher brain activity. While there has been a very wide use of mathematical/physical methodologies, less effort has been made to formulate a comprehensive and integrative theory of brain function. This review concentrates on recent developments, uses and abuses of mathematical formalisms and techniques that are being applied in brain research, particularly the current trend of using dynamical system theory to unravel the global, collective dynamics of brain activity. It is worth emphasising that the theoretician-neuroscientist, eager to apply mathematical analysis to neuronal recordings, has to consider carefully some crucial anatomo-physiological assumptions, that may not be as accurate as the specific methods require. On the other hand, the experimentalist neuro-physicist, with an inclination to implement mathematical thoughts in brain science, has to make an effort to comprehend the bases of the theoretical concepts that can be used as frameworks or as analysis methods of brain electrophysiological recordings, and to critically inspect the accuracy of the interpretations of the results based on the neurophysiological ground. It is hoped that this brief overview of anatomical and physiological presumptions and their relation to theoretical paradigms will help clarify some particular points of interest in current trends in brain science, and may provoke further reflections on how certain or uncertain it is to conceptualise brain function based on these theoretical frameworks, if the physiological and experimental constraints are not as accurate as the models prescribe.

Microwave Brightness Of Land Surfaces From Outer Space

NASA Technical Reports Server (NTRS)

Kerr, Yann H.; Njoku, Eni G.

1991-01-01

Mathematical model approximates microwave radiation emitted by land surfaces traveling to microwave radiometer in outer space. Applied to measurements made by Scanning Multichannel Microwave Radiometer (SMMR). Developed for interpretation of microwave imagery of Earth to obtain distributions of various chemical, physical, and biological characteristics across its surface. Intended primarily for use in mapping moisture content of soil and fraction of Earth covered by vegetation. Advanced Very-High-Resolution Radiometer (AVHRR), provides additional information on vegetative cover, thereby making possible retrieval of soil-moisture values from SMMR measurements. Possible to monitor changes of land surface during intervals of 5 to 10 years, providing significant data for mathematical models of evolution of climate.

Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G'/G)-expansion method.

PubMed

Alam, Md Nur; Akbar, M Ali

2013-01-01

The new approach of the generalized (G'/G)-expansion method is an effective and powerful mathematical tool in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in science, engineering and mathematical physics. In this article, the new approach of the generalized (G'/G)-expansion method is applied to construct traveling wave solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation. The solutions are expressed in terms of the hyperbolic functions, the trigonometric functions and the rational functions. By means of this scheme, we found some new traveling wave solutions of the above mentioned equation.

Finite-element approach to Brownian dynamics of polymers.

PubMed

Cyron, Christian J; Wall, Wolfgang A

2009-12-01

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

Summary of research in applied mathematics, numerical analysis, and computer sciences

NASA Technical Reports Server (NTRS)

1986-01-01

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.

NASA Tech Briefs, Summer 1976. Volume 1, No. 2

NASA Technical Reports Server (NTRS)

1976-01-01

Topics covered include: Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Life Sciences; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences. Also included are; NASA TU Services: Technology Utilization services that can assist you in learning about and applying NASA technology; and New Product Ideas: A summary of selected innovations of value to manufacturers for the development of new products.

Physics Teacher Demonstrations for the Classroom

NASA Astrophysics Data System (ADS)

Murfee, Lee

2005-04-01

A sharing of physics and physics teaching demonstrations by Lee Murfee, a teacher of students learning physics and mathematics at Berkeley Preparatory School and the United States Military Academy for 21 years, and active member of the Florida Section of American Association of Physics Teachers (AAPT). Presentation is a fast paced array of physics and physics teaching demonstrations. Topics include who and what we teach, a successful science department philosophy, forces, acceleration, impulse, momentum, observations, pendulums, springs, friction, inclined plane, rotational motion, moment of inertia, teaching description of motion with data, equations and graphing, slope, uniform circular motion, derivatives, integrals, PASCO Data Studio sensor applications, students presenting to students, flashboards, sound, pressure, and sensitivity analysis in determining specific heat. Demonstrations apply to high school and college introductory physics teaching; handouts and some door prizes/gifts will be provided.

A Physics Show Performed by Students for Kids: From Mechanics to Elementary Particle Physics

NASA Astrophysics Data System (ADS)

Dreiner, Herbi K.

2008-09-01

Physics students spend the early part of their training attending physics and mathematics lectures, solving problem sets, and experimenting in laboratory courses. The program is typically intensive and fairly rigid. They have little opportunity to follow their own curiosity or apply their knowledge. There have been many attempts to address this deficiency, specifically through outreach activities.1-23 For example, since 1984 Clint Sprott (University of Wisconsin) hosts a physics show entitled "The Wonders of Physics!" Dressed up as a circus director and assisted by students, Professor Sprott presents entertaining and educating experiments to a regularly packed auditorium of all age groups.5 This was in turn inspired by the "Chemistry is Fun" presentations of Basam Shakhashiri (University of Wisconsin), where the students are also involved.6

Comparison of university students' understanding of graphs in different contexts

NASA Astrophysics Data System (ADS)

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-12-01

This study investigates university students’ understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was administered to 385 first year students at University of Zagreb who were either prospective physics or mathematics teachers or prospective physicists or mathematicians. Rasch analysis of data was conducted and linear measures for item difficulties were obtained. Average difficulties of items in three domains (mathematics, physics, and other contexts) and over two concepts (graph slope, area under the graph) were computed and compared. Analysis suggests that the variation of average difficulty among the three domains is much smaller for the concept of graph slope than for the concept of area under the graph. Most of the slope items are very close in difficulty, suggesting that students who have developed sufficient understanding of graph slope in mathematics are generally able to transfer it almost equally successfully to other contexts. A large difference was found between the difficulty of the concept of area under the graph in physics and other contexts on one side and mathematics on the other side. Comparison of average difficulty of the three domains suggests that mathematics without context is the easiest domain for students. Adding either physics or other context to mathematical items generally seems to increase item difficulty. No significant difference was found between the average item difficulty in physics and contexts other than physics, suggesting that physics (kinematics) remains a difficult context for most students despite the received instruction on kinematics in high school.

Modeling and simulation of high dimensional stochastic multiscale PDE systems at the exascale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zabaras, Nicolas J.

2016-11-08

Predictive Modeling of multiscale and Multiphysics systems requires accurate data driven characterization of the input uncertainties, and understanding of how they propagate across scales and alter the final solution. This project develops a rigorous mathematical framework and scalable uncertainty quantification algorithms to efficiently construct realistic low dimensional input models, and surrogate low complexity systems for the analysis, design, and control of physical systems represented by multiscale stochastic PDEs. The work can be applied to many areas including physical and biological processes, from climate modeling to systems biology.

On Boundaries of the Language of Physics

NASA Astrophysics Data System (ADS)

Kvasz, Ladislav

The aim of the present paper is to outline a method of reconstruction of the historical development of the language of physical theories. We will apply the theory presented in Patterns of Change, Linguistic Innovations in the Development of Classical Mathematics to the analysis of linguistic innovations in physics. Our method is based on a reconstruction of the following potentialities of language: analytical power, expressive power, integrative power, and explanatory power, as well as analytical boundaries and expressive boundaries. One of the results of our reconstruction is a new interpretation of Kant's antinomies of pure reason. If we relate Kant's antinomies to the language, they retain validity.

Quantitative Analysis of the Interdisciplinarity of Applied Mathematics.

PubMed

Xie, Zheng; Duan, Xiaojun; Ouyang, Zhenzheng; Zhang, Pengyuan

2015-01-01

The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999-2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.

Quantum Chemistry in Great Britain: Developing a Mathematical Framework for Quantum Chemistry

NASA Astrophysics Data System (ADS)

Simões, Ana; Gavroglu, Kostas

By 1935 quantum chemistry was already delineated as a distinct sub-discipline due to the contributions of Fritz London, Walter Heitler, Friedrich Hund, Erich Hückel, Robert Mulliken, Linus Pauling, John van Vleck and John Slater. These people are credited with showing that the application of quantum mechanics to the solution of chemical problems was, indeed, possible, especially so after the introduction of a number of new concepts and the adoption of certain approximation methods. And though a number of chemists had started talking of the formation of theoretical or, even, mathematical chemistry, a fully developed mathematical framework of quantum chemistry was still wanting. The work of three persons in particular-of John E. Lennard-Jones, Douglas R. Hartree, and Charles Alfred Coulson-has been absolutely crucial in the development of such a framework. In this paper we shall discuss the work of these three researchers who started their careers in the Cambridge tradition of mathematical physics and who at some point of their careers all became professors of applied mathematics. We shall argue that their work consisted of decisive contributions to the development of such a mathematical framework for quantum chemistry.

A new mathematical approach for shock-wave solution in a dusty plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Das, G.C.; Dwivedi, C.B.; Talukdar, M.

1997-12-01

The problem of nonlinear Burger equation in a plasma contaminated with heavy dust grains has been revisited. As discussed earlier [C. B. Dwivedi and B. P. Pandey, Phys. Plasmas {bold 2}, 9 (1995)], the Burger equation originates due to dust charge fluctuation dynamics. A new alternate mathematical approach based on a simple traveling wave formalism has been applied to find out the solution of the derived Burger equation, and the method recovers the known shock-wave solution. This technique, although having its own limitation, predicts successfully the salient features of the weak shock-wave structure in a dusty plasma with dust chargemore » fluctuation dynamics. It is emphasized that this approach of the traveling wave formalism is being applied for the first time to solve the nonlinear wave equation in plasmas. {copyright} {ital 1997 American Institute of Physics.}« less

Modelling Mathematical Reasoning in Physics Education

ERIC Educational Resources Information Center

Uhden, Olaf; Karam, Ricardo; Pietrocola, Mauricio; Pospiech, Gesche

2012-01-01

Many findings from research as well as reports from teachers describe students' problem solving strategies as manipulation of formulas by rote. The resulting dissatisfaction with quantitative physical textbook problems seems to influence the attitude towards the role of mathematics in physics education in general. Mathematics is often seen as a…

The solution of the sixth Hilbert problem: the ultimate Galilean revolution

NASA Astrophysics Data System (ADS)

D'Ariano, Giacomo Mauro

2018-04-01

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: `physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as `clock', `rigid rod', `force', `inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory. This article is part of the theme issue `Hilbert's sixth problem'.

The solution of the sixth Hilbert problem: the ultimate Galilean revolution.

PubMed

D'Ariano, Giacomo Mauro

2018-04-28

I argue for a full mathematization of the physical theory, including its axioms, which must contain no physical primitives. In provocative words: 'physics from no physics'. Although this may seem an oxymoron, it is the royal road to keep complete logical coherence, hence falsifiability of the theory. For such a purely mathematical theory the physical connotation must pertain only the interpretation of the mathematics, ranging from the axioms to the final theorems. On the contrary, the postulates of the two current major physical theories either do not have physical interpretation (as for von Neumann's axioms for quantum theory), or contain physical primitives as 'clock', 'rigid rod', 'force', 'inertial mass' (as for special relativity and mechanics). A purely mathematical theory as proposed here, though with limited (but relentlessly growing) domain of applicability, will have the eternal validity of mathematical truth. It will be a theory on which natural sciences can firmly rely. Such kind of theory is what I consider to be the solution of the sixth Hilbert problem. I argue that a prototype example of such a mathematical theory is provided by the novel algorithmic paradigm for physics, as in the recent information-theoretical derivation of quantum theory and free quantum field theory.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).

Task force on applied mathematics

NASA Technical Reports Server (NTRS)

Prieto, A.

1979-01-01

Tomas Garza relates how the Research Center for Applied Mathematics Systems and Services in Mexico became the Research Institute for Applied Mathematics and Systems and what the type of work performed is.

Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning

NASA Astrophysics Data System (ADS)

Afthina, H.; Mardiyana; Pramudya, I.

2017-09-01

This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.

Mathematical Physics in the Style of Gabriel Lamé and the Treatise of Emile Mathieu

NASA Astrophysics Data System (ADS)

Barbin, Évelyne; Guitart, René

The Treatise of Mathematical Physics of Emile Mathieu, published from 1873 to 1890, provided an exposition of the specific French "Mathematical Physics" inherited from Lamé, himself an heir of Poisson, Fourier, and Laplace. The works of all these authors had significant differences, but they were pursuing the same goal, described here with its relation to Theoretical Physics.

Studies in Mathematics, Volume XVI. Some Uses of Mathematics: A Source Book for Teachers and Students of School Mathematics.

ERIC Educational Resources Information Center

Bell, Max S., Ed.

This is a collection of articles dealing with mathematical applications for use by high school teachers and students. The articles are intended to illustrate several themes: (1) how mathematics is applied via construction of mathematical models; (2) the various types of activities in applied mathematics; (3) the role of pure mathematics in applied…

Mathematical modeling of a process the rolling delivery

NASA Astrophysics Data System (ADS)

Stepanov, Mikhail A.; Korolev, Andrey A.

2018-03-01

An adduced analysis of the scientific researches in a domain of the rolling equipments, also research of properties the working material. A one of perspective direction of scientific research this is mathematical modeling. That is broadly used in many scientific disciplines and especially at the technical, applied sciences. With the aid of mathematical modeling it can be study of physical properties of the researching objects and systems. A research of the rolling delivery and transporting devices realized with the aid of a construction of mathematical model of appropriate process. To be described the basic principles and conditions of a construction of mathematical models of the real objects. For example to be consider a construction of mathematical model the rolling delivery device. For a construction that is model used system of the equations, which consist of: Lagrange’s equation of a motion, describing of the law conservation of energy of a mechanical system, and the Navier - Stokes equations, which characterize of the flow of a continuous non-compressed fluid. A construction of mathematical model the rolling deliver to let determined of a total energy of device, and therefore to got the dependence upon the power of drive to a gap between of rolls. A corroborate the hypothesis about laminar the flow of a material into the rolling gap of deliver.

Analytical derivation: An epistemic game for solving mathematically based physics problems

NASA Astrophysics Data System (ADS)

Bajracharya, Rabindra R.; Thompson, John R.

2016-06-01

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.

Rationale and study protocol of the EASY Minds (Encouraging Activity to Stimulate Young Minds) program: cluster randomized controlled trial of a primary school-based physical activity integration program for mathematics.

PubMed

Riley, Nicholas; Lubans, David R; Holmes, Kathryn; Morgan, Philip J

2014-08-08

Novel strategies are required to increase school-based physical activity levels of children. Integrating physical activity in mathematics lessons may lead to improvements in students' physical activity levels as well as enjoyment, engagement and learning. The primary aim of this study is to evaluate the impact of a curriculum-based physical activity integration program known as EASY Minds (Encouraging Activity to Stimulate Young Minds) on children's daily school time physical activity levels. Secondary aims include exploring the impact of EASY Minds on their engagement and 'on task' behaviour in mathematics. Grade 5/6 classes from eight public schools in New South Wales, Australia will be randomly allocated to intervention (n = 4) or control (n = 4) groups. Teachers from the intervention group will receive one day of professional development, a resource pack and asked to adapt their lessons to embed movement-based learning in their daily mathematics program in at least three lessons per week over a six week period. Intervention support will be provided via a weekly email and three lesson observations. The primary outcomes will be children's physical activity levels (accelerometry) across both the school day and during mathematics lessons (moderate-to-vigorous physical activity and sedentary time). Children's 'on-task' behaviour, enjoyment of mathematics and mathematics attainment will be assessed as secondary outcomes. A detailed process evaluation will be undertaken. EASY Minds is an innovative intervention that has the potential to improve key physical and academic outcomes for primary school aged children and help guide policy and practice regarding the teaching of mathematics. Australian and New Zealand Clinical Trials Register ACTRN12613000637741 13/05/2013.

Comparison of Student Understanding of Line Graph Slope in Physics and Mathematics

ERIC Educational Resources Information Center

Planinic, Maja; Milin-Sipus, Zeljka; Katic, Helena; Susac, Ana; Ivanjek, Lana

2012-01-01

This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school…

Promoting the Understanding of Mathematics in Physics at Secondary Level

ERIC Educational Resources Information Center

Thompson, Alaric

2016-01-01

This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…

Well test mathematical model for fractures network in tight oil reservoirs

NASA Astrophysics Data System (ADS)

Diwu, Pengxiang; Liu, Tongjing; Jiang, Baoyi; Wang, Rui; Yang, Peidie; Yang, Jiping; Wang, Zhaoming

2018-02-01

Well test, especially build-up test, has been applied widely in the development of tight oil reservoirs, since it is the only available low cost way to directly quantify flow ability and formation heterogeneity parameters. However, because of the fractures network near wellbore, generated from artificial fracturing linking up natural factures, traditional infinite and finite conductivity fracture models usually result in significantly deviation in field application. In this work, considering the random distribution of natural fractures, physical model of fractures network is proposed, and it shows a composite model feature in the large scale. Consequently, a nonhomogeneous composite mathematical model is established with threshold pressure gradient. To solve this model semi-analytically, we proposed a solution approach including Laplace transform and virtual argument Bessel function, and this method is verified by comparing with existing analytical solution. The matching data of typical type curves generated from semi-analytical solution indicates that the proposed physical and mathematical model can describe the type curves characteristic in typical tight oil reservoirs, which have up warping in late-term rather than parallel lines with slope 1/2 or 1/4. It means the composite model could be used into pressure interpretation of artificial fracturing wells in tight oil reservoir.

Qualitative investigation into students' use of divergence and curl in electromagnetism

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; Baily, Charles; De Cock, Mieke

2016-12-01

Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector calculus. To gain insight into student reasoning when solving problems involving divergence and curl, we conducted eight semistructured individual student interviews. During these interviews, students discussed the divergence and curl of electromagnetic fields using graphical representations, mathematical calculations, and the differential form of Maxwell's equations. We observed that while many students attempt to clarify the problem by making a sketch of the electromagnetic field, they struggle to interpret graphical representations of vector fields in terms of divergence and curl. In addition, some students confuse the characteristics of field line diagrams and field vector plots. By interpreting our results within the conceptual blending framework, we show how a lack of conceptual understanding of the vector operators and difficulties with graphical representations can account for an improper understanding of Maxwell's equations in differential form. Consequently, specific learning materials based on a multiple representation approach are required to clarify Maxwell's equations.

Obituary: Eugene Richard Tomer, 1932-2007

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2009-01-01

Dr. Eugene R. Tomer passed away on 2 July 2007 at his home in San Francisco, California. The cause of death was cancer. Tomer was a consulting applied mathematician with a wide range of interests in dynamical astronomy, electromagnetic theory for use in communications, and computational methods of applied mathematics. He was a member of AAS, and the Society for Applied and Industrial Mathematics [SIAM]. With K. H. Prendergast, he co-wrote the influential paper "Self-consistent Models of Elliptical Galaxies," published in the Astronomical Journal 75 (1970), 674-679. This paper has been cited over eighty times. Tomer was born on 13 June 1932. He earned the Ph.D. in Mathematics at the University of California-Berkeley in 1978 (title of dissertation: On the C*-algebra of the Hermite Operator). In 1996 he and A. F. Peterson wrote "Meeting the Challenges Presented by Computational Electromagnetics," a publication of the Naval Postgraduate School at Monterey, California. This writer met Eugene at the 1992 Annual SIAM meeting in Los Angeles in connection with the Activity Group on Orthogonal Polynomials and Special Functions, which the writer chaired at the time. Eugene volunteered to edit the Newsletter of the group, which he did from July 1992 to July 1995. Thanks to his skills and efforts, the Newsletter became a carefully edited, professional publication. Eugene not only organized a Problems Column, attracting questions in pure and applied mathematics, but he also designed the logo for the group. He gave much time and effort to this service, in an era when copy had to be physically assembled and mailed to SIAM Headquarters. Eventually he felt he had done what he could for the Activity Group. He told me that he hoped the Group would get seriously involved with applications such as in astronomy, physics, and sciences that use special function solutions of differential equations. During Tomer's editorship, we communicated mostly by e-mail, our homes being far apart. He was a good friend to the Group and to me, as much as one can be over a separation of thousands of miles. As well, Eugene was an active amateur radio operator, much appreciated by his local amateur radio community, with call sign WI6X. He left behind family, friends, and one son.

A consistent modelling methodology for secondary settling tanks in wastewater treatment.

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

The role of mathematics for physics teaching and understanding

NASA Astrophysics Data System (ADS)

Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette

2016-05-01

-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.

Thermal loading in the laser holography nondestructive testing of a composite structure

NASA Technical Reports Server (NTRS)

Liu, H. K.; Kurtz, R. L.

1975-01-01

A laser holographic interferometry method that has variable sensitivity to surface deformation was applied to the investigation of composite test samples under thermal loading. A successful attempt was made to detect debonds in a fiberglass-epoxy-ceramic plate. Experimental results are presented along with the mathematical analysis of the physical model of the thermal loading and current conduction in the composite material.

Some New Mathematical Methods for Variational Objective Analysis

NASA Technical Reports Server (NTRS)

Wahba, G.; Johnson, D. R.

1984-01-01

New and/or improved variational methods for simultaneously combining forecast, heterogeneous observational data, a priori climatology, and physics to obtain improved estimates of the initial state of the atmosphere for the purpose of numerical weather prediction are developed. Cross validated spline methods are applied to atmospheric data for the purpose of improved description and analysis of atmospheric phenomena such as the tropopause and frontal boundary surfaces.

quantum mechanics

PubMed Central

Bender, Carl M; DeKieviet, Maarten; Klevansky, S. P.

2013-01-01

-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics. PMID:23509390

Open problems in mathematical physics

NASA Astrophysics Data System (ADS)

Coley, Alan A.

2017-09-01

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr. 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.

Design Steps for Physic STEM Education Learning in Secondary School

NASA Astrophysics Data System (ADS)

Teevasuthonsakul, C.; Yuvanatheeme, V.; Sriput, V.; Suwandecha, S.

2017-09-01

This study aimed to develop the process of STEM Education activity design used in Physics subjects in the Thai secondary schools. The researchers have conducted the study by reviewing the literature and related works, interviewing Physics experts, designing and revising the process accordingly, and experimenting the designed process in actual classrooms. This brought about the five-step process of STEM Education activity design which Physics teachers applied to their actual teaching context. The results from the after-class evaluation revealed that the students’ satisfaction level toward Physics subject and critical thinking skill was found higher statistically significant at p < .05. Moreover, teachers were advised to integrate the principles of science, mathematics, technology, and engineering design process as the foundation when creating case study of problems and solutions.

Statistical physics of hard combinatorial optimization: Vertex cover problem

NASA Astrophysics Data System (ADS)

Zhao, Jin-Hua; Zhou, Hai-Jun

2014-07-01

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

A new method of search design of refrigerating systems containing a liquid and gaseous working medium based on the graph model of the physical operating principle

NASA Astrophysics Data System (ADS)

Yakovlev, A. A.; Sorokin, V. S.; Mishustina, S. N.; Proidakova, N. V.; Postupaeva, S. G.

2017-01-01

The article describes a new method of search design of refrigerating systems, the basis of which is represented by a graph model of the physical operating principle based on thermodynamical description of physical processes. The mathematical model of the physical operating principle has been substantiated, and the basic abstract theorems relatively semantic load applied to nodes and edges of the graph have been represented. The necessity and the physical operating principle, sufficient for the given model and intended for the considered device class, were demonstrated by the example of a vapour-compression refrigerating plant. The example of obtaining a multitude of engineering solutions of a vapour-compression refrigerating plant has been considered.

REVIEWS OF TOPICAL PROBLEMS: Analytic calculations on digital computers for applications in physics and mathematics

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Tarasov, O. V.; Shirkov, Dmitrii V.

1980-01-01

The present state of analytic calculations on computers is reviewed. Several programming systems which are used for analytic calculations are discussed: SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK, MACSYMA, etc. It is shown that these systems can be used to solve a wide range of problems in physics and mathematics. Some physical applications are discussed in celestial mechanics, the general theory of relativity, quantum field theory, plasma physics, hydrodynamics, atomic and molecular physics, and quantum chemistry. Some mathematical applications which are discussed are evaluating indefinite integrals, solving differential equations, and analyzing mathematical expressions. This review is addressed to physicists and mathematicians working in a wide range of fields.

An Introduction to Atmospheric Physics

NASA Astrophysics Data System (ADS)

Andrews, David G.

2000-09-01

This advanced undergraduate textbook clearly details how physics can be used to understand many important aspects of atmospheric behavior. Coverage presents a broad overview of atmospheric physics, including atmospheric thermodynamics, radiative transfer, atmospheric fluid dynamics and elementary atmospheric chemistry. Armed with an understanding of these topics, the interested student will be able to grasp the essential physics behind issues of current concern, such as the enhanced greenhouse effect and associated questions of climate change, the Antarctic ozone hole and global ozone depletion, as well as more familiar processes such as the formation of raindrops and the development of weather systems. This introductory textbook is ideal for advanced undergraduates studying atmospheric physics as part of physics, meteorology or environmental science courses. It will also be useful for graduate students studying atmospheric physics for the first time and for students of applied mathematics, physical chemistry and engineering who have an interest in the atmosphere.

Use of model analysis to analyse Thai students’ attitudes and approaches to physics problem solving

NASA Astrophysics Data System (ADS)

Rakkapao, S.; Prasitpong, S.

2018-03-01

This study applies the model analysis technique to explore the distribution of Thai students’ attitudes and approaches to physics problem solving and how those attitudes and approaches change as a result of different experiences in physics learning. We administered the Attitudes and Approaches to Problem Solving (AAPS) survey to over 700 Thai university students from five different levels, namely students entering science, first-year science students, and second-, third- and fourth-year physics students. We found that their inferred mental states were generally mixed. The largest gap between physics experts and all levels of the students was about the role of equations and formulas in physics problem solving, and in views towards difficult problems. Most participants of all levels believed that being able to handle the mathematics is the most important part of physics problem solving. Most students’ views did not change even though they gained experiences in physics learning.

Mathematics and Physics: The Idea of a Pre-Established Harmony

ERIC Educational Resources Information Center

Kragh, Helge

2015-01-01

For more than a century the notion of a pre-established harmony between the mathematical and physical sciences has played an important role not only in the rhetoric of mathematicians and theoretical physicists, but also as a doctrine guiding much of their research. Strongly mathematized branches of physics, such as the vortex theory of atoms…

Notes for Applied Mathematics in Trigonometry and Earth Geometry/Navigation

ERIC Educational Resources Information Center

Faulkner, Peter

2004-01-01

As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that…

An epistemic framing analysis of upper level physics students' use of mathematics

NASA Astrophysics Data System (ADS)

Bing, Thomas Joseph

Mathematics is central to a professional physicist's work and, by extension, to a physics student's studies. It provides a language for abstraction, definition, computation, and connection to physical reality. This power of mathematics in physics is also the source of many of the difficulties it presents students. Simply put, many different activities could all be described as "using math in physics". Expertise entails a complicated coordination of these various activities. This work examines the many different kinds of thinking that are all facets of the use of mathematics in physics. It uses an epistemological lens, one that looks at the type of explanation a student presently sees as appropriate, to analyze the mathematical thinking of upper level physics undergraduates. Sometimes a student will turn to a detailed calculation to produce or justify an answer. Other times a physical argument is explicitly connected to the mathematics at hand. Still other times quoting a definition is seen as sufficient, and so on. Local coherencies evolve in students' thought around these various types of mathematical justifications. We use the cognitive process of framing to model students' navigation of these various facets of math use in physics. We first demonstrate several common framings observed in our students' mathematical thought and give several examples of each. Armed with this analysis tool, we then give several examples of how this framing analysis can be used to address a research question. We consider what effects, if any, a powerful symbolic calculator has on students' thinking. We also consider how to characterize growing expertise among physics students. Framing offers a lens for analysis that is a natural fit for these sample research questions. To active physics education researchers, the framing analysis presented in this dissertation can provide a useful tool for addressing other research questions. To physics teachers, we present this analysis so that it may make them more explicitly aware of the various types of reasoning, and the dynamics among them, that students employ in our physics classes. This awareness will help us better hear students' arguments and respond appropriately.

Mathematics in chemistry: indeterminate forms and their meaning

NASA Astrophysics Data System (ADS)

Segurado, Manuel A. P.; Silva, Margarida F. B.; Castro, Rita

2011-07-01

The mathematical language and its tools are complementary to the formalism in chemistry, in particular at an advanced level. It is thus crucial, for its understanding, that students acquire a solid knowledge in Calculus and that they know how to apply it. The frequent occurrence of indeterminate forms in multiple areas, particularly in Physical Chemistry, justifies the need to properly understand the limiting process in such cases. This article emphasizes the importance of the L'Hôpital's rule as a practical tool, although often neglected, to obtain the more common indeterminate limits, through the use of some specific examples as the radioactive decay, spectrophotometric error, Planck's radiation law, second-order kinetics, or consecutive reactions.

The mathematics of virus shell assembly. Progress report 1995--1996

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berger, B.

1996-08-01

This research focuses on applying computational and mathematical techniques to problems in biology, and more specifically to problems in protein folding. Significant progress has been made in the following areas relating to virus shell assembly: the local rules theory has been further developed; development has begun on a second-generation simulator which provides a more physically realistic model of assembly, collaborative efforts have continued with an experimental biologist to verify and inspire the local rules theory; an investigation has been initiated into the mechanics of virus shell assembly; laboratory experiments have been conducted on bacteriophage T4 which verify that the previouslymore » believed structure for the core may be incorrect.« less

Superposition Quantification

NASA Astrophysics Data System (ADS)

Chang, Li-Na; Luo, Shun-Long; Sun, Yuan

2017-11-01

The principle of superposition is universal and lies at the heart of quantum theory. Although ever since the inception of quantum mechanics a century ago, superposition has occupied a central and pivotal place, rigorous and systematic studies of the quantification issue have attracted significant interests only in recent years, and many related problems remain to be investigated. In this work we introduce a figure of merit which quantifies superposition from an intuitive and direct perspective, investigate its fundamental properties, connect it to some coherence measures, illustrate it through several examples, and apply it to analyze wave-particle duality. Supported by Science Challenge Project under Grant No. TZ2016002, Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing, Key Laboratory of Random Complex Structures and Data Science, Chinese Academy of Sciences, Grant under No. 2008DP173182

Anaerobic Threshold by Mathematical Model in Healthy and Post-Myocardial Infarction Men.

PubMed

Novais, L D; Silva, E; Simões, R P; Sakabe, D I; Martins, L E B; Oliveira, L; Diniz, C A R; Gallo, L; Catai, A M

2016-02-01

The aim of this study was to determine the anaerobic threshold (AT) in a population of healthy and post-myocardial infarction men by applying Hinkley's mathematical method and comparing its performance to the ventilatory visual method. This mathematical model, in lieu of observer-dependent visual determination, can produce more reliable results due to the uniformity of the procedure. 17 middle-aged men (55±3 years) were studied in 2 groups: 9 healthy men (54±2 years); and 8 men with previous myocardial infarction (57±3 years). All subjects underwent an incremental ramp exercise test until physical exhaustion. Breath-by-breath ventilatory variables, heart rate (HR), and vastus lateralis surface electromyography (sEMG) signal were collected throughout the test. Carbon dioxide output (V˙CO2), HR, and sEMG were studied, and the AT determination methods were compared using correlation coefficients and Bland-Altman plots. Parametric statistical tests were applied with significance level set at 5%. No significant differences were found in the HR, sEMG, and ventilatory variables at AT between the different methods, such as the intensity of effort relative to AT. Moreover, important concordance and significant correlations were observed between the methods. We concluded that the mathematical model was suitable for detecting the AT in both healthy and myocardial infarction subjects. © Georg Thieme Verlag KG Stuttgart · New York.

Magic in the machine: a computational magician's assistant.

PubMed

Williams, Howard; McOwan, Peter W

2014-01-01

A human magician blends science, psychology, and performance to create a magical effect. In this paper we explore what can be achieved when that human intelligence is replaced or assisted by machine intelligence. Magical effects are all in some form based on hidden mathematical, scientific, or psychological principles; often the parameters controlling these underpinning techniques are hard for a magician to blend to maximize the magical effect required. The complexity is often caused by interacting and often conflicting physical and psychological constraints that need to be optimally balanced. Normally this tuning is done by trial and error, combined with human intuitions. Here we focus on applying Artificial Intelligence methods to the creation and optimization of magic tricks exploiting mathematical principles. We use experimentally derived data about particular perceptual and cognitive features, combined with a model of the underlying mathematical process to provide a psychologically valid metric to allow optimization of magical impact. In the paper we introduce our optimization methodology and describe how it can be flexibly applied to a range of different types of mathematics based tricks. We also provide two case studies as exemplars of the methodology at work: a magical jigsaw, and a mind reading card trick effect. We evaluate each trick created through testing in laboratory and public performances, and further demonstrate the real world efficacy of our approach for professional performers through sales of the tricks in a reputable magic shop in London.

The Challenge of Learning Physics Before Mathematics: A Case Study of Curriculum Change in Taiwan

NASA Astrophysics Data System (ADS)

Chiu, Mei-Shiu

2016-12-01

The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without prior learning experiences of trigonometry in mathematics. The perspectives of three curriculum developers, 22 mathematics and physics teachers, two principals, and 45 science students were obtained by interview. The results of qualitative data analysis revealed six challenges and suggested likely solutions. The national level includes political and social challenges, resolved by respecting teachers as professionals; the teacher level includes knowledge and teaching challenges, resolved by increasing teacher trans-literal capacities; and the student level includes learning and justice challenges, resolved by focusing on students' diverse developments in cross-domain learning.

Constructing and predicting solitary pattern solutions for nonlinear time-fractional dispersive partial differential equations

NASA Astrophysics Data System (ADS)

Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher

2015-07-01

Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.

Implementing 'The Math You Need' in an Introductory Physical Geology Course at California State University East Bay

NASA Astrophysics Data System (ADS)

Moran, J. E.

2011-12-01

The wide range of abilities in the student population at California State University East Bay, with a significant fraction of students under-prepared and requiring mathematics remediation, is a challenge to including mathematical concepts and exercises in our introductory geoscience courses. Student expectations that a geoscience course will not include quantitative work may result in math-phobics choosing the course and resisting quantitative work when presented with it. Introductory courses that are required for Geology and Environmental Science majors are also designated as General Education, which gives rise to a student group with a wide range of abilities and expectations. This presentation will focus on implementation of a series of online math tutorials for students in introductory geoscience courses called 'The Math You Need' (TMYN; http://serc.carleton.edu/mathyouneed/index.html). The program is implemented in a Physical Geology course, in which 2/3 of the students are typically non-majors. The Physical Geology course has a three hour lab each week and the lab exercises and lab manual offer several opportunities for application of TMYN. Many of the lab exercises include graphing, profiling, working with map scales, converting units, or using equations to calculate some parameter or solve for an unknown. Six TMYN modules covering topics using density calculations as applied to mineral properties and isostasy, graphing as applied to rock properties, earthquake location, and radiometric dating, and calculation of rates as applied to plate movement, stream discharge, and groundwater flow, are assigned as pre-labs to be completed before lab classes. TMYN skills are reinforced during lectures and lab exercises, as close in time as possible to students' exposure via TMYN. Pre- and post-tests give a measure of the effectiveness of TMYN in improving students' quantitative literacy.

Topological data analysis (TDA) applied to reveal pedogenetic principles of European topsoil system.

PubMed

Savic, Aleksandar; Toth, Gergely; Duponchel, Ludovic

2017-05-15

Recent developments in applied mathematics are bringing new tools that are capable to synthesize knowledge in various disciplines, and help in finding hidden relationships between variables. One such technique is topological data analysis (TDA), a fusion of classical exploration techniques such as principal component analysis (PCA), and a topological point of view applied to clustering of results. Various phenomena have already received new interpretations thanks to TDA, from the proper choice of sport teams to cancer treatments. For the first time, this technique has been applied in soil science, to show the interaction between physical and chemical soil attributes and main soil-forming factors, such as climate and land use. The topsoil data set of the Land Use/Land Cover Area Frame survey (LUCAS) was used as a comprehensive database that consists of approximately 20,000 samples, each described by 12 physical and chemical parameters. After the application of TDA, results obtained were cross-checked against known grouping parameters including five types of land cover, nine types of climate and the organic carbon content of soil. Some of the grouping characteristics observed using standard approaches were confirmed by TDA (e.g., organic carbon content) but novel subtle relationships (e.g., magnitude of anthropogenic effect in soil formation), were discovered as well. The importance of this finding is that TDA is a unique mathematical technique capable of extracting complex relations hidden in soil science data sets, giving the opportunity to see the influence of physicochemical, biotic and abiotic factors on topsoil formation through fresh eyes. Copyright © 2017 Elsevier B.V. All rights reserved.

Computer analysis of ATR-FTIR spectra of paint samples for forensic purposes

NASA Astrophysics Data System (ADS)

Szafarska, Małgorzata; Woźniakiewicz, Michał; Pilch, Mariusz; Zięba-Palus, Janina; Kościelniak, Paweł

2009-04-01

A method of subtraction and normalization of IR spectra (MSN-IR) was developed and successfully applied to extract mathematically the pure paint spectrum from the spectrum of paint coat on different bases, both acquired by the Attenuated Total Reflectance Fourier Transform Infrared (ATR-FTIR) technique. The method consists of several stages encompassing several normalization and subtraction processes. The similarity of the spectrum obtained with the reference spectrum was estimated by means of the normalized Manhattan distance. The utility and performance of the method proposed were tested by examination of five different paints sprayed on plastic (polyester) foil and on fabric materials (cotton). It was found that the numerical algorithm applied is able - in contrast to other mathematical approaches conventionally used for the same aim - to reconstruct a pure paint IR spectrum effectively without a loss of chemical information provided. The approach allows the physical separation of a paint from a base to be avoided, hence a time and work-load of analysis to be considerably reduced. The results obtained prove that the method can be considered as a useful tool which can be applied to forensic purposes.

Obstacles Related to Structuring for Mathematization Encountered by Students When Solving Physics Problems

ERIC Educational Resources Information Center

Niss, Martin

2017-01-01

This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called "structuring for mathematization," where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four…

Problem Solving in the Borderland between Mathematics and Physics

ERIC Educational Resources Information Center

Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas

2017-01-01

The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it focuses on solving so-called unformalized problems,…

Students' difficulties with vector calculus in electrodynamics

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; De Cock, Mieke

2015-12-01

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven encounter with the divergence and curl of a vector field in mathematical and physical contexts. We have found that they are quite skilled at doing calculations, but struggle with interpreting graphical representations of vector fields and applying vector calculus to physical situations. We have found strong indications that traditional instruction is not sufficient for our students to fully understand the meaning and power of Maxwell's equations in electrodynamics.

Noise elimination algorithm for modal analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bao, X. X., E-mail: baoxingxian@upc.edu.cn; Li, C. L.; Xiong, C. B.

2015-07-27

Modal analysis is an ongoing interdisciplinary physical issue. Modal parameters estimation is applied to determine the dynamic characteristics of structures under vibration excitation. Modal analysis is more challenging for the measured vibration response signals are contaminated with noise. This study develops a mathematical algorithm of structured low rank approximation combined with the complex exponential method to estimate the modal parameters. Physical experiments using a steel cantilever beam with ten accelerometers mounted, excited by an impulse load, demonstrate that this method can significantly eliminate noise from measured signals and accurately identify the modal frequencies and damping ratios. This study provides amore » fundamental mechanism of noise elimination using structured low rank approximation in physical fields.« less

What is the problem in problem-based learning in higher education mathematics

NASA Astrophysics Data System (ADS)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

Evaluating High School Students' Conceptions of the Relationship between Mathematics and Physics: Development of a Questionnaire

ERIC Educational Resources Information Center

Kapucu, S.; Öçal, M. F.; Simsek, M.

2016-01-01

The purposes of this study were (1) to develop a questionnaire measuring high school students' conceptions of the relationship between mathematics and physics, (2) and to determine the students' conceptions of the relationship between mathematics and physics. A total of 718 high school students (343 male, 375 female) participated in this study.…

Shadows constructing a relationship between light and color pigments by physical and mathematical perspectives

NASA Astrophysics Data System (ADS)

Yurumezoglu, Kemal; Karabey, Burak; Yigit Koyunkaya, Melike

2017-03-01

Full shadows, partial shadows and multilayer shadows are explained based on the phenomenon of the linear dispersion of light. This paper focuses on progressing the understanding of shadows from physical and mathematical perspectives. A significant relationship between light and color pigments is demonstrated with the help of the concept of sets. This integration of physical and mathematical reasoning not only manages an operational approach to the concept of shadows, it also outputs a model that can be used in science, technology, engineering and mathematics (STEM) curricula by providing a concrete and physical example for abstract concept of the empty set.

Predicting Physics Achievement: Attitude towards Physics, Self-Efficacy of Learning Physics, and Mathematics Achievement

ERIC Educational Resources Information Center

Kapucu, Serkan

2017-01-01

This study aims to explore the relationships among Turkish high school students' attitude towards physics, self-efficacy of learning physics, mathematics achievement, and physics achievement. To investigate the relationships, a unique questionnaire that identifies the attitude, self-efficacy and achievements were delivered to a total of 301 high…

Shift scheduling model considering workload and worker’s preference for security department

NASA Astrophysics Data System (ADS)

Herawati, A.; Yuniartha, D. R.; Purnama, I. L. I.; Dewi, LT

2018-04-01

Security department operates for 24 hours and applies shift scheduling to organize its workers as well as in hotel industry. This research has been conducted to develop shift scheduling model considering the workers physical workload using rating of perceived exertion (RPE) Borg’s Scale and workers’ preference to accommodate schedule flexibility. The mathematic model is developed in integer linear programming and results optimal solution for simple problem. Resulting shift schedule of the developed model has equally distribution shift allocation among workers to balance the physical workload and give flexibility for workers in working hours arrangement.

History of Modern Applied Mathematics in Mathematics Education

ERIC Educational Resources Information Center

Jankvist, Uffe Thomas

2009-01-01

This article discusses the integration of history of modern applied mathematics in mathematics education as well as the possible teaching and learning benefits of introducing a newer history of mathematics over an old(er) one--something that seems to be done most often when integrating history. Three cases of the history of modern applied…

Discussing Perception, Determining Provision: Teachers' Perspectives on the Applied Options of A-Level Mathematics

ERIC Educational Resources Information Center

Ward-Penny, Robert; Johnston-Wilder, Sue; Johnston-Wilder, Peter

2013-01-01

One-third of the current A-level mathematics curriculum is determined by choice, constructed out of "applied mathematics" modules in mechanics, statistics and decision mathematics. Although this choice arguably involves the most sizeable instance of choice in the current English school mathematics curriculum, and it has a significant…

Girls Talk Math - Engaging Girls Through Math Media

NASA Astrophysics Data System (ADS)

Bernardi, Francesca; Morgan, Katrina

2017-11-01

``Girls Talk Math: Engaging Girls through Math Media'' is a free two-week long summer day camp for high-school girls in the Triangle area of NC. This past June the camp had its second run thanks to renewed funding from the Mathematical Association of America Tensor Women and Mathematics Grant. The camp involved 35 local high-school students who identify as female. Campers complete challenging problem sets and research the life of a female scientist who worked on similar problems. They report their work in a blog post and record a podcast about the scientist they researched. The curriculum has been developed by Mathematics graduate students at UNC from an inquiry based learning perspective; problem sets topics include some theoretical mathematics, but also more applied physics-based material. Campers worked on fluid dynamics, special relativity, and quantum mechanics problem sets which included experiments. The camp has received positive feedback from the local community and the second run saw a large increase in the number of participants. The program is evaluated using pre and post surveys, which measure campers' confidence and interest in pursuing higher level courses in STEM. The results from the past two summers have been encouraging. Mathematical Association of America Tensor Women and Mathematics Grant.

Energy regeneration model of self-consistent field of electron beams into electric power*

NASA Astrophysics Data System (ADS)

Kazmin, B. N.; Ryzhov, D. R.; Trifanov, I. V.; Snezhko, A. A.; Savelyeva, M. V.

2016-04-01

We consider physic-mathematical models of electric processes in electron beams, conversion of beam parameters into electric power values and their transformation into users’ electric power grid (onboard spacecraft network). We perform computer simulation validating high energy efficiency of the studied processes to be applied in the electric power technology to produce the power as well as electric power plants and propulsion installation in the spacecraft.

Frontiers in Applied and Computational Mathematics 05’

DTIC Science & Technology

2005-03-01

dynamics, forcing subsets to have the same oscillation numbers and interleaving spiking times . Our analysis follows the theory of coupled systems of...continuum is described by a continuous- time stochastic process, as are their internal dynamics. Soluble factors, such as cytokines, are represent- ed...scale of a partide pas- sage time through the reaction zone. Both are realistic for many systems of physical interest. A higher order theory includes

Hydrodynamic equations for electrons in graphene obtained from the maximum entropy principle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barletti, Luigi, E-mail: luigi.barletti@unifi.it

2014-08-15

The maximum entropy principle is applied to the formal derivation of isothermal, Euler-like equations for semiclassical fermions (electrons and holes) in graphene. After proving general mathematical properties of the equations so obtained, their asymptotic form corresponding to significant physical regimes is investigated. In particular, the diffusive regime, the Maxwell-Boltzmann regime (high temperature), the collimation regime and the degenerate gas limit (vanishing temperature) are considered.

Marriages of mathematics and physics: A challenge for biology.

PubMed

Islami, Arezoo; Longo, Giuseppe

2017-12-01

The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the mathematical practices and their foundations. Yet, the collapse of Euclidean certitudes, of over 2300 years, and the crisis in the mathematical analysis of the 19th century, led to the exclusion of "geometric judgments" from the foundations of Mathematics. After the success and the limits of the logico-formal analysis, it is necessary to broaden our foundational tools and re-examine the interactions with natural sciences. In particular, the way the geometric and algebraic approaches organize knowledge is analyzed as a cross-disciplinary and cross-cultural issue and will be examined in Mathematical Physics and Biology. We finally discuss how the current notions of mathematical (phase) "space" should be revisited for the purposes of life sciences. Copyright © 2017. Published by Elsevier Ltd.

Methods of Mathematical and Computational Physics for Industry, Science, and Technology

NASA Astrophysics Data System (ADS)

Melnik, Roderick V. N.; Voss, Frands

2006-11-01

Many industrial problems provide scientists with important and challenging problems that need to be solved today rather than tomorrow. The key role of mathematical physics, modelling, and computational methodologies in addressing such problems continues to increase. Science has never been exogenous to applied research. Gigantic ships and steam engines, repeating catapult of Dionysius and the Antikythera `computer' invented around 80BC are just a few examples demonstrating a profound link between theoretical and applied science in the ancient world. Nowadays, many industrial problems are typically approached by groups of researchers who are working as a team bringing their expertise to the success of the entire enterprise. Since the late 1960s several groups of European mathematicians and scientists have started organizing regular meetings, seeking new challenges from industry and contributing to the solution of important industrial problems. In particular, this often took the format of week-long workshops originally initiated by the Oxford Study Groups with Industry in 1968. Such workshops are now held in many European countries (typically under the auspices of the European Study Groups with Industry - ESGI), as well as in Australia, Canada, the United States, and other countries around the world. Problems given by industrial partners are sometimes very difficult to complete within a week. However, during a week of brainstorming activities these problems inevitably stimulate developing fruitful new ideas, new approaches, and new collaborations. At the same time, there are cases where as soon as the problem is formulated mathematically, it is relatively easy to solve. Hence, putting the industrial problem into a mathematical framework, based on physical laws, often provides a key element to the success. In addition to this important first step, the value in such cases is the real, practical applicability of the results obtained for an industrial partner who presents the problem. Under both outlined scenarios, scientists and mathematicians are provided with an opportunity to challenge themselves with real-world problems and to work together in a team on important industrial issues. This issue is a result of selected contributions by participants of the meeting that took place in the Sønderborg area of Denmark, one of the most important centers for information technology, telecommunication and electronics in the country. The meeting was hosted by the University of Southern Denmark in a picturesque area of Southern Jutland. It brought together about 65 participants, among whom were professional mathematicians, engineers, physicists, and industrial participants. The meeting was a truly international one, with delegates from four major Danish Universities, the UK, Norway, Italy, Czech Republic, Turkey, China, Germany, Latvia, Canada, the United States, and Finland. Five challenging projects were presented by leading industrial companies, including Grundfos, Danfoss Industrial Control, Unisensor, and Danfoss Flow Division (now Siemens). The meeting featured also the Mathematics for Industry Workshop with several distinguished international speakers. This volume of Journal of Physics: Conference Series on `Methods of Mathematical and Computational Physics for Industry, Science, and Technology' contains contributions from some of the participants of the workshop as well as the papers produced as a result of collaborative efforts with the above mentioned industrial companies. We would like to thank all authors and participants for their contributions and for bearing with us during the review process and preparation of this issue. We thank also all our referees for their timely and detailed reports. The publication of the proceedings of this meeting in Denmark was delayed due to problems with a previous publisher. We are very grateful that Journal of Physics: Conference Series kindly agreed to publish the proceedings rapidly at this late stage. As industrial problems become increasingly multidisciplinary, their successful solutions are often contingent on effective collaborative efforts between scientists, mathematicians, industrialists, and engineers. This volume has provided several examples of such collaborative efforts in the context of real-world industrial problems along with the analysis of important physics-based mathematical models applicable in a range of industrial contexts. Roderick V N Melnik, Professor of Mathematical Modelling, Syddansk Universitet (Denmark) and Professor and Canada Research Chair, Wilfrid Laurier University, Waterloo, Canada E-mail: rmelnik@wlu.ca Frands Voss, Director of the Mads Clausen Institute, Syddansk Universitet (Denmark)

A Guided Tour of Mathematical Methods - 2nd Edition

NASA Astrophysics Data System (ADS)

Snieder, Roel

2004-09-01

Mathematical methods are essential tools for all physical scientists. This second edition provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates, and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks. All the material is presented in the form of problems Mathematical insights are gained by getting the reader to develop answers themselves Many applications of the mathematics are given

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

The Mathematics of Four or More N-Localizers for Stereotactic Neurosurgery.

PubMed

Brown, Russell A

2015-10-13

The mathematics that were originally developed for the N-localizer apply to three N-localizers that produce three sets of fiducials in a tomographic image. Some applications of the N-localizer use four N-localizers that produce four sets of fiducials; however, the mathematics that apply to three sets of fiducials do not apply to four sets of fiducials. This article presents mathematics that apply to four or more sets of fiducials that all lie within one planar tomographic image. In addition, these mathematics are extended to apply to four or more fiducials that do not all lie within one planar tomographic image, as may be the case with magnetic resonance (MR) imaging where a volume is imaged instead of a series of planar tomographic images. Whether applied to a planar image or a volume image, the mathematics of four or more N-localizers provide a statistical measure of the quality of the image data that may be influenced by factors, such as the nonlinear distortion of MR images.

The Real and the Mathematical in Quantum Modeling: From Principles to Models and from Models to Principles

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2017-06-01

The history of mathematical modeling outside physics has been dominated by the use of classical mathematical models, C-models, primarily those of a probabilistic or statistical nature. More recently, however, quantum mathematical models, Q-models, based in the mathematical formalism of quantum theory have become more prominent in psychology, economics, and decision science. The use of Q-models in these fields remains controversial, in part because it is not entirely clear whether Q-models are necessary for dealing with the phenomena in question or whether C-models would still suffice. My aim, however, is not to assess the necessity of Q-models in these fields, but instead to reflect on what the possible applicability of Q-models may tell us about the corresponding phenomena there, vis-à-vis quantum phenomena in physics. In order to do so, I shall first discuss the key reasons for the use of Q-models in physics. In particular, I shall examine the fundamental principles that led to the development of quantum mechanics. Then I shall consider a possible role of similar principles in using Q-models outside physics. Psychology, economics, and decision science borrow already available Q-models from quantum theory, rather than derive them from their own internal principles, while quantum mechanics was derived from such principles, because there was no readily available mathematical model to handle quantum phenomena, although the mathematics ultimately used in quantum did in fact exist then. I shall argue, however, that the principle perspective on mathematical modeling outside physics might help us to understand better the role of Q-models in these fields and possibly to envision new models, conceptually analogous to but mathematically different from those of quantum theory, helpful or even necessary there or in physics itself. I shall suggest one possible type of such models, singularized probabilistic, SP, models, some of which are time-dependent, TDSP-models. The necessity of using such models may change the nature of mathematical modeling in science and, thus, the nature of science, as it happened in the case of Q-models, which not only led to a revolutionary transformation of physics but also opened new possibilities for scientific thinking and mathematical modeling beyond physics.

Integrating Mathematics into the Introductory Biology Laboratory Course

ERIC Educational Resources Information Center

White, James D.; Carpenter, Jenna P.

2008-01-01

Louisiana Tech University has an integrated science curriculum for its mathematics, chemistry, physics, computer science, biology-research track and secondary mathematics and science education majors. The curriculum focuses on the calculus sequence and introductory labs in biology, physics, and chemistry. In the introductory biology laboratory…

TIMSS Advanced 2008 Assessment Frameworks

ERIC Educational Resources Information Center

Garden, Robert A.; Lie, Svein; Robitaille, David F.; Angell, Carl; Martin, Michael O.; Mullis, Ina V.S.; Foy, Pierre; Arora, Alka

2006-01-01

Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…

A Mathematics Entrance Exam for General (Non-Majors) Physics

ERIC Educational Resources Information Center

Chediak, Alex

2010-01-01

In a previous issue of "The Physics Teacher", John Hubisz explained how a mathematics background check has been used at three different colleges to determine the appropriate physics sequence for incoming students. Based on their performance, students are placed into either calculus-based physics (CBP), algebra-trig physics (ATP), or a year of…

Advancement of understanding in physical science and reduction of mathematical anxiety through the use of supplemental mathematics material

NASA Astrophysics Data System (ADS)

Roberson, James Chadwick

The purpose of this study was to determine if supplementary mathematics materials (created to be complementary to a physical science course) could provide a significant change in the attitudes and performance of the students involved. The supplementary text was provided in the form of a booklet. Participants were students in a physical science class. Students were given surveys to evaluate existing knowledge of physical science, mathematics skill, and mathematics anxiety in the context of a science class. Students were divided into control and experimental groups by lab section, with the experimental group receiving a supplemental booklet. At the end of the semester, another anxiety survey was given. The anxiety surveys and test grades were compared between groups. Anxiety scores were compared between the beginning and end of the semester within each group. Too few students reported using the booklets for a reliable statistical comparison (of grades) to be made. A statistically significant difference in mathematics anxiety levels was found between the groups.

The reasonable effectiveness of mathematics in the natural sciences

NASA Astrophysics Data System (ADS)

Harvey, Alex

2011-12-01

Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.

Introductory Physics Students' Physics and Mathematics Epistemologies

ERIC Educational Resources Information Center

Scanlon, Erin M.

2017-01-01

The purpose of this three study dissertation is to investigate why students are enrolled in introductory physics courses experience difficulties in being successful; one possible source of their difficulties is related to their epistemology. In order to investigate students' epistemologies about mathematics and physics, students were observed…

Quantum-like Modeling of Cognition

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2015-09-01

This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).

Students' Mathematical Modeling of Motion

ERIC Educational Resources Information Center

Marshall, Jill A.; Carrejo, David J.

2008-01-01

We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…

Research in progress in applied mathematics, numerical analysis, and computer science

NASA Technical Reports Server (NTRS)

1990-01-01

Research conducted at the Institute in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized. The Institute conducts unclassified basic research in applied mathematics in order to extend and improve problem solving capabilities in science and engineering, particularly in aeronautics and space.

Changes in Elementary Mathematics Teachers' Understanding of Cognitive Demand: When Adapting, Creating, and Using Mathematical Performance Tasks

ERIC Educational Resources Information Center

Jamieson, Thad Spencer

2015-01-01

The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…

Simulations of string vibrations with boundary conditions of third kind using the functional transformation method

NASA Astrophysics Data System (ADS)

Trautmann, L.; Petrausch, S.; Bauer, M.

2005-09-01

The functional transformation method (FTM) is an established mathematical method for accurate simulation of multidimensional physical systems from various fields of science, including optics, heat and mass transfer, electrical engineering, and acoustics. It is a frequency-domain method based on the decomposition into eigenvectors and eigenfrequencies of the underlying physical problem. In this article, the FTM is applied to real-time simulations of vibrating strings which are ideally fixed at one end while the fixing at the other end is modeled by a frequency-dependent input impedance. Thus, boundary conditions of third kind are applied to the model at the end fixed with the input impedance. It is shown that accurate and stable simulations are achieved with nearly the same computational cost as with strings ideally fixed at both ends.

Analysis of entry of additional energy to gunpowder in electrothermal chemical shot

NASA Astrophysics Data System (ADS)

Burkin, Viktor; Ishchenko, Alexandr; Kasimov, Vladimir; Samorokova, Nina; Sidorov, Aleksey

2017-11-01

In the article two series of ballistic experiments conducted according to the scheme of electrothermal chemical control of ballistic parameters of the shot at the Research Institute of Applied Mathematics and Mechanics of Tomsk State University (RIAMM TSU, Russia) are considered. The experimental part of the work is described. The analysis of the electro physical data of ballistic experiments is carried out. A methodical approach that allows to take into account the entry of an electric discharge plasma in a gunpowder in the mathematical model of internal ballistic processes in barrel systems is proposed and tested. Under the conditions of these experiments, the effects of various characteristics of the plasmatron on the nature of the energy entry are estimated.

The stability issues in problems of mathematical modeling

NASA Astrophysics Data System (ADS)

Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

2018-03-01

In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

Bridging the Gulf between Formal Calculus and Physical Reasoning.

ERIC Educational Resources Information Center

Van Der Meer, A.

1980-01-01

Some ways to link calculus instruction with the mathematical models used in physics courses are presented. The activity of modelling is presented as a major tool in synchronizing physics and mathematics instruction in undergraduate engineering programs. (MP)

Transforming a fourth year modern optics course using a deliberate practice framework

NASA Astrophysics Data System (ADS)

Jones, David J.; Madison, Kirk W.; Wieman, Carl E.

2015-12-01

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present a study of active learning pedagogies in an upper-division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15% improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier transforms, partial differential equations, and vector calculus), we expect the transformation process could be applied to most upper-division physics courses having a similar mathematical base.

The Trouble with Trig

ERIC Educational Resources Information Center

Galle, Gillian; Meredith, Dawn

2014-01-01

A few years ago we began to revamp our introductory physics course for life science students. We knew that this cohort would be less prepared and less adventurous mathematically than engineering, physical science, or mathematics majors. Moreover, from our own experience and the mathematics education literature, we knew that trigonometry would be…

Applied Mathematics in the Undergraduate Curriculum.

ERIC Educational Resources Information Center

Committee on the Undergraduate Program in Mathematics, Berkeley, CA.

After considering the growth in the use of mathematics in the past 25 years, this report makes four major recommendations regarding the undergraduate curriculum: (1) The mathematics department should offer a course or two in applied mathematics which treat some realistic situations completely, including the steps of problem formulation, model…

Stability Analysis of Finite Difference Schemes for Hyperbolic Systems, and Problems in Applied and Computational Linear Algebra.

DTIC Science & Technology

FINITE DIFFERENCE THEORY, * LINEAR ALGEBRA , APPLIED MATHEMATICS, APPROXIMATION(MATHEMATICS), BOUNDARY VALUE PROBLEMS, COMPUTATIONS, HYPERBOLAS, MATHEMATICAL MODELS, NUMERICAL ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS, STABILITY.

Study of coupled nonlinear partial differential equations for finding exact analytical solutions.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Koppelaar, H

2015-07-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Transactions of the Army Conference on Applied Mathematics and Computing (1st) Held at Washington, DC on 9-11 May 1983

DTIC Science & Technology

1984-02-01

I . . . . . . An Introduction to Geometric Programming Patrick D. Allen and David W. Baker . . . . . . , . . . . . . . Space and Time...Zarwyn, US-Army Electronics R & D Comhiand GEOMETRIC PROGRAMING SPACE AND TIFFE ANALYSIS IN DYNAMIC PROGRAMING ALGORITHMS Renne..tf Stizti, AkeanXa...physical and parameter space can be connected by asymptotic matching. The purpose of the asymptotic analysis is to define the simplest problems

Proceedings of the International Symposium on Multiple-Valued Logic (13th) Held at Kyoto, Japan on May 23-25, 1983.

DTIC Science & Technology

1983-05-01

would like to thank the members of the Organizing Committee of ISMVL-Japan, listed on page vii of this Proceedings, for their generous support. Hisashi ...8217 °. °- . ’. . 6% Organizing Commnittee I *Chairman: Hisashi Mine Department of Applied Mathematics and Physics Kcyoto University, Kyoto...Masayuki Kimura (Tohoku University, Japan) Tadahiro Kitahashi (Toyohashi University of Technology, Japan) Yoshiaki Koga (National Defense Academy, Japan

Educating Physicists for the 21st Century Industrial Arena

NASA Astrophysics Data System (ADS)

Levine, Alaina G.

2001-03-01

At the University of Arizona, a new Professional Master's Degree in Applied and Industrial Physics has been initiated to meet the demands of a new industrial era. A 1995 report by the National Academy of Sciences, et al, concluded, "A world of work that has become more interdisciplinary, collaborative, and global requires that we produce young people who are adaptable and flexible, as well as technically proficient." To better prepare students for this new "world of work", a new degree was launched in 2000 sponsored by the Sloan Foundation as part of a national initiative. The Professional Master's Degree in Applied and Industrial Physics educates students to 1) work in interdisciplinary teams on complex problems involving rapidly changing science and technology, 2) gain proficiency in computational techniques, 3) effectively communicate their scientific mission at all levels, and 4) understand business and legal issues associated with their scientific projects. I will discuss these goals, the roles of our industrial partners, and Arizona's parallel programs in Applied Biosciences and Mathematical Sciences.

Magic in the machine: a computational magician's assistant

PubMed Central

Williams, Howard; McOwan, Peter W.

2014-01-01

A human magician blends science, psychology, and performance to create a magical effect. In this paper we explore what can be achieved when that human intelligence is replaced or assisted by machine intelligence. Magical effects are all in some form based on hidden mathematical, scientific, or psychological principles; often the parameters controlling these underpinning techniques are hard for a magician to blend to maximize the magical effect required. The complexity is often caused by interacting and often conflicting physical and psychological constraints that need to be optimally balanced. Normally this tuning is done by trial and error, combined with human intuitions. Here we focus on applying Artificial Intelligence methods to the creation and optimization of magic tricks exploiting mathematical principles. We use experimentally derived data about particular perceptual and cognitive features, combined with a model of the underlying mathematical process to provide a psychologically valid metric to allow optimization of magical impact. In the paper we introduce our optimization methodology and describe how it can be flexibly applied to a range of different types of mathematics based tricks. We also provide two case studies as exemplars of the methodology at work: a magical jigsaw, and a mind reading card trick effect. We evaluate each trick created through testing in laboratory and public performances, and further demonstrate the real world efficacy of our approach for professional performers through sales of the tricks in a reputable magic shop in London. PMID:25452736

Students’ epistemic understanding of mathematical derivations in physics

NASA Astrophysics Data System (ADS)

Sirnoorkar, Amogh; Mazumdar, Anwesh; Kumar, Arvind

2017-01-01

We propose an epistemic measure of physics in terms of the ability to discriminate between the purely mathematical, physical (i.e. dependent on empirical inputs) and nominal (i.e. empty of mathematical or physical content) propositions appearing in a typical derivation in physics. The measure can be relevant in understanding the maths-physics link hurdles among college students. To illustrate the idea, we construct a tool for a familiar derivation (involving specific heats of an ideal gas), and use it for a sample of students from three different institutes. The reliability of the tool is examined. The results indicate, as intuitively expected, that epistemic clarity correlates with content clarity. Data yield several significant trends on the extent and kinds of epistemic pitfalls prevalent among physics undergraduates.

Women Physicists in Academia

NASA Astrophysics Data System (ADS)

Berrah, Nora

2010-02-01

The last decade marked the emergence of several important studies and workshops worldwide that focused attention on women in science, technology, engineering and mathematics (STEM). The Committee on the Status of Women in Physics (CSWP) of the American Physical Society (APS) is very active in organizing national workshops and follow up ``conversations'' with physics departments and national laboratories [1,2] to address the gender gap in the field of physics. The International Union of Pure and Applied Physics (IUPAP) is also very devoted to this issue, and the US is involved by contributing our lesson learned and our plans to increase the number of women in physics. In the US, our goal of doubling the number of women in physics by 2022 is ambitious but could be achieved. I will present the present status on this issue and our plans for the future. [4pt] [1] http://www.aps.org/programs/women/workshops/gender-equity/index.cfm [0pt] [2] Report, ``Gender Equity: Strengthening the Physics Enterprise in Universities and National Laboratories'', 2007. )

Obstacles to Mathematization in Physics: The Case of the Differential

ERIC Educational Resources Information Center

López-Gay, R.; Martinez Sáez, J.; Martinez Torregrosa, J.

2015-01-01

The process of the mathematization of physical situations through differential calculus requires an understanding of the justification for and the meaning of the differential in the context of physics. In this work, four different conceptions about the differential in physics are identified and assessed according to their utility for the…

Effects of Vigorous Intensity Physical Activity on Mathematics Test Performance

ERIC Educational Resources Information Center

Phillips, David S.; Hannon, James C.; Castelli, Darla M.

2015-01-01

The effect of an acute bout of physical activity on academic performance in school-based settings is under researched. The purpose of this study was to examine associations between a single, vigorous (70-85%) bout of physical activity completed during physical education on standardized mathematics test performance among 72, eighth grade students…

On the Role of Mathematics in Physics: A Constructivist Epistemic Perspective

ERIC Educational Resources Information Center

Quale, Andreas

2011-01-01

The association between the observable physical world and the mathematical models used in theoretical physics to describe this world is examined. Such models will frequently exhibit solutions that are "unexpected," in the sense that they describe physical situations which are different from that which the physicist may initially have had in mind…

The Effect of Manipulatives on Achievement Scores in the Middle School Mathematics Class

ERIC Educational Resources Information Center

Doias, Elaine D.

2013-01-01

When applied to mathematics education, manipulatives help students to visualize mathematical concepts and apply them to everyday situations. Interest in mathematics instruction has increased dramatically over the past two decades with the introduction of virtual manipulatives, as opposed to the concrete manipulatives that have been employed for…

Strategies to Recruit and Retain Students in Physical Science and Mathematics on a Diverse College Campus

ERIC Educational Resources Information Center

Chang, Jen-Mei; Kwon, Chuhee; Stevens, Lora; Buonora, Paul

2016-01-01

This article presents implementation details and findings of a National Science Foundation Scholarship in Science, Technology, Engineering, and Mathematics Program (S-STEM) consisting of many high-impact practices to recruit and retain students in the physical sciences and mathematics programs, particularly first-generation and underrepresented…

Increasing Mathematical Computation Skills for Students with Physical and Health Disabilities

ERIC Educational Resources Information Center

Webb, Paula

2017-01-01

Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…

Addendum to foundations of multidimensional wave field signal theory: Gaussian source function

NASA Astrophysics Data System (ADS)

Baddour, Natalie

2018-02-01

Many important physical phenomena are described by wave or diffusion-wave type equations. Recent work has shown that a transform domain signal description from linear system theory can give meaningful insight to multi-dimensional wave fields. In N. Baddour [AIP Adv. 1, 022120 (2011)], certain results were derived that are mathematically useful for the inversion of multi-dimensional Fourier transforms, but more importantly provide useful insight into how source functions are related to the resulting wave field. In this short addendum to that work, it is shown that these results can be applied with a Gaussian source function, which is often useful for modelling various physical phenomena.

[On the founders of the Institute of Mathematics and Physics, University of Bahia].

PubMed

Dias, A L

The reduced number of female students of mathematics at the University of Bahia School of Philosophy (Faculdade de Filosofia, Universidade da Bahia - FF/UBa) is quite surprising. To date, they are concentrated in areas traditionally viewed as feminine whereas men predominate in the mathematical fields. I have examined interview data from a few women who graduated in mathematics and went on to teach at the University of Bahia School of Mathematics (Faculdade de Filosofia - FF) and at the Institute of Mathematics and Physics (Instituto de Matemática e Física - IMF), where they were soon to outnumber men and constitute the majority of the mathematics teaching staff. In this study, I have investigated the course of their careers over time: from their early student days, through their time as teaching assistants and professors, and finally as founders of the Institute of Mathematics and Physics, in 1960. Special reference is made to Martha Maria de Souza Dantas, organizer of the I Brazilian Conference on Mathematics Teaching, an event which has provided the groundwork for what was to become the Institute (IMF); and to Arlete Cerqueira Lima, the mastermind behind its creation.

NSF appointment

NASA Astrophysics Data System (ADS)

President Ronald Reagan has announced his intention to nominate Richard S. Nicholson as assistant director of the National Science Foundation (NSF) for mathematical and physical sciences. Nicholson has been acting deputy director and staff director of NSF since 1983.A research chemist by training, Nicholson was an associate professor of chemistry at Michigan State University before joining NSF in 1970. He served in a number of capacities at NSF, including executive director of the National Science Board commission on precollege education in mathematics, science, and technology, deputy assistant director for the mathematical and physical sciences, and senior planning officer for mathematical and physical sciences. The nomination is subject to Senate confirmation.

Quotable Quotes in Mathematics

ERIC Educational Resources Information Center

Lo, Bruce W. N.

1983-01-01

As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)

Instrumentation for Scientific Computing in Neural Networks, Information Science, Artificial Intelligence, and Applied Mathematics.

DTIC Science & Technology

1987-10-01

include Security Classification) Instrumentation for scientific computing in neural networks, information science, artificial intelligence, and...instrumentation grant to purchase equipment for support of research in neural networks, information science, artificail intellignece , and applied mathematics...in Neural Networks, Information Science, Artificial Intelligence, and Applied Mathematics Contract AFOSR 86-0282 Principal Investigator: Stephen

Learning physical descriptors for materials science by compressed sensing

NASA Astrophysics Data System (ADS)

Ghiringhelli, Luca M.; Vybiral, Jan; Ahmetcik, Emre; Ouyang, Runhai; Levchenko, Sergey V.; Draxl, Claudia; Scheffler, Matthias

2017-02-01

The availability of big data in materials science offers new routes for analyzing materials properties and functions and achieving scientific understanding. Finding structure in these data that is not directly visible by standard tools and exploitation of the scientific information requires new and dedicated methodology based on approaches from statistical learning, compressed sensing, and other recent methods from applied mathematics, computer science, statistics, signal processing, and information science. In this paper, we explain and demonstrate a compressed-sensing based methodology for feature selection, specifically for discovering physical descriptors, i.e., physical parameters that describe the material and its properties of interest, and associated equations that explicitly and quantitatively describe those relevant properties. As showcase application and proof of concept, we describe how to build a physical model for the quantitative prediction of the crystal structure of binary compound semiconductors.

Student Reasoning about Graphs in Different Contexts

ERIC Educational Resources Information Center

Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

2016-01-01

This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the…

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts.

PubMed

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Simplification of Markov chains with infinite state space and the mathematical theory of random gene expression bursts

NASA Astrophysics Data System (ADS)

Jia, Chen

2017-09-01

Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the concept of fast transition paths and show that the effective transitions of the reduced chain can be represented as the superposition of the direct transitions and the indirect transitions via all the fast transition paths. Furthermore, we apply our simplification approach to the standard Markov model of single-cell stochastic gene expression and provide a mathematical theory of random gene expression bursts. We give the precise mathematical conditions for the bursting kinetics of both mRNAs and proteins. It turns out that random bursts exactly correspond to the fast transition paths of the Markov model. This helps us gain a better understanding of the physics behind the bursting kinetics as an emergent behavior from the fundamental multiscale biochemical reaction kinetics of stochastic gene expression.

Sex, Class, and Physical Science Educational Attainment: Portions due to Achievement Versus Recruitment

NASA Astrophysics Data System (ADS)

Simon, Richard M.; Farkas, George

Nationally representative data from the National Education Longitudinal Study are used to investigate why males (rather than females) and children of parents with advanced degrees (rather than those from less-educated parents) are more highly represented among physical science bachelor's degrees and graduate students. Parental education is measured by three categories: neither parent has a bachelor's degree, at least one parent has a bachelor's degree, or at least one parent has a degree beyond the bachelor's. Physical science is defined as students majoring in physics, engineering, mathematics, or computer science. The effects of mathematics achievement and effects not accounted for by mathematics achievement (what the authors call "recruitment" effects) are isolated for parental education categories and for sex, allowing inequality in physical science degree attainment to be decomposed into portions due to achievement and portions due to recruitment. Additionally, the results from logistic regressions predicting the attainment of a bachelor's degree in physical science as well as the pursuit of a graduate degree in physical science are presented. It is found that for parental education categories, the gaps in physical science educational attainment are nearly entirely accounted for by differences in mathematics achievement, suggesting that if achievement could be equalized, physical science educational attainment differences among parental education categories would disappear. However, the sex gap in physical science educational attainment operates almost entirely independent of achievement effects, suggesting that if the mathematics achievement distributions of males and females were identical, the sex gap in physical science educational attainment would be unchanged from what it is today.

Introductory Physics Students' Physics and Mathematics Epistemologies

NASA Astrophysics Data System (ADS)

Scanlon, Erin M.

The purpose of this three study dissertation is to investigate why students are enrolled in introductory physics courses experience difficulties in being successful; one possible source of their difficulties is related to their epistemology. In order to investigate students' epistemologies about mathematics and physics, students were observed solving physics problems in groups during a laboratory course (study 1) and while solving physics and mathematics problems individually during office-hour sessions (study 2). The Epistemological Resources theoretical framework was employed (Hammer & Elby, 2002). Using emergent and a priori epistemological resource operationalizations (Jones, 2015), 25 distinct epistemological resources were identified in study 1. Differences in physics epistemological resource usage between students of varying academic background (as measured by their number of previously completed mathematics and science classes were identified. By employing an external (Jones, 2015) and internal (Scanlon, 2016) a priori epistemological resource coding scheme, a total of 17 distinct epistemological resources were identified in study 2. The data were sampled to compare the mathematics and physics epistemological resource usage of participants with consistent and inconsistent sign usage in an energy conservation physics problem in order to provide a meaningful context for discussion. Participants of the same sign usage group employed epistemological resources similarly. Conversely, participants in different groups had significantly different physics epistemological resource usage patterns. Finally, student epistemological resource usage patterns from the first two studies were compared to course outcomes in order to determine implications for practice (study 3). Educators must be aware of and address the epistemological underpinnings of students' difficulties in introductory physics courses.

Zimbabwean Female Participation in Physics: Facets of Identity Formation Considered to Be of Significance by Female Students in Relation to Physics

ERIC Educational Resources Information Center

Gudyanga, Anna

2016-01-01

The study explored facets of identity formation considered to be of significance by Zimbabwean female adolescent students in physics. Four high schools that were offering physics at A' level in the Midlands Province, in Zimbabwe were targeted. Nine female adolescents doing mathematics and physics and only mathematics were chosen. Data generation…

A Study of the Relationship between Physical Skills and Achievement in Listening Comprehension, Mathematics, and Reading.

ERIC Educational Resources Information Center

Templeton, Josey; Jones, Robbie

To determine if a relationship existed between physical skills and achievement in reading, mathematics, and listening comprehension of fifth-grade students, a study evaluated 334 fifth-graders in Starkville, Mississippi, on 20 physical fitness, motor fitness, and sports skills, as well as the Stanford Achievement Tests. The physical skills test…

Problem Solving and the Use of Math in Physics Courses

ERIC Educational Resources Information Center

Redish, Edward F.

2006-01-01

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend to blend conceptual physics with mathematical symbolism in a way that profoundly affects the way equations are…

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

Mathematical methods of studying physical phenomena

NASA Astrophysics Data System (ADS)

Man'ko, Margarita A.

2013-03-01

In recent decades, substantial theoretical and experimental progress was achieved in understanding the quantum nature of physical phenomena that serves as the foundation of present and future quantum technologies. Quantum correlations like the entanglement of the states of composite systems, the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, connected with these phenomena, uncertainty relations for conjugate variables and entropies, like Shannon and Rényi entropies, and the inequalities for spin states, like Bell inequalities, reflect the recently understood quantum properties of micro and macro systems. The mathematical methods needed to describe all quantum phenomena mentioned above were also the subject of intense studies in the end of the last, and beginning of the new, century. In this section of CAMOP 'Mathematical Methods of Studying Physical Phenomena' new results and new trends in the rapidly developing domain of quantum (and classical) physics are presented. Among the particular topics under discussion there are some reviews on the problems of dynamical invariants and their relations with symmetries of the physical systems. In fact, this is a very old problem of both classical and quantum systems, e.g. the systems of parametric oscillators with time-dependent parameters, like Ermakov systems, which have specific constants of motion depending linearly or quadratically on the oscillator positions and momenta. Such dynamical invariants play an important role in studying the dynamical Casimir effect, the essence of the effect being the creation of photons from the vacuum in a cavity with moving boundaries due to the presence of purely quantum fluctuations of the electromagnetic field in the vacuum. It is remarkable that this effect was recently observed experimentally. The other new direction in developing the mathematical approach in physics is quantum tomography that provides a new vision of quantum states. In the tomographic picture of quantum mechanics, the states are identified with fair conditional probability distributions, which contain the same information on the states as the wave function or the density matrix. The mathematical methods of the tomographic approach are based on studying the star-product (associative product) quantization scheme. The tomographic star-product technique provides an additional understanding of the associative product, which is connected with the existence of specific pairs of operators called quantizers and dequantizers. These operators code information on the kernels of all the star-product schemes, including the traditional phase-space Weyl-Wigner-Moyal picture describing the quantum-system evolution. The new equation to find quantizers, if the kernel of the star product of functions is given, is presented in this CAMOP section. For studying classical systems, the mathematical methods developed in quantum mechanics can also be used. The case of paraxial-radiation beams propagating in waveguides is a known example of describing a purely classical phenomenon by means of quantum-like equations. Thus, some quantum phenomenon like the entanglement can be mimicked by the properties of classical beams, for example, Gaussian modes. The mathematical structures and relations to the symplectic symmetry group are analogous for both classical and quantum phenomena. Such analogies of the mathematical classical and quantum methods used in research on quantum-like communication channels provide new tools for constructing a theoretical basis of the new information-transmission technologies. The conventional quantum mechanics and its relation to classical mechanics contain mathematical recipes of the correspondence principle and quantization rules. Attempts to find rules for deriving the quantum-mechanical formalism starting from the classical field theory, taking into account the influence of classical fluctuations of the field, is considered in these papers. The methods to solve quantum equations and formulate the boundary conditions in the problems with singular potentials are connected with the mathematical problems of self-adjointness of the Hamiltonians. The progress and some new results in this direction are reflected in this CAMOP section. The Gaussian states of the photons play an important role in quantum optics. The multimode electromagnetic field and quantum correlations in the Gaussian states are considered in this section. The new results in the statistical properties of the laser radiation discussed here are based on applications of mathematical methods in this traditional domain of physics. It is worth stressing that the universality of the mathematical procedures permitted to consider the physical phenomena in the ocean is on the same footing as the phenomena in the microworld. In this CAMOP section, there are also papers devoted to traditional problems of solving the Schrödinger equation for interesting quantum systems. Recently obtained results related to different domains of theoretical physics are united by applying mathematical methods and tools, that provide new possibilities to better understand the theoretical foundations needed to develop new quantum technologies like quantum computing and quantum communications. The papers are arranged alphabetically by the name of the first author. We are grateful to all authors who accepted our invitation to contribute to this CAMOP section.

The Mathematics of "Star Trek"--An Honors Colloquium

ERIC Educational Resources Information Center

Karls, Michael A.

2011-01-01

After the success of a course on cryptography for a general audience, based on Simon Singh's "The Code Book" [49], I decided to try again and create a mathematics course for a general audience based on "The Physics of Star Trek" by Lawrence Krauss [32]. This article looks at the challenges of designing a physics-based mathematics course "from…

Material Encounters with Mathematics: The Case for Museum Based Cross-Curricular Integration

ERIC Educational Resources Information Center

de Freitas, Elizabeth; Bentley, Sean J.

2012-01-01

This paper reports on research from a network of high school and museum partnerships designed to explore techniques for integrating mathematics and physics learning experiences during the first year of high school. The foundation of the curriculum is a problem-based, museum-based, and hands-on approach to mathematics and physics. In this paper, we…

Stealing from Physics: Modeling with Mathematical Functions in Data-Rich Contexts

ERIC Educational Resources Information Center

Erickson, Tim

2006-01-01

In the course of a project to create physics education materials for secondary schools in the USA we have, not surprisingly, had insights into how students develop certain mathematical understandings. Some of these translate directly into the mathematics classroom. With our materials, students get data from a variety of sources, data that arise in…

Acquire an Bruker Dimension FastScan (trademark) Atomic Force Microscope (AFM) for Materials, Physical and Biological Science Research and Education

DTIC Science & Technology

2016-04-14

two super users, Drs. Biswajit Sannigrahi and Guangchang Zhou were trained by the Senior Engineer for Product Service, Dr. Teddy Huang from the... Engineering : The number of undergraduates funded by your agreement who graduated during this period and intend to work for the Department of Defense The...science, mathematics, engineering or technology fields: Student Metrics This section only applies to graduating undergraduates supported by this

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

PubMed Central

Khan, Kamruzzaman; Akbar, M. Ali; Koppelaar, H.

2015-01-01

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd–Sokolov–Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics. PMID:26587256

A cluster bootstrap for two-loop MHV amplitudes

DOE PAGES

Golden, John; Spradlin, Marcus

2015-02-02

We apply a bootstrap procedure to two-loop MHV amplitudes in planar N=4 super-Yang-Mills theory. We argue that the mathematically most complicated part (the Λ 2 B 2 coproduct component) of the n-particle amplitude is uniquely determined by a simple cluster algebra property together with a few physical constraints (dihedral symmetry, analytic structure, supersymmetry, and well-defined collinear limits). Finally, we present a concise, closed-form expression which manifests these properties for all n.

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

NASA Technical Reports Server (NTRS)

Baty, Roy S.; Farassat, Fereidoun; Hargreaves, John

2007-01-01

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Teaching group theory using Rubik's cubes

NASA Astrophysics Data System (ADS)

Cornock, Claire

2015-10-01

Being situated within a course at the applied end of the spectrum of maths degrees, the pure mathematics modules at Sheffield Hallam University have an applied spin. Pure topics are taught through consideration of practical examples such as knots, cryptography and automata. Rubik's cubes are used to teach group theory within a final year pure elective based on physical examples. Abstract concepts, such as subgroups, homomorphisms and equivalence relations are explored with the cubes first. In addition to this, conclusions about the cubes can be made through the consideration of algebraic approaches through a process of discovery. The teaching, learning and assessment methods are explored in this paper, along with the challenges and limitations of the methods. The physical use of Rubik's cubes within the classroom and examination will be presented, along with the use of peer support groups in this process. The students generally respond positively to the teaching methods and the use of the cubes.

Influence of mathematical and physical background of drought indices on their complementarity and drought recognition ability

NASA Astrophysics Data System (ADS)

Frank, Anna; Armenski, Tanja; Gocic, Milan; Popov, Srdjan; Popovic, Ljiljana; Trajkovic, Slavisa

2017-09-01

The aim of this study is to test how effective and physically correct are the mathematical approaches of operational indices used by relevant National Agencies across the globe. To do so, the following indices were analysed Standardized Precipitation Index (SPI) -1, 3, 6, 12 and 24, Standardized Precipitation - Evapotranspiration Index (SPEI) - 1, 3, 6, 12 and 24, Effective Drought Index (EDI) and Index of Drying Efficiency of Air (IDEA). To make regions more comparable to each other and follow the spatial development of drought SPI index was advised by World Meteorological Organisation to be used widely by official meteorological services. The SPI and SPEI are used for Drought Early Warning in the USA, National Drought Mitigation Center and NASA, and in the EU by the European Drought Centre (EDC) and in the Balkan Region by National Meteorological Agencies. The EDI Index has wide application in Asia. In this paper four different issues were investigated: 1) how the mathematical method used in a drought indicator's computation influence drought indices' (DI) comparative analyses; 2) the sensitivity of the DIs on any change of the length of observational period; 3) similarities between the DIs time series; 4) and how accurate DIs are when compared to historical drought records. Results suggest that it is necessary to apply a few crucial changes in the Drought Monitoring and Early Warning Systems: 1) reconsider use of SPI and SPEI family indices as a measure of quality of other indices; and for Drought Early Recognition Programs 2) switch to DIs with a solid physical background, such as EDI; 3) Adopt solid physics for modelling drought processes and define the physical measure of drought, e.g. EDI and IDEA indices; 4) investigate further the IDEA index, which, supported by our study as well, is valuable for simulation of a drought process.

Adam Smith's invisible hand is unstable: physics and dynamics reasoning applied to economic theorizing

NASA Astrophysics Data System (ADS)

McCauley, Joseph L.

2002-11-01

Neo-classical economic theory is based on the postulated, nonempiric notion of utility. Neo-classical economists assume that prices, dynamics, and market equilibria are supposed to be derived from utility. The results are supposed to represent mathematically the stabilizing action of Adam Smith's invisible hand. In deterministic excess demand dynamics, however, a utility function generally does not exist mathematically due to nonintegrability. Price as a function of demand does not exist and all equilibria are unstable. Qualitatively, and empirically, the neo-classical prediction of price as a function of demand describes neither consumer nor trader demand. We also discuss five inconsistent definitions of equilibrium used in economics and finance, only one of which is correct, and then explain the fallacy in the economists’ notion of ‘temporary price equilibria’.

Model for growth of fractal solid state surface and possibility of its verification by means of atomic force microscopy

NASA Astrophysics Data System (ADS)

Kulikov, D. A.; Potapov, A. A.; Rassadin, A. E.; Stepanov, A. V.

2017-10-01

In the paper, methods of verification of models for growth of solid state surface by means of atomic force microscopy are suggested. Simulation of growth of fractals with cylindrical generatrix on the solid state surface is presented. Our mathematical model of this process is based on generalization of the Kardar-Parisi-Zhang equation. Corner stones of this generalization are both conjecture of anisotropy of growth of the surface and approximation of small angles. The method of characteristics has been applied to solve the Kardar-Parisi-Zhang equation. Its solution should be considered up to the gradient catastrophe. The difficulty of nondifferentiability of fractal initial generatrix has been overcome by transition from a mathematical fractal to a physical one.

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

Investigation of possible observable e ects in a proposed theory of physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freidan, Daniel

2015-03-31

The work supported by this grant produced rigorous mathematical results on what is possible in quantum field theory. Quantum field theory is the well-established mathematical language for fundamental particle physics, for critical phenomena in condensed matter physics, and for Physical Mathematics (the numerous branches of Mathematics that have benefitted from ideas, constructions, and conjectures imported from Theoretical Physics). Proving rigorous constraints on what is possible in quantum field theories thus guides the field, puts actual constraints on what is physically possible in physical or mathematical systems described by quantum field theories, and saves the community the effort of trying tomore » do what is proved impossible. Results were obtained in two dimensional qft (describing, e.g., quantum circuits) and in higher dimensional qft. Rigorous bounds were derived on basic quantities in 2d conformal field theories, i.e., in 2d critical phenomena. Conformal field theories are the basic objects in quantum field theory, the scale invariant theories describing renormalization group fixed points from which all qfts flow. The first known lower bounds on the 2d boundary entropy were found. This is the entropy- information content- in junctions in critical quantum circuits. For dimensions d > 2, a no-go theorem was proved on the possibilities of Cauchy fields, which are the analogs of the holomorphic fields in d = 2 dimensions, which have had enormously useful applications in Physics and Mathematics over the last four decades. This closed o the possibility of finding analogously rich theories in dimensions above 2. The work of two postdoctoral research fellows was partially supported by this grant. Both have gone on to tenure track positions.« less

Mind map learning for advanced engineering study: case study in system dynamics

NASA Astrophysics Data System (ADS)

Woradechjumroen, Denchai

2018-01-01

System Dynamics (SD) is one of the subjects that were use in learning Automatic Control Systems in dynamic and control field. Mathematical modelling and solving skills of students for engineering systems are expecting outcomes of the course which can be further used to efficiently study control systems and mechanical vibration; however, the fundamental of the SD includes strong backgrounds in Dynamics and Differential Equations, which are appropriate to the students in governmental universities that have strong skills in Mathematics and Scientifics. For private universities, students are weak in the above subjects since they obtained high vocational certificate from Technical College or Polytechnic School, which emphasize the learning contents in practice. To enhance their learning for improving their backgrounds, this paper applies mind maps based problem based learning to relate the essential relations of mathematical and physical equations. With the advantages of mind maps, each student is assigned to design individual mind maps for self-leaning development after they attend the class and learn overall picture of each chapter from the class instructor. Four problems based mind maps learning are assigned to each student. Each assignment is evaluated via mid-term and final examinations, which are issued in terms of learning concepts and applications. In the method testing, thirty students are tested and evaluated via student learning backgrounds in the past. The result shows that well-design mind maps can improve learning performance based on outcome evaluation. Especially, mind maps can reduce time-consuming and reviewing for Mathematics and Physics in SD significantly.

The "Human Factor" in Pure and in Applied Mathematics. Systems Everywhere: Their Impact on Mathematics Education.

ERIC Educational Resources Information Center

Fischer, Roland

1992-01-01

Discusses the impact that the relationship between people and mathematics could have on the development of pure and applied mathematics. Argues for (1) a growing interest in philosophy, history and sociology of science; (2) new models in educational and psychological research; and (3) a growing awareness of the human factor in technology,…

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints.

PubMed

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M

2016-10-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. Copyright © 2016. Published by Elsevier Ltd.

Modeling mammary organogenesis from biological first principles: Cells and their physical constraints

PubMed Central

Montévil, Maël; Speroni, Lucia; Sonnenschein, Carlos; Soto, Ana M.

2017-01-01

In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing non-identical cells, which organize in tri-dimensional patterns. These association patterns and cells types change as tissues and organs are formed. This contextuality and circularity makes it difficult to establish detailed cause and effect relationships. Here we propose an approach to overcome these intrinsic difficulties by combining the use of two models; 1) an experimental one that employs 3D culture technology to obtain the structures of the mammary gland, namely, ducts and acini, and 2) a mathematical model based on biological principles. The typical approach for mathematical modeling in biology is to apply mathematical tools and concepts developed originally in physics or computer sciences. Instead, we propose to construct a mathematical model based on proper biological principles. Specifically, we use principles identified as fundamental for the elaboration of a theory of organisms, namely i) the default state of cell proliferation with variation and motility and ii) the principle of organization by closure of constraints. This model has a biological component, the cells, and a physical component, a matrix which contains collagen fibers. Cells display agency and move and proliferate unless constrained; they exert mechanical forces that i) act on collagen fibers and ii) on other cells. As fibers organize, they constrain the cells on their ability to move and to proliferate. The model exhibits a circularity that can be interpreted in terms of closure of constraints. Implementing the mathematical model shows that constraints to the default state are sufficient to explain ductal and acinar formation, and points to a target of future research, namely, to inhibitors of cell proliferation and motility generated by the epithelial cells. The success of this model suggests a step-wise approach whereby additional constraints imposed by the tissue and the organism could be examined in silico and rigorously tested by in vitro and in vivo experiments, in accordance with the organicist perspective we embrace. PMID:27544910

Comparison of University Students' Understanding of Graphs in Different Contexts

ERIC Educational Resources Information Center

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-01-01

This study investigates university students' understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was…

The Physics of Vibration

NASA Astrophysics Data System (ADS)

Pippard, A. B.

1989-11-01

The study of vibration in physical systems is an important part of almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. Following this the book turns to the treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar. In Part II the emphasis turns to quantum systems, that is those systems which can only be adequately described by quantum mechanics. The treatment concentrates on vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is illustrated with many examples and theory and experiment are compared. Although the reader may find that the physics discussed is demanding and the concepts are subtle in places, all mathematics used is familiar to both engineers and experimental scientists. Although not a textbook this is a useful introduction to the more advanced mathematical treatment of vibrations as it bridges the gap between the basic principles and more specialized concepts. It will be of great interest to advanced undergraduates and postgraduates as well as applied mathematicians, physicists and engineers in university and industry.

75 FR 10328 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2010-03-05

... Person: Dr. Morris L. Aizenman, Senior Science Associate, Directorate for Mathematical and Physical... Directorate; Report of NSF Advisory Working Groups; Meeting of MPSAC with Divisions within MPS Directorate...

Theoretical studies of the physics of the solar atmosphere

NASA Technical Reports Server (NTRS)

Hollweg, Joseph V.

1992-01-01

Significant advances in our theoretical basis for understanding several physical processes related to dynamical phenomena on the sun were achieved. We have advanced a new model for spicules and fibrils. We have provided a simple physical view of resonance absorption of MHD surface waves; this allowed an approximate mathematical procedure for obtaining a wealth of new analytical results which we applied to coronal heating and p-mode absorption at magnetic regions. We provided the first comprehensive models for the heating and acceleration of the transition region, corona, and solar wind. We provided a new view of viscosity under coronal conditions. We provided new insights into Alfven wave propagation in the solar atmosphere. And recently we have begun work in a new direction: parametric instabilities of Alfven waves.

What your mother never told you about ... physics teaching

NASA Astrophysics Data System (ADS)

Roudebush, Deborah

2010-03-01

When I entered high school teaching after working in industry for several years, I was sure I knew exactly what to do. I was convinced that I would be the sage on the stage and would wow the students with my clear explanations, amazing problem-solving techniques, and perfect lab instructions. I was convinced that the students would soak up the wisdom and insight that I was offering and that, if the students just followed my directions exactly, they would be able to solve new and exciting problems. Instead, I found that the students became amazingly adept at applied mathematics and understood few of the underlying physics concepts. In fact, some of my star students who headed off to become physics majors were unprepared for the thought required and changed majors within two years.

Quantum cosmology: a review.

PubMed

Bojowald, Martin

2015-02-01

In quantum cosmology, one applies quantum physics to the whole universe. While no unique version and no completely well-defined theory is available yet, the framework gives rise to interesting conceptual, mathematical and physical questions. This review presents quantum cosmology in a new picture that tries to incorporate the importance of inhomogeneity. De-emphasizing the traditional minisuperspace view, the dynamics is rather formulated in terms of the interplay of many interacting 'microscopic' degrees of freedom that describe the space-time geometry. There is thus a close relationship with more-established systems in condensed-matter and particle physics even while the large set of space-time symmetries (general covariance) requires some adaptations and new developments. These extensions of standard methods are needed both at the fundamental level and at the stage of evaluating the theory by effective descriptions.

Enhancing Interpretation of Natural Phenomena through a Mathematical Apparatus: A Proposal of an Interactive Unit in Optics

ERIC Educational Resources Information Center

Sokolowski, Andrzej

2012-01-01

This paper integrates technology, in the form of a physics simulation; science concepts, via image formation by lenses; and a mathematics apparatus, in the form of rational functions. All constituents merge into an instructional unit that can be embedded into a high school or undergraduate mathematics or physics course. The cognitive purpose of…

Student reasoning about graphs in different contexts

NASA Astrophysics Data System (ADS)

Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

2016-06-01

This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the Faculty of Science, University of Zagreb. Students were asked to provide explanations and/or mathematical procedures with their answers. Students' main strategies and difficulties identified through the analysis of those explanations and procedures are described. Student strategies of graph interpretation were found to be largely context dependent and domain specific. A small fraction of students have used the same strategy in all three domains (mathematics, physics, and other contexts) on most sets of parallel questions. Some students have shown indications of transfer of knowledge in the sense that they used techniques and strategies developed in physics for solving (or attempting to solve) other context problems. In physics, the preferred strategy was the use of formulas, which sometimes seemed to block the use of other, more productive strategies which students displayed in other domains. Students' answers indicated the presence of slope-height confusion and interval-point confusion in all three domains. Students generally better interpreted graph slope than the area under a graph, although the concept of slope still seemed to be quite vague for many. The interpretation of the concept of area under a graph needs more attention in both physics and mathematics teaching.

Interfacing mathematics and biology: a discussion on training, research, collaboration, and funding.

PubMed

Miller, Laura A; Alben, Silas

2012-11-01

This article summarizes the discussion at a workshop on "Working at the Interface of Mathematics and Biology" at the 2012 Annual Meeting of the Society for Integrative and Comparative Biology. The goal of this workshop was to foster an ongoing discussion by the community on how to effectively train students from the biological, physical, engineering, and mathematical sciences to work at the intersection of these fields. One major point of discussion centered on how to be a successful interdisciplinary researcher in terms of where to publish, how to successfully write grants, and how to navigate evaluations for tenure and promotion. An emphasis was placed on the importance of developing strong multidisciplinary collaborations and clearly defining one's career trajectory to the home discipline. Another focus of the discussion was on the training of students and postdoctoral fellows in interdisciplinary work and helping these junior researchers to launch their careers. The group emphasized the need for the development of publicly available resources for biologists to learn basic tools for mathematical modeling and for mathematicians and engineers to see how their fields may be applied to current topics in the life sciences.

Pattern of mathematic representation ability in magnetic electricity problem

NASA Astrophysics Data System (ADS)

Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.

2018-03-01

The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.

Applied aerodynamics experience for secondary science teachers and students

NASA Technical Reports Server (NTRS)

Abbitt, John D., III; Carroll, Bruce F.

1992-01-01

The Department of Aerospace Engineering, Mechanics & Engineering Science at the University of Florida in conjunction with the Alachua County, Florida School Board has embarked on a four-year project of university-secondary school collaboration designed to enhance mathematics and science instruction in secondary school classrooms. The goals are to provide teachers with a fundamental knowledge of flight sciences, and to stimulate interest among students, particularly women and minorities, toward careers in engineering, mathematics, and science. In the first year of the project, all thirteen of the eighth grade physical science teachers and all 1200 of the eighth grade physical science students in the county participated. The activities consisted of a three-day seminar taught at the college level for the teachers, several weeks of classroom instruction for all the students, and an airport field trip for a subgroup of about 430 students that included an orientation flight in a Cessna 172 aircraft. The project brought together large numbers of middle school students, teachers, undergraduate and graduate engineering students, school board administrators, and university engineering faculty.

Infiltration into soils: Conceptual approaches and solutions

NASA Astrophysics Data System (ADS)

Assouline, Shmuel

2013-04-01

Infiltration is a key process in aspects of hydrology, agricultural and civil engineering, irrigation design, and soil and water conservation. It is complex, depending on soil and rainfall properties and initial and boundary conditions within the flow domain. During the last century, a great deal of effort has been invested to understand the physics of infiltration and to develop quantitative predictors of infiltration dynamics. Jean-Yves Parlange and Wilfried Brutsaert have made seminal contributions, especially in the area of infiltration theory and related analytical solutions to the flow equations. This review retraces the landmark discoveries and the evolution of the conceptual approaches and the mathematical solutions applied to the problem of infiltration into porous media, highlighting the pivotal contributions of Parlange and Brutsaert. A historical retrospective of physical models of infiltration is followed by the presentation of mathematical methods leading to analytical solutions of the flow equations. This review then addresses the time compression approximation developed to estimate infiltration at the transition between preponding and postponding conditions. Finally, the effects of special conditions, such as the presence of air and heterogeneity in soil properties, on infiltration are considered.

Which Kind of Mathematics for Quantum Mechanics? the Relevance of H. Weyl's Program of Research

NASA Astrophysics Data System (ADS)

Drago, Antonino

In 1918 Weyl's book Das Kontinuum planned to found anew mathematics upon more conservative bases than both rigorous mathematics and set theory. It gave birth to the so-called Weyl's elementary mathematics, i.e. an intermediate mathematics between the mathematics rejecting at all actual infinity and the classical one including it almost freely. The present paper scrutinises the subsequent Weyl's book Gruppentheorie und Quantenmechanik (1928) as a program for founding anew theoretical physics - through quantum theory - and at the same time developing his mathematics through an improvement of group theory; which, according to Weyl, is a mathematical theory effacing the old distinction between discrete and continuous mathematics. Evidence from Weyl's writings is collected for supporting this interpretation. Then Weyl's program is evaluated as unsuccessful, owing to some crucial difficulties of both physical and mathematical nature. The present clear-cut knowledge of Weyl's elementary mathematics allows us to re-evaluate Weyl's program in order to look for more adequate formulations of quantum mechanics in any weaker kind of mathematics than the classical one.

76 FR 14996 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2011-03-18

.... Aizenman, Senior Science Associate, Directorate for Mathematical and Physical Sciences, Room 1005, National... Committee of Visitors Report of NSF Advisory Working Groups Meeting of MPSAC with Divisions within MPS...

Essential Mathematics for the Physical Sciences; Volume I: Homogeneous boundary value problems, Fourier methods, and special functions

NASA Astrophysics Data System (ADS)

Borden, Brett; Luscombe, James

2017-10-01

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.

Validation and upgrading of physically based mathematical models

NASA Technical Reports Server (NTRS)

Duval, Ronald

1992-01-01

The validation of the results of physically-based mathematical models against experimental results was discussed. Systematic techniques are used for: (1) isolating subsets of the simulator mathematical model and comparing the response of each subset to its experimental response for the same input conditions; (2) evaluating the response error to determine whether it is the result of incorrect parameter values, incorrect structure of the model subset, or unmodeled external effects of cross coupling; and (3) modifying and upgrading the model and its parameter values to determine the most physically appropriate combination of changes.

Students' Understanding of Mathematical Expressions in Physical Chemistry Contexts: An Analysis Using Sherin's Symbolic Forms

ERIC Educational Resources Information Center

Becker, Nicole; Towns, Marcy

2012-01-01

Undergraduate physical chemistry courses require students to be proficient in calculus in order to develop an understanding of thermodynamics concepts. Here we present the findings of a study that examines student understanding of mathematical expressions, including partial derivative expressions, in two undergraduate physical chemistry courses.…

The Mathematics of High School Physics: Models, Symbols, Algorithmic Operations and Meaning

ERIC Educational Resources Information Center

Kanderakis, Nikos

2016-01-01

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and…

Analytical Derivation: An Epistemic Game for Solving Mathematically Based Physics Problems

ERIC Educational Resources Information Center

Bajracharya, Rabindra R.; Thompson, John R.

2016-01-01

Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the "analytical derivation" game. This game involves deriving an…

A Summer Math and Physics Program for High School Students: Student Performance and Lessons Learned in the Second Year

ERIC Educational Resources Information Center

Timme, Nicholas; Baird, Michael; Bennett, Jake; Fry, Jason; Garrison, Lance; Maltese, Adam

2013-01-01

For the past two years, the Foundations in Physics and Mathematics (FPM) summer program has been held at Indiana University in order to fulfill two goals: provide additional physics and mathematics instruction at the high school level, and provide physics graduate students with experience and autonomy in designing curricula and teaching courses.…

Wyoming Mathematics Curriculum Guide, Grades 7-12.

ERIC Educational Resources Information Center

Wyoming State Dept. of Education, Cheyenne.

GRADES OR AGES: 7-12; SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The guide has an introduction and four chapters: 1) A Sample Mathematics Curriculum; 2) The Exceptional Student in Mathematics; 3) Mathematics Components for Comprehensive Occupational Education; 4) Reference Materials. The guide is printed and spiral bound…

Exact soliton of (2 + 1)-dimensional fractional Schrödinger equation

NASA Astrophysics Data System (ADS)

Rizvi, S. T. R.; Ali, K.; Bashir, S.; Younis, M.; Ashraf, R.; Ahmad, M. O.

2017-07-01

The nonlinear fractional Schrödinger equation is the basic equation of fractional quantum mechanics introduced by Nick Laskin in 2002. We apply three tools to solve this mathematical-physical model. First, we find the solitary wave solutions including the trigonometric traveling wave solutions, bell and kink shape solitons using the F-expansion and Improve F-expansion method. We also obtain the soliton solution, singular soliton solutions, rational function solution and elliptic integral function solutions, with the help of the extended trial equation method.

Transactions of the Army Conference on Applied Mathematics and Computing (4th) Held in Ithaca, New York on 27-31 May 1986

DTIC Science & Technology

1987-02-01

positive, nonincreaslng on 0 < t < *, and m decays rapidly at Infinity. Stronger power singularities at zero (a < 0) are also...considered. In this case the wavenumber appears to power four in the differential equation, the Orr-Sommerfeld equation, and to power five in the wall...normal mode, appears to power four in the differential equation. However it is this problem that is physically realistic in which fixed real frequency

Electro-Optics In Two Years

NASA Astrophysics Data System (ADS)

Simcik, John C.

1989-04-01

Texas State Technical Institute-Waco (TSTI-WACO) was the first school in the United States to offer an Associate of Applied Science degree in Laser Electro-Optics Technology. The program began in September 1969 and has produced 1,827 graduates since inception. These graduates are readily adaptable to any area of the laser electro-optics industry. Areas of study include Optics, Electronics, Vacuum, Physics, Mathematics, and English with emphasis on Electro-Optics. Graduate placement is centered around research and development, life sciences and manufacturing in technical and engineering areas.

PREFACE: 3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015 (ScieTech 2015)

NASA Astrophysics Data System (ADS)

Gaol, F. L.

2015-06-01

The 3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015 (ScieTech 2015), was held at The Westin Resort Nusa Dua, Bali on 31 January - 1 February 2015. The ScieTech 2015 conference is aimed to bring together researchers, engineers and scientists from around the world. ScieTech 2015 is placed on promoting interaction between the theoretical, experimental, and applied communities, so that a high level exchange is achieved in new and emerging areas within mathematics, chemistry and physics. As we already know that science and technology have brought tremendous benefits for human civilization. People are becoming healthier, wealthier, better educated, more peaceful, increasingly connected, and living longer. Of course, science and technology provide many answers to global challenges, but we will face more complex problems in the next decade due to increasing world population, limitation of energy, and climate change. Therefore, researchers should be more active in conducting research that enables collaboration between one and the others. Interdisciplinary cooperation is absolutely necessary in order to create a smart system for solving the global problems. We need a global and general long-term view of the future with long-range goals for solving complex problems in next decade. Therefore the conference was held to be a forum for researchers from different disciplines to start collaborating and conducting research that provides a solution to the global issues. The theme of ScieTech 2015 was ''The interdisciplinary Application between Mathematics, Chemistry and Physics to enhance the Quality of Life''. We would like to express our sincere gratitude to all in the Technical Program Committee who have reviewed the papers and developed a very interesting conference program as well as the invited and plenary speakers. This year, we received 197 papers and after rigorous review, 59 papers were accepted. The participants came from 19 countries, and there were six paralell sessions and four keynote speakers. It is an honour to present this volume of Journal of Physics: Conference Series (JPCS) and we deeply thank the authors for their enthusiastic and high-grade contributions. Finally, we would like to thank the conference chairmen, members of the steering committee, the organizing committee, the organizing secretariat and the financial support from the conference sponsors that allowed the success of ScieTech 2015.

Atiyah-Patodi-Singer index theorem for domain-wall fermion Dirac operator

NASA Astrophysics Data System (ADS)

Fukaya, Hidenori; Onogi, Tetsuya; Yamaguchi, Satoshi

2018-03-01

Recently, the Atiyah-Patodi-Singer(APS) index theorem attracts attention for understanding physics on the surface of materials in topological phases. Although it is widely applied to physics, the mathematical set-up in the original APS index theorem is too abstract and general (allowing non-trivial metric and so on) and also the connection between the APS boundary condition and the physical boundary condition on the surface of topological material is unclear. For this reason, in contrast to the Atiyah-Singer index theorem, derivation of the APS index theorem in physics language is still missing. In this talk, we attempt to reformulate the APS index in a "physicist-friendly" way, similar to the Fujikawa method on closed manifolds, for our familiar domain-wall fermion Dirac operator in a flat Euclidean space. We find that the APS index is naturally embedded in the determinant of domain-wall fermions, representing the so-called anomaly descent equations.

Epistemic Views of the Relationship between Physics and Mathematics: Its Influence on the Approach of Undergraduate Students to Problem Solving

ERIC Educational Resources Information Center

Pereira de Ataide, Ana Raquel; Greca, Ileana Maria

2013-01-01

The relationship between physics and mathematics is hardly ever presented with sufficient clarity to satisfy either physicists or mathematicians. It is a situation that often leads to misunderstandings that may spread quickly from teacher to student, such as the idea that mathematics is a mere instrument for the physicist. In this paper, we…

Geometry and Integrability

NASA Astrophysics Data System (ADS)

Mason, Lionel; Nutku, Yavuz

2003-12-01

Based on courses held at the Feza GÜrsey Institute, this collection of survey articles introduces advanced graduate students to an exciting area on the border of mathematics and mathematical physics. Including articles by key names such as Calogero, Donagi and Mason, it features the algebro-geometric material from Donagi as well as the twistor space methods in Woodhouse's contribution, forming a bridge between the pure mathematics and the more physical approaches.

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

On the Reasonable and Unreasonable Effectiveness of Mathematics in Classical and Quantum Physics

NASA Astrophysics Data System (ADS)

Plotnitsky, Arkady

2011-03-01

The point of departure for this article is Werner Heisenberg's remark, made in 1929: "It is not surprising that our language [or conceptuality] should be incapable of describing processes occurring within atoms, for … it was invented to describe the experiences of daily life, and these consist only of processes involving exceedingly large numbers of atoms. … Fortunately, mathematics is not subject to this limitation, and it has been possible to invent a mathematical scheme—the quantum theory [quantum mechanics]—which seems entirely adequate for the treatment of atomic processes." The cost of this discovery, at least in Heisenberg's and related interpretations of quantum mechanics (such as that of Niels Bohr), is that, in contrast to classical mechanics, the mathematical scheme in question no longer offers a description, even an idealized one, of quantum objects and processes. This scheme only enables predictions, in general, probabilistic in character, of the outcomes of quantum experiments. As a result, a new type of the relationships between mathematics and physics is established, which, in the language of Eugene Wigner adopted in my title, indeed makes the effectiveness of mathematics unreasonable in quantum but, as I shall explain, not in classical physics. The article discusses these new relationships between mathematics and physics in quantum theory and their implications for theoretical physics—past, present, and future.

Negotiating the Boundaries Between Mathematics and Physics

NASA Astrophysics Data System (ADS)

Radtka, Catherine

2015-07-01

This paper examines physics and mathematics textbooks published in France at the end of the 1950s and at the beginning of the 1960s for children aged 11-15 years old. It argues that at this "middle school" level, textbooks contributed to shape cultural representations of both disciplines and their mutual boundaries through their contents and their material aspect. Further, this paper argues that far from presenting clearly delimited subjects, late 1950s textbooks offered possible connections between mathematics and physics. It highlights that such connections depended upon the type of schools the textbooks aimed at, at a time when educational organization still differentiated pupils of this age. It thus stresses how the audience and its projected aptitudes and needs, as well as the cultural teaching traditions of the teachers in charge, were inseparable from the diverse conceptions of mathematics and physics and their relationships promoted through textbooks of the time.

Identifying potential dropouts from college physics classes

NASA Astrophysics Data System (ADS)

Wollman, Warren; Lawrenz, Frances

Hudson and Rottman (1981) established that mathematics ability is probably a secondary factor influencing dropout from college physics courses. Other factors remain to be found for predicting who will drop out or at least have difficulty with the course. When mathematics ability is coupled with general indicators of performance (total GPA and ACT natural science), prediction of performance for those who complete the course is substantially improved. Moreover, discriminant analyses reveal who will have at least some difficulty, but not who will drop out. The problem of isolating specific weaknesses of students who have difficulty persists. Physics achievement appears to depend on mathematics ability only to the extent that students possess the ability to utilize mathematics knowledge for solving physics problems. Identification of the specific aspects of this ability as well as the specific deficiencies leading to dropout should be the object of future research. For the present, interviews might be more revealing than group testing methods.

A celebration of mechanics: from nano to macro. The J. Michael T. Thompson Festschrift issue.

PubMed

Elishakoff, Isaac

2013-06-28

This Theme Issue is dedicated to the topic 'Mechanics: from nano to macro' and marks the 75th birthday of Dr J. Michael T. Thompson, Fellow of the Royal Society, whose current affiliations are as follows: (i) Honorary Fellow, Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge; (ii) Emeritus Professor of Nonlinear Dynamics, Department of Civil, Environmental and Geomatic Engineering, University College London; and (iii) Professor of Theoretical and Applied Dynamics (Distinguished Sixth Century Chair, part-time), University of Aberdeen. He also serves as Chairman of the Board of Directors at ES-Consult (consulting engineers) in Copenhagen, Denmark. The pertinent question that arises from the very start is: should we first salute Michael and then describe the Theme Issue, or vice versa? Indeed, according to Blaise Pascal (1623-1662), the last thing one discovers in composing a work is what to put first. I would like to take the liberty of deviating from the tradition of the Philosophical Transactions and start with the tribute to Michael; after all he is the prime cause of this Theme Issue.

Mathematics applied to the climate system: outstanding challenges and recent progress

PubMed Central

Williams, Paul D.; Cullen, Michael J. P.; Davey, Michael K.; Huthnance, John M.

2013-01-01

The societal need for reliable climate predictions and a proper assessment of their uncertainties is pressing. Uncertainties arise not only from initial conditions and forcing scenarios, but also from model formulation. Here, we identify and document three broad classes of problems, each representing what we regard to be an outstanding challenge in the area of mathematics applied to the climate system. First, there is the problem of the development and evaluation of simple physically based models of the global climate. Second, there is the problem of the development and evaluation of the components of complex models such as general circulation models. Third, there is the problem of the development and evaluation of appropriate statistical frameworks. We discuss these problems in turn, emphasizing the recent progress made by the papers presented in this Theme Issue. Many pressing challenges in climate science require closer collaboration between climate scientists, mathematicians and statisticians. We hope the papers contained in this Theme Issue will act as inspiration for such collaborations and for setting future research directions. PMID:23588054

Incorporating Student Activities into Climate Change Education

NASA Astrophysics Data System (ADS)

Steele, H.; Kelly, K.; Klein, D.; Cadavid, A. C.

2013-12-01

Under a NASA grant, Mathematical and Geospatial Pathways to Climate Change Education, students at California State University, Northridge integrated Geographic Information Systems (GIS), remote sensing, satellite data technologies, and climate modelling into the study of global climate change under a Pathway for studying the Mathematics of Climate Change (PMCC). The PMCC, which is an interdisciplinary option within the BS in Applied Mathematical Sciences, consists of courses offered by the departments of Mathematics, Physics, and Geography and is designed to prepare students for careers and Ph.D. programs in technical fields relevant to global climate change. Under this option students are exposed to the science, mathematics, and applications of climate change science through a variety of methods including hands-on experience with computer modeling and image processing software. In the Geography component of the program, ESRI's ArcGIS and ERDAS Imagine mapping, spatial analysis and image processing software were used to explore NASA satellite data to examine the earth's atmosphere, hydrosphere and biosphere in areas that are affected by climate change or affect climate. These technology tools were incorporated into climate change and remote sensing courses to enhance students' knowledge and understanding of climate change through hands-on application of image processing techniques to NASA data. Several sets of exercises were developed with specific learning objectives in mind. These were (1) to increase student understanding of climate change and climate change processes; (2) to develop student skills in understanding, downloading and processing satellite data; (3) to teach remote sensing technology and GIS through applications to climate change; (4) to expose students to climate data and methods they can apply to solve real world problems and incorporate in future research projects. In the Math and Physics components of the course, students learned about atmospheric circulation with applications of the Lorenz model, explored the land-sea breeze problem with the Dynamics and Thermodynamics Circulation Model (DTDM), and developed simple radiative transfer models. Class projects explored the effects of varying the content of CO2 and CH4 in the atmosphere, as well as the properties of paleoclimates in atmospheric simulations using EdGCM. Initial assessment of student knowledge, attitudes, and behaviors associated with these activities, particularly about climate change, was measured. Pre- and post-course surveys provided student perspectives about the courses and their learning about remote sensing and climate change concepts. Student performance on the tutorials and course projects evaluated students' ability to learn and apply their knowledge about climate change and skills with remote sensing to assigned problems or proposed projects of their choice. Survey and performance data illustrated that the exercises were successful in meeting their intended learning objectives as well as opportunities for further refinement and expansion.

"MAPHICS", its development and influence on the future of Science.

NASA Astrophysics Data System (ADS)

Castellano, Doc

2001-11-01

On the fifth 'anniversary' of his conferences with Einstein, the Author reviewed the State of the Art of Mathematical Physics. During this review, 1960, the Author formulated an Omega Science. Namely, combining the Philosophy of Mathematics with the Philosophy of Physics into ONE Philosophy, "MAPHICS". "MA from MAthematics and PH--ICS" from Physics; "MAPHICS" (TM). The PhD co. views Science in general, and Mathematical Physics in particular, from a Historic-Philosophical viewpoint. Thus, it remained anonymous and 'in the background' as publicly known Mathematicians and Physicists, with their great reservoir of rhetoric expertise in said Fields; gradually presented and refined the essence of what the Author calls "Spirito Mathematics". A Philosophical concept that now appears to be publicly developing, with the utilization of some its speed and resolution power. The Author will give at least three examples of its speed and resolution power. One being the partial differential equation in the development of Wave Mechanics & Quantum Mechanics. Namely, [(-ih bar(squared)/2m)(2nd Part.Der. psi/ respect to x)] + V psi = ih bar -(Part.Der. psi/respect to t).

Physical Concepts and Mathematical Symbols

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

2007-12-01

According to traditional empiricist philosophy of science, concepts and meaning grow out of sense experience, and the mathematical structure of a physical theory is nothing but a formalisation of a given meaning-content. This view seems to work well in classical mechanics. But it breaks down in quantum physics, where we have a self-supported mathematical structure which resists any conceptual or pictorial interpretation in the traditional sense. Thus, traditional empiricism is flawed. Quantum physics teaches us that mathematics is a language in itself which extends beyond ordinary language. To understand the meaning of this extended language, we have to explore how new concepts and intuitions grow out of mathematics, not the other way around. The symbolic structure is prior to its meaning. This point of view is called linguistic empiricism, to stress that the connection with experience is still crucial. As cases, I compare the concept of stiffness in classical mechanics and the concept of electron density in quantum mechanics. The last case demonstrates that the wave function has a richer interpretation than the probabilistic one concerning measurement of position.

Oulipo: Applying Mathematical Constraints to Literature and the Arts in a Mathematics for the Liberal Arts Classroom

ERIC Educational Resources Information Center

Despeaux, Sloan Evans

2015-01-01

Oulipo (Ouvroir de Littérature potentielle, or Workshop on potential literature), an over 50-year old movement that began in France, seeks to apply mathematical constraints to literature and the arts. In this article, I will give a brief survey of this movement and how I have built a learning module based on it for my mathematics for the liberal…

Case Studies in Applied Mathematics.

ERIC Educational Resources Information Center

Mathematical Association of America, Washington, DC.

This collection of nine case studies in applied mathematics was written primarily for the use of the instructor by a Conference sponsored by the Committee on the Undergraduate Program in Mathematics (CUPM). Each chapter contains exercises of varying degrees of difficulty and several include student projects. The materials were used on a trial…

Applied Mathematics. Florida Teaching Supplement.

ERIC Educational Resources Information Center

Florida State Dept. of Education, Tallahassee. Div. of Vocational, Adult, and Community Education.

The information in this supplementary notebook is intended to provide teachers with additional materials, ideas and suggestions, and activities to help in implementing the first 21 units of the Applied Mathematics modules that help develop and refine job-related mathematics skills. An introduction lists the 36 units of the complete Applied…

Throw Away Your Mathematical Handbook! Undergraduate Physics with Wolfram|Alpha, a FREE(!) Internet-Based Mathematical Engine

NASA Astrophysics Data System (ADS)

Looney, Craig W.

2009-10-01

Wolfram|Alpha (http://www.wolframalpha.com/), a free internet-based mathematical engine released earlier this year, represents an orders-of magnitude advance in mathematical power freely available - without money, passwords, or downloads - on the web. Wolfram|Alpha is based on Mathematica, so it can plot functions, take derivatives, solve systems of equations, perform symbolic and numerical integration, and more. These capabilities (especially plotting and integration) will be explored in the context of topics covered in upper level undergraduate physics courses.

Mathematical Modeling: A Structured Process

ERIC Educational Resources Information Center

Anhalt, Cynthia Oropesa; Cortez, Ricardo

2015-01-01

Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…

Use of the "Moodle" Platform to Promote an Ongoing Learning When Lecturing General Physics in the Physics, Mathematics and Electronic Engineering Programmes at the University of the Basque Country UPV/EHU

ERIC Educational Resources Information Center

López, Gabriel A.; Sáenz, Jon; Leonardo, Aritz; Gurtubay, Idoia G.

2016-01-01

The "Moodle" platform has been used to put into practice an ongoing evaluation of the students' Physics learning process. The evaluation has been done on the frame of the course General Physics, which is lectured during the first year of the Physics, Mathematics and Electronic Engineering Programmes at the Faculty of Science and…

CICART Center For Integrated Computation And Analysis Of Reconnection And Turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhattacharjee, Amitava

CICART is a partnership between the University of New Hampshire (UNH) and Dartmouth College. CICART addresses two important science needs of the DoE: the basic understanding of magnetic reconnection and turbulence that strongly impacts the performance of fusion plasmas, and the development of new mathematical and computational tools that enable the modeling and control of these phenomena. The principal participants of CICART constitute an interdisciplinary group, drawn from the communities of applied mathematics, astrophysics, computational physics, fluid dynamics, and fusion physics. It is a main premise of CICART that fundamental aspects of magnetic reconnection and turbulence in fusion devices, smaller-scalemore » laboratory experiments, and space and astrophysical plasmas can be viewed from a common perspective, and that progress in understanding in any of these interconnected fields is likely to lead to progress in others. The establishment of CICART has strongly impacted the education and research mission of a new Program in Integrated Applied Mathematics in the College of Engineering and Applied Sciences at UNH by enabling the recruitment of a tenure-track faculty member, supported equally by UNH and CICART, and the establishment of an IBM-UNH Computing Alliance. The proposed areas of research in magnetic reconnection and turbulence in astrophysical, space, and laboratory plasmas include the following topics: (A) Reconnection and secondary instabilities in large high-Lundquist-number plasmas, (B) Particle acceleration in the presence of multiple magnetic islands, (C) Gyrokinetic reconnection: comparison with fluid and particle-in-cell models, (D) Imbalanced turbulence, (E) Ion heating, and (F) Turbulence in laboratory (including fusion-relevant) experiments. These theoretical studies make active use of three high-performance computer simulation codes: (1) The Magnetic Reconnection Code, based on extended two-fluid (or Hall MHD) equations, in an Adaptive Mesh Refinement (AMR) framework, (2) the Particle Simulation Code, a fully electromagnetic 3D Particle-In-Cell (PIC) code that includes a collision operator, and (3) GS2, an Eulerian, electromagnetic, kinetic code that is widely used in the fusion program, and simulates the nonlinear gyrokinetic equations, together with a self-consistent set of Maxwell’s equations.« less

Identification of biomechanical nonlinearity in whole-body vibration using a reverse path multi-input-single-output method

NASA Astrophysics Data System (ADS)

Huang, Ya; Ferguson, Neil S.

2018-04-01

The study implements a classic signal analysis technique, typically applied to structural dynamics, to examine the nonlinear characteristics seen in the apparent mass of a recumbent person during whole-body horizontal random vibration. The nonlinearity in the present context refers to the amount of 'output' that is not correlated or coherent to the 'input', usually indicated by values of the coherence function that are less than unity. The analysis is based on the longitudinal horizontal inline and vertical cross-axis apparent mass of twelve human subjects exposed to 0.25-20 Hz random acceleration vibration at 0.125 and 1.0 ms-2 r.m.s. The conditioned reverse path frequency response functions (FRF) reveal that the uncorrelated 'linear' relationship between physical input (acceleration) and outputs (inline and cross-axis forces) has much greater variation around the primary resonance frequency between 0.5 and 5 Hz. By reversing the input and outputs of the physical system, it is possible to assemble additional mathematical inputs from the physical output forces and mathematical constructs (e.g. square root of inline force). Depending on the specific construct, this can improve the summed multiple coherence at frequencies where the response magnitude is low. In the present case this is between 6 and 20 Hz. The statistical measures of the response force time histories of each of the twelve subjects indicate that there are potential anatomical 'end-stops' for the sprung mass in the inline axis. No previous study has applied this reverse path multi-input-single-output approach to human vibration kinematic and kinetic data before. The implementation demonstrated in the present study will allow new and existing data to be examined using this different analytical tool.

Dilemma in Teaching Mathematics

ERIC Educational Resources Information Center

Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain

2012-01-01

The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…

Exploring Differential Effects of Mathematics Courses on Mathematics Achievement

ERIC Educational Resources Information Center

Ma, Xin; McIntyre, Laureen J.

2005-01-01

Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…

Mathematics Underground

ERIC Educational Resources Information Center

Luther, Kenneth H.

2012-01-01

Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…

Applied Physics Education: PER focused on Physics-Intensive Careers

NASA Astrophysics Data System (ADS)

Zwickl, Benjamin

2017-01-01

Physics education research is moving beyond classroom learning to study the application of physics education within STEM jobs and PhD-level research. Workforce-related PER is vital to supporting physics departments as they educate students for a diverse range of careers. Results from an on-going study involving interviews with entry-level employees, academic researchers, and supervisors in STEM jobs describe the ways that mathematics, physics, and communication are needed for workplace success. Math and physics are often used for solving ill-structured problems that involve data analysis, computational modeling, or hands-on work. Communication and collaboration are utilized in leadership, sales, and as way to transfer information capital throughout the organization through documentation, emails, memos, and face-to-face discussions. While managers and advisors think a physics degree typically establishes technical competency, communication skills are vetted through interviews and developed on the job. Significant learning continues after graduation, showing the importance of cultivating self-directed learning habits and the critical role of employers as educators of specialized technical abilities through on-the-job training. Supported by NSF DGE-1432578.

An Analysis of the Changes in Ability and Knowledge of Students Taking A-Level Physics and Mathematics over a 35 Year Period

ERIC Educational Resources Information Center

Barham, Peter J.

2012-01-01

New undergraduate students arriving to study physics at the University of Bristol from 1975 onwards have all taken the same test of their knowledge and understanding of physics and mathematics. Many of the questions test knowledge of material that has been in the A-level syllabus for maths or physics throughout this period. The ability of incoming…

Do Students Trust in Mathematics or Intuition during Physics Problem Solving? An Epistemic Game Perspective

ERIC Educational Resources Information Center

Yavuz, Ahmet

2015-01-01

This study aims to investigate (1) students' trust in mathematics calculation versus intuition in a physics problem solving and (2) whether this trust is related to achievement in physics in the context of epistemic game theoretical framework. To achieve this research objective, paper-pencil and interview sessions were conducted. A paper-pencil…

Interdisciplinary Mathematics-Physics Approaches to Teaching the Concept of Angle in Elementary School

ERIC Educational Resources Information Center

Munier, Valerie; Merle, Helene

2009-01-01

The present study takes an interdisciplinary mathematics-physics approach to the acquisition of the concept of angle by children in Grades 3-5. This paper first presents the theoretical framework we developed, then we analyse the concept of angle and the difficulties pupils have with it. Finally, we report three experimental physics-based teaching…

Mathematical Physics in Italy in the XIX Century: The Theory of Elasticity

NASA Astrophysics Data System (ADS)

Capecchi, Danilo

In the second half of the nineteenth century there was in Italy an important group of mathematicians who focused their attention on mathematical physics. The most prominent of them were Enrico Betti, Eugenio Beltrami, Gregorio Ricci-Curbastro and some others (Vito Volterra, Carlo Somigliana and Tullio Levi Civita) whose activity persevered for many years in the twentieth century. In this article, I will write about the contribution of this group to the theory of elasticity. The best representative writing on continuum mechanics and elasticity as theories of mathematical physics is presented in the book Teoria della elasticità by Enrico Betti. The book is interesting not only for the particular results found but also for its structure which became paradigmatic for the development of subsequent texts on elasticity, not only those in Italian. Betti's interest was concentrated on the mathematical aspects of a physical theory. Physical principles are not discussed; they are only exposed in the most formal way possible. The objective is to arrive, without discussing epistemological or empirical problems, at the formulation and solution of differential equations that rule elasticity, as had become classic in the emerging mathematical physics. Beltrami wrote no complete books on elasticity; however, his contribution to this field was perhaps more original than that of Betti. A similar consideration holds true for Volterra and Somigliana.

Optimisation by hierarchical search

NASA Astrophysics Data System (ADS)

Zintchenko, Ilia; Hastings, Matthew; Troyer, Matthias

2015-03-01

Finding optimal values for a set of variables relative to a cost function gives rise to some of the hardest problems in physics, computer science and applied mathematics. Although often very simple in their formulation, these problems have a complex cost function landscape which prevents currently known algorithms from efficiently finding the global optimum. Countless techniques have been proposed to partially circumvent this problem, but an efficient method is yet to be found. We present a heuristic, general purpose approach to potentially improve the performance of conventional algorithms or special purpose hardware devices by optimising groups of variables in a hierarchical way. We apply this approach to problems in combinatorial optimisation, machine learning and other fields.

Nonlinear Elasticity

NASA Astrophysics Data System (ADS)

Fu, Y. B.; Ogden, R. W.

2001-05-01

This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

A class of traveling wave solutions for space-time fractional biological population model in mathematical physics

NASA Astrophysics Data System (ADS)

Akram, Ghazala; Batool, Fiza

2017-10-01

The (G'/G)-expansion method is utilized for a reliable treatment of space-time fractional biological population model. The method has been applied in the sense of the Jumarie's modified Riemann-Liouville derivative. Three classes of exact traveling wave solutions, hyperbolic, trigonometric and rational solutions of the associated equation are characterized with some free parameters. A generalized fractional complex transform is applied to convert the fractional equations to ordinary differential equations which subsequently resulted in number of exact solutions. It should be mentioned that the (G'/G)-expansion method is very effective and convenient for solving nonlinear partial differential equations of fractional order whose balancing number is a negative integer.

Rethinking Mathematics.

ERIC Educational Resources Information Center

Abad, Ernesto A.

1994-01-01

Poses solutions for our failure to show students how well mathematics interlocks with the physical structures of the Universe. Some examples are provided to illustrate the natural integration of mathematics and science. (ZWH)

Mathematics Ab Ovo: Hans Driesch and Entwicklungsmechanik.

PubMed

Priven, Silvia Waisse; Alfonso-Goldfarb, Ana M

2009-01-01

One of the factors leading to the creation of embryology as a modern discipline at the end of the 19th century was Wilhelm Roux's formulation of the program of Entwicklungsmechanik (developmental mechanics). A look into the work of Hans Driesch, an equal contributor to developmental mechanics, may shed further light on this process. For Roux, developmental mechanics was an anatomical science, but for Driesch it was associated with a mathematical and physical approach to the natural world. Likewise, Roux used the concept of mechanics as an analogy, but Driesch used it literally. Driesch's generation had been trained in a pedagogic context that emphasized mathematics and physics, which may explain why he went a step further than Roux to state that a true "mechanics" of development required the reduction of morphogenetic problems to the known laws of physics. It is argued here that this difference in background is behind the enthusiastic adoption and further development of Roux's program by Driesch's generation, a generation that conceived Entwicklungsmechanik to be the reduction of embryological processes to "the laws of matter in motion." This same mathematical and physical mindset would underscore Driesch's later construction of entelechy as a regulating factor in embryogenesis, through mathematical analysis grounded on the notion of mathematical functions.

Poly (lactic-co-glycolic acid) controlled release systems: experimental and modeling insights

PubMed Central

Hines, Daniel J.; Kaplan, David L.

2013-01-01

Poly-lactic-co-glycolic acid (PLGA) has been the most successful polymeric biomaterial for use in controlled drug delivery systems. There are several different chemical and physical properties of PLGA that impact the release behavior of drugs from PLGA delivery devices. These properties must be considered and optimized in drug release device formulation. Mathematical modeling is a useful tool for identifying, characterizing, and predicting the mechanisms of controlled release. The advantages and limitations of poly (lactic-co-glycolic acid) for controlled release are reviewed, followed by a review of current approaches in controlled release technology that utilize PLGA. Mathematical modeling applied towards controlled release rates from PLGA-based devices will also be discussed to provide a complete picture of state of the art understanding of the control achievable with this polymeric system, as well as the limitations. PMID:23614648

Acceleration of neutrons in a scheme of a tautochronous mathematical pendulum (physical principles)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rivlin, Lev A

We consider the physical principles of neutron acceleration through a multiple synchronous interaction with a gradient rf magnetic field in a scheme of a tautochronous mathematical pendulum. (laser applications and other aspects of quantum electronics)

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-02-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-12-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-11-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Moving beyond the Barriers: Supporting Meaningful Teacher Collaboration to Improve Secondary School Mathematics

ERIC Educational Resources Information Center

Jao, Limin; McDougall, Doug

2016-01-01

The Collaborative Teacher Inquiry Project was a professional development initiative that sought to improve the teaching and learning of Grade 9 Applied mathematics by encouraging teachers to work collaboratively. The project brought together Grade 9 Applied mathematics teachers from 11 schools across four neighboring public school boards in the…

How High Is the Tramping Track? Mathematising and Applying in a Calculus Model-Eliciting Activity

ERIC Educational Resources Information Center

Yoon, Caroline; Dreyfus, Tommy; Thomas, Michael O. J.

2010-01-01

Two complementary processes involved in mathematical modelling are mathematising a realistic situation and applying a mathematical technique to a given realistic situation. We present and analyse work from two undergraduate students and two secondary school teachers who engaged in both processes during a mathematical modelling task that required…

High-Productivity Computing in Computational Physics Education

NASA Astrophysics Data System (ADS)

Tel-Zur, Guy

2011-03-01

We describe the development of a new course in Computational Physics at the Ben-Gurion University. This elective course for 3rd year undergraduates and MSc. students is being taught during one semester. Computational Physics is by now well accepted as the Third Pillar of Science. This paper's claim is that modern Computational Physics education should deal also with High-Productivity Computing. The traditional approach of teaching Computational Physics emphasizes ``Correctness'' and then ``Accuracy'' and we add also ``Performance.'' Along with topics in Mathematical Methods and case studies in Physics the course deals a significant amount of time with ``Mini-Courses'' in topics such as: High-Throughput Computing - Condor, Parallel Programming - MPI and OpenMP, How to build a Beowulf, Visualization and Grid and Cloud Computing. The course does not intend to teach neither new physics nor new mathematics but it is focused on an integrated approach for solving problems starting from the physics problem, the corresponding mathematical solution, the numerical scheme, writing an efficient computer code and finally analysis and visualization.

Quantifying Astronaut Tasks: Robotic Technology and Future Space Suit Design

NASA Technical Reports Server (NTRS)

Newman, Dava

2003-01-01

The primary aim of this research effort was to advance the current understanding of astronauts' capabilities and limitations in space-suited EVA by developing models of the constitutive and compatibility relations of a space suit, based on experimental data gained from human test subjects as well as a 12 degree-of-freedom human-sized robot, and utilizing these fundamental relations to estimate a human factors performance metric for space suited EVA work. The three specific objectives are to: 1) Compile a detailed database of torques required to bend the joints of a space suit, using realistic, multi- joint human motions. 2) Develop a mathematical model of the constitutive relations between space suit joint torques and joint angular positions, based on experimental data and compare other investigators' physics-based models to experimental data. 3) Estimate the work envelope of a space suited astronaut, using the constitutive and compatibility relations of the space suit. The body of work that makes up this report includes experimentation, empirical and physics-based modeling, and model applications. A detailed space suit joint torque-angle database was compiled with a novel experimental approach that used space-suited human test subjects to generate realistic, multi-joint motions and an instrumented robot to measure the torques required to accomplish these motions in a space suit. Based on the experimental data, a mathematical model is developed to predict joint torque from the joint angle history. Two physics-based models of pressurized fabric cylinder bending are compared to experimental data, yielding design insights. The mathematical model is applied to EVA operations in an inverse kinematic analysis coupled to the space suit model to calculate the volume in which space-suited astronauts can work with their hands, demonstrating that operational human factors metrics can be predicted from fundamental space suit information.

Tables of the Inverse Laplace Transform of the Function [Formula: see text].

PubMed

Dishon, Menachem; Bendler, John T; Weiss, George H

1990-01-01

The inverse transform, [Formula: see text], 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g ( t ). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g ( t ) for a number of values of β between 0.25 and 0.999. In addition, since g ( t ), regarded as a function of β , is uni-modal with a peak occurring at t = t max we both tabulate and graph t max and 1/ g ( t max ) as a function of β , as well as giving polynomial approximations to 1/ g ( t max ).

Tables of the Inverse Laplace Transform of the Function e−sβ

PubMed Central

Dishon, Menachem; Bendler, John T.; Weiss, George H.

1990-01-01

The inverse transform, g(t)=L−1(e−sβ), 0 < β < 1, is a stable law that arises in a number of different applications in chemical physics, polymer physics, solid-state physics, and applied mathematics. Because of its important applications, a number of investigators have suggested approximations to g(t). However, there have so far been no accurately calculated values available for checking or other purposes. We present here tables, accurate to six figures, of g(t) for a number of values of β between 0.25 and 0.999. In addition, since g(t), regarded as a function of β, is uni-modal with a peak occurring at t = tmax we both tabulate and graph tmax and 1/g(tmax) as a function of β, as well as giving polynomial approximations to 1/g(tmax). PMID:28179785

Deriving Accessible Science Books for the Blind Students of Physics

NASA Astrophysics Data System (ADS)

Kouroupetroglou, Georgios; Kacorri, Hernisa

2010-01-01

We present a novel integrated methodology for the development and production of accessible physics and science books from the elementary up to tertiary educational levels. This language independent approach adopts the Design-for-All principles, the available international standards for alternative formats and the Universal Design for Learning (UDL) Guidelines. Moreover it supports both static (embossed and refreshable tactile) and dynamic (based on synthetic speech and other sounds) accessibility. It can produce Tactile Books (Embossed Braille and Tactile Graphics), Digital Talking Books (or Digital Audio Books), Large Print Books as well as Acoustic-Tactile Books for the blind and visually impaired students as well as but for the print-disabled. This methodology has been successfully applied in the case of blind students of the Physics, Mathematics and Informatics Departments in the University of Athens.

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2014-12-01

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

Physics through the 1990s: Elementary-particle physics

NASA Astrophysics Data System (ADS)

The volume begins with a non-mathematical discussion of the motivation behind, and basic ideas of, elementary-particle physics theory and experiment. The progress over the past two decades with the quark model and unification of the electromagnetic and weak interactions is reviewed. Existing theoretical problems in the field, such as the origin of mass and the unification of the fundamental forces, are detailed, along with experimental programs to test the new theories. Accelerators, instrumentation, and detectors are described for both current and future facilities. Interactions with other areas of both theoretical and applied physics are presented. The sociology of the field is examined regarding the education of graduate students, the organization necessary in large-scale experiments, and the decision-making process involved in high-cost experiments. Finally, conclusions and recommendations for maintaining US excellence in theory and experiment are given. Appendices list both current and planned accelerators, and present statistical data on the US elementary-particle physics program. A glossary is included.

Physics through the 1990s: elementary-particle physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1986-01-01

The volume begins with a non-mathematical discussion of the motivation behind, and basic ideas of, elementary-particle physics theory and experiment. The progress over the past two decades with the quark model and unification of the electromagnetic and weak interactions is reviewed. Existing theoretical problems in the field, such as the origin of mass and the unification of the fundamental forces, are detailed, along with experimental programs to test the new theories. Accelerators, instrumentation, and detectors are described for both current and future facilities. Interactions with other areas of both theoretical and applied physics are presented. The sociology of the fieldmore » is examined regarding the education of graduate students, the organization necessary in large-scale experiments, and the decision-making process involved in high-cost experiments. Finally, conclusions and recommendations for maintaining US excellence in theory and experiment are given. Appendices list both current and planned accelerators, and present statistical data on the US elementary-particle physics program. A glossary is included.« less

Physics through the 1990s: Elementary-particle physics

NASA Technical Reports Server (NTRS)

1986-01-01

The volume begins with a non-mathematical discussion of the motivation behind, and basic ideas of, elementary-particle physics theory and experiment. The progress over the past two decades with the quark model and unification of the electromagnetic and weak interactions is reviewed. Existing theoretical problems in the field, such as the origin of mass and the unification of the fundamental forces, are detailed, along with experimental programs to test the new theories. Accelerators, instrumentation, and detectors are described for both current and future facilities. Interactions with other areas of both theoretical and applied physics are presented. The sociology of the field is examined regarding the education of graduate students, the organization necessary in large-scale experiments, and the decision-making process involved in high-cost experiments. Finally, conclusions and recommendations for maintaining US excellence in theory and experiment are given. Appendices list both current and planned accelerators, and present statistical data on the US elementary-particle physics program. A glossary is included.

Double density dynamics: realizing a joint distribution of a physical system and a parameter system

NASA Astrophysics Data System (ADS)

Fukuda, Ikuo; Moritsugu, Kei

2015-11-01

To perform a variety of types of molecular dynamics simulations, we created a deterministic method termed ‘double density dynamics’ (DDD), which realizes an arbitrary distribution for both physical variables and their associated parameters simultaneously. Specifically, we constructed an ordinary differential equation that has an invariant density relating to a joint distribution of the physical system and the parameter system. A generalized density function leads to a physical system that develops under nonequilibrium environment-describing superstatistics. The joint distribution density of the physical system and the parameter system appears as the Radon-Nikodym derivative of a distribution that is created by a scaled long-time average, generated from the flow of the differential equation under an ergodic assumption. The general mathematical framework is fully discussed to address the theoretical possibility of our method, and a numerical example representing a 1D harmonic oscillator is provided to validate the method being applied to the temperature parameters.

Fermilab Today

Science.gov Websites

standard for special mathematical functions A new standard for mathematical special functions in C++ has the standard are frequently used in applications of high-energy physics and other mathematical

The Effect of Syllabus on Mathematical Knowledge

ERIC Educational Resources Information Center

Belsom, C. G. H.; Elton, L. R. B.

1974-01-01

Item analysis of a mathematics preknowledge test given to physics students revealed that significant differences existed on certain items between groups of students who had followed different mathematics syllabuses. (MLH)

PREFACE: Counting Complexity: An international workshop on statistical mechanics and combinatorics

NASA Astrophysics Data System (ADS)

de Gier, Jan; Warnaar, Ole

2006-07-01

On 10-15 July 2005 the conference `Counting Complexity: An international workshop on statistical mechanics and combinatorics' was held on Dunk Island, Queensland, Australia in celebration of Tony Guttmann's 60th birthday. Dunk Island provided the perfect setting for engaging in almost all of Tony's life-long passions: swimming, running, food, wine and, of course, plenty of mathematics and physics. The conference was attended by many of Tony's close scientific friends from all over the world, and most talks were presented by his past and present collaborators. This volume contains the proceedings of the meeting and consists of 24 refereed research papers in the fields of statistical mechanics, condensed matter physics and combinatorics. These papers provide an excellent illustration of the breadth and scope of Tony's work. The very first contribution, written by Stu Whittington, contains an overview of the many scientific achievements of Tony over the past 40 years in mathematics and physics. The organizing committee, consisting of Richard Brak, Aleks Owczarek, Jan de Gier, Emma Lockwood, Andrew Rechnitzer and Ole Warnaar, gratefully acknowledges the Australian Mathematical Society (AustMS), the Australian Mathematical Sciences Institute (AMSI), the ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS), the ARC Complex Open Systems Research Network (COSNet), the Institute of Physics (IOP) and the Department of Mathematics and Statistics of The University of Melbourne for financial support in organizing the conference. Tony, we hope that your future years in mathematics will be numerous. Count yourself lucky! Tony Guttman

How Much Space Does a Library Need? Justifying Collections Space in an Electronic Age

ERIC Educational Resources Information Center

Butkovich, Nancy J.

2010-01-01

In 2002, plans to merge Penn State's Physical Sciences Library and Mathematics Library provoked a controversy in the Eberly College of Science over the size of the library needed to support its departments. The College contended that a physical collection no more than 5 years old was adequate. A study of astronomy, chemistry, mathematics, physics,…

Behaviour of mathematics and physics students in solving problem of Vector-Physics context

NASA Astrophysics Data System (ADS)

Sardi; Rizal, M.; Mansyur, J.

2018-04-01

This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.

Bell's Inequality: Revolution in Quantum Physics or Just AN Inadequate Mathematical Model?

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

The main aim of this review is to stress the role of mathematical models in physics. The Bell inequality (BI) is often called the "most famous inequality of the 20th century." It is commonly accepted that its violation in corresponding experiments induced a revolution in quantum physics. Unlike "old quantum mechanics" (of Einstein, Schrodinger Bohr, Heisenberg, Pauli, Landau, Fock), "modern quantum mechanics" (of Bell, Aspect, Zeilinger, Shimony, Green-berger, Gisin, Mermin) takes seriously so called quantum non-locality. We will show that the conclusion that one has to give up the realism (i.e., a possibility to assign results of measurements to physical systems) or the locality (i.e., to assume action at a distance) is heavily based on one special mathematical model. This model was invented by A. N. Kolmogorov in 1933. One should pay serious attention to the role of mathematical models in physics. The problems of the realism and locality induced by Bell's argument can be solved by using non-Kolmogorovian probabilistic models. We compare this situation with non-Euclidean geometric models in relativity theory.

Mathematics and complex systems.

PubMed

Foote, Richard

2007-10-19

Contemporary researchers strive to understand complex physical phenomena that involve many constituents, may be influenced by numerous forces, and may exhibit unexpected or emergent behavior. Often such "complex systems" are macroscopic manifestations of other systems that exhibit their own complex behavior and obey more elemental laws. This article proposes that areas of mathematics, even ones based on simple axiomatic foundations, have discernible layers, entirely unexpected "macroscopic" outcomes, and both mathematical and physical ramifications profoundly beyond their historical beginnings. In a larger sense, the study of mathematics itself, which is increasingly surpassing the capacity of researchers to verify "by hand," may be the ultimate complex system.

Bouncing Balls and Graphing Derivatives

ERIC Educational Resources Information Center

Cory, Beth

2010-01-01

National Council of Teachers of Mathematics' (NCTM's) (2000) Connections Standard states that students should "recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect ...; [and] recognize and apply mathematics in contexts outside of mathematics" (p. 354). This article presents an in-depth…

Stochastic theory of nonequilibrium steady states and its applications. Part I

NASA Astrophysics Data System (ADS)

Zhang, Xue-Juan; Qian, Hong; Qian, Min

2012-01-01

The concepts of equilibrium and nonequilibrium steady states are introduced in the present review as mathematical concepts associated with stationary Markov processes. For both discrete stochastic systems with master equations and continuous diffusion processes with Fokker-Planck equations, the nonequilibrium steady state (NESS) is characterized in terms of several key notions which are originated from nonequilibrium physics: time irreversibility, breakdown of detailed balance, free energy dissipation, and positive entropy production rate. After presenting this NESS theory in pedagogically accessible mathematical terms that require only a minimal amount of prerequisites in nonlinear differential equations and the theory of probability, it is applied, in Part I, to two widely studied problems: the stochastic resonance (also known as coherent resonance) and molecular motors (also known as Brownian ratchet). Although both areas have advanced rapidly on their own with a vast amount of literature, the theory of NESS provides them with a unifying mathematical foundation. Part II of this review contains applications of the NESS theory to processes from cellular biochemistry, ranging from enzyme catalyzed reactions, kinetic proofreading, to zeroth-order ultrasensitivity.

A numerical solution of the problem of crown forest fire initiation and spread

NASA Astrophysics Data System (ADS)

Marzaeva, S. I.; Galtseva, O. V.

2018-05-01

Mathematical model of forest fire was based on an analysis of known experimental data and using concept and methods from reactive media mechanics. The study takes in to account the mutual interaction of the forest fires and three-dimensional atmosphere flows. The research is done by means of mathematical modeling of physical processes. It is based on numerical solution of Reynolds equations for chemical components and equations of energy conservation for gaseous and condensed phases. It is assumed that the forest during a forest fire can be modeled as a two-temperature multiphase non-deformable porous reactive medium. A discrete analog for the system of equations was obtained by means of the control volume method. The developed model of forest fire initiation and spreading would make it possible to obtain a detailed picture of the variation in the velocity, temperature and chemical species concentration fields with time. Mathematical model and the result of the calculation give an opportunity to evaluate critical conditions of the forest fire initiation and spread which allows applying the given model for of means for preventing fires.

Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques - project status and first results

NASA Astrophysics Data System (ADS)

Schmidt, M.; Hugentobler, U.; Jakowski, N.; Dettmering, D.; Liang, W.; Limberger, M.; Wilken, V.; Gerzen, T.; Hoque, M.; Berdermann, J.

2012-04-01

Near real-time high resolution and high precision ionosphere models are needed for a large number of applications, e.g. in navigation, positioning, telecommunications or astronautics. Today these ionosphere models are mostly empirical, i.e., based purely on mathematical approaches. In the DFG project 'Multi-scale model of the ionosphere from the combination of modern space-geodetic satellite techniques (MuSIK)' the complex phenomena within the ionosphere are described vertically by combining the Chapman electron density profile with a plasmasphere layer. In order to consider the horizontal and temporal behaviour the fundamental target parameters of this physics-motivated approach are modelled by series expansions in terms of tensor products of localizing B-spline functions depending on longitude, latitude and time. For testing the procedure the model will be applied to an appropriate region in South America, which covers relevant ionospheric processes and phenomena such as the Equatorial Anomaly. The project connects the expertise of the three project partners, namely Deutsches Geodätisches Forschungsinstitut (DGFI) Munich, the Institute of Astronomical and Physical Geodesy (IAPG) of the Technical University Munich (TUM) and the German Aerospace Center (DLR), Neustrelitz. In this presentation we focus on the current status of the project. In the first year of the project we studied the behaviour of the ionosphere in the test region, we setup appropriate test periods covering high and low solar activity as well as winter and summer and started the data collection, analysis, pre-processing and archiving. We developed partly the mathematical-physical modelling approach and performed first computations based on simulated input data. Here we present information on the data coverage for the area and the time periods of our investigations and we outline challenges of the multi-dimensional mathematical-physical modelling approach. We show first results, discuss problems in modelling and possible solution strategies and finally, we address open questions.

Teachers' Perception of Their Preparedness to Apply Facilitation Teaching in Secondary School Mathematics Instruction by Teacher Characteristics

ERIC Educational Resources Information Center

Ng'eno, J. K.; Chesimet, M. C.

2015-01-01

This study set out to find out the differences in teachers' perception of their preparedness to apply facilitation methods in teaching secondary school mathematics. Facilitation methods allow learners to be actively involved in the teaching and learning of mathematics hence making them be co-creators of knowledge. Facilitation teaching allow…

Why do we need theories?

PubMed Central

Longo, Giuseppe; Soto, Ana M.

2017-01-01

Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetries, and thus the opposite of symmetry conservation, a central component of physical theories. This instability corresponds to the changes of the environment and the phenotypes. Inspired by Galileo’s principle of inertia, the “default state” of inert matter, we propose a “default state” for biological dynamics following Darwin’s first principle, “descent with modification” that we transform into “proliferation with variation and motility” as a property that spans life, including cells in an organism. These dissimilarities between theories of the inert and of biology also apply to causality: biological causality is to be understood in relation to the distinctive role that constraints assume in this discipline. Consequently, the notion of cause will be reframed in a context where constraints to activity are seen as the core component of biological analyses. Finally, we assert that the radical materiality of life rules out distinctions such as “software vs. hardware.” PMID:27390105

Why do we need theories?

PubMed

Longo, Giuseppe; Soto, Ana M

2016-10-01

Theories organize knowledge and construct objectivity by framing observations and experiments. The elaboration of theoretical principles is examined in the light of the rich interactions between physics and mathematics. These two disciplines share common principles of construction of concepts and of the proper objects of inquiry. Theory construction in physics relies on mathematical symmetries that preserve the key invariants observed and proposed by such theory; these invariants buttress the idea that the objects of physics are generic and thus interchangeable and they move along specific trajectories which are uniquely determined, in classical and relativistic physics. In contrast to physics, biology is a historical science that centers on the changes that organisms experience while undergoing ontogenesis and phylogenesis. Biological objects, namely organisms, are not generic but specific; they are individuals. The incessant changes they undergo represent the breaking of symmetries, and thus the opposite of symmetry conservation, a central component of physical theories. This instability corresponds to the changes of the environment and the phenotypes. Inspired by Galileo's principle of inertia, the "default state" of inert matter, we propose a "default state" for biological dynamics following Darwin's first principle, "descent with modification" that we transform into "proliferation with variation and motility" as a property that spans life, including cells in an organism. These dissimilarities between theories of the inert and of biology also apply to causality: biological causality is to be understood in relation to the distinctive role that constraints assume in this discipline. Consequently, the notion of cause will be reframed in a context where constraints to activity are seen as the core component of biological analyses. Finally, we assert that the radical materiality of life rules out distinctions such as "software vs. hardware." Copyright © 2016 Elsevier Ltd. All rights reserved.

MO-DE-BRA-05: Developing Effective Medical Physics Knowledge Structures: Models and Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sprawls, P

Purpose: Develop a method and supporting online resources to be used by medical physics educators for teaching medical imaging professionals and trainees so they develop highly-effective physics knowledge structures that can contribute to improved diagnostic image quality on a global basis. Methods: The different types of mental knowledge structures were analyzed and modeled with respect to both the learning and teaching process for their development and the functions or tasks that can be performed with the knowledge. While symbolic verbal and mathematical knowledge structures are very important in medical physics for many purposes, the tasks of applying physics in clinicalmore » imaging--especially to optimize image quality and diagnostic accuracy--requires a sensory conceptual knowledge structure, specifically, an interconnected network of visually based concepts. This type of knowledge supports tasks such as analysis, evaluation, problem solving, interacting, and creating solutions. Traditional educational methods including lectures, online modules, and many texts are serial procedures and limited with respect to developing interconnected conceptual networks. A method consisting of the synergistic combination of on-site medical physics teachers and the online resource, CONET (Concept network developer), has been developed and made available for the topic Radiographic Image Quality. This was selected as the inaugural topic, others to follow, because it can be used by medical physicists teaching the large population of medical imaging professionals, such as radiology residents, who can apply the knowledge. Results: Tutorials for medical physics educators on developing effective knowledge structures are being presented and published and CONET is available with open access for all to use. Conclusion: An adjunct to traditional medical physics educational methods with the added focus on sensory concept development provides opportunities for medical physics teachers to share their knowledge and experience at a higher cognitive level and produce medical professionals with the enhanced ability to apply physics to clinical procedures.« less

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, B.; Wood, R.T.

1997-04-22

A method is described for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical model. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system. 1 fig.

Automated method for the systematic interpretation of resonance peaks in spectrum data

DOEpatents

Damiano, Brian; Wood, Richard T.

1997-01-01

A method for spectral signature interpretation. The method includes the creation of a mathematical model of a system or process. A neural network training set is then developed based upon the mathematical model. The neural network training set is developed by using the mathematical model to generate measurable phenomena of the system or process based upon model input parameter that correspond to the physical condition of the system or process. The neural network training set is then used to adjust internal parameters of a neural network. The physical condition of an actual system or process represented by the mathematical model is then monitored by extracting spectral features from measured spectra of the actual process or system. The spectral features are then input into said neural network to determine the physical condition of the system or process represented by the mathematical. More specifically, the neural network correlates the spectral features (i.e. measurable phenomena) of the actual process or system with the corresponding model input parameters. The model input parameters relate to specific components of the system or process, and, consequently, correspond to the physical condition of the process or system.

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

44 CFR 67.6 - Basis of appeal.

Code of Federal Regulations, 2010 CFR

2010-10-01

... absolute (except where mathematical or measurement error or changed physical conditions can be demonstrated... a mathematical or measurement error or changed physical conditions, then the specific source of the... registered professional engineer or licensed land surveyor, of the new data necessary for FEMA to conduct a...

PHYS-MA-TECH. An Integrated Partnership.

ERIC Educational Resources Information Center

Scarborough, Jule Dee

This document contains 45 integrated physics, mathematics, and technology curriculum modules developed by teachers at 5 Illinois schools. An introduction discusses the collaborative project, in which teams of one mathematics, physics, and technology teacher from each school developed innovative instructional delivery models that enabled the three…

Aviation Maintenance Technology. General. G101 Aviation Mathematics and Physics. Instructor Material.

ERIC Educational Resources Information Center

Oklahoma State Board of Vocational and Technical Education, Stillwater. Curriculum and Instructional Materials Center.

These instructor materials for an aviation maintenance technology course contain three instructional modules covering safety, aviation mathematics, and aviation physics. Each module may contain an introduction and module objective, specific objectives, an instructor's module implementation guide, technical information supplements, transparency…

An appraisal of an online tutorial system for the teaching and learning of engineering physics in conjunction with contextual physics and mathematics, and relevant mathematics

NASA Astrophysics Data System (ADS)

Bhathal, Ragbir

2016-09-01

The number of students entering engineering schools in Australian universities has increased tremendously over the last few years because of the Australian Federal Government's policy of increasing the participation rates of Higher School Certificate students and students from low social economic status backgrounds in the tertiary sector. They now come with a diverse background of skills, motivations and prior knowledge. It is imperative that new methods of teaching and learning be developed. This paper describes an online tutorial system used in conjunction with contextual physics and mathematics, and the revision of the relevant mathematical knowledge at the appropriate time before a new topic is introduced in the teaching and learning of engineering physics. Taken as a whole, this study shows that students not only improved their final examination results but there was also an increase in the retention rate of first-year engineering students which has financial implications for the university.

The Combination of Just-in-Time Teaching and Wikispaces in Physics Classrooms

NASA Astrophysics Data System (ADS)

Mohottala, Hashini E.

2013-01-01

The general student population enrolled in today's physics classrooms is diverse. They come from a variety of different educational backgrounds. Some demonstrate a good knowledge of natural laws of physics with a better understanding of mathematical concepts, while others show a fair knowledge in fundamentals of physics with a minimum knowledge in mathematics. There are few who have not been exposed to physics or mathematics in their high schools (or at least they claim it to be the case). In addition, now we have "nontraditional" students: working part-time students, older students, commuting students, and, occasionally, military veterans. Regardless of the background, the majority of the students show little or no interest in physics and exhibit anxiety toward learning the subject. In order to address such a diverse and often unmotivated student population, and excite them about physics in a timely manner, we should deviate from conventional teaching techniques. Just-in-Time Teaching (JiTT) combined with wikis is an excellent way to accomplish this goal.

Comparison of anaerobic threshold determined by visual and mathematical methods in healthy women.

PubMed

Higa, M N; Silva, E; Neves, V F C; Catai, A M; Gallo, L; Silva de Sá, M F

2007-04-01

Several methods are used to estimate anaerobic threshold (AT) during exercise. The aim of the present study was to compare AT obtained by a graphic visual method for the estimate of ventilatory and metabolic variables (gold standard), to a bi-segmental linear regression mathematical model of Hinkley's algorithm applied to heart rate (HR) and carbon dioxide output (VCO2) data. Thirteen young (24 +/- 2.63 years old) and 16 postmenopausal (57 +/- 4.79 years old) healthy and sedentary women were submitted to a continuous ergospirometric incremental test on an electromagnetic braking cycloergometer with 10 to 20 W/min increases until physical exhaustion. The ventilatory variables were recorded breath-to-breath and HR was obtained beat-to-beat over real time. Data were analyzed by the nonparametric Friedman test and Spearman correlation test with the level of significance set at 5%. Power output (W), HR (bpm), oxygen uptake (VO2; mL kg(-1) min(-1)), VO2 (mL/min), VCO2 (mL/min), and minute ventilation (VE; L/min) data observed at the AT level were similar for both methods and groups studied (P > 0.05). The VO2 (mL kg(-1) min(-1)) data showed significant correlation (P < 0.05) between the gold standard method and the mathematical model when applied to HR (rs = 0.75) and VCO2 (rs = 0.78) data for the subjects as a whole (N = 29). The proposed mathematical method for the detection of changes in response patterns of VCO2 and HR was adequate and promising for AT detection in young and middle-aged women, representing a semi-automatic, non-invasive and objective AT measurement.

PREFACE: Physics-Based Mathematical Models for Nanotechnology

NASA Astrophysics Data System (ADS)

Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten

2008-03-01

In November 2007, some of the world's best nanoscientists and nanoengineers met at the Banff Centre, where the Banff International Research Station hosted a workshop on recent developments in the mathematical study of the physics of nanomaterials and nanostructures. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located in a scenic part of Alberta, Canada and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). We would like to thank the BIRS and its sponsors for the given opportunity and the BIRS staff for their excellent support during the workshop. Nanotechnology is the study and application of phenomena at or below the dimensions of 100 nm and has received a lot of public attention following popular accounts such as in the bestselling book by Michael Crichton, Prey. It is an area where fundamental questions of applied mathematics and mathematical physics, design of computational methodologies, physical insight, engineering and experimental techniques are meeting together in a quest for an adequate description of nanomaterials and nanostructures for applications in optoelectronics, medicine, energy-saving, bio- and other key technologies which will profoundly influence our life in the 21st century and beyond. There are already hundreds of applications in daily life such as in cosmetics and the hard drives in MP3 players (the 2007 Nobel prize in physics was recently awarded for the science that allowed the miniaturization of the drives), delivering drugs, high-definition DVD players and stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a task of enormous computational complexity in solving a large-scale many-body problem. On the other hand, taking each quantum dot in isolation would lead to a manageable task for modern supercomputers, but accounting for the wetting layer even in the individual quantum dot model would increase the computational complexity of the problem in several times. As a result, the entire problem in its generality would be hardly feasible from a practical, routine-based simulation, point of view. Moreover, in calculating atomic positions the definitions of atomic forces that enter the Hamiltonian in such large scale atomic simulations are approximate by nature and a number of important coupled effects, such as piezoelectric, remain frequently outside the scope of the analysis. To attack the problem in hand, one needs to resort to some clever averaging over atomic scales. Such averaging can be achieved by empirical tight-binding, pseudopotential, and k.p approximations. These approximations are very important in further development of mathematical models for LDSNs due to the fact they are well suited for incorporating additional effects into the model, including strain, piezoelectric effects, spontaneous polarization, geometric and materials nonlinearities. These effects, despite their importance, have not been studied with vigor they deserve, in particular in the context of mathematical models for bandstructure calculations. There is a growing interest to such models as they should provide a key to better predicting optoelectromechanical properties of LDSNs. With anticipated new discoveries in theoretical and experimental analysis of LDSNs in the coming years, one of the main emphases of the workshop was on the models that would allow incorporating these effects consistently into the state-of-the-art models for LDSNs. From a mathematical point of view, many such models can be reduced to a large eigenvalue PDE problem (e.g., with the Hamiltonian accounting for the Burt-Foreman correction) coupled to strain and piezoelectric potential calculation. In its turn, in its general setting the problem of strain and piezoelectric potential calculation requires the solution of a nonlinear system of partial differential equation. A large experience in solving these two parts of the problem separately, independently of each other, has been already accumulated in the distinct communities of the researchers. This BIRS workshop effectively combined expertise of these research communities, summarized the state-of-the-art for modeling LDSNs and key challenges facing these communities, and explored ways to address those challenges in interdisciplinary team settings. The workshop brought together researchers working on different aspects of the analysis and modeling of LDSNs which require a concerted efforts of teams of researchers with close interactions between applied and pure mathematicians, physicists (theoreticians and experimentalists), computational scientists, and engineers. These scientific and engineering communities were represented in Banff by the researchers from Japan, Canada, the USA, Russia, France, Denmark, Germany, and the UK (further details can be found at http://www.m2netlab.wlu.ca/ldsn-banff/). We had four main plenary talks of one hour duration that gave state-of-the-art overviews of the subject from perspectives of applied mathematics (Professor Russel Caflisch of the University of California at Los Angeles), physics (Professor Antti-Pekka Jauho of the Danish Technical University), and computational science and engineering communities (Professor Gerhard Klimeck of Purdue University), as well as from a point of view of experimentalists (Dr Gail Brown of the Materials Lab/Air Force Research Lab at Wright-Patterson AFB). These talks helped identify the areas where joint efforts needed to be directed to, and they set up the scene for further work during the workshop, including discussions at the workshop open problem sessions. All participants had time to present their research and a specific time was allocated for on-site demonstrations of software and explanations of tools applied in the LDSN analysis. This special issue provides a flavor of the problems discussed at the workshop. It contains 12 refereed papers. Additional information, including the abstracts of all presented talks, can be found at http://www.m2netlab.wlu.ca/ldsn-banff/. Using this opportunity, we would like to thank the referees of this volume for their time and efforts. Without their timely professional comments this volume would not have been made possible. In conclusion, we note that advances in mathematics, physics and computation of LDSNs, impact such seemingly distant applications as biotechnology and medicine, quantum information processing and optoelectronics. The research into LDSNs offered exciting new challenges that are intrinsically interdisciplinary in nature and should be addressed by a multidisciplinary team of applied mathematicians, theoretical and experimental physicists, engineers and computational scientists. We hope that we are able to pass this idea to the reader. Lok C Lew Yan Voon(Wright State University, OH, USA) Roderick Melnik(M2NeT Lab, Wilfrid Laurier University, ON, Canada) Morten Willatzen(MCI, University of Southern Denmark, Denmark)

PREFACE: Physics and Mathematics of Nonlinear Phenomena 2013 (PMNP2013)

NASA Astrophysics Data System (ADS)

Konopelchenko, B. G.; Landolfi, G.; Martina, L.; Vitolo, R.

2014-03-01

Modern theory of nonlinear integrable equations is nowdays an important and effective tool of study for numerous nonlinear phenomena in various branches of physics from hydrodynamics and optics to quantum filed theory and gravity. It includes the study of nonlinear partial differential and discrete equations, regular and singular behaviour of their solutions, Hamitonian and bi- Hamitonian structures, their symmetries, associated deformations of algebraic and geometrical structures with applications to various models in physics and mathematics. The PMNP 2013 conference focused on recent advances and developments in Continuous and discrete, classical and quantum integrable systems Hamiltonian, critical and geometric structures of nonlinear integrable equations Integrable systems in quantum field theory and matrix models Models of nonlinear phenomena in physics Applications of nonlinear integrable systems in physics The Scientific Committee of the conference was formed by Francesco Calogero (University of Rome `La Sapienza', Italy) Boris A Dubrovin (SISSA, Italy) Yuji Kodama (Ohio State University, USA) Franco Magri (University of Milan `Bicocca', Italy) Vladimir E Zakharov (University of Arizona, USA, and Landau Institute for Theoretical Physics, Russia) The Organizing Committee: Boris G Konopelchenko, Giulio Landolfi, Luigi Martina, Department of Mathematics and Physics `E De Giorgi' and the Istituto Nazionale di Fisica Nucleare, and Raffaele Vitolo, Department of Mathematics and Physics `E De Giorgi'. A list of sponsors, speakers, talks, participants and the conference photograph are given in the PDF. Conference photograph

Success in introductory college physics: The role of gender, high school preparation, and student learning perceptions

NASA Astrophysics Data System (ADS)

Chen, Jean Chi-Jen

Physics is fundamental for science, engineering, medicine, and for understanding many phenomena encountered in people's daily lives. The purpose of this study was to investigate the relationships between student success in college-level introductory physics courses and various educational and background characteristics. The primary variables of this study were gender, high school mathematics and science preparation, preference and perceptions of learning physics, and performance in introductory physics courses. Demographic characteristics considered were age, student grade level, parents' occupation and level of education, high school senior grade point average, and educational goals. A Survey of Learning Preference and Perceptions was developed to collect the information for this study. A total of 267 subjects enrolled in six introductory physics courses, four algebra-based and two calculus-based, participated in the study conducted during Spring Semester 2002. The findings from the algebra-based physics courses indicated that participant's educational goal, high school senior GPA, father's educational level, mother's educational level, and mother's occupation in the area of science, engineering, or computer technology were positively related to performance while participant age was negatively related. Biology preparation, mathematics preparation, and additional mathematics and science preparation in high school were also positively related to performance. The relationships between the primary variables and performance in calculus-based physics courses were limited to high school senior year GPA and high school physics preparation. Findings from all six courses indicated that participant's educational goal, high school senior GPA, father's educational level, and mother's occupation in the area of science, engineering, or computer technology, high school preparation in mathematics, biology, and the completion of additional mathematics and science courses were positively related to performance. No significant performance differences were found between male and female students. However, there were significant gender differences in physics learning perceptions. Female participants tended to try to understand physics materials and relate the physics problems to real world situations while their male counterparts tended to rely on rote learning and equation application. This study found that participants performed better by trying to understand the physics material and relate physics problems to real world situations. Participants who relied on rote learning did not perform well.

TIMSS Advanced 2015 and Advanced Placement Calculus & Physics. A Framework Analysis. Research in Review 2016-1

ERIC Educational Resources Information Center

Lazzaro, Christopher; Jones, Lee; Webb, David C.; Grover, Ryan; Di Giacomo, F. Tony; Marino, Katherine Adele

2016-01-01

This report will determine to what degree the AP Physics 1 and 2 and AP Calculus AB and BC frameworks are aligned with the Trends in International Mathematics and Science Study (TIMSS) Advanced Physics and Mathematics frameworks. This will enable an exploration of any differences in content coverage and levels of complexity, and will set the stage…

Theoretical and experimental physical methods of neutron-capture therapy

NASA Astrophysics Data System (ADS)

Borisov, G. I.

2011-09-01

This review is based to a substantial degree on our priority developments and research at the IR-8 reactor of the Russian Research Centre Kurchatov Institute. New theoretical and experimental methods of neutron-capture therapy are developed and applied in practice; these are: A general analytical and semi-empiric theory of neutron-capture therapy (NCT) based on classical neutron physics and its main sections (elementary theories of moderation, diffuse, reflection, and absorption of neutrons) rather than on methods of mathematical simulation. The theory is, first of all, intended for practical application by physicists, engineers, biologists, and physicians. This theory can be mastered by anyone with a higher education of almost any kind and minimal experience in operating a personal computer.

An ansatz for solving nonlinear partial differential equations in mathematical physics.

PubMed

Akbar, M Ali; Ali, Norhashidah Hj Mohd

2016-01-01

In this article, we introduce an ansatz involving exact traveling wave solutions to nonlinear partial differential equations. To obtain wave solutions using direct method, the choice of an appropriate ansatz is of great importance. We apply this ansatz to examine new and further general traveling wave solutions to the (1+1)-dimensional modified Benjamin-Bona-Mahony equation. Abundant traveling wave solutions are derived including solitons, singular solitons, periodic solutions and general solitary wave solutions. The solutions emphasize the nobility of this ansatz in providing distinct solutions to various tangible phenomena in nonlinear science and engineering. The ansatz could be more efficient tool to deal with higher dimensional nonlinear evolution equations which frequently arise in many real world physical problems.

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energymore » for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.« less

Impact of Interdisciplinary Undergraduate Research in Mathematics and Biology on the Development of a New Course Integrating Five STEM Disciplines

PubMed Central

Caudill, Lester; Hill, April; Lipan, Ovidiu

2010-01-01

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a course for first-year students that integrates the material in the first course of the major in each of biology, chemistry, mathematics, computer science, and physics. PMID:20810953

Impact of Interdisciplinary Undergraduate Research in mathematics and biology on the development of a new course integrating five STEM disciplines.

PubMed

Caudill, Lester; Hill, April; Hoke, Kathy; Lipan, Ovidiu

2010-01-01

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a course for first-year students that integrates the material in the first course of the major in each of biology, chemistry, mathematics, computer science, and physics.

Cluster functions and scattering amplitudes for six and seven points

DOE PAGES

Harrington, Thomas; Spradlin, Marcus

2017-07-05

Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. Here, we explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4, 6) and Gr(4, 7) cluster polylogarithm functions of [15] at weight 4.

Using History to Teach Mathematics: The Case of Logarithms

ERIC Educational Resources Information Center

Panagiotou, Evangelos N.

2011-01-01

Many authors have discussed the question "why" we should use the history of mathematics to mathematics education. For example, Fauvel ("For Learn Math," 11(2): 3-6, 1991) mentions at least fifteen arguments for applying the history of mathematics in teaching and learning mathematics. Knowing "how" to introduce history into mathematics lessons is a…

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

Outcomes from the DOE Workshop on Turbulent Flow Simulation at the Exascale

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sprague, Michael; Boldyrev, Stanislav; Chang, Choong-Seock

This paper summarizes the outcomes from the Turbulent Flow Simulation at the Exascale: Opportunities and Challenges Workshop, which was held 4-5 August 2015, and was sponsored by the U.S. Department of Energy Office of Advanced Scientific Computing Research. The workshop objective was to define and describe the challenges and opportunities that computing at the exascale will bring to turbulent-flow simulations in applied science and technology. The need for accurate simulation of turbulent flows is evident across the U.S. Department of Energy applied-science and engineering portfolios, including combustion, plasma physics, nuclear-reactor physics, wind energy, and atmospheric science. The workshop brought togethermore » experts in turbulent-flow simulation, computational mathematics, and high-performance computing. Building upon previous ASCR workshops on exascale computing, participants defined a research agenda and path forward that will enable scientists and engineers to continually leverage, engage, and direct advances in computational systems on the path to exascale computing.« less

Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

NASA Astrophysics Data System (ADS)

Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

2017-12-01

In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

Life as an Ex-Physicist on Wall Street

NASA Astrophysics Data System (ADS)

Derman, Emanuel

2001-06-01

Financial theory looks deceptively like physics because of the techniques it uses. But physics models deal with the relatively unchanging parameters of the external world; in contrast, the parameters of financial theory are people's current estimates of, and sentiments about, future behavior. Life as a Ph.D. on Wall St is therefore very different from the way most people in academic life imagine it to be. For most of us, most of the time, it involves neither finding miraculous and previously undiscovered arbitrages, nor doing boring mindless programming. Instead, it demands an interdisciplinary mix of inventive computation, applied mathematics, financial understanding, self-education and educating others, applied in a hectic environment, to help build and maintain a business. Financial modeling as a practitioner means suffering many interruptions when you want to think quietly, and making many pragmatic compromises dictated by constraints on time and resources. It also means a stimulating and lively environment, using your imagination, avoiding complexity, and always trying to bridge the gap between analysis and intuition (yours and others).

Adjoint equations and analysis of complex systems: Application to virus infection modelling

NASA Astrophysics Data System (ADS)

Marchuk, G. I.; Shutyaev, V.; Bocharov, G.

2005-12-01

Recent development of applied mathematics is characterized by ever increasing attempts to apply the modelling and computational approaches across various areas of the life sciences. The need for a rigorous analysis of the complex system dynamics in immunology has been recognized since more than three decades ago. The aim of the present paper is to draw attention to the method of adjoint equations. The methodology enables to obtain information about physical processes and examine the sensitivity of complex dynamical systems. This provides a basis for a better understanding of the causal relationships between the immune system's performance and its parameters and helps to improve the experimental design in the solution of applied problems. We show how the adjoint equations can be used to explain the changes in hepatitis B virus infection dynamics between individual patients.

An Excursion in Applied Mathematics.

ERIC Educational Resources Information Center

von Kaenel, Pierre A.

1981-01-01

An excursion in applied mathematics is detailed in a lesson deemed well-suited for the high school student or undergraduate. The problem focuses on an experimental missile guidance system simulated in the laboratory. (MP)

Some Mathematics and Physics of Ball Games.

ERIC Educational Resources Information Center

Hughes, D. E.

1985-01-01

Gives examples on the applications of arithmetic, geometry, and some calculus, vector algebra, and mechanics to ball games. Suggestions for further interesting investigations are provided together with references to other articles and books on applications of mathematics and physics to ball games and sports in general. (JN)

Elaine Hale | NREL

Science.gov Websites

Analysis Center. Areas of Expertise Mathematical modeling, simulation, and optimization of complex Industrial and Applied Mathematics Mathematical Optimization Society Featured Publications Stoll, Brady

Exploring the relations among physical fitness, executive functioning, and low academic achievement.

PubMed

de Bruijn, A G M; Hartman, E; Kostons, D; Visscher, C; Bosker, R J

2018-03-01

Physical fitness seems to be related to academic performance, at least when taking the role of executive functioning into account. This assumption is highly relevant for the vulnerable population of low academic achievers because their academic performance might benefit from enhanced physical fitness. The current study examined whether physical fitness and executive functioning are independent predictors of low mathematics and spelling achievement or whether the relation between physical fitness and low achievement is mediated by specific executive functions. In total, 477 students from second- and third-grade classes of 12 primary schools were classified as either low or average-to-high achievers in mathematics and spelling based on their scores on standardized achievement tests. Multilevel structural equation models were built with direct paths between physical fitness and academic achievement and added indirect paths via components of executive functioning: inhibition, verbal working memory, visuospatial working memory, and shifting. Physical fitness was only indirectly related to low achievement via specific executive functions, depending on the academic domain involved. Verbal working memory was a mediator between physical fitness and low achievement in both domains, whereas visuospatial working memory had a mediating role only in mathematics. Physical fitness interventions aiming to improve low academic achievement, thus, could potentially be successful. The mediating effect of executive functioning suggests that these improvements in academic achievement will be preceded by enhanced executive functions, either verbal working memory (in spelling) or both verbal and visuospatial working memory (in mathematics). Copyright © 2017 Elsevier Inc. All rights reserved.

Mathematics at A-Level. A Discussion Paper on the Applied Content. No. 93.

ERIC Educational Resources Information Center

Mathematical Association, Leicester (England).

In September 1979, the Mathematical Association in England held a weekend seminar on the scope of Applied Mathematics at A-level, and a subcommittee was established to consider the topic at more length. This paper is the first product of the subcommittee's deliberations. Sections 1 and 2 describe the background to current A-level courses: (1) who…

Preparing Teachers to Apply Research to Mathematics Teaching: Using Design-Based Research to Define and Assess the Process of Evidence-Based Practice

ERIC Educational Resources Information Center

van Ingen, Sarah

2013-01-01

Persistent lack of mathematics achievement and disparity in achievement has led to the publication of research findings related to equitable teaching practices. Although the publication of such research provides insights about approaches for potentially increasing equity in mathematics education, teachers must be able to apply what has been…

Activities for the Promotion of Gender Equality in Japan—Japan Society of Applied Physics

NASA Astrophysics Data System (ADS)

Kodate, Kashiko; Tanaka, Kazuo

2005-10-01

Since 1946, the Japan Society of Applied Physics (JSAP) has strived to promote research and development in applied physics for benefits beyond national boundaries. Activities of JSAP involve multidisciplinary fields, from physics and engineering to life sciences. Of its 23,000 members, 48% are from industry, 29% from academia, and about 7% from semi-autonomous national research laboratories. Its large industrial membership is one of the distinctive features of JSAP. In preparation for the First IUPAP International Conference on Women in Physics (Paris, 2002), JSAP members took the first step under the strong leadership of then-JSAP President Toshio Goto, setting up the Committee for the Promotion Equal Participation of Men and Women in Science and Technology. Equality rather than women's advancement is highlighted to further development in science and technology. Attention is also paid to balancing the number of researchers from different age groups and affiliations. The committee has 22 members: 12 female and 10 male; 7 from corporations, 12 from universities, and 3 from semi-autonomous national research institutes. Its main activities are to organize symposia and meetings, conduct surveys among JSAP members, and provide child-care facilities at meetings and conferences. In 2002 the Japan Physics Society and the Chemical Society of Japan jointly created the Japan Inter-Society Liaison Association for the Promotion of Equal Participation of Men and Women in Science and Engineering. Membership has grown to 44 societies (of which 19 are observers) ranging from mathematics, information, and life sciences to civil engineering. Joint activities across sectors and empower the whole. The Gender Equality Bureau in the Cabinet Office recently launched a large-scale project called "Challenge Campaign" to encourage girls to major in natural science and engineering, which JSAP is co-sponsoring.

Mathematics make microbes beautiful, beneficial, and bountiful.

PubMed

Jungck, John R

2012-01-01

Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning. Copyright © 2012 Elsevier Inc. All rights reserved.

Numerical simulation of phase transition problems with explicit interface tracking

DOE PAGES

Hu, Yijing; Shi, Qiangqiang; de Almeida, Valmor F.; ...

2015-12-19

Phase change is ubiquitous in nature and industrial processes. Started from the Stefan problem, it is a topic with a long history in applied mathematics and sciences and continues to generate outstanding mathematical problems. For instance, the explicit tracking of the Gibbs dividing surface between phases is still a grand challenge. Our work has been motivated by such challenge and here we report on progress made in solving the governing equations of continuum transport in the presence of a moving interface by the front tracking method. The most pressing issue is the accounting of topological changes suffered by the interfacemore » between phases wherein break up and/or merge takes place. The underlying physics of topological changes require the incorporation of space-time subscales not at reach at the moment. Therefore we use heuristic geometrical arguments to reconnect phases in space. This heuristic approach provides new insight in various applications and it is extensible to include subscale physics and chemistry in the future. We demonstrate the method on applications such as simulating freezing, melting, dissolution, and precipitation. The later examples also include the coupling of the phase transition solution with the Navier-Stokes equations for the effect of flow convection.« less

Task-level robot programming: Integral part of evolution from teleoperation to autonomy

NASA Technical Reports Server (NTRS)

Reynolds, James C.

1987-01-01

An explanation is presented of task-level robot programming and of how it differs from the usual interpretation of task planning for robotics. Most importantly, it is argued that the physical and mathematical basis of task-level robot programming provides inherently greater reliability than efforts to apply better known concepts from artificial intelligence (AI) to autonomous robotics. Finally, an architecture is presented that allows the integration of task-level robot programming within an evolutionary, redundant, and multi-modal framework that spans teleoperation to autonomy.

Wave refraction diagrams for the Baltimore Canyon region of the mid-Atlantic continental shelf computed by using three bottom topography approximation techniques

NASA Technical Reports Server (NTRS)

Poole, L. R.

1976-01-01

The Langley Research Center and Virginia Institute of Marine Science wave refraction computer model was applied to the Baltimore Canyon region of the mid-Atlantic continental shelf. Wave refraction diagrams for a wide range of normally expected wave periods and directions were computed by using three bottom topography approximation techniques: quadratic least squares, cubic least squares, and constrained bicubic interpolation. Mathematical or physical interpretation of certain features appearing in the computed diagrams is discussed.

Scaling Limit for a Generalization of the Nelson Model and its Application to Nuclear Physics

NASA Astrophysics Data System (ADS)

Suzuki, Akito

We study a mathematically rigorous derivation of a quantum mechanical Hamiltonian in a general framework. We derive such a Hamiltonian by taking a scaling limit for a generalization of the Nelson model, which is an abstract interaction model between particles and a Bose field with some internal degrees of freedom. Applying it to a model for the field of the nuclear force with isospins, we obtain a Schrödinger Hamiltonian with a matrix-valued potential, the one pion exchange potential, describing an effective interaction between nucleons.

Derivation of an applied nonlinear Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pitts, Todd Alan; Laine, Mark Richard; Schwarz, Jens

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

A new asymptotic method for jump phenomena

NASA Technical Reports Server (NTRS)

Reiss, E. L.

1980-01-01

Physical phenomena involving rapid and sudden transitions, such as snap buckling of elastic shells, explosions, and earthquakes, are characterized mathematically as a small disturbance causing a large-amplitude response. Because of this, standard asymptotic and perturbation methods are ill-suited to these problems. In the present paper, a new method of analyzing jump phenomena is proposed. The principal feature of the method is the representation of the response in terms of rational functions. For illustration, the method is applied to the snap buckling of an elastic arch and to a simple combustion problem.

The Kitchen as a Lab

NASA Astrophysics Data System (ADS)

Adria, Ferran; Andres, Jose; Brenner, Michael P.

2012-02-01

Provocative world-famous Chef Ferran Adria, often associated with originating the modernist cuisine movement, and Washington DC chef Jose Andres, credited with bring the ``small plates" movement to North America, will discuss their views on the creative preparation of food with unexpected contrasts of flavor, temperature, and texture. Their discussion will be followed by a talk by Michael P. Brenner, a professor of applied mathematics, who (along with physics professor David A. Weitz) teaches a course at Harvard University on science and cooking. Come learn about the science and the art of food preparation!