Advances in Reactor physics, mathematics and computation. Volume 3
Energy Technology Data Exchange (ETDEWEB)
1987-01-01
These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume 3, are divided into sessions bearing on: - poster sessions on benchmark and codes: 35 conferences - review of status of assembly spectrum codes: 9 conferences - Numerical methods in fluid mechanics and thermal hydraulics: 16 conferences - stochastic transport and methods: 7 conferences.
Advances in Reactor Physics, Mathematics and Computation. Volume 2
Energy Technology Data Exchange (ETDEWEB)
1987-01-01
These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, Volume 2, are divided into 7 sessions bearing on: - session 7: Deterministic transport methods 1 (7 conferences), - session 8: Interpretation and analysis of reactor instrumentation (6 conferences), - session 9: High speed computing applied to reactor operations (5 conferences), - session 10: Diffusion theory and kinetics (7 conferences), - session 11: Fast reactor design, validation and operating experience (8 conferences), - session 12: Deterministic transport methods 2 (7 conferences), - session 13: Application of expert systems to physical aspects of reactor design and operation.
Advances in Reactor Physics, Mathematics and Computation. Volume 1
Energy Technology Data Exchange (ETDEWEB)
1987-01-01
These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume one, are divided into 6 sessions bearing on: - session 1: Advances in computational methods including utilization of parallel processing and vectorization (7 conferences) - session 2: Fast, epithermal, reactor physics, calculation, versus measurements (9 conferences) - session 3: New fast and thermal reactor designs (9 conferences) - session 4: Thermal radiation and charged particles transport (7 conferences) - session 5: Super computers (7 conferences) - session 6: Thermal reactor design, validation and operating experience (8 conferences).
Physics and mathematics of strings memorial volume for Vadim Knizhnik
Polyakov, A M; Brink, Lars
1990-01-01
Vadim Knizhnik was one of the most promising theoretical physicists in the world. Unfortunately, he passed away at the very young age of 25 years. This memorial volume is to honor his contributions in Theoretical Physics. This is perhaps one of the most important collections of articles on the theoretical developments in String Theory, Conformal Field Theory and related topics. It consists of contributions from world-renowned physicists who have met Vadim Knizhnik personally and whom the late Knizhnik really respected. The contributions are systematic and pedagogical in format.
Geroch, Robert
1985-01-01
Mathematical Physics is an introduction to such basic mathematical structures as groups, vector spaces, topological spaces, measure spaces, and Hilbert space. Geroch uses category theory to emphasize both the interrelationships among different structures and the unity of mathematics. Perhaps the most valuable feature of the book is the illuminating intuitive discussion of the ""whys"" of proofs and of axioms and definitions. This book, based on Geroch's University of Chicago course, will be especially helpful to those working in theoretical physics, including such areas as relativity, particle
Cahill, Kevin
2013-01-01
Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
Contemporary mathematical physics
Dobrushin, R L; Shubin, M A; Vershik, Anatoly M
1996-01-01
This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics
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.
XVIIth Interntional Congress on Mathematical Physics
DEFF Research Database (Denmark)
This volume contains the proceedings of the XVIIth International Congress on Mathematical Physics. It is the main scientific event of the International Association of Mathematical Physics (IAMP). The Congress was held in Aalborg, Denmark, August 6-11, 2012.......This volume contains the proceedings of the XVIIth International Congress on Mathematical Physics. It is the main scientific event of the International Association of Mathematical Physics (IAMP). The Congress was held in Aalborg, Denmark, August 6-11, 2012....
Methods of modern mathematical physics
Reed, Michael
1980-01-01
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. Later volumes describe various advanced topics in functional analysis and give numerous applications in classical physics, modern physics, and partial differential equations.
Manin, Yu I
1981-01-01
A bird's eye view of mathematics ; physical quantities, dimensions and constants : the source of numbers in physics ; a drop of milk : observer, observation, observable and unobservable ; space-time as a physical system ; action and symmetry.
Mathematics for physical chemistry
Mortimer, Robert G
2013-01-01
Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, wit
Supersymmetry in mathematics and physics
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio [CERN, Geneve (Switzerland). Div. Theorie; Fioresi, Rita [Bologna Univ. (Italy). Dept. of Mathematics; Varadarajan, V.S. (eds.) [UCLA, Los Angeles, CA (United States). Dept. of Mathematics
2011-07-01
Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised. (orig.)
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Mathematization in introductory physics
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
Mathematics for physical chemistry
Mortimer, Robert G
2005-01-01
Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses. The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.* Numerous examples and problems interspersed throughout the presentations * Each extensive chapter contains a preview, objectives, and ...
Mathematical physics classical mechanics
Knauf, Andreas
2018-01-01
As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
Introduction to mathematical statistical physics
Minlos, R A
1999-01-01
This book presents a mathematically rigorous approach to the main ideas and phenomena of statistical physics. The introduction addresses the physical motivation, focussing on the basic concept of modern statistical physics, that is the notion of Gibbsian random fields. Properties of Gibbsian fields are analyzed in two ranges of physical parameters: "regular" (corresponding to high-temperature and low-density regimes) where no phase transition is exhibited, and "singular" (low temperature regimes) where such transitions occur. Next, a detailed approach to the analysis of the phenomena of phase transitions of the first kind, the Pirogov-Sinai theory, is presented. The author discusses this theory in a general way and illustrates it with the example of a lattice gas with three types of particles. The conclusion gives a brief review of recent developments arising from this theory. The volume is written for the beginner, yet advanced students will benefit from it as well. The book will serve nicely as a supplement...
Mathematical physics applied mathematics for scientists and engineers
Kusse, Bruce R
2006-01-01
What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations
Nuclear physics mathematical methods
International Nuclear Information System (INIS)
Balian, R.; Gervois, A.; Giannoni, M.J.; Levesque, D.; Maille, M.
1984-01-01
The nuclear physics mathematical methods, applied to the collective motion theory, to the reduction of the degrees of freedom and to the order and disorder phenomena; are investigated. In the scope of the study, the following aspects are discussed: the entropy of an ensemble of collective variables; the interpretation of the dissipation, applying the information theory; the chaos and the universality; the Monte-Carlo method applied to the classical statistical mechanics and quantum mechanics; the finite elements method, and the classical ergodicity [fr
Jungnickel, Christa; McCormmach, Russell
Intellectual mastery of nature was the stated goal of the German physicists of the nineteenth century. In this first of two volumes, an attempt is made to bridge social, institutional, and intellectual history. Separate sections of the book deal with: (1) establishing physics at the universities; (2) German physicists before 1830; (3) promoting…
International Nuclear Information System (INIS)
Anon.
1995-01-01
The International Conference on Mathematics and Computations, Reactor Physics, and Environmental Analyses marks the sixteenth biennial topical meeting of the Mathematics and Computation (M ampersand C) Division of the American Nuclear Society (ANS). This conference combines many traditional features of M ampersand C conferences with several new aspects. The meeting is, for the first time, being held in Portland, Oregon and sponsored by the ANS Eastern Washington Section. Three of the cosponsors - the ANS Reactor Physics Division, the European Nuclear Society, and the Atomic Energy Society of Japan - have participated in a series of such meetings, with very successful results. The fourth cosponsor, the ANS Environmental Science Division, is participating for the first time as a cosponsor of a M ampersand C topical meeting, as a result of the M ampersand C Division's decision to formally include the area of environmental analyses as a major focus of the conference, another 'first.' Separate abstracts have been submitted to the energy database for contributions to this conference
Mathematics for physics with calculus
Das, Biman
2005-01-01
Designed for students who plan to take or who are presently taking calculus-based physics courses. This book will develop necessary mathematical skills and help students gain the competence to use precalculus, calculus, vector algebra, vector calculus, and the statistical analysis of experimental data. Students taking intermediate physics, engineering, and other science courses will also find the book useful-and will be able to use the book as a mathematical resource for these intermediate level courses. The book emphasizes primarily the use of mathematical techniques and mathematical concepts in Physics and does not go into their rigorous developments.
Mathematical aspects of superspace, volume 132
International Nuclear Information System (INIS)
Seifert, H.J.
1984-01-01
Through a continually increasing wave of activity in the physics community, super-gravity has come to be regarded as one of the most promising ways of unifying gravity with other particle interaction as a finite gauge theory to explain the particle-spectrum. Concurrently, important mathematical work on graded manifolds and superspace as proposed arenas of supergravity has been carried out. There remains a gap between the mathematical and physical approaches expressed by such unanswered questions as: Does there exist a superspace having the properties that physicists require. Does it make sense to perform a path-integral in such spaces. Does a sensible classical supergravity exist. It is hoped that this volume will stimulate the dialogue between mathematicians and physicists dealing with these questions
Workshop on Supersymmetry in Mathematics and Physics
Fioresi, Rita; Varadarajan, VS
2011-01-01
Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.
Obstacle problems in mathematical physics
Rodrigues, J-F
1987-01-01
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.
The functions of mathematical physics
Hochstadt, Harry
2012-01-01
A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics.In the 18th and 19th centuries, the theorists who devoted themselves to this field - pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel - were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating
Open problems in mathematical physics
International Nuclear Information System (INIS)
Coley, Alan A
2017-01-01
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. (invited comment)
Open problems in mathematical physics
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.
Mathematical methods of classical physics
Cortés, Vicente
2017-01-01
This short primer, geared towards students with a strong interest in mathematically rigorous approaches, introduces the essentials of classical physics, briefly points out its place in the history of physics and its relation to modern physics, and explains what benefits can be gained from a mathematical perspective. As a starting point, Newtonian mechanics is introduced and its limitations are discussed. This leads to and motivates the study of different formulations of classical mechanics, such as Lagrangian and Hamiltonian mechanics, which are the subjects of later chapters. In the second part, a chapter on classical field theories introduces more advanced material. Numerous exercises are collected in the appendix.
Cluster algebras in mathematical physics
International Nuclear Information System (INIS)
Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2014-01-01
This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm
Mathematical Rigor in Introductory Physics
Vandyke, Michael; Bassichis, William
2011-10-01
Calculus-based introductory physics courses intended for future engineers and physicists are often designed and taught in the same fashion as those intended for students of other disciplines. A more mathematically rigorous curriculum should be more appropriate and, ultimately, more beneficial for the student in his or her future coursework. This work investigates the effects of mathematical rigor on student understanding of introductory mechanics. Using a series of diagnostic tools in conjunction with individual student course performance, a statistical analysis will be performed to examine student learning of introductory mechanics and its relation to student understanding of the underlying calculus.
Equations in mathematical physics a practical course
Pikulin, Victor P
2001-01-01
This handbook is addressed to students of technology institutf's where a course on mathematical physics of relatively reduced volume is offered, as well as to engineers and scientists. The aim of the handbook is to treat (demonstrate) the basic methods for solving the simplest problems of classical mathematical physics. The most basic among the methods considered hrre i8 the superposition method. It allows one, based on particular linearly indepmdent HolutionH (solution "atoms"), to obtain the solution of a given problem. To that end the "Hupply" of solution atoms must be complete. This method is a development of the well-known method of particular solutions from the theory of ordinar~' differelltial equations. In contrast to the case of ordinary differential equations, where the number of linearly independent 80lutions is always finite, for a linear partial differrntial equation a complete "supply" of solution atoms is always infinite. This infinite set of Holutions may be discrete (for example, for regular ...
PREFACE: Algebra, Geometry, and Mathematical Physics 2010
Stolin, A.; Abramov, V.; Fuchs, J.; Paal, E.; Shestopalov, Y.; Silvestrov, S.
2012-02-01
This proceedings volume presents results obtained by the participants of the 6th Baltic-Nordic workshop 'Algebra, Geometry, and Mathematical Physics (AGMP-6)' held at the Sven Lovén Centre for Marine Sciences in Tjärnö, Sweden on October 25-30, 2010. The Baltic-Nordic Network AGMP 'Algebra, Geometry, and Mathematical Physics' http://www.agmp.eu was created in 2005 on the initiative of two Estonian universities and two Swedish universities: Tallinn University of Technology represented by Eugen Paal (coordinator of the network), Tartu University represented by Viktor Abramov, Lund University represented by Sergei Silvestrov, and Chalmers University of Technology and the University of Gothenburg represented by Alexander Stolin. The goal was to promote international and interdisciplinary cooperation between scientists and research groups in the countries of the Baltic-Nordic region in mathematics and mathematical physics, with special emphasis on the important role played by algebra and geometry in modern physics, engineering and technologies. The main activities of the AGMP network consist of a series of regular annual international workshops, conferences and research schools. The AGMP network also constitutes an important educational forum for scientific exchange and dissimilation of research results for PhD students and Postdocs. The network has expanded since its creation, and nowadays its activities extend beyond countries in the Baltic-Nordic region to universities in other European countries and participants from elsewhere in the world. As one of the important research-dissimilation outcomes of its activities, the network has a tradition of producing high-quality research proceedings volumes after network events, publishing them with various international publishers. The PDF also contains the following: List of AGMP workshops and other AGMP activities Main topics discussed at AGMP-6 Review of AGMP-6 proceedings Acknowledgments List of Conference Participants
Some mathematical methods of physics
Goertzel, Gerald
2014-01-01
This well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics.The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts u
Physical Consequences of Mathematical Principles
Directory of Open Access Journals (Sweden)
Comay E.
2009-10-01
Full Text Available Physical consequences are derived from the following mathematical structures: the variational principle, Wigner’s classifications of the irreducible representations of the Poincar ́ e group and the duality invariance of the homogeneous Maxwell equations. The analysis is carried out within the validity domain of special relativity. Hierarchical re- lations between physical theories are used. Some new results are pointed out together with their comparison with experimental data. It is also predicted that a genuine Higgs particle will not be detected.
Interactions Between Mathematics and Physics
DEFF Research Database (Denmark)
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 var......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...
Differential geometry and mathematical physics
Rudolph, Gerd
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous d...
Mathematical methods in physics and engineering
Dettman, John W
2011-01-01
Intended for college-level physics, engineering, or mathematics students, this volume offers an algebraically based approach to various topics in applied math. It is accessible to undergraduates with a good course in calculus which includes infinite series and uniform convergence. Exercises follow each chapter to test the student's grasp of the material; however, the author has also included exercises that extend the results to new situations and lay the groundwork for new concepts to be introduced later. A list of references for further reading will be found at the end of each chapter. For t
Mathematics in physics and engineering
Irving, J; Massey, H S W; Brueckner, Keith A
1959-01-01
Mathematics in Physics and Engineering describes the analytical and numerical (desk-machine) methods that arise in pure and applied science, including wave equations, Bessel and Legendre functions, and matrices. The manuscript first discusses partial differential equations, as well as the method of separation of variables, three-dimensional wave equation, diffusion or heat flow equation, and wave equation in plane and cylindrical polar coordinates. The text also ponders on Frobenius' and other methods of solution. Discussions focus on hypergeometric equation, Bessel's equation, confluent hyper
Introduction to mathematical physics methods and concepts
Wong, Chun Wa
2013-01-01
Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages...
Interaction between Mathematics and Physics
Directory of Open Access Journals (Sweden)
Hitchin, Nigel
2007-06-01
Full Text Available There is at the moment a highly active interface between mathematics and theoretical physics, which extends into completely new areas of both disciplines. This article, based on a round table discussion which took place as part of the activities around the 2006 International Congress of Mathematicians in Madrid, explores some of the issues involved: the differing goals and backgrounds of the two communities, today’s interactions and their precedents, the possibilities for the future and the role of mathematics itself in understanding the world in which we live.Actualmente existe una importante interfaz entre matemáticas y física teórica, que ha producido áreas completamente nuevas. Este artículo está basado en un debate en una mesa redonda organizada en el entorno del International Congress of Mathematicians en 2006 de Madrid, explora algunos de estos temas: los diferentes objetivos y pasado de ambas disciplinas, las interacciones actuales y sus precedentes, las posibilidades para el futuro y el papel de las matemáticas para entender el mundo en que vivimos.
Modelling Mathematical Reasoning in Physics Education
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.
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
15th International Congress on Mathematical Physics
New Trends in Mathematical Physics
2009-01-01
This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad ov...
Attitude Towards Physics and Additional Mathematics Achievement Towards Physics Achievement
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 and conceptual foundations of 20th-century physics
International Nuclear Information System (INIS)
Emch, G.G.
1984-01-01
This volume presents a unified mathematical account of the conceptual foundations of 20th-century Physics. Part 1 provides a survey of classical physics divided in separate chapters on mechanics, thermodynamics and statistical mechanics, and electromagnetism. This study provides opportunities to place in perspective the successive advents of calculus, of probability and statistics, of differential and sympletic geometry, and of classical functional analysis. Relativity is presented in part 2 of this book and quantum theory in part 3. The motivation provided by physical problems in the development of mathematical disciplines such as, for instance, pseudo-Riemannian geometries, Hilbert spaces and operator algebras, are emphasized. (H.W.). refs.; figs.; schemes
Partial differential equations of mathematical physics
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
Journal of the Nigerian Association of Mathematical Physics
African Journals Online (AJOL)
Bibliometric techniques were used to study the authorship characteristics of the Journal of the Nigerian Association of Mathematical Physics (JNAMP). Relevant data was obtained through an examination of volume 10 of the Journal. Author productivity, average productivity per author, authorship collaboration, most ...
Mathematical methods for physical and analytical chemistry
Goodson, David Z
2011-01-01
Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical
Mathematics and the physical world
Kline, Morris
1981-01-01
Stimulating account of development of mathematics from arithmetic, algebra, geometry and trigonometry, to calculus, differential equations, and non-Euclidean geometries. Also describes how math is used in optics, astronomy, and other phenomena.
The logical structure of mathematical physics
Sneed, Joseph D
1971-01-01
This book is about scientific theories of a particular kind - theories of mathematical physics. Examples of such theories are classical and relativis tic particle mechanics, classical electrodynamics, classical thermodynamics, statistical mechanics, hydrodynamics, and quantum mechanics. Roughly, these are theories in which a certain mathematical structure is employed to make statements about some fragment of the world. Most of the book is simply an elaboration of this rough characterization of theories of mathematical physics. It is argued that each theory of mathematical physics has associated with it a certain characteristic mathematical struc ture. This structure may be used in a variety of ways to make empirical claims about putative applications of the theory. Typically - though not necessarily - the way this structure is used in making such claims requires that certain elements in the structure play essentially different roles. Some playa "theoretical" role; others playa "non-theoretical" role. For ...
Computer Algebra Recipes for Mathematical Physics
Enns, Richard H
2005-01-01
Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is use...
Contributions in mathematical physics a tribute to Gerard G. Emch
Sinha, Kalyan
2007-01-01
Professor Gerard G. Emch has been one of the pioneers of the C-algebraic approach to quantum and classical statistical mechanics. In a prolific scientific career, spanning nearly five decades, Professor Emch has been one of the creative influences in the general area of mathematical physics. The present volume is a collection of tributes, from former students, colleagues and friends of Professor Emch, on the occasion of his 70th birthday. The articles featured here are a small yet representative sample of the breadth and reach of some of the ideas from mathematical physics.It is also a testimony to the impact that Professor Emch's work has had on several generations of mathematical physicists as well as to the diversity of mathematical methods used to understand them.
The Physical Origin of Physically Useful Mathematics
DEFF Research Database (Denmark)
Lützen, Jesper
2011-01-01
Der argumenteres for at anvendelser i fysik er afgørende i udviklingen af de dele af matematikken, som har været nyttig for beskrivelsen af den fysiske verden. Dermed kastes et nyt lys på Eugine Wigner's 50 år gamle artikel om The unreasonable effectiveness of mathematics. Der gives en række hist...
Mathematical and physical theory of turbulence
Cannon, John
2006-01-01
Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier-Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities a...
6th International School of Mathematical Physics "Ettore Majorana"
Wightman, Arthur Strong
1986-01-01
The sixth Ettore Majorana International School of Mathematical Physics was held at the Centro della Cultura Scientifica Erice, Sicily, 1-14 July 1985. The present volume collects lecture notes on the ses sion which was devoted to Fundamental Problems of Gauge Field Theory. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now pro vides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lectures and seminars of the school concentrated on the many unsolved pro...
International Nuclear Information System (INIS)
1981-01-01
In this 1981 ISABELLE Workshop, for the Physics category, eight groups worked on eight topics. The mission for each group was to survey the status of each topic, ask new questions, and try to answer them. The organizers of each group were responsible for the organization of meetings, discussions and the final reports of the results from each working group. The mission was completed splendidly. The members enthusiastically participated in the group meetings. Each topic was thoroughly surveyed and many new understandings resulted. Twenty-seven individual items were prepared separately for the data base in addition to five previously prepared
Algebra, Geometry and Mathematical Physics Conference
Paal, Eugen; Silvestrov, Sergei; Stolin, Alexander
2014-01-01
This book collects the proceedings of the Algebra, Geometry and Mathematical Physics Conference, held at the University of Haute Alsace, France, October 2011. Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and applications; non-commutative and Lie algebra and more. The papers explore the interplay between research in contemporary mathematics and physics concerned with generalizations of the main structures of Lie theory aimed at quantization, and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, non-commutative geometry and applications in physics and beyond. The book benefits a broad audience of researchers a...
The mysterious connection between mathematics and physics.
Kauffman, Louis H; Ul-Haq, Rukhsan
2015-12-01
The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of "It from Bit" as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed. Copyright © 2015. Published by Elsevier Ltd.
International Conference on Quantum Mathematical Physics : a Bridge between Mathematics and Physics
Kleiner, Johannes; Röken, Christian; Tolksdorf, Jürgen
2016-01-01
Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fu...
Negotiating the Boundaries Between Mathematics and Physics
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.
DOE Fundamentals Handbook: Mathematics, Volume 1
International Nuclear Information System (INIS)
1992-06-01
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations
DOE Fundamentals Handbook: Mathematics, Volume 2
International Nuclear Information System (INIS)
1992-06-01
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations
Symmetry and the Standard Model mathematics and particle physics
Robinson, Matthew
2011-01-01
While elementary particle physics is an extraordinarily fascinating field, the huge amount of knowledge necessary to perform cutting-edge research poses a formidable challenge for students. The leap from the material contained in the standard graduate course sequence to the frontiers of M-theory, for example, is tremendous. To make substantial contributions to the field, students must first confront a long reading list of texts on quantum field theory, general relativity, gauge theory, particle interactions, conformal field theory, and string theory. Moreover, waves of new mathematics are required at each stage, spanning a broad set of topics including algebra, geometry, topology, and analysis. Symmetry and the Standard Model: Mathematics and Particle Physics, by Matthew Robinson, is the first volume of a series intended to teach math in a way that is catered to physicists. Following a brief review of classical physics at the undergraduate level and a preview of particle physics from an experimentalist's per...
The interface of mathematics and particle physics
Energy Technology Data Exchange (ETDEWEB)
Quillen, D.G.; Segal, G.B.; Tsousheung Tsun (Oxford Univ. (UK). Mathematical Inst.) (eds.)
1990-01-01
This collection of papers is based on the proceedings of a conference organized by the Institute of Mathematics and its Applications on the Interface of Mathematics and Particle Physics held at Oxford University in September 1988. There are twenty-five papers, all of which are indexed separately. Many contribute to the search for an understanding of how gravity can be unified with other interactions in one field theory. String and twistor theories are important in this search and many of the papers refer to strings, superstrings or twistor. All the papers seek a physical interpretation of theories and elementary particles. (author).
Birds and frogs in mathematics and physics
Energy Technology Data Exchange (ETDEWEB)
Dyson, Freeman J [Institute for Advanced Study, Princeton, NJ (United States)
2010-11-15
Some scientists are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. A brief history of mathematics and its applications in physics is presented in this article. (from the history of physics)
Attractors for equations of mathematical physics
Chepyzhov, Vladimir V
2001-01-01
One of the major problems in the study of evolution equations of mathematical physics is the investigation of the behavior of the solutions to these equations when time is large or tends to infinity. The related important questions concern the stability of solutions or the character of the instability if a solution is unstable. In the last few decades, considerable progress in this area has been achieved in the study of autonomous evolution partial differential equations. For a number of basic evolution equations of mathematical physics, it was shown that the long time behavior of their soluti
Birds and frogs in mathematics and physics
International Nuclear Information System (INIS)
Dyson, Freeman J
2010-01-01
Some scientists are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time. A brief history of mathematics and its applications in physics is presented in this article. (from the history of physics)
A first course in mathematical physics
Whelan, Colm T
2016-01-01
The book assumes next to no prior knowledge of the topic. The first part introduces the core mathematics, always in conjunction with the physical context. In the second part of the book, a series of examples showcases some of the more conceptually advanced areas of physics, the presentation of which draws on the developments in the first part. A large number of problems helps students to hone their skills in using the presented mathematical methods. Solutions to the problems are available to instructors on an associated password-protected website for lecturers.
Curvature in mathematics and physics
Sternberg, Shlomo
2012-01-01
This original Dover textbook is based on an advanced undergraduate course taught by the author for more than 50 years. It introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.
Models and structures: mathematical physics
International Nuclear Information System (INIS)
2003-01-01
This document gathers research activities along 5 main directions. 1) Quantum chaos and dynamical systems. Recent results concern the extension of the exact WKB method that has led to a host of new results on the spectrum and wave functions. Progress have also been made in the description of the wave functions of chaotic quantum systems. Renormalization has been applied to the analysis of dynamical systems. 2) Combinatorial statistical physics. We see the emergence of new techniques applied to various such combinatorial problems, from random walks to random lattices. 3) Integrability: from structures to applications. Techniques of conformal field theory and integrable model systems have been developed. Progress is still made in particular for open systems with boundary conditions, in connection to strings and branes physics. Noticeable links between integrability and exact WKB quantization to 2-dimensional disordered systems have been highlighted. New correlations of eigenvalues and better connections to integrability have been formulated for random matrices. 4) Gravities and string theories. We have developed aspects of 2-dimensional string theory with a particular emphasis on its connection to matrix models as well as non-perturbative properties of M-theory. We have also followed an alternative path known as loop quantum gravity. 5) Quantum field theory. The results obtained lately concern its foundations, in flat or curved spaces, but also applications to second-order phase transitions in statistical systems
Mathematical and physical models and radiobiology
International Nuclear Information System (INIS)
Lokajicek, M.
1980-01-01
The hit theory of the mechanism of biological radiation effects in the cell is discussed with respect to radiotherapy. The mechanisms of biological effects and of intracellular recovery, the cumulative radiation effect and the cumulative biological effect in fractionated irradiation are described. The benefit is shown of consistent application of mathematical and physical models in radiobiology and radiotherapy. (J.P.)
Applied Mathematical Methods in Theoretical Physics
Masujima, Michio
2005-04-01
All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.
Equations in mathematical physics a practical course
Pikulin, Victor P
2001-01-01
Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demonstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution. The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers. ------------ [A] manual for future engineers must strongly differ from the textbook for pure mathematicians, and the book by Pikulin and Pohozaev is the good example. (…) The purpose (…) is to offer quick access to the principal facts (…) This well written book is a...
Mathematical and conceptual foundations of 20th-century physics
International Nuclear Information System (INIS)
Emch, G.G.
1984-01-01
This book is primarily intended for Mathematicians, but it is also hoped that students in the physical sciences, will find here information not usually available in physics texts. The main aim of the book is to provide a unified mathematical account of the conceptual foundations of 20th-century Physics, in a form suitable for a one-year survey course in Mathematics or Mathematical Physics. Emphasis is laid on the interlocked historical development of mathematical and physical ideas. (Auth.)
International Nuclear Information System (INIS)
Zeidler, Eberhard
2009-01-01
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Zeidler, Eberhard [Max-Planck-Institut fuer Mathematik in den Naturwissenschaften, Leipzig (Germany)
2009-07-01
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics. (orig.)
Physics and Mathematics as Interwoven Disciplines in Science Education
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.
Archives: Journal of the Nigerian Association of Mathematical Physics
African Journals Online (AJOL)
Items 1 - 14 of 14 ... Archives: Journal of the Nigerian Association of Mathematical Physics. Journal Home > Archives: Journal of the Nigerian Association of Mathematical Physics. Log in or Register to get access to full text downloads.
Journal of the Nigerian Association of Mathematical Physics: Journal ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics: Journal Sponsorship. Journal Home > About the Journal > Journal of the Nigerian Association of Mathematical Physics: Journal Sponsorship. Log in or Register to get access to full text downloads.
Global Conference on Applied Physics and Mathematics
2016-01-01
The Global Conference on Applied Physics and Mathematics is organized by academics and researchers belonging to different scientific areas of the C3i/Polytechnic Institute of Portalegre (Portugal) and the University of Extremadura (Spain) with the technical support of ScienceKnow Conferences. The event has the objective of creating an international forum for academics, researchers and scientists from worldwide to discuss worldwide results and proposals regarding to the soundest issues related to Applied Physics and Mathematics. This event will include the participation of renowned keynote speakers, oral presentations, posters sessions and technical conferences related to the topics dealt with in the Scientific Program as well as an attractive social and cultural program. The papers will be published in the Proceedings e-books. The proceedings of the conference will be sent to possible indexing on Thomson Reuters (selective by Thomson Reuters, not all-inclusive) and Google Scholar. Those communications con...
Trajectory attractors of equations of mathematical physics
International Nuclear Information System (INIS)
Vishik, Marko I; Chepyzhov, Vladimir V
2011-01-01
In this survey the method of trajectory dynamical systems and trajectory attractors is described, and is applied in the study of the limiting asymptotic behaviour of solutions of non-linear evolution equations. This method is especially useful in the study of dissipative equations of mathematical physics for which the corresponding Cauchy initial-value problem has a global (weak) solution with respect to the time but the uniqueness of this solution either has not been established or does not hold. An important example of such an equation is the 3D Navier-Stokes system in a bounded domain. In such a situation one cannot use directly the classical scheme of construction of a dynamical system in the phase space of initial conditions of the Cauchy problem of a given equation and find a global attractor of this dynamical system. Nevertheless, for such equations it is possible to construct a trajectory dynamical system and investigate a trajectory attractor of the corresponding translation semigroup. This universal method is applied for various types of equations arising in mathematical physics: for general dissipative reaction-diffusion systems, for the 3D Navier-Stokes system, for dissipative wave equations, for non-linear elliptic equations in cylindrical domains, and for other equations and systems. Special attention is given to using the method of trajectory attractors in approximation and perturbation problems arising in complicated models of mathematical physics. Bibliography: 96 titles.
Mathematical models of physics problems (physics research and technology)
Anchordoqui, Luis Alfredo
2013-01-01
This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research. The book focuses on two cor...
The mathematics and physics of knots
Energy Technology Data Exchange (ETDEWEB)
Kauffman, Louis H [Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7045 (United States)
2005-12-01
This paper is an introduction to relationships between knot theory and theoretical physics. We give an exposition of the theory of polynomial invariants of knots and links, the Witten functional integral formulation of knot and link invariants, and the beginnings of topological quantum field theory, and show how the theory of knots is related to a number of key issues in mathematical physics, including loop quantum gravity and quantum information theory. Along with the references cited in the text below, we also recommend the following as sources of background information.
Focus group discussion in mathematical physics learning
Ellianawati; Rudiana, D.; Sabandar, J.; Subali, B.
2018-03-01
The Focus Group Discussion (FGD) activity in Mathematical Physics learning has helped students perform the stages of problem solving reflectively. The FGD implementation was conducted to explore the problems and find the right strategy to improve the students' ability to solve the problem accurately which is one of reflective thinking component that has been difficult to improve. The research method used is descriptive qualitative by using single subject response in Physics student. During the FGD process, one student was observed of her reflective thinking development in solving the physics problem. The strategy chosen in the discussion activity was the Cognitive Apprenticeship-Instruction (CA-I) syntax. Based on the results of this study, it is obtained the information that after going through a series of stages of discussion, the students' reflective thinking skills is increased significantly. The scaffolding stage in the CA-I model plays an important role in the process of solving physics problems accurately. Students are able to recognize and formulate problems by describing problem sketches, identifying the variables involved, applying mathematical equations that accord to physics concepts, executing accurately, and applying evaluation by explaining the solution to various contexts.
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 Mathematics and Further Mathematics. The findings suggest that physics undergraduates would benefit from studying Further Mathematics and specialising in mechanics during their A-level studies. As both A-level Mathematics and Further Mathematics are being reformed, universities should look closely at the benefits of Further Mathematics as preparation for their physics courses and either increase their admissions requirements, or recommend that students take Further Mathematics.
Fifty years of mathematical physics selected works of Ludwig Faddeev
Faddeev, Ludwig; Niemi, Antti J
2016-01-01
This unique volume summarizes with a historical perspective several of the major scientific achievements of Ludwig Faddeev, with a foreword by Nobel Laureate C N Yang. The volume that spans over fifty years of Faddeev's career begins where he started his own scientific research, in the subject of scattering theory and the three-body problem. It then continues to describe Faddeev's contributions to automorphic functions, followed by an extensive account of his many fundamental contributions to quantum field theory including his original article on ghosts with Popov. Faddeev's contributions to soliton theory and integrable models are then described, followed by a survey of his work on quantum groups. The final scientific section is devoted to Faddeev's contemporary research including articles on his long-term interest in constructing knotted solitons and understanding confinement. The volume concludes with his personal view on science and mathematical physics in particular.
International Conference on Differential Equations and Mathematical Physics
Saitō, Yoshimi
1987-01-01
The meeting in Birmingham, Alabama, provided a forum for the discussion of recent developments in the theory of ordinary and partial differential equations, both linear and non-linear, with particular reference to work relating to the equations of mathematical physics. The meeting was attended by about 250 mathematicians from 22 countries. The papers in this volume all involve new research material, with at least outline proofs; some papers also contain survey material. Topics covered include: Schrödinger theory, scattering and inverse scattering, fluid mechanics (including conservative systems and inertial manifold theory attractors), elasticity, non-linear waves, and feedback control theory.
Mathematical Reasoning Requirements in Swedish National Physics Tests
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…
Foundations of mathematics and physics one century after Hilbert new perspectives
2018-01-01
This book explores the rich and deep interplay between mathematics and physics one century after David Hilbert’s works from 1891 to 1933, published by Springer in six volumes. The most prominent scientists in various domains of these disciplines contribute to this volume providing insight to their works, and analyzing the impact of the breakthrough and the perspectives of their own contributions. The result is a broad journey through the most recent developments in mathematical physics, such as string theory, quantum gravity, noncommutative geometry, twistor theory, Gauge and Quantum fields theories, just to mention a few. The reader, accompanied on this journey by some of the fathers of these theories, explores some far reaching interfaces where mathematics and theoretical physics interact profoundly and gets a broad and deep understanding of subjects which are at the core of recent developments in mathematical physics. The journey is not confined to the present state of the art, but sheds light on future ...
Modellus: Learning Physics with Mathematical Modelling
Teodoro, Vitor
Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations
African Journals Online: Chemistry, Mathematics & Physics
African Journals Online (AJOL)
Items 1 - 36 of 36 ... African Journal of Educational Studies in Mathematics and Sciences ... statistics, operational research, financial mathematics and about the annexes ... research work in all areas of mathematical sciences and application at all ...
A Moonshine Dialogue in Mathematical Physics
Directory of Open Access Journals (Sweden)
Michel Planat
2015-08-01
Full Text Available Phys and Math are two colleagues at the University of Saçenbon (Crefan Kingdom, dialoguing about the remarkable efficiency of mathematics for physics. They talk about the notches on the Ishango bone and the various uses of psi in maths and physics; they arrive at dessins d’enfants, moonshine concepts, Rademacher sums and their significance in the quantum world. You should not miss their eccentric proposal of relating Bell’s theorem to the Baby Monster group. Their hyperbolic polygons show a considerable singularity/cusp structure that our modern age of computers is able to capture. Henri Poincaré would have been happy to see it.
My view of mathematics and physics (integration of mathematics into physics
Directory of Open Access Journals (Sweden)
Safronov S.V.
2017-09-01
Full Text Available this paper explores a new view of modern physics. New material is added to the modern mathematical physics. Filling a gap in physics theory and physical laws already in existence is the purpose of the article. The paper is devoted to contemporary issues. The work contains first development of formulas: gravitational pulse formula, vibration in pendulum formula, photon formula, three field energy density in atom formula, neutrino energy formula, equal energy of two kinds conversion formula and ray of light energy formula. The author introduces the conversion sign for scientific use in this article. The practical importance of the work involves innovative technology development.
Problem solving in the borderland between mathematics and physics
DEFF Research Database (Denmark)
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 fo......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...
Partial differential equations of mathematical physics and integral equations
Guenther, Ronald B
1996-01-01
This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t
XIII Modave Summer School in Mathematical Physics
2017-09-01
The Modave Summer School on Mathematical Physics is a yearly summer school in topics of theoretical physics. Various topics ranging from quantum gravity and cosmology to theoretical particle physics and string theory. The school takes place in Modave, a charming village in the Belgian Ardennes close to Huy. Modave School is organised by PhD students for PhD students, and this makes it rather unique. The courses are taught by Post-Docs or late PhD students, and they are all made of pedagogical, basic blackboard lectures about recent topics in theoretical physics. Participants and lecturers eat and sleep in the same place where the lectures are given. The absence of senior members, and the fact of spending day and night together in an isolated, peaceful place contribute to creating an informal atmosphere and facilitating interactions. Lectures of the thirteenth edition are centered around the following subjects: bulk reconstruction in AdS/CFT, twistor theory, AdS_2/CFT_1 and SYK, geometry and topology, and asymptotic charges.
Twareque Ali, Syed; Antoine, Jean-Pierre; Bagarello, Fabio; Gazeau, Jean-Pierre
2011-07-01
This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to coherent states. The motivation behind this special issue is to gather in a single comprehensive volume the main aspects (past and present), latest developments, different viewpoints and directions being followed in this multidisciplinary field. Given the impressive development of the field in the past two decades, the topicality of such a volume can hardly be overemphasized. We strongly believe that such a special issue could become a particularly valuable reference for the broad scientific community working in mathematical and theoretical physics, as well as in signal processing and mathematics. Editorial policy The Guest Editors for this issue will be Syed Twareque Ali, Jean-Pierre Antoine, Fabio Bagarello and Jean-Pierre Gazeau. Potential topics include, but are not limited to, developments in the theory and applications of coherent states in: quantum optics, optomechanics, Bose-Einstein condensates quantum information, quantum measurement signal processing quantum gravity pseudo-Hermitian quantum mechanics supersymmetric quantum mechanics non-commutative quantum mechanics quantization theory harmonic and functional analysis operator theory Berezin-Toeplitz operators, PT-symmetric operators holomorphic representation theory, reproducing kernel spaces generalization of coherent states All contributions will be refereed and processed according to the usual procedure of the journal. Papers should report original and significant research that has not already been published. Guidelines for preparation of contributions The deadline for contributed papers will be 31 October 2011. This deadline will allow the special issue to appear before the end of May 2012 There is a nominal page limit of 15 printed pages per contribution (invited review papers can be longer). For papers exceeding this limit, the Guest Editors reserve the right to request a
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…
Theoretical mechanics an introduction to mathematical physics
Sweetman Ames, Joseph
1958-01-01
In this book Professors Ames and Murnaghan undertake a mathematically rigorous development of theoretical mechanics from the point of view of modern physics. It gives an intensive survey of this basis field with extensive and extremely thorough discussions of vector and tensor methods, the displacement and motion of a rigid body, dynamics of inertial and non-inertial reference frames, dynamics of a particle, harmonic vibrations, nonrectilinear motion of a particle, central forces and universal gravitation, dynamics of a systems of material particle,impulsive forces, motion of a rigid body about a fixed point, gyroscopic and barygyroscopic theory, general dynamical theorems, vibrations about a point of equilibrium, the principle of least action, holonomic and nonholonomic systems, the principle of least constraint, general methods of integration and the three body problem, the potential function (including simple-layer and double-layer potentials), wave motion, the Lorentz-Einstein transformation and an illumi...
Current problems in applied mathematics and mathematical physics
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.
Simple mathematical models of symmetry breaking. Application to particle physics
International Nuclear Information System (INIS)
Michel, L.
1976-01-01
Some mathematical facts relevant to symmetry breaking are presented. A first mathematical model deals with the smooth action of compact Lie groups on real manifolds, a second model considers linear action of any group on real or complex finite dimensional vector spaces. Application of the mathematical models to particle physics is considered. (B.R.H.)
Index Theory with Applications to Mathematics and Physics
DEFF Research Database (Denmark)
Booss-Bavnbek, Bernhelm; Bleecker, David
Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has giv...... birth to many mathematical research areas and exposed profound connections between analysis, geometry, topology, algebra, and mathematical physics. Hardly any topic of modern mathematics stands independent of its influence.......Index Theory with Applications to Mathematics and Physics describes, explains, and explores the Index Theorem of Atiyah and Singer, one of the truly great accomplishments of twentieth-century mathematics whose influence continues to grow, fifty years after its discovery. The Index Theorem has given...
Promoting the Understanding of Mathematics in Physics at Secondary Level
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…
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…
Mathematical and physical aspects of gauge theories
International Nuclear Information System (INIS)
Chatelet, G.; Paris-13 Univ., 93 - Saint-Denis
1981-01-01
We present here a survey of gauge theories, trying to relate the main mathematical and physical concepts. Part I is devoted to exhibiting parallel transport and connection as the adequate concepts for the constitution of the parametrized internal space of a particle. A covariant derivative provides the differential calculus, which is needed when one leaves the point-like description in microphysics. Part II deals with the so-called pure gauge theory and sketches the construction of the self-dual solutions of Yang-Mills equations. We briefly explain Guersey's method to get SU 2 self-dual potentials as quarternionic analytic maps from S 4 (first quarternionic projective space) into HPsub(n) (n-dimensional quarternionic projective space). Part III is devoted to the Goldstone's theorem and Higgs' mechanism used to provide a mass to gauge mesons. We describe a Salam-Weinberg model to illustrate these techniques. Part IV deals with the perturbative aspect. The Faddeev-Popov method, formerly conceived as a technique to get correct Feynmann rules, actually leads to a systematic study of the affine space of connections factored out by gauge transformations. (orig.)
Mathematics and physics of emerging biomedical imaging
National Research Council Canada - National Science Library
Committee on the Mathematics and Physics of Emerging Dynamic Biomedical Imaging, National Research Council
.... Incorporating input from dozens of biomedical researchers who described what they perceived as key open problems of imaging that are amenable to attack by mathematical scientists and physicists...
Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics
Chill, Ralph; Tomilov, Yuri
2015-01-01
This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern...
Simple and Intuitive Mathematics for Learning Elementary Physics
Kobayashi, Yukio
Mathematics is the language of physics and simple and intuitive mathematics is effective for imaging physical pictures of phenomena. This is important because geometrical viewpoints inspire ideas in physics. For example, some problems on the motion of a particle in a uniform gravitational field can be well illustrated by simple diagrams. Calculus is not only a way of calculating but is also closely related to the law of inertia through slope on a position-time graph. As such, cross-curricular study between mathematics and physics is effective for broadly developing thinking power at the high school and college levels.
Addressing Mathematization Obstacles with Unformalized Problems in Physics Education
DEFF Research Database (Denmark)
Niss, Martin
2018-01-01
Abstract: Solving a physics problem requires that the problem solver either implicitly or explicitly structure the problem situation in such a way that she can set up the mathematical equations based on the relevant physics. This part of the mathematization process has been shown to cause obstacles...... for students (Niss, 2016). In the paper, we show how the students’ ability to perform this mathematization process can be trained by using so-called unformalized physics problems. Some examples of how this training can be done are provided from a course on problem solving in physics taught at Roskilde...
An excursion through elementary mathematics, volume iii discrete mathematics and polynomial algebra
Caminha Muniz Neto, Antonio
2018-01-01
This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Ol...
XI. The Relation between Mathematics and Physic
Indian Academy of Sciences (India)
of mathematics in this scheme is to represent the laws of motion by equations, and to obtain solutions ... What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical peauty. This is a quality ... The difference may be expressed concisely, but in·a ...
Some applications of mathematics in theoretical physics - A review
Energy Technology Data Exchange (ETDEWEB)
Bora, Kalpana [Physics Department, Gauhati University, Guwahati-781014, Assam (India)
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 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.
Some applications of mathematics in theoretical physics - A review
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.
Some applications of mathematics in theoretical physics - A review
International Nuclear Information System (INIS)
Bora, Kalpana
2016-01-01
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.
Developmental Physical Education Accountability; Volume I.
Guarnieri, Barbara; Sandeen, Cecile
Presented in the first of a two volume series is a developmental physical education checklist which provides teachers of trainable mentally retarded students with a permanent and accountable record of pupil progress and needs. The checklist is intended to be used with the accompanying volume of curricular activities in a nongraded enviroment for…
Scattering theory in quantum mechanics. Physical principles and mathematical methods
International Nuclear Information System (INIS)
Amrein, W.O.; Jauch, J.M.; Sinha, K.B.
1977-01-01
A contemporary approach is given to the classical topics of physics. The purpose is to explain the basic physical concepts of quantum scattering theory, to develop the necessary mathematical tools for their description, to display the interrelation between the three methods (the Schroedinger equation solutions, stationary scattering theory, and time dependence) to derive the properties of various quantities of physical interest with mathematically rigorous methods
Quantum Gravity (Cambridge Monographs on Mathematical Physics)
International Nuclear Information System (INIS)
Kiefer, C
2005-01-01
mechanics, general relativity and other topics. According to the level of the reader, this part can be skipped or studied as interesting material on its own. The penetrating theme of the whole book (its leitmotiv) is background independence. In non-gravitational theories, dynamical fields are formulated on a fixed background spacetime that plays the role of an absolute structure in the theory. In general relativity, on the other hand, there is no background structure - all fields are dynamical. This was a confusing point already during the development of general relativity and led Albert Einstein in 1913 erroneously to give up general covariance before recognizing his error and presenting his final correct field equations that are of course covariant. This story is instructive, circling around the famous 'hole problem', and is told in detail in Rovelli's book. Its solution is that points on a bare manifold do not make sense in physics; everything, including the gravitational field, is dragged around by a diffeomorphism - there is just no background available, only the fields exist. In loop quantum gravity, physical space (called 'quantum geometry') itself is formed by loop-like quantum states: a suitable orthonormal basis is provided by spin-network states (a spin-network is a graph with edges and nodes, where spins are assigned to the edges), and the quantum geometry is a superposition of such states. Time and space in the usual sense have disappeared. In the second half of his book, Rovelli discusses at length the major successes of this approach. First of all, the formalism yields a unique kinematical Hilbert space for the quantum states obeying the Gauss and diffeomorphism constraints. Secondly, there exist two important operators that are connected, respectively, with area and volume in the classical limit. These operators have a discrete spectrum and thus provide elementary 'quanta' of area and volume. This gives a vague hint of a discrete structure at the Planck
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.
Co-operation Between Science Teachers and Mathematics Teachers. Volumes 1-6.
Rogerson, Alan, Ed.
This document contains six separate works, titled: (1) Functions and Physics; (2) Links Between Geography and Mathematics; (3) Our Inheritance: Common Ground for the Mathematics and Biology Teacher; (4) Mathematics and Chemistry: The Classroom Interface; (5) Mathematical Modeling; and (6) Mathematical Modeling with Calculus. This series of…
The philosophical aspect of learning inverse problems of mathematical physics
Directory of Open Access Journals (Sweden)
Виктор Семенович Корнилов
2018-12-01
Full Text Available The article describes specific questions student learning inverse problems of mathematical physics. When teaching inverse problems of mathematical physics to the understanding of the students brought the information that the inverse problems of mathematical physics with a philosophical point of view are the problems of determining the unknown causes of known consequences, and the search for their solutions have great scientific and educational potential. The reasons are specified in the form of unknown coefficients, right side, initial conditions of the mathematical model of inverse problems, and as a consequence are functionals of the solution of this mathematical model. In the process of learning the inverse problems of mathematical physics focuses on the philosophical aspects of the phenomenon of information and identify cause-effect relations. It is emphasized that in the process of logical analysis applied and humanitarian character, students realize that information is always related to the fundamental philosophical questions that the analysis applied and the humanitarian aspects of the obtained results the inverse problem of mathematical physics allows students to make appropriate inferences about the studied process and to, ultimately, new information, to study its properties and understand its value. Philosophical understanding of the notion of information opens up to students a new methodological opportunities to comprehend the world and helps us to reinterpret existing science and philosophy of the theory related to the disclosure of the interrelationship of all phenomena of reality.
Mathematics, Physics and Computer Sciences The computation of ...
African Journals Online (AJOL)
Mathematics, Physics and Computer Sciences The computation of system matrices for biquadraticsquare finite ... Global Journal of Pure and Applied Sciences ... The computation of system matrices for biquadraticsquare finite elements.
Fractional derivative and its application in mathematics and physics
International Nuclear Information System (INIS)
Namsrai, K.
2004-12-01
We propose fractional derivatives and to study those mathematical and physical consequences. It is shown that fractional derivatives possess noncommutative and nonassociative properties and within which motion of a particle, differential and integral calculuses are investigated. (author)
Effects of Vigorous Intensity Physical Activity on Mathematics Test Performance
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…
An excursion through elementary mathematics, volume ii euclidean geometry
Caminha Muniz Neto, Antonio
2018-01-01
This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This second volume covers Plane Geometry, Trigonometry, Space Geometry, Vectors in the Plane, Solids and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Olympiads, as well as many...
Support of Study on Engineering Technology from Physics and Mathematics
Mynbaev, Djafar K.; Cabo, Candido; Kezerashvili, Roman Ya.; Liou-Mark, Janet
2008-01-01
An approach that provides students with an ability to transfer learning in physics and mathematics to the engineering-technology courses through e-teaching and e-learning process is proposed. E-modules of courses in mathematics, physics, computer systems technology, and electrical and telecommunications engineering technology have been developed. These modules being used in the Blackboard and Web-based communications systems create a virtual interdisciplinary learning community, which helps t...
The role of a posteriori mathematics in physics
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.
Directory of Open Access Journals (Sweden)
Syarifah Fadillah
2017-03-01
Full Text Available The problem in this research is to know how the process of developing mathematics physics instructional book based on inquiry approach and its supporting documents to improve students' mathematical problem-solving ability. The purpose of this research is to provide mathematical physics instruction based on inquiry approach and its supporting documents (semester learning activity plan, lesson plan and mathematical problem-solving test to improve students' mathematical problem-solving ability. The development of textbook refers to the ADDIE model, including analysis, design, development, implementation, and evaluation. The validation result from the expert team shows that the textbook and its supporting documents are valid. The test results of the mathematical problem-solving skills show that all test questions are valid and reliable. The result of the incorporation of the textbook in teaching and learning process revealed that students' mathematical problem-solving ability using mathematical physics instruction based on inquiry approach book was better than the students who use the regular book.
A mathematical look at a physical power prediction model
DEFF Research Database (Denmark)
Landberg, L.
1998-01-01
This article takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations and to give guidelines as to where simplifications can be made and where they cannot....... The article shows that there is a linear dependence between the geostrophic wind and the local wind at the surface, but also that great care must be taken in the selection of the simple mathematical models, since physical dependences play a very important role, e.g. through the dependence of the turning...
A few recent examples of mathematics at work in physics
International Nuclear Information System (INIS)
Zee, A.
1984-01-01
In this paper, the authors discuss some recent applications of mathematics to physics, in the hope that the mathematical sophisticates among you may be able to see ways of carrying the discussion further. The authors believe that mathematics is sometimes a necessary fact of life but in general to be avoided if possible. The absence of significant experimental result can do strange things to a field of physics. They highlight some recent developments and they focus exclusively on papers to which the reader is referred for further details
Mathematical mechanic using physical reasoning to solve problems
Levi, Mark
2009-01-01
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can
PREFACE: Physics-Based Mathematical Models for Nanotechnology
Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten
2008-03-01
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)
Mathematics and physics of neutron radiography
International Nuclear Information System (INIS)
Harms, A.A.; Wyman, D.R.
1985-01-01
This book provides detailed descriptions and analyses of selected experiments and their mathematical characterization. Also included are illustrative and quantitative procedures for applications. This book also discusses the radiography, nondestructive testing and nuclear reactor utilization. The contents discussed are: I: Introduction. II: Component Characterization. III: Object-Image Relations. IV: Rectangular Geometry. V: Cylindrical Geometry. VI: Two-Dimensional Analysis. VII: Object Scattering. VIII: Linear Systems Formulation. IX: Selected Topics. X: Neutron Radiographs. XI: Bibliography and References. Subject Index
Mathematics and physics of emerging biomedical imaging
International Nuclear Information System (INIS)
1996-01-01
Although the mathematical sciences were used in a general way for image processing, they were of little importance in biomedical work until the development in the 1970s of computed tomography (CT) for the imaging of x-rays and isotope emission tomography. In the 1980s, MRI eclipsed the other modalities in many ways as the most informative medical imaging methodology. Besides these well-established techniques, computer-based mathematical methods are being explored in applications to other well-known methods, such as ultrasound and electroencephalography, as well as new techniques of optical imaging, impedance tomography, and magnetic source imaging. It is worth pointing out that, while the final images of many of these techniques bear many similarities to each other, the technologies involved in each are completely different and the parameters represented in the images are very different in character as well as in medical usefulness. In each case, rather different mathematical or statistical models are used, with different equations. One common thread is the paradigm of reconstruction from indirect measurements--this is the unifying theme of this report. The imaging methods used in biomedical applications that this report discusses include: (1) x-ray projection imaging; (2) x-ray computed tomography (CT); (3) magnetic resonance imaging (MRI) and magnetic resonance spectroscopy; (4) single photon emission computed tomography (SPECT); (5) positron emission tomography (PET); (6) ultrasonics; (7) electrical source imaging (ESI); (8) electrical impedance tomography (EIT); (9) magnetic source imaging (MSI); and (10) medical optical imaging
Marriages of mathematics and physics: A challenge for biology.
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.
Quaternions and the heuristic role of mathematical structures in physics
International Nuclear Information System (INIS)
Anderson, R.S.J.; Joshi, G.C.
1992-07-01
One of the important ways development takes place in mathematics is via a process of generalization. On the basis of a recent characterization of the process the authors propose that generalizations of mathematical structures that are already part of successful physical theories serve as good guides for the development of new physical theories. The principle is a more formal presentation and extension of a position stated earlier this century by Dirac. Quaternions form an excellent example of such a generalization, and a number of the ways in which their use in physical theories illustrates this principle, are discussed. 114 refs
Summer Workshop on Physics, Mathematics, and All That Quantum Jazz
Bando, Masamitsu; Güngördü, Utkan; Physics, Mathematics, and All That Quantum Jazz
2014-01-01
This book is a collection of contributions from a Summer Workshop on Physics, Mathematics, and All That Quantum Jazz . Subjects of the symposium include quantum information theory, quantum annealing, Bose gases, and thermodynamics from a viewpoint of quantum physics. Contributions to this book are prepared in a self-contained manner so that readers with a modest background may understand the subjects.
Exercises and problems in mathematical methods of physics
Cicogna, Giampaolo
2018-01-01
This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students...
Topics in the mathematical physics of E-infinity theory
International Nuclear Information System (INIS)
El Naschie, M.S.
2006-01-01
This is the fourth contribution in a series of papers aimed at directing the attention of the prospective E-infinity researcher to the most important mathematical background and sources needed for an easy understanding and successful application of this theory. The present paper is mainly concerned with the mathematical physics relevant to E-infinity theory with emphasis on super Yang-Mills theory and superstrings
The Pythagorean world why mathematics is unreasonably effective in physics
McDonnell, Jane
2017-01-01
This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.
Cardall, Christian Y.; Budiardja, Reuben D.
2018-01-01
The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.
The role of mathematics for physics teaching and understanding
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.
High-Precision Computation and Mathematical Physics
International Nuclear Information System (INIS)
Bailey, David H.; Borwein, Jonathan M.
2008-01-01
At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.
Essentials of Mathematica With Applications to Mathematics and Physics
Boccara, Nino
2007-01-01
Essentials of Mathematica: With Applications to Mathematics and Physics, based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergraduate and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. The text assumes no previous exposure to Mathematica. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy-to-read Mathematica programs. It includes many detailed graphics, with instructions to students on how to achieve similar results. The aim of Essentials of Mathematica is to provide the reader with Mathematica proficiency quickly and efficiently. The first part, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. The second part covers a broad range of applications in physics and applied mathematics, including negative and complex bases, the double pendulum, fractals,...
Nature's longest threads new frontiers in the mathematics and physics of information in biology
Sreekantan, B V
2014-01-01
Organisms endowed with life show a sense of awareness, interacting with and learning from the universe in and around them. Each level of interaction involves transfer of information of various kinds, and at different levels. Each thread of information is interlinked with the other, and woven together, these constitute the universe — both the internal self and the external world — as we perceive it. They are, figuratively speaking, Nature's longest threads. This volume reports inter-disciplinary research and views on information and its transfer at different levels of organization by reputed scientists working on the frontier areas of science. It is a frontier where physics, mathematics and biology merge seamlessly, binding together specialized streams such as quantum mechanics, dynamical systems theory, and mathematics. The topics would interest a broad cross-section of researchers in life sciences, physics, cognition, neuroscience, mathematics and computer science, as well as interested amateurs, familia...
The role of mathematics for physics teaching and understanding
International Nuclear Information System (INIS)
Pospiech, G; Geyer, M.A.; Eylon, B.; Bagno, E.; Lehavi, Y.
2015-01-01
That 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.
ALICE: Physics Performance Report, Volume II
International Nuclear Information System (INIS)
Alessandro, B; Antinori, F; Belikov, J A
2006-01-01
ALICE is a general-purpose heavy-ion experiment designed to study the physics of strongly interacting matter and the quark-gluon plasma in nucleus-nucleus collisions at the LHC. It currently involves more than 900 physicists and senior engineers, from both the nuclear and high-energy physics sectors, from over 90 institutions in about 30 countries. The ALICE detector is designed to cope with the highest particle multiplicities above those anticipated for Pb-Pb collisions (dN ch /dy up to 8000) and it will be operational at the start-up of the LHC. In addition to heavy systems, the ALICE Collaboration will study collisions of lower-mass ions, which are a means of varying the energy density, and protons (both pp and pA), which primarily provide reference data for the nucleus-nucleus collisions. In addition, the pp data will allow for a number of genuine pp physics studies. The detailed design of the different detector systems has been laid down in a number of Technical Design Reports issued between mid-1998 and the end of 2004. The experiment is currently under construction and will be ready for data taking with both proton and heavy-ion beams at the start-up of the LHC. Since the comprehensive information on detector and physics performance was last published in the ALICE Technical Proposal in 1996, the detector, as well as simulation, reconstruction and analysis software have undergone significant development. The Physics Performance Report (PPR) provides an updated and comprehensive summary of the performance of the various ALICE subsystems, including updates to the Technical Design Reports, as appropriate. The PPR is divided into two volumes. Volume I, published in 2004 (CERN/LHCC 2003-049, ALICE Collaboration 2004 J. Phys. G: Nucl. Part. Phys. 30 1517-1763), contains in four chapters a short theoretical overview and an extensive reference list concerning the physics topics of interest to ALICE, the experimental conditions at the LHC, a short summary and update
Mathematical methods in engineering and physics
Felder, Gary N
2016-01-01
This text is intended for the undergraduate course in math methods, with an audience of physics and engineering majors. As a required course in most departments, the text relies heavily on explained examples, real-world applications and student engagement. Supporting the use of active learning, a strong focus is placed upon physical motivation combined with a versatile coverage of topics that can be used as a reference after students complete the course. Each chapter begins with an overview that includes a list of prerequisite knowledge, a list of skills that will be covered in the chapter, and an outline of the sections. Next comes the motivating exercise, which steps the students through a real-world physical problem that requires the techniques taught in each chapter.
A mathematical look at a physical power prediction model
Energy Technology Data Exchange (ETDEWEB)
Landberg, L. [Riso National Lab., Roskilde (Denmark)
1997-12-31
This paper takes a mathematical look at a physical model used to predict the power produced from wind farms. The reason is to see whether simple mathematical expressions can replace the original equations, and to give guidelines as to where the simplifications can be made and where they can not. This paper shows that there is a linear dependence between the geostrophic wind and the wind at the surface, but also that great care must be taken in the selection of the models since physical dependencies play a very important role, e.g. through the dependence of the turning of the wind on the wind speed.
Some beautiful equations of mathematical physics
International Nuclear Information System (INIS)
Freedman, D.Z.
1995-01-01
The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism and the standard model, the spin-2 gauge principle of general relativity, and the spin-3/2 gauge principle of supergravity. (author)
Mathematics of classical and quantum physics
Byron, Frederick W
Well-organized text designed to complement graduate-level physics texts in classical mechanics, electricity, magnetism, and quantum mechanics. Topics include theory of vector spaces, analytic function theory, Green's function method of solving differential and partial differential equations, theory of groups, more. Many problems, suggestions for further reading.
Some beautiful equations of mathematical physics
Energy Technology Data Exchange (ETDEWEB)
Freedman, D Z [Theoretical Physics Division, CERN, Geneva (Switzerland); [Department of Mathematics and Center for Theoretical Physics, M.I.T., Cambridge, MA (United States)
1996-12-31
The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism and the standard model, the spin-2 gauge principle of general relativity, and the spin-3/2 gauge principle of supergravity. (author)
Physical and mathematical modelling of extrusion processes
DEFF Research Database (Denmark)
Arentoft, Mogens; Gronostajski, Z.; Niechajowics, A.
2000-01-01
The main objective of the work is to study the extrusion process using physical modelling and to compare the findings of the study with finite element predictions. The possibilities and advantages of the simultaneous application of both of these methods for the analysis of metal forming processes...
Rays, waves, and scattering topics in classical mathematical physics
Adam, John A
2017-01-01
This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technica...
Methods of contemporary mathematical statistical physics
2009-01-01
This volume presents a collection of courses introducing the reader to the recent progress with attention being paid to laying solid grounds and developing various basic tools. An introductory chapter on lattice spin models is useful as a background for other lectures of the collection. The topics include new results on phase transitions for gradient lattice models (with introduction to the techniques of the reflection positivity), stochastic geometry reformulation of classical and quantum Ising models, the localization/delocalization transition for directed polymers. A general rigorous framework for theory of metastability is presented and particular applications in the context of Glauber and Kawasaki dynamics of lattice models are discussed. A pedagogical account of several recently discussed topics in nonequilibrium statistical mechanics with an emphasis on general principles is followed by a discussion of kinetically constrained spin models that are reflecting important peculiar features of glassy dynamic...
Analytical calculations by computer in physics and mathematics
International Nuclear Information System (INIS)
Gerdt, V.P.; Tarasov, O.V.; Shirokov, D.V.
1978-01-01
The review of present status of analytical calculations by computer is given. Some programming systems for analytical computations are considered. Such systems as SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK which are implemented or will be implemented in JINR, and MACSYMA - one of the most developed systems - are discussed. It is shown on the basis of mathematical operations, realized in these systems, that they are appropriated for different problems of theoretical physics and mathematics, for example, for problems of quantum field theory, celestial mechanics, general relativity and so on. Some problems solved in JINR by programming systems for analytical computations are described. The review is intended for specialists in different fields of theoretical physics and mathematics
Mathematical methods for students of physics and related fields
Hassani, Sadri
2000-01-01
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics This new edition has been made more user-friendly through organization into convenient, shorter chapters Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms Some praise for the previous edi...
Mathematical Methods For Students of Physics and Related Fields
Hassani, Sadri
2009-01-01
Intended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material. Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics. This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms. Some praise for the previo...
Interpreting mathematics in physics: Charting the applications of SU(2) in 20th century physics
International Nuclear Information System (INIS)
Anderson, Ronald; Joshi, G.C.
2008-01-01
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has played in three key episodes in 20th century physics - intrinsic spin, isospin, and gauge theory and electroweak unification. We also briefly consider its role in loop quantum gravity. Each episode has led to profound and new physical notions of a space other than the traditional ones of space and spacetime, and each has had associated with it a complex and in places, contested history. The episodes also reveal ways mathematical structures provide resources for new physical theorizing and we propose our study as a contribution to a need Roger Penrose has identified to develop a 'profoundly sensitive aesthetic' sense for locating physically relevant mathematics
Interpreting mathematics in physics: Charting the applications of SU(2) in 20th century physics
Energy Technology Data Exchange (ETDEWEB)
Anderson, Ronald [Department of Philosophy, Boston College, Chestnut Hill, MA 02467 (United States)], E-mail: ronald.anderson@bc.edu; Joshi, G.C. [School of Physics, University of Melbourne, Victoria 3010 (Australia)], E-mail: joshi@physics.unimelb.edu.au
2008-04-15
The role mathematics plays within physics has been of sustained interest for physicists as well as for philosophers and historians of science. We explore this topic by tracing the role the mathematical structure associated with SU(2) has played in three key episodes in 20th century physics - intrinsic spin, isospin, and gauge theory and electroweak unification. We also briefly consider its role in loop quantum gravity. Each episode has led to profound and new physical notions of a space other than the traditional ones of space and spacetime, and each has had associated with it a complex and in places, contested history. The episodes also reveal ways mathematical structures provide resources for new physical theorizing and we propose our study as a contribution to a need Roger Penrose has identified to develop a 'profoundly sensitive aesthetic' sense for locating physically relevant mathematics.
The essential harmony in the classical equations of mathematical physics
Nucci, M C
2001-01-01
The possibility to transform any system of linear ordinary differential equations into a system of constant coefficient equations is demonstrated using Lie theory. Some examples relate the classical equations of mathematical physics to the simple harmonic oscillator. The roles of the third order form of the Ermakov-Pinney equation and of Fleischen-von Weltunter systems are explained.
Quantum algebras and Poisson geometry in mathematical physics
Karasev, M V
2005-01-01
This collection presents new and interesting applications of Poisson geometry to some fundamental well-known problems in mathematical physics. The methods used by the authors include, in addition to advanced Poisson geometry, unexpected algebras with non-Lie commutation relations, nontrivial (quantum) Kählerian structures of hypergeometric type, dynamical systems theory, semiclassical asymptotics, etc.
Physics to Mathematics: from Lintearia to Lemniscate - I
Indian Academy of Sciences (India)
Physics to Mathematics: from Lintearia to Lemniscate - I. R Sridharan. The elastic curve, also called elastica, is the name given to the shape assumed by a uniform elastic rod when bent into a plane curve under a stress of a certain kind. This curve, defined by James Bernoulli in the lSth century has been an interesting object ...
Journal of the Nigerian Association of Mathematical Physics ...
African Journals Online (AJOL)
This journal is aimed at any scientist who applies fairly rigorous mathematics to physics, chemistry, engineering or other sciences and also any mathematician ... Section Policies. Articles ... Browse By Category · Browse Alphabetically · Browse By Country · List All Titles · Free To Read Titles This Journal is Open Access.
PREFACE: X Workshop of the Gravitation and Mathematical Physics Division, Mexican Physical Society
2014-11-01
The collection of papers in this volume was presented during the X Workshop of the Gravitation and Mathematical Physics Division of the Mexican Physical Society (DGFM-SMF), which was held in Pachuca, Hidalgo, México, December 2-6, 2013. The Workshop is a bi-annual series of conferences sponsored by the DGFM-SMF that started in 1993 with the purposes of discussing and exchanging the research and experience of the gravitational and mathematical physics communities in Mexico. Each Mexican Workshop has been devoted to subjects of broad interest, so that students, in particular, can have access to specialized courses and talks that allow them to raise up their qualifications as professional researchers. Recurrent topics in the Mexican Workshop are supergravity, branes, black holes, the early Universe, observational cosmology, quantum gravity and cosmology and numerical relativity. Following our previous Workshops, distinguished researchers in the field, working in Mexico, were invited to give courses, whereas young researchers were invited for plenary lectures. More specialized talks were also presented in parallel sessions, with ample participation of researchers, and graduate and undergraduate students; most of the presentations have been included in these proceedings. The contributions in this volume have been peer-reviewed, and they represent most of the courses, plenary talks and contributed talks presented during our Workshop. We are indebted to the contributors of these proceedings, as well as to the other participants and organizers, all for making the event a complete success. We acknowledge the professionalism of our reviewers, who helped us to keep high quality standards in all manuscripts. Acknowledgments The organizing committee would like to acknowledge the financial support of the Mexican National Science and Technology Council (CONACyT), the Mexican Physical Society (SMF), as well as several Institutions including: Centro de Investigación y Estudios
78 FR 37590 - Advisory Committee for Mathematical and Physical Sciences #66; Notice of Meeting
2013-06-21
... Science Foundation and to provide advice and recommendations concerning research in mathematics and... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences 66; Notice... National Science Foundation announces the following meeting. Name: Advisory Committee for Mathematical and...
Directory of Open Access Journals (Sweden)
Trude Nilsen
2013-10-01
Full Text Available As students advance in their learning of physics over the course of their education, the requirement of mathematical applications in physics-related tasks increases, especially so in upper secondary school and in higher education. Yet there is little empirical work (particularly large-scale or longitudinal on the application of mathematics in physics education compared with the research related to the conceptual knowledge of physics. In order to clarify the nature of mathematics in physics education, we developed a theoretical framework for mathematical competencies pertinent to various physics tasks based on theoretical frameworks from mathematics and physics education. We used this synthesis of frameworks as a basis to create a model for physics competence. The framework also served as a tool for analyzing and categorizing trend items from the international large-scale survey, TIMSS Advanced 1995 and 2008. TIMSS Advanced assessed students in upper secondary school with special preparation in advanced physics and mathematics. We then investigated the changes in achievements on these categorized items across time for nations who participated in both surveys. The results from our analysis indicate that students whose overall physics achievement declined struggled the most with items requiring mathematics, especially items requiring them to handle symbols, such as manipulating equations. This finding suggests the importance of collaboration between mathematics and physics education as well as the importance of traditional algebra for physics education.
The role of mathematics in physical sciences interdisciplinary and philosophical aspects
Boniolo, Giovanni; Trobok, Majda
2005-01-01
Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.
Chern-Simons terms and cocycles in physics and mathematics
Energy Technology Data Exchange (ETDEWEB)
Jackiw, R.
1984-12-01
Contemporary topological research in Yang-Mills theory is reviewed, emphasizing the Chern-Simons terms and their relatives. Three applications of the Chern-Simons terms in physical theory are described: to help understanding gauge theories in even dimensional space-time; gauge field dynamics in odd dimensional space-time; and mathematically coherent description of even-dimensional gauge theories with chiral fermions that are apparently inconsistent due to chiral anomalies. Discussion of these applications is preceded by explanation of the mathematical preliminaries and examples in simple quantum mechanical settings. 24 refs. (LEW)
Mathematical methods for mathematicians, physical scientists and engineers
Dunning-Davies, J
2003-01-01
This practical introduction encapsulates the entire content of teaching material for UK honours degree courses in mathematics, physics, chemistry and engineering, and is also appropriate for post-graduate study. It imparts the necessary mathematics for use of the techniques, with subject-related worked examples throughout. The text is supported by challenging problem exercises (and answers) to test student comprehension. Index notation used in the text simplifies manipulations in the sections on vectors and tensors. Partial differential equations are discussed, and special functions introduced
The mathematical knowledge of physics graduates: Primary data and conclusions
Breitenberger, Ernst
1992-04-01
Systematic observations were made of the mathematical knowledge of physics students from the U.S. and other countries during their first years of graduate study at Ohio University. It was found that all were deficient in general and in ``modern'' mathematical concepts, and in problem-solving skills. Sizable fractions of them did not even possess adequate concepts of ``derivative,'' ``integration,'' and ``truth.'' Nearly all were limited to some familiarity with rather elementary calculus, and with equally elementary differential and linear equations, but they showed some ability and a pronounced willingness to perform manipulations. Roughly, they regarded mathematics as mechanical method, not as constructive thinking. In view of the significantly higher levels of mathematical fluency demanded by contemporary advances in physics and in computer usage, none of these students was adequately prepared for future-oriented study, or for research and employment in physics and related areas at the close of the 20th century. It is intended to discuss the likely causes of this state of affairs elsewhere with a view toward remedial actions.
Framing the Structural Role of Mathematics in Physics Lectures: A Case Study on Electromagnetism
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.…
Mathematics for plasma physics; Mathematiques pour la physique des plasmas
Energy Technology Data Exchange (ETDEWEB)
Sentis, R. [CEA Bruyeres-le-Chatel, 91 (France)
2011-01-15
The plasma physics is in the heart of the research of the CEA-DAM. Using mathematics in this domain is necessary, particularly for a precise statement of the partial differential equations systems which are on the basis of the numerical simulations. Examples are given concerning hydrodynamics, models for the thermal conduction and laser-plasma interaction. For the bi-temperature compressible Euler model, the mathematical study of the problem has allowed us to understand why the role of the energy equations dealing with ions on one hand and electrons on the other hand are not identical despite the symmetrical appearance of the system. The mathematical study is also necessary to be sure of the existence and uniqueness of the solution
Studies in Mathematics, Volume X. Applied Mathematics in the High School.
Schiffer, Max M.
This publication contains a sequence of lectures given to high school mathematics teachers by the author. Applications of mathematics emphasized are elementary algebra, geometry, and matrix algebra. Included are: (1) an introduction concerning teaching applications of mathematics; (2) Chapter 1: Mechanics for the High School Student; (3) Chapter…
Mathematical analogies in physics. Thin-layer wave theory
Directory of Open Access Journals (Sweden)
José M. Carcione
2014-03-01
Full Text Available Field theory applies to elastodynamics, electromagnetism, quantum mechanics, gravitation and other similar fields of physics, where the basic equations describing the phenomenon are based on constitutive relations and balance equations. For instance, in elastodynamics, these are the stress-strain relations and the equations of momentum conservation (Euler-Newton law. In these cases, the same mathematical theory can be used, by establishing appropriate mathematical equivalences (or analogies between material properties and field variables. For instance, the wave equation and the related mathematical developments can be used to describe anelastic and electromagnetic wave propagation, and are extensively used in quantum mechanics. In this work, we obtain the mathematical analogy for the reflection/refraction (transmission problem of a thin layer embedded between dissimilar media, considering the presence of anisotropy and attenuation/viscosity in the viscoelastic case, conductivity in the electromagnetic case and a potential barrier in quantum physics (the tunnel effect. The analogy is mainly illustrated with geophysical examples of propagation of S (shear, P (compressional, TM (transverse-magnetic and TE (transverse-electric waves. The tunnel effect is obtained as a special case of viscoelastic waves at normal incidence.
Intuitive physics knowledge, physics problem solving and the role of mathematical equations
Directory of Open Access Journals (Sweden)
Laura Buteler
2012-09-01
Full Text Available The present work explores the role that mathematical equations play in modifying students’ physical intuition (diSessa, 1993. The work is carried out assuming that students achieve a great deal of the refinement in their physical intuitions during problem solving (Sherin, 2006. The study is guided by the question of how the use of mathematical equations contributes to this refinement. The authors aim at expanding on Sherin´s (2006 hypothesis, suggesting a more bounding relation between physical intuitions and mathematics. In this scenario, intuitions play a more compelling role in “deciding” which equations are acceptable and which are not. Our hypothesis is constructed on the basis of three cases: the first published by Sherin (2006 and two more from registries of our own. The three cases are compared and analyzed in relation to the role of mathematical equations in refining – or not – the intuitive knowledge students bring to play during problem solving.
Special issue on cluster algebras in mathematical physics
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
The limitations of mathematical modeling in high school physics education
Forjan, Matej
The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems
The Bogolyubov renormalization group in theoretical and mathematical physics
International Nuclear Information System (INIS)
Shirkov, D.V.
1999-01-01
This text follows the line of a talk on Ringberg symposium dedicated to Wolfhart Zimmermann 70th birthday. The historical overview (Part I) partially overlaps with corresponding text of my previous commemorative paper - see Ref. [6] in the list. At the same time the second part includes some fresh results in QFT (Sect. 2.1.) and summarizes (Sect. 2.4) an impressive recent progress of the 'QFT renormalization group' application in mathematical physics
d=4 N=2 Field Theory And Physical Mathematics
CERN. Geneva
2017-01-01
I will explain the meaning of the two phrases in the title. Much of the talk will be a review of the renowned Seiberg-Witten formulation of the low-energy physics of certain four dimensional supersymmetric interacting quantum field theories. In the latter part of the talk I will briefly describe some of the significant progress that has been made in solving for the so-called BPS sector of the Hilbert space of these theories. Investigations into these physical questions have had a nontrivial impact on mathematics.
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major…
Rock Burst Mechanics: Insight from Physical and Mathematical Modelling
Directory of Open Access Journals (Sweden)
J. Vacek
2008-01-01
Full Text Available Rock burst processes in mines are studied by many groups active in the field of geomechanics. Physical and mathematical modelling can be used to better understand the phenomena and mechanisms involved in the bursts. In the present paper we describe both physical and mathematical models of a rock burst occurring in a gallery of a coal mine.For rock bursts (also called bumps to occur, the rock has to possess certain particular rock burst properties leading to accumulation of energy and the potential to release this energy. Such materials may be brittle, or the rock burst may arise at the interfacial zones of two parts of the rock, which have principally different material properties (e.g. in the Poíbram uranium mines.The solution is based on experimental and mathematical modelling. These two methods have to allow the problem to be studied on the basis of three presumptions:· the solution must be time dependent,· the solution must allow the creation of cracks in the rock mass,· the solution must allow an extrusion of rock into an open space (bump effect.
Physical and mathematical modeling of antimicrobial photodynamic therapy
Bürgermeister, Lisa; López, Fernando Romero; Schulz, Wolfgang
2014-07-01
Antimicrobial photodynamic therapy (aPDT) is a promising method to treat local bacterial infections. The therapy is painless and does not cause bacterial resistances. However, there are gaps in understanding the dynamics of the processes, especially in periodontal treatment. This work describes the advances in fundamental physical and mathematical modeling of aPDT used for interpretation of experimental evidence. The result is a two-dimensional model of aPDT in a dental pocket phantom model. In this model, the propagation of laser light and the kinetics of the chemical reactions are described as coupled processes. The laser light induces the chemical processes depending on its intensity. As a consequence of the chemical processes, the local optical properties and distribution of laser light change as well as the reaction rates. The mathematical description of these coupled processes will help to develop treatment protocols and is the first step toward an inline feedback system for aPDT users.
Blanchard, Philippe
2015-01-01
The second edition of this textbook presents the basic mathematical knowledge and skills that are needed for courses on modern theoretical physics, such as those on quantum mechanics, classical and quantum field theory, and related areas. The authors stress that learning mathematical physics is not a passive process and include numerous detailed proofs, examples, and over 200 exercises, as well as hints linking mathematical concepts and results to the relevant physical concepts and theories. All of the material from the first edition has been updated, and five new chapters have been added on such topics as distributions, Hilbert space operators, and variational methods. The text is divided into three main parts. Part I is a brief introduction to distribution theory, in which elements from the theories of ultradistributions and hyperfunctions are considered in addition to some deeper results for Schwartz distributions, thus providing a comprehensive introduction to the theory of generalized functions. P...
Special functions of mathematical physics a unified introduction with applications
Nikiforov, Arnold F
1988-01-01
With students of Physics chiefly in mind, we have collected the material on special functions that is most important in mathematical physics and quan tum mechanics. We have not attempted to provide the most extensive collec tion possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other natural sciences, since it pro vides a simple and effective method for the independent solution of problems that arise in practice in physics, engineering and mathematics. For the American edition we have been able to improve a number of proofs; in particular, we have given a new proof of the basic theorem (§3). This is the fundamental theorem of the book; it has now been extended to cover difference equations of hypergeometric type (§§12, 13). Several sections have been simplified and contain new material. We believe that this is the first time that the theory of classical or th...
Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics
Directory of Open Access Journals (Sweden)
Peter A. Horváthy
2006-12-01
Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.
Fundamentals of Cryobiology Physical Phenomena and Mathematical Models
Zhmakin, Alexander I
2009-01-01
The book gives a summary of the state-of-the-art of cryobiology and its applications. The accent is on the underlying physical phenomena, which are common in such opposite applications as cryosurgery and cryoconservation, and the corresponding mathematical models, including numerical ones. The treatment of some more special issues is moved to the appendices. The glossary contains definitions and explanations of the major entities. All the topics considered are well referenced. The book is useful to both biologists and physicits of different level including practioners and graduate students.
Weyl's search for a difference between 'physical' and 'mathematical' automorphisms
Scholz, Erhard
2018-02-01
During his whole scientific life Hermann Weyl was fascinated by the interrelation of physical and mathematical theories. From the mid 1920s onward he reflected also on the typical difference between the two epistemic fields and tried to identify it by comparing their respective automorphism structures. In a talk given at the end of the 1940s (ETH, Hs 91a:31) he gave the most detailed and coherent discussion of his thoughts on this topic. This paper presents his arguments in the talk and puts it in the context of the later development of gauge theories.
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Proceedings, 3rd International Satellite Conference on Mathematical Methods in Physics (ICMP13)
2013-01-01
The aim of the Conference is to present the latest advances in Mathematical Methods to researchers, post-docs and graduated students acting in the areas of Physics of Particles and Fields, Mathematical Physics and Applied Mathematics. Topics: Methods of Spectral and Group Theory, Differential and Algebraic Geometry and Topology in Field Theory, Quantum Gravity, String Theory and Cosmology.
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 complex road to mathematization in physics instruction
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo; Pietrocola, Maurício; Pospiech, Gesche
2012-01-01
to the research in this field, we have analysed a set of lectures given by a distinguished physics professor. In this proposal we present the analysis of two lectures where the abstract concepts of charge density and electric flux are taught. The complexity of the mathematization of these concepts is evident both...... explicitly and made punctual metacognitive remarks. Taking into account the future perspectives of our research, the categorization of the didactical strategies used by this professor shall allows us to develop comparative studies with other lectures on the same topic. Moreover, the derivation promising......How to facilitate students’ understanding of science’s abstract concepts is definitely a major concern of every dedicated physics teacher. However, discussions about promising ways to be successful at this task are not always part of teacher training curricula. With the goal of contributing...
Mathematical physics a modern introduction to its foundations
Hassani, Sadri
2013-01-01
The goal of this book is to expose the reader to the indispensable role that mathematics---often very abstract---plays in modern physics. Starting with the notion of vector spaces, the first half of the book develops topics as diverse as algebras, classical orthogonal polynomials, Fourier analysis, complex analysis, differential and integral equations, operator theory, and multi-dimensional Green's functions. The second half of the book introduces groups, manifolds, Lie groups and their representations, Clifford algebras and their representations, and fiber bundles and their applications to differential geometry and gauge theories. This second edition is a substantial revision of the first one with a complete rewriting of many chapters and the addition of new ones, including chapters on algebras, representation of Clifford algebras and spinors, fiber bundles, and gauge theories. The spirit of the first edition, namely the balance between rigor and physical application, has been maintained, as is the abundance...
A course in mathematical physics 2 classical field theory
Thirring, Walter
1978-01-01
In the past decade the language and methods ofmodern differential geometry have been increasingly used in theoretical physics. What seemed extravagant when this book first appeared 12 years ago, as lecture notes, is now a commonplace. This fact has strengthened my belief that today students of theoretical physics have to learn that language-and the sooner the better. Afterall, they willbe the professors ofthe twenty-first century and it would be absurd if they were to teach then the mathematics of the nineteenth century. Thus for this new edition I did not change the mathematical language. Apart from correcting some mistakes I have only added a section on gauge theories. In the last decade it has become evident that these theories describe fundamental interactions, and on the classical level their structure is suffi cientlyclear to qualify them for the minimum amount ofknowledge required by a theoretician. It is with much regret that I had to refrain from in corporating the interesting developments in Kal...
Physical correlates of radiologic heart volume
International Nuclear Information System (INIS)
Christie, D.
1978-01-01
Radiologic heart volume was calculated on a 10 per cent random sample of subjects examined in the London Civil Service Health Survey. Data were available for 1 188 men over the age of 40, and the importance of correcting radiologic heart volume for body size, age and heart rate was demonstrated. After these variables were taken into account, the most important association found was with blood pressure. Radiologic heart volume has potential value in cardiovascular screening programmes. (Auth.)
14th National Conference on Physics. Abstracts. Volume 2
International Nuclear Information System (INIS)
Calboreanu, Alexandru; Grecu, Dan
2005-01-01
The National Conference on Physics 2005, is dedicated to 'The International Year of Physics' by the scientific community of physicists in Romania. Within the frame of this 'Festival of Physics', The First Symposium on Technical Physics and Physical Engineering' TPPE 2005, was organized as a satellite event at the Polytechnic University of Bucharest. As it is well known, the contributed papers to the National Conference on Physics were structured on chapters, corresponding to 'the sections' of The Romanian Society of Physics, their abstracts being then published in a two volume 'Book of Abstracts'. All the chapters of this book, except the 8th and the 9th, can be found in 'Abstracts Volume I'. According to the topics of the TPPE 2005, these two chapters, namely: 8. Technical Physics and Physical Engineering and 9. Physics and Energy are published separately in the 'Abstracts Volume II', but as it can be seen, the unitary character of the Conference is preserved and developed. The most important topics of this second volume are: optoelectronics; advanced materials and technologies; physics, electronics and electrical engineering; physics and mechanical engineering; physics and chemical engineering; physics, information and computer engineering; physics and industry; physics, biology and medical engineering; renewable energy sources and energy efficiency; nuclear engineering. We present the progress made in physics education concerning: physics teaching in technical education; E-learning and modern methods in physics teaching; physics education in schools and universities, in a special section of the first volume of abstracts. Regarding the essential role of physics in the realizing of a knowledge-based society of the new millennium the strengthening of the relationship between researchers and academics becomes thus the main message of this scientific meeting. (P.S.)
An aqueous physical and mathematical modelling of ultrasonic degassing of molten metals
International Nuclear Information System (INIS)
Meidani, A.R.N.; Hasan, M.
1999-01-01
A comprehensive mathematical model, combined with an aqueous physical modelling, have been developed to simulate the ultrasonic degassing of a gassy liquid. The mathematical model forms a set of coupled, highly nonlinear and stiff differential equations. Therefore, the modified Gear method, which is a good numerical scheme for solving extremely fast moving boundary problems is applied. The threshold pressure and the effects of ultrasonic specifications on rectified diffusion of the dissolved air in water with different initial concentrations are studied. The results show that the air bubble grows when the ultrasonic pressure amplitude is more than the threshold pressure. In this case, the bubble volume reaches several times of its initial value in a fraction of second and the gas bubble may float to the surface due to the buoyancy force. A parametric study on the present model is carried out. The results of aqueous physical modelling for bubble growth are compared to the results of the mathematical model which show a reasonable agreement between the experiments and the predictions. (author)
Mathematical models for volume rendering and neutron transport
International Nuclear Information System (INIS)
Max, N.
1994-09-01
This paper reviews several different models for light interaction with volume densities of absorbing, glowing, reflecting, or scattering material. They include absorption only, glow only, glow and absorption combined, single scattering of external illumination, and multiple scattering. The models are derived from differential equations, and illustrated on a data set representing a cloud. They are related to corresponding models in neutron transport. The multiple scattering model uses an efficient method to propagate the radiation which does not suffer from the ray effect
The Challenge of Learning Physics before Mathematics: A Case Study of Curriculum Change in Taiwan
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…
Understanding space weather with new physical, mathematical and philosophical approaches
Mateev, Lachezar; Velinov, Peter; Tassev, Yordan
2016-07-01
The actual problems of solar-terrestrial physics, in particular of space weather are related to the prediction of the space environment state and are solved by means of different analyses and models. The development of these investigations can be considered also from another side. This is the philosophical and mathematical approach towards this physical reality. What does it constitute? We have a set of physical processes which occur in the Sun and interplanetary space. All these processes interact with each other and simultaneously participate in the general process which forms the space weather. Let us now consider the Leibniz's monads (G.W. von Leibniz, 1714, Monadologie, Wien; Id., 1710, Théodicée, Amsterdam) and use some of their properties. There are total 90 theses for monads in the Leibniz's work (1714), f.e. "(1) The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts'. (Theod. 10.); … (56) Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.); (59) … this universal harmony, according to which every substance exactly expresses all others through the relations it has with them. (63) … every Monad is, in its own way, a mirror of the universe, and the universe is ruled according to a perfect order. (Theod. 403.)", etc. Let us introduce in the properties of monads instead of the word "monad" the word "process". We obtain the following statement: Each process reflects all other processes and all other processes reflect this process. This analogy is not formal at all, it reflects accurately the relation between the physical processes and their unity. The category monad which in the Leibniz's Monadology reflects generally the philosophical sense is fully identical with the
Electroweak properties of particle physics. Volume 2
International Nuclear Information System (INIS)
Aleksan, R.; Ellis, N.; Falvard, A.; Fayard, L.; Frere, J.M.; Kuehn, J.H.; Le Yaouanc, A.; Roudeau, P.; Wormser, G.
1991-01-01
The 23th GIf school was held at Ecole Polytechnique, Palaiseau, France from 16 to 20 September 1991. The subject was large: Electroweak properties of heavy quarks. The second part has been devoted to B physics at hadron machines, search for Top, Charm particle physics and Quarkonium physics
Dynamical chaos and uniformly hyperbolic attractors: from mathematics to physics
Energy Technology Data Exchange (ETDEWEB)
Kuznetsov, Sergei P [Saratov Branch, Kotel' nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov (Russian Federation)
2011-02-28
Research is reviewed on the identification and construction of physical systems with chaotic dynamics due to uniformly hyperbolic attractors (such as the Plykin attraction or the Smale-Williams solenoid). Basic concepts of the mathematics involved and approaches proposed in the literature for constructing systems with hyperbolic attractors are discussed. Topics covered include periodic pulse-driven models; dynamics models consisting of periodically repeated stages, each described by its own differential equations; the construction of systems of alternately excited coupled oscillators; the use of parametrically excited oscillations; and the introduction of delayed feedback. Some maps, differential equations, and simple mechanical and electronic systems exhibiting chaotic dynamics due to the presence of uniformly hyperbolic attractors are presented as examples. (reviews of topical problems)
VIPRE-01. a thermal-hydraulic analysis code for reactor cores. Volume 1. Mathematical modeling
International Nuclear Information System (INIS)
Stewart, C.W.; Cuta, J.M.; Koontz, A.S.; Kelly, J.M.; Basehore, K.L.; George, T.L.; Rowe, D.S.
1983-04-01
VIPRE (Versatile Internals and Component Program for Reactors; EPRI) has been developed for nuclear power utility thermal-hydraulic analysis applications. It is designed to help evaluate nuclear reactor core safety limits including minimum departure from nucleate boiling ratio (MDNBR), critical power ratio (CPR), fuel and clad temperatures, and coolant state in normal operation and assumed accident conditions. This volume (Volume 1: Mathematical Modeling) explains the major thermal hydraulic models and supporting correlations in detail
Behaviour of mathematics and physics students in solving problem of Vector-Physics context
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.
Tuminaro, Jonathan
Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of
DEFF Research Database (Denmark)
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...
Explorations in Mathematical Physics The Concepts Behind an Elegant Language
Koks, Don
2006-01-01
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis buil...
Pursell, David P
2009-01-01
BIO2010 advocates enhancing the interdisciplinary, mathematics, and physical science components of the undergraduate biology curriculum. The Department of Chemistry and Life Science at West Point responded by developing a required physical chemistry course tailored to the interests of life science majors. To overcome student resistance to physical chemistry, students were enabled as long-term stakeholders who would shape the syllabus by selecting life science topics of interest to them. The initial 2 yr of assessment indicates that students have a positive view of the course, feel they have succeeded in achieving course outcome goals, and that the course is relevant to their professional future. Instructor assessment of student outcome goal achievement via performance on exams and labs is comparable to that of students in traditional physical chemistry courses. Perhaps more noteworthy, both student and instructor assessment indicate positive trends from year 1 to year 2, presumably due to the student stakeholder effect.
Engineering Physics and Mathematics Division progress report for period ending August 31, 1989
International Nuclear Information System (INIS)
1989-12-01
This paper contains abstracts on research performed at the Engineering Physics and Mathematics Division of Oak Ridge National Laboratory. The areas covered are: mathematical science; nuclear-data measurement and evaluation; intelligent systems; nuclear analysis and shielding; and Engineering Physics Information Center
Engineering Physics and Mathematics Division progress report for period ending August 31, 1989
Energy Technology Data Exchange (ETDEWEB)
1989-12-01
This paper contains abstracts on research performed at the Engineering Physics and Mathematics Division of Oak Ridge National Laboratory. The areas covered are: mathematical science; nuclear-data measurement and evaluation; intelligent systems; nuclear analysis and shielding; and Engineering Physics Information Center. (LSP)
Noted astrophysicist Michael S. Turner to Head NSF'S mathematical and physical sciences directorate
2003-01-01
"The National Science Foundation has named celebrated astrophysicist Michael S. Turner of the University of Chicago as Assistant Director for Mathematical and Physical Sciences. He will head a $1 billion directorate that supports research in mathematics, physics, chemistry, materials and astronomy, as well as multidisciplinary programs and education" (1/2 page).
A course in mathematical physics 3 quantum mechanics of atoms and molecules
Thirring, Walter
1981-01-01
In this third volume of A Course in Mathematical Physics I have attempted not simply to introduce axioms and derive quantum mechanics from them, but also to progress to relevant applications. Reading the axiomatic litera ture often gives one the impression that it largely consists of making refined axioms, thereby freeing physics from any trace of down-to-earth residue and cutting it off from simpler ways of thinking. The goal pursued here, however, is to come up with concrete results that can be compared with experimental facts. Everything else should be regarded only as a side issue, and has been chosen for pragmatic reasons. It is precisely with this in mind that I feel it appropriate to draw upon the most modern mathematical methods. Only by their means can the logical fabric of quantum theory be woven with a smooth structure; in their absence, rough spots would . inevitably appear, especially in the theory of unbounded operators, where the details are too intricate to be comprehended easily. Great care...
Energy Technology Data Exchange (ETDEWEB)
Lepore, J.V. (ed.)
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during 1977. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics, although there is a relatively small program of medium-energy research. The High Energy Physics research program in the Physics Division is concerned with fundamental research which will enable man to comprehend the nature of the physical world. The major effort is now directed toward experiments with positron-electron colliding beam at PEP. The Medium Energy Physics program is concerned with research using mesons and nucleons to probe the properties of matter. This research is concerned with the study of nuclear structure, nuclear reactions, and the interactions between nuclei and electromagnetic radiation and mesons. The Computer Science and Applied Mathematics Department engages in research in a variety of computer science and mathematics disciplines. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The Computer Center provides large-scale computational support to LBL's scientific programs. Descriptions of the various activities are quite short; references to published results are given. 24 figures. (RWR)
Physics, Computer Science and Mathematics Division. Annual report, 1 January--31 December 1977
International Nuclear Information System (INIS)
Lepore, J.V.
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during 1977. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics, although there is a relatively small program of medium-energy research. The High Energy Physics research program in the Physics Division is concerned with fundamental research which will enable man to comprehend the nature of the physical world. The major effort is now directed toward experiments with positron-electron colliding beam at PEP. The Medium Energy Physics program is concerned with research using mesons and nucleons to probe the properties of matter. This research is concerned with the study of nuclear structure, nuclear reactions, and the interactions between nuclei and electromagnetic radiation and mesons. The Computer Science and Applied Mathematics Department engages in research in a variety of computer science and mathematics disciplines. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The Computer Center provides large-scale computational support to LBL's scientific programs. Descriptions of the various activities are quite short; references to published results are given. 24 figures
Directory of Open Access Journals (Sweden)
Mihailova A.
2016-01-01
Reduced lung volumes were associated with lower aerobic fitness, lower physical fitness and lower amount of weekly physical activity. Healthier body mass index was associated with higher aerobic fitness (relative VO2max in both female and male.
Engineering Physics and Mathematics Division progress report for period ending December 31, 1994
International Nuclear Information System (INIS)
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 January 1, 1993, through December 31, 1994. This report is the final archival record of the EPM Division. On October 1, 1994, ORELA was transferred to Physics Division and on January 1, 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
Engineering Physics and Mathematics Division progress report for period ending December 31, 1994
Energy Technology Data Exchange (ETDEWEB)
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 January 1, 1993, through December 31, 1994. This report is the final archival record of the EPM Division. On October 1, 1994, ORELA was transferred to Physics Division and on January 1, 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.
ALICE: Physics performance report, volume II
Czech Academy of Sciences Publication Activity Database
Cortese, P.; Adamová, Dagmar; Kugler, Andrej; Šumbera, Michal; Wagner, Vladimír
2006-01-01
Roč. 32, č. 10 (2006), s. 1295-2040 ISSN 0954-3899 Institutional research plan: CEZ:AV0Z10480505 Keywords : LHC Subject RIV: BF - Elementary Particles and High Energy Physics Impact factor: 1.781, year: 2006
Are there common mathematical structures in economics and physics?
Mimkes, Jürgen
2016-12-01
Economics is a field that looks into the future. We may know a few things ahead (ex ante), but most things we only know, afterwards (ex post). How can we work in a field, where much of the important information is missing? Mathematics gives two answers: 1. Probability theory leads to microeconomics: the Lagrange function optimizes utility under constraints of economic terms (like costs). The utility function is the entropy, the logarithm of probability. The optimal result is given by a probability distribution and an integrating factor. 2. Calculus leads to macroeconomics: In economics we have two production factors, capital and labour. This requires two dimensional calculus with exact and not-exact differentials, which represent the "ex ante" and "ex post" terms of economics. An integrating factor turns a not-exact term (like income) into an exact term (entropy, the natural production function). The integrating factor is the same as in microeconomics and turns the not-exact field of economics into an exact physical science.
Fourier series, Fourier transform and their applications to mathematical physics
Serov, Valery
2017-01-01
This text serves as an introduction to the modern theory of analysis and differential equations with applications in mathematical physics and engineering sciences. Having outgrown from a series of half-semester courses given at University of Oulu, this book consists of four self-contained parts. The first part, Fourier Series and the Discrete Fourier Transform, is devoted to the classical one-dimensional trigonometric Fourier series with some applications to PDEs and signal processing. The second part, Fourier Transform and Distributions, is concerned with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic Schrödinger operations. The third part, Operator Theory and Integral Equations, is devoted mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to integral equations in such spaces. The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory o...
Introduction of the Thematic Issue on the Interplay of Physics and Mathematics
DEFF Research Database (Denmark)
Avelar Sotomaior Karam, Ricardo
2015-01-01
for the students. They have a hard time understanding where mathematical concepts come from and why physics has little to do with their experiential world. This problem demands a systematic research effort from experts in different fields, especially the ones who aim at informing educational practices......Since their beginnings Physics (natural philosophy) and mathematics have been deeply interrelated, and this mutual influence has played an essential role in both their developments. However, the image typically found in educational contexts is often quite different. In physics education......, it is usual to find mathematics being seen as a mere tool to describe and calculate, whereas in mathematics education, physics is commonly viewed as a possible context for the application of mathematical concepts that were previously defined abstractly. This dichotomy creates significant learning problems...
Analytical derivation: An epistemic game for solving mathematically based physics problems
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.
Keller, Agathe
2006-01-01
In the 5th century the Indian mathematician Aryabhata (476-499) wrote a small but famous work on astronomy, the Aryabhatiya. This treatise, written in 118 verses, gives in its second chapter a summary of Hindu mathematics up to that time. Two hundred years later, an Indian astronomer called Bhaskara glossed this mathematial chapter of the Aryabhatiya. An english translation of Bhaskara's commentary and a mathematical supplement are presented in two volumes. Subjects treated in Bhaskara's commentary range from computing the volume of an equilateral tetrahedron to the interest on a loaned capital, from computations on series to an elaborate process to solve a Diophantine equation. This volume contains explanations for each verse commentary translated in Volume 1. These supplements discuss the linguistic and mathematical matters exposed by the commentator. Particularly helpful for readers are an appendix on Indian astronomy, elaborate glossaries, and an extensive bibliography.
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…
Framing the structural role of mathematics in physics lectures: A case study on electromagnetism
Directory of Open Access Journals (Sweden)
Ricardo Karam
2014-05-01
Full Text Available 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.
Institutional supporting research highlights in physics and mathematics, fiscal year 1983
International Nuclear Information System (INIS)
Vigil, J.C.
1984-03-01
Highlights of FY 1983 Institutional Supporting Research and Development activities within the six Physics and Mathematics divisions and the Center for Nonlinear Studies are presented. The highlights are but a fraction of the ISRD activities in the Directorate and are intended to be a representative sample of progress in the various research areas. FY 1983 ISRD activities within the Physics and Mathematics divisions included both basic and applied research and were divided into 11 research areas: mathematics and numerical methods, low-energy nuclear physics, medium- and high-energy nuclear physics, atomic and molecular physics, solid-state physics and materials science, fluid dynamics, plasma physics and intense particle beam theory, astrophysics and space physics, particle transport methods, accelerator and fusion technology, and biophysics. Highlights from each of these areas are presented
Physics, Computer Science and Mathematics Division annual report, 1 January--31 December 1975
International Nuclear Information System (INIS)
Lepore, J.L.
1975-01-01
This annual report describes the scientific research and other work carried out during the calendar year 1975. The report is nontechnical in nature, with almost no data. A 17-page bibliography lists the technical papers which detail the work. The contents of the report include the following: experimental physics (high-energy physics--SPEAR, PEP, SLAC, FNAL, BNL, Bevatron; particle data group; medium-energy physics; astrophysics, astronomy, and cosmic rays; instrumentation development), theoretical physics (particle theory and accelerator theory and design), computer science and applied mathematics (data management systems, socio-economic environment demographic information system, computer graphics, computer networks, management information systems, computational physics and data analysis, mathematical modeling, programing languages, applied mathematics research), real-time systems (ModComp and PDP networks), and computer center activities (systems programing, user services, hardware development, computer operations). A glossary of computer science and mathematics terms is also included. 32 figures
Mathematical gauge theory with applications to the standard model of particle physics
Hamilton, Mark J D
2017-01-01
The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of d...
Physics, Computer Science and Mathematics Division annual report, 1 January--31 December 1975. [LBL
Energy Technology Data Exchange (ETDEWEB)
Lepore, J.L. (ed.)
1975-01-01
This annual report describes the scientific research and other work carried out during the calendar year 1975. The report is nontechnical in nature, with almost no data. A 17-page bibliography lists the technical papers which detail the work. The contents of the report include the following: experimental physics (high-energy physics--SPEAR, PEP, SLAC, FNAL, BNL, Bevatron; particle data group; medium-energy physics; astrophysics, astronomy, and cosmic rays; instrumentation development), theoretical physics (particle theory and accelerator theory and design), computer science and applied mathematics (data management systems, socio-economic environment demographic information system, computer graphics, computer networks, management information systems, computational physics and data analysis, mathematical modeling, programing languages, applied mathematics research), real-time systems (ModComp and PDP networks), and computer center activities (systems programing, user services, hardware development, computer operations). A glossary of computer science and mathematics terms is also included. 32 figures. (RWR)
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…
The dialectic relation between physics and mathematics in the XIXth century
Pisano, Raffaele
2013-01-01
The aim of this book is to analyse historical problems related to the use of mathematics in physics as well as to the use of physics in mathematics and to investigate Mathematical Physics as precisely the new discipline which is concerned with this dialectical link itself. So the main question is: When and why did the tension between mathematics and physics, explicitly practised at least since Galileo, evolve into such a new scientific theory? The authors explain the various ways in which this science allowed an advanced mathematical modelling in physics on the one hand, and the invention of new mathematical ideas on the other hand. Of course this problem is related to the links between institutions, universities, schools for engineers, and industries, and so it has social implications as well. The link by which physical ideas had influenced the world of mathematics was not new in the 19th century, but it came to a kind of maturity at that time. Recently, much historical research has been done into math...
Hobbes on natural philosophy as "True Physics" and mixed mathematics.
Adams, Marcus P
2016-04-01
In this paper, I offer an alternative account of the relationship of Hobbesian geometry to natural philosophy by arguing that mixed mathematics provided Hobbes with a model for thinking about it. In mixed mathematics, one may borrow causal principles from one science and use them in another science without there being a deductive relationship between those two sciences. Natural philosophy for Hobbes is mixed because an explanation may combine observations from experience (the 'that') with causal principles from geometry (the 'why'). My argument shows that Hobbesian natural philosophy relies upon suppositions that bodies plausibly behave according to these borrowed causal principles from geometry, acknowledging that bodies in the world may not actually behave this way. First, I consider Hobbes's relation to Aristotelian mixed mathematics and to Isaac Barrow's broadening of mixed mathematics in Mathematical Lectures (1683). I show that for Hobbes maker's knowledge from geometry provides the 'why' in mixed-mathematical explanations. Next, I examine two explanations from De corpore Part IV: (1) the explanation of sense in De corpore 25.1-2; and (2) the explanation of the swelling of parts of the body when they become warm in De corpore 27.3. In both explanations, I show Hobbes borrowing and citing geometrical principles and mixing these principles with appeals to experience. Copyright © 2015 Elsevier Ltd. All rights reserved.
Engineering Physics and Mathematics Division progress report for period ending June 30, 1985
International Nuclear Information System (INIS)
1986-02-01
The report is divided into eight sections: (1) nuclear data measurements and evaluation; (2) systems analysis and shielding; (3) applied physics and fusion reactor analysis; (4) mathematical modeling and intelligent control; (5) reliability and human factors research; (6) applied risk and decision analysis; (7) information analysis and data management; and (8) mathematical sciences. Each section then consists of abstracts of presented or published papers
Increasing Mathematical Computation Skills for Students with Physical and Health Disabilities
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…
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…
Stealing from Physics: Modeling with Mathematical Functions in Data-Rich Contexts
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…
International Nuclear Information System (INIS)
Kotel'nikov, G.A.
1994-01-01
An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry
National Research Council Canada - National Science Library
Stuhmiller, James H; Bykanova, Lucy; Chan, Philemon; Dang, Xinglai; Fournier, Adam; Long, Diane W; Lu, Zi; Masiello, Paul; Ng, Laurel; Niu, Eugene
2006-01-01
This report summarizes the first year of a 5-year program to develop physiologically and biomechanically based mathematical models that will allow the estimation of physical and cognitive performance...
The importante of physical and mathematical models for nuclear power plants site selection
International Nuclear Information System (INIS)
Rios, J.L.P.
1989-01-01
The importance of the release of effluents from nuclear installations for the site selection of nuclear power plants is discussed. The main available analysis methods, physical and mathematical, is presented [pt
Physics, Computer Science and Mathematics Division. Annual report, 1 January-31 December 1979
International Nuclear Information System (INIS)
Lepore, J.V.
1980-09-01
This annual report describes the research work carried out by the Physics, Computer Science and Mathematics Division during 1979. The major research effort of the Division remained High Energy Particle Physics with emphasis on preparing for experiments to be carried out at PEP. The largest effort in this field was for development and construction of the Time Projection Chamber, a powerful new particle detector. This work took a large fraction of the effort of the physics staff of the Division together with the equivalent of more than a hundred staff members in the Engineering Departments and shops. Research in the Computer Science and Mathematics Department of the Division (CSAM) has been rapidly expanding during the last few years. Cross fertilization of ideas and talents resulting from the diversity of effort in the Physics, Computer Science and Mathematics Division contributed to the software design for the Time Projection Chamber, made by the Computer Science and Applied Mathematics Department
THE EFFECTS OF ACUTE PHYSICAL EXERCISE TRAINING ON MATHEMATICAL COMPUTATION IN CHILDREN
Directory of Open Access Journals (Sweden)
Gustav Bala
2014-12-01
The results showed that the children’s computation performance was enhanced significantly in the groups with 30, or 45, or 60 min of physical exercise, but not in the groups without physical exercise. This means that even acute intensive physical training can yield positive effects on children's mathematical abilities.
Physics, Computer Science and Mathematics Division. Annual report, January 1-December 31, 1980
International Nuclear Information System (INIS)
Birge, R.W.
1981-12-01
Research in the physics, computer science, and mathematics division is described for the year 1980. While the division's major effort remains in high energy particle physics, there is a continually growing program in computer science and applied mathematics. Experimental programs are reported in e + e - annihilation, muon and neutrino reactions at FNAL, search for effects of a right-handed gauge boson, limits on neutrino oscillations from muon-decay neutrinos, strong interaction experiments at FNAL, strong interaction experiments at BNL, particle data center, Barrelet moment analysis of πN scattering data, astrophysics and astronomy, earth sciences, and instrument development and engineering for high energy physics. In theoretical physics research, studies included particle physics and accelerator physics. Computer science and mathematics research included analytical and numerical methods, information analysis techniques, advanced computer concepts, and environmental and epidemiological studies
Physics, Computer Science and Mathematics Division. Annual report, January 1-December 31, 1980
Energy Technology Data Exchange (ETDEWEB)
Birge, R.W.
1981-12-01
Research in the physics, computer science, and mathematics division is described for the year 1980. While the division's major effort remains in high energy particle physics, there is a continually growing program in computer science and applied mathematics. Experimental programs are reported in e/sup +/e/sup -/ annihilation, muon and neutrino reactions at FNAL, search for effects of a right-handed gauge boson, limits on neutrino oscillations from muon-decay neutrinos, strong interaction experiments at FNAL, strong interaction experiments at BNL, particle data center, Barrelet moment analysis of ..pi..N scattering data, astrophysics and astronomy, earth sciences, and instrument development and engineering for high energy physics. In theoretical physics research, studies included particle physics and accelerator physics. Computer science and mathematics research included analytical and numerical methods, information analysis techniques, advanced computer concepts, and environmental and epidemiological studies. (GHT)
Physics, Computer Science and Mathematics Division annual report, January 1--December 31, 1976
Energy Technology Data Exchange (ETDEWEB)
Lepore, J.V. (ed.)
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during the calendar year 1976. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics; a vigorous program is maintained in this pioneering field. The high-energy physics research program in the Division now focuses on experiments with e/sup +/e/sup -/ colliding beams using advanced techniques and developments initiated and perfected at the Laboratory. The Division continues its work in medium energy physics, with experimental work carried out at the Bevatron and at the Los Alamos Pi-Meson Facility. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The computer center serves the Laboratory by constantly upgrading its facility and by providing day-to-day service. This report is descriptive in nature; references to detailed publications are given. (RWR)
Physics, Computer Science and Mathematics Division annual report, January 1--December 31, 1976
International Nuclear Information System (INIS)
Lepore, J.V.
1977-01-01
This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during the calendar year 1976. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics; a vigorous program is maintained in this pioneering field. The high-energy physics research program in the Division now focuses on experiments with e + e - colliding beams using advanced techniques and developments initiated and perfected at the Laboratory. The Division continues its work in medium energy physics, with experimental work carried out at the Bevatron and at the Los Alamos Pi-Meson Facility. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The computer center serves the Laboratory by constantly upgrading its facility and by providing day-to-day service. This report is descriptive in nature; references to detailed publications are given
Martin, B R
2015-01-01
Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets. Mathematics for Physicists features: * Interfaces with modern school mathematics syllabuses * All topics usually taught in the first two years of a physics degree * Worked examples throughout * Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website This text will ...
Tayurskii, Dmitrii; Abe, Sumiyoshi; Alexandre Wang, Q.
2012-11-01
The 3rd International Workshop on Statistical Physics and Mathematics for Complex Systems (SPMCS2012) was held between 25-30 August at Kazan (Volga Region) Federal University, Kazan, Russian Federation. This workshop was jointly organized by Kazan Federal University and Institut Supérieur des Matériaux et Mécaniques Avancées (ISMANS), France. The series of SPMCS workshops was created in 2008 with the aim to be an interdisciplinary incubator for the worldwide exchange of innovative ideas and information about the latest results. The first workshop was held at ISMANS, Le Mans (France) in 2008, and the third at Huazhong Normal University, Wuhan (China) in 2010. At SPMCS2012, we wished to bring together a broad community of researchers from the different branches of the rapidly developing complexity science to discuss the fundamental theoretical challenges (geometry/topology, number theory, statistical physics, dynamical systems, etc) as well as experimental and applied aspects of many practical problems (condensed matter, disordered systems, financial markets, chemistry, biology, geoscience, etc). The program of SPMCS2012 was prepared based on three categories: (i) physical and mathematical studies (quantum mechanics, generalized nonequilibrium thermodynamics, nonlinear dynamics, condensed matter physics, nanoscience); (ii) natural complex systems (physical, geophysical, chemical and biological); (iii) social, economical, political agent systems and man-made complex systems. The conference attracted 64 participants from 10 countries. There were 10 invited lectures, 12 invited talks and 28 regular oral talks in the morning and afternoon sessions. The book of Abstracts is available from the conference website (http://www.ksu.ru/conf/spmcs2012/?id=3). A round table was also held, the topic of which was 'Recent and Anticipated Future Progress in Science of Complexity', discussing a variety of questions and opinions important for the understanding of the concept of
Methods of Mathematical and Computational Physics for Industry, Science, and Technology
Melnik, Roderick V. N.; Voss, Frands
2006-11-01
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
Implicit Lagrangian equations and the mathematical modeling of physical systems
Moreau, Luc; van der Schaft, Arjan
2002-01-01
We introduce a class of optimal control problems on manifolds which gives rise (via the Pontryagin maximum principle) to a class of implicit Lagrangian systems (a notion which is introduced in the paper). We apply this to the mathematical modeling of interconnected mechanical systems and mechanical
Journal of the Nigerian Association of Mathematical Physics
African Journals Online (AJOL)
We modify existing mathematical models for HIV that account for observation from hemodialysis. Of particular interest are the criteria under which the disease infected equilibrium could be stable we indicate treatment that is adequate to significantly lower gp 120 levels and help T cells to recover to normal level. Journal of ...
CLASSICS On Teaching Mathematics
Indian Academy of Sciences (India)
give a better and more correct idea of modern mathematics than whole volumes of the. Bourbaki ... The de-geometrisation of mathematical education and the divorce from physics sever these ties. ... is their traditional national trait. I do not ...
ACER: A framework on the use of mathematics in upper-division physics
Caballero, Marcos D.; Wilcox, Bethany R.; Pepper, Rachel E.; Pollock, Steven J.
2013-01-01
At the University of Colorado Boulder, as part of our broader efforts to transform middle- and upper-division physics courses, we research students' difficulties with particular concepts, methods, and tools in classical mechanics, electromagnetism, and quantum mechanics. Unsurprisingly, a number of difficulties are related to students' use of mathematical tools (e.g., approximation methods). Previous work has documented a number of challenges that students must overcome to use mathematical tools fluently in introductory physics (e.g., mapping meaning onto mathematical symbols). We have developed a theoretical framework to facilitate connecting students' difficulties to challenges with specific mathematical and physical concepts. In this paper, we motivate the need for this framework and demonstrate its utility for both researchers and course instructors by applying it to frame results from interview data on students' use of Taylor approximations.
International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards
Kouteva-Guentcheva, Mihaela
2015-01-01
This book is devoted to current advances in the field of nonlinear mathematical physics and modeling of critical phenomena that can lead to catastrophic events. Pursuing a multidisciplinary approach, it gathers the work of scientists who are developing mathematical and computational methods for the study and analysis of nonlinear phenomena and who are working actively to apply these tools and create conditions to mitigate and reduce the negative consequences of natural and socio-economic disaster risk. This book summarizes the contributions of the International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, organized within the framework of the South East Europe Network in Mathematical and Theoretical Physics (SEENET MTP) and supported by UNESCO. It was held at the Bulgarian Academy of Sciences from November 28 to December 2, 2013. The contributions are divided into two major parts in keeping with the scientific program of the meeting. Among the topics covered in Part I (Nonlinear...
Nonlinear optical and atomic systems at the interface of physics and mathematics
Garreau, Jean-Claude
2015-01-01
Focusing on the interface between mathematics and physics, this book offers an introduction to the physics, the mathematics, and the numerical simulation of nonlinear systems in optics and atomic physics. The text covers a wide spectrum of current research on the subject, which is an extremely active field in physics and mathematical physics, with a very broad range of implications, both for fundamental science and technological applications: light propagation in microstructured optical fibers, Bose-Einstein condensates, disordered systems, and the newly emerging field of nonlinear quantum mechanics. Accessible to PhD students, this book will also be of interest to post-doctoral researchers and seasoned academics.
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
Kalanov, Temur Z.
2016-03-01
Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
The Maslov dequantization, idempotent and tropical mathematics: a very brief introduction
Litvinov, Grigori
2005-01-01
Comment: 24 pages, 2 figures. An introductory paper to the volume "Idempotent Mathematics and Mathematical Physics" (G.L. Ltvinov, V.P. Maslov, eds.; AMS Contemporary Mathematics, 2005). More misprints corrected
From Calculus to Wavelets: ANew Mathematical Technique
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 4. From Calculus to Wavelets: A New Mathematical Technique Wavelet Analysis Physical Properties. Gerald B Folland. General Article Volume 2 Issue 4 April 1997 pp 25-37 ...
Methods of Approximation Theory in Complex Analysis and Mathematical Physics
Saff, Edward
1993-01-01
The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. ...
Measurement and the mathematical apparatus of quantum physics
International Nuclear Information System (INIS)
Slavnov, D.A.
2007-01-01
A scheme for constructing quantum mechanics in which the Hilbert space and linear operators are not primary elements on the theory is described. Some variant of the algebraic approach is instead considered. The elements of a noncommutative algebra (observables) and functionals in this algebra serve as the primary components of the theory. Such a scheme allows one to use the formalism of the classical (Kolmogorovian) theory of probability, and to reproduce the mathematical formalism of standard quantum mechanics and to specify borders of its applicability. A brief review of necessary data from the theory of algebras and probability theory is given. The manner is described in which the considered mathematical scheme agrees with the theory of quantum measurements and allows one to avoid quantum paradoxes [ru
Quantization, geometry and noncommutative structures in mathematics and physics
Morales, Pedro; Ocampo, Hernán; Paycha, Sylvie; Lega, Andrés
2017-01-01
This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf a...
[On the founders of the Institute of Mathematics and Physics, University of Bahia].
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.
Mathematical and physical modeling of rainfall in centrifuge
CAICEDO, Bernardo; THOREL, Luc; TRISTANCHO, Julian
2015-01-01
Rainfall simulation in centrifuge models is important for modelling soil-atmosphere interactions. However, the presence of Coriolis force, drag forces, evaporation and wind within the centrifuge may affect the distribution of rainfall over the model. As a result, development of appropriate centrifuge rain simulators requires a demanding process of experimental trial and error. This paper highlights the key factors involved in controlling rainfall in centrifuge simulations, develops a mathemat...
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1983
International Nuclear Information System (INIS)
Jackson, J.D.
1984-08-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1983. The major activity of the Division is research in high-energy physics, both experimental and theoretical, and research and development in associated technologies. A smaller, but still significant, program is in computer science and applied mathematics. During 1983 there were approximately 160 people in the Division active in or supporting high-energy physics research, including about 40 graduate students. In computer science and mathematics, the total staff, including students and faculty, was roughly 50. Because of the creation in late 1983 of a Computing Division at LBL and the transfer of the Computer Science activities to the new Division, this annual report is the last from the Physics, Computer Science and Mathematics Division. In December 1983 the Division reverted to its historic name, the Physics Division. Its future annual reports will document high energy physics activities and also those of its Mathematics Department
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1983
Energy Technology Data Exchange (ETDEWEB)
Jackson, J.D.
1984-08-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1983. The major activity of the Division is research in high-energy physics, both experimental and theoretical, and research and development in associated technologies. A smaller, but still significant, program is in computer science and applied mathematics. During 1983 there were approximately 160 people in the Division active in or supporting high-energy physics research, including about 40 graduate students. In computer science and mathematics, the total staff, including students and faculty, was roughly 50. Because of the creation in late 1983 of a Computing Division at LBL and the transfer of the Computer Science activities to the new Division, this annual report is the last from the Physics, Computer Science and Mathematics Division. In December 1983 the Division reverted to its historic name, the Physics Division. Its future annual reports will document high energy physics activities and also those of its Mathematics Department.
Developing A-level physics students' mathematical skills - a way forward?
Raw, A. J.
1999-09-01
This article outlines research that details the mathematical difficulties of physics students and it also discusses various projects to overcome these difficulties. The successes of these projects are very encouraging and show a way forward for A-level physics teaching.
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…
de Mul, F.F.M.; Martin Batlle, C.; Martin i Batlle, Cristina; de Bruijn, Imme; Rinzema, K.; Rinzema, Kees
2003-01-01
Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential
Physics Letters B, Volume 716, Issue 1- Cover Page
CERN
2012-01-01
The cover page of the Physics Letters B Journal, Volume 716, Issue 1, dedicated to the observation of a new particle in the search for the Standard Model Higgs boson. To celebrate this historical discovery, Elsevier reprinted the ATLAS and the CMS articles together with a foreword by Peter Higgs and the other scientists that predicted the existence of the so-called Higgs boson and published this in a separate booklet.
Masters of Theory Cambridge and the Rise of Mathematical Physics
Warwick, Andrew
2011-01-01
Winner of the the Susan Elizabeth Abrams Prize in History of Science.When Isaac Newton published the Principia three centuries ago, only a few scholars were capable of understanding his conceptually demanding work. Yet this esoteric knowledge quickly became accessible in the nineteenth and early twentieth centuries when Britain produced many leading mathematical physicists. In this book, Andrew Warwick shows how the education of these "masters of theory" led them to transform our understanding of everything from the flight of a boomerang to the structure of the universe. Warwick focuses on Cam
STP: A mathematically and physically consistent library of steam properties
International Nuclear Information System (INIS)
Aguilar, F.; Hutter, A.C.; Tuttle, P.G.
1982-01-01
A new FORTRAN library of subroutines has been developed from the fundamental equation of Keenan et al. to evaluate a large set of water properties including derivatives such as sound speed and isothermal compressibility. The STP library uses the true saturation envelope of the Keenan et al. fundamental equation. The evaluation of the true envelope by a continuation method is explained. This envelope, along with other design features, imparts an exceptionally high degree of thermodynamic and mathematical consistency to the STP library, even at the critical point. Accuracy and smoothness, library self-consistency, and designed user convenience make the STP library a reliable and versatile water property package
Soliton-type solutions for two models in mathematical physics
Al-Ghafri, K. S.
2018-04-01
In this paper, the generalised Klein-Gordon and Kadomtsov-Petviashvili Benjamin-Bona-Mahony equations with power law nonlinearity are investigated. Our study is based on reducing the form of both equations to a first-order ordinary differential equation having the travelling wave solutions. Subsequently, soliton-type solutions such as compacton and solitary pattern solutions are obtained analytically. Additionally, the peaked soliton has been derived where it exists under a specific restrictions. In addition to the soliton solutions, the mathematical method which is exploited in this work also creates a few amount of travelling wave solutions.
Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals
Schwalm, William A.
2015-12-01
This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.
International Nuclear Information System (INIS)
Povinec, P.; Florek, M.; Chudy, M.
1983-01-01
The Science Faculty of the Comenius University in Bratislava established the nuclear physics specialization in 1962. Students enrolled in the study course acquired basic knowledge in mathematics and physics, foundations of the microstructure of matter and experimental methods of nuclear physics and technics. Since 1976 nuclear physics has been a separate study field which from the fourth year of study has its narrow specializations, namely applied nuclear physics, experimental nuclear physics and physics of the atomic nucleus and elementary particles. A change has recently been made in the system of optional lectures with the aim of providing the students with a wider range of knowledge in the physics of nuclear reactors and the use of computer technology and microelectronics in nuclear physics and technology. In 1980 a postgraduate study course was opened oriented to nuclear power and the environment. (E.S.)
Bohmian mechanics. The physics and mathematics of quantum theory
International Nuclear Information System (INIS)
Duerr, Detlef; Teufel, Stefan
2009-01-01
Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)
Bohmian mechanics. The physics and mathematics of quantum theory
Energy Technology Data Exchange (ETDEWEB)
Duerr, Detlef [Muenchen Univ. (Germany). Fakultaet Mathematik; Teufel, Stefan [Tuebingen Univ. (Germany). Mathematisches Inst.
2009-07-01
Bohmian Mechanics was formulated in 1952 by David Bohm as a complete theory of quantum phenomena based on a particle picture. It was promoted some decades later by John S. Bell, who, intrigued by the manifestly nonlocal structure of the theory, was led to his famous Bell's inequalities. Experimental tests of the inequalities verified that nature is indeed nonlocal. Bohmian mechanics has since then prospered as the straightforward completion of quantum mechanics. This book provides a systematic introduction to Bohmian mechanics and to the mathematical abstractions of quantum mechanics, which range from the self-adjointness of the Schroedinger operator to scattering theory. It explains how the quantum formalism emerges when Boltzmann's ideas about statistical mechanics are applied to Bohmian mechanics. The book is self-contained, mathematically rigorous and an ideal starting point for a fundamental approach to quantum mechanics. It will appeal to students and newcomers to the field, as well as to established scientists seeking a clear exposition of the theory. (orig.)
Engineering Physics and Mathematics Division progress report for period ending June 30, 1985
Energy Technology Data Exchange (ETDEWEB)
1986-02-01
The report is divided into eight sections: (1) nuclear data measurements and evaluation; (2) systems analysis and shielding; (3) applied physics and fusion reactor analysis; (4) mathematical modeling and intelligent control; (5) reliability and human factors research; (6) applied risk and decision analysis; (7) information analysis and data management; and (8) mathematical sciences. Each section then consists of abstracts of presented or published papers. (WRF)
International Nuclear Information System (INIS)
Shirvanimoghaddam, K.; Khayyam, H.; Abdizadeh, H.; Karbalaei Akbari, M.; Pakseresht, A.H.; Ghasali, E.; Naebe, M.
2016-01-01
This paper investigates the manufacturing of aluminium–boron carbide composites using the stir casting method. Mechanical and physical properties tests to obtain hardness, ultimate tensile strength (UTS) and density are performed after solidification of specimens. The results show that hardness and tensile strength of aluminium based composite are higher than monolithic metal. Increasing the volume fraction of B_4C, enhances the tensile strength and hardness of the composite; however over-loading of B_4C caused particle agglomeration, rejection from molten metal and migration to slag. This phenomenon decreases the tensile strength and hardness of the aluminium based composite samples cast at 800 °C. For Al-15 vol% B_4C samples, the ultimate tensile strength and Vickers hardness of the samples that were cast at 1000 °C, are the highest among all composites. To predict the mechanical properties of aluminium matrix composites, two key prediction modelling methods including Neural Network learned by Levenberg–Marquardt Algorithm (NN-LMA) and Thin Plate Spline (TPS) models are constructed based on experimental data. Although the results revealed that both mathematical models of mechanical properties of Al–B_4C are reliable with a high level of accuracy, the TPS models predict the hardness and tensile strength values with less error compared to NN-LMA models.
An epistemic framing analysis of upper level physics students' use of mathematics
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
Special matrices of mathematical physics stochastic, circulant and Bell matrices
Aldrovandi, R
2001-01-01
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas co
Open-closed homotopy algebra in mathematical physics
International Nuclear Information System (INIS)
Kajiura, Hiroshige; Stasheff, Jim
2006-01-01
In this paper we discuss various aspects of open-closed homotopy algebras (OCHAs) presented in our previous paper, inspired by Zwiebach's open-closed string field theory, but that first paper concentrated on the mathematical aspects. Here we show how an OCHA is obtained by extracting the tree part of Zwiebach's quantum open-closed string field theory. We clarify the explicit relation of an OCHA with Kontsevich's deformation quantization and with the B-models of homological mirror symmetry. An explicit form of the minimal model for an OCHA is given as well as its relation to the perturbative expansion of open-closed string field theory. We show that our open-closed homotopy algebra gives us a general scheme for deformation of open string structures (A ∞ algebras) by closed strings (L ∞ algebras)
Non-commuting variations in mathematics and physics a survey
Preston, Serge
2016-01-01
This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...
Mrs. Perkins's electric quilt and other intriguing stories of mathematical physics
Nahin, Paul J
2009-01-01
What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, andinteresting than either is by itself. In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier ...
GeoGebra and eXe Learning: applicability in the teaching of Physics and Mathematics
Directory of Open Access Journals (Sweden)
Eunice Maria Mussoi
2011-04-01
Full Text Available Today, education in the field of sciences is still characterized by excessive attention to repetitive exercises at the expense of understanding and visualizing the concepts of mathematical and physical phenomena. This article will show the potential of the software GeoGebra to build content and / or activities in Physics and Mathematics usable in isolation or engaged in other activities, such as eXe Learning. For this we constructed two activities: a mathematical content - Application of successive derivatives, and a content of physics - Application of uniform rectilinear motion. These contents were built in eXe Learning, and the graphics was built in GeoGebra and imported into the eXe by Java Applet. The content was done with the exported SCORM to Moodle, it is within this framework that the student will study the movement and display of graphic content.
Efficient decision-making by volume-conserving physical object
International Nuclear Information System (INIS)
Kim, Song-Ju; Aono, Masashi; Nameda, Etsushi
2015-01-01
Decision-making is one of the most important intellectual abilities of not only humans but also other biological organisms, helping their survival. This ability, however, may not be limited to biological systems and may be exhibited by physical systems. Here we demonstrate that any physical object, as long as its volume is conserved when coupled with suitable operations, provides a sophisticated decision-making capability. We consider the multi-armed bandit problem (MBP), the problem of finding, as accurately and quickly as possible, the most profitable option from a set of options that gives stochastic rewards. Efficient MBP solvers are useful for many practical applications, because MBP abstracts a variety of decision-making problems in real-world situations in which an efficient trial-and-error is required. These decisions are made as dictated by a physical object, which is moved in a manner similar to the fluctuations of a rigid body in a tug-of-war (TOW) game. This method, called ‘TOW dynamics’, exhibits higher efficiency than conventional reinforcement learning algorithms. We show analytical calculations that validate statistical reasons for TOW dynamics to produce the high performance despite its simplicity. These results imply that various physical systems in which some conservation law holds can be used to implement an efficient ‘decision-making object’. The proposed scheme will provide a new perspective to open up a physics-based analog computing paradigm and to understanding the biological information-processing principles that exploit their underlying physics. (paper)
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Directory of Open Access Journals (Sweden)
Neisy Rodríguez Morales
2014-03-01
Full Text Available The article shows the theoretical elements related with the conception of the curricular strategies and its instrumentation in the process of the student's of the Mathematical career formation - Physics. Examples are presented that demonstrate how to deal with the computer science's curricular strategy from the teaching process - learning of the subject Algebra I in the third year of the career. They give the possibility that the formation process be more effective, they facilitate the systematizing knowledge and abilities as well as the development of the integral general culture in the future professors of Mathematics - Physics.
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 116; Issue 4 ... by application to a number of examples arising in physics and probability. ... Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, ...
Strict finitism and the logic of mathematical applications
Ye, Feng
2011-01-01
Exploring the logic behind applied mathematics to the physical world, this volume illustrates how radical naturalism, nominalism and strict finitism can account for the applications of classical mathematics in current theories about natural phenomena.
Partial volume effect correction in nuclear medicine: assessment with a mathematical phantom
International Nuclear Information System (INIS)
Silva, Murilo Collete da; Pozzo, Lorena
2009-01-01
Objective: assessment of Van Cittert partial volume effect correction method in nuclear medicine images, with a mathematical phantom. Material and method: we simulated an image of four circular sources of different diameters and intensity of 255 per pixel. The iterative algorithm was applied with 20 iterations and α = 1. We obtained the maximum and average counts on the entire image and in regions of interest placed on each of the sources. We also extracted count profiles plotted along the diameter of each of the sources. Results: the local convergence depends on the size of the source studied: the smaller the source, the greater the number of iterations required. It also depends on the information extracted: the use of average counts provides more homogeneous results than the maximum count. There is a significant improvement in image contrast. Conclusion: this study showed the possibility of qualitative and quantitative improvement in applying the bidimensional iterative Van Cittert method to images of simple geometry. (author)
High-Precision Computation: Mathematical Physics and Dynamics
International Nuclear Information System (INIS)
Bailey, D.H.; Barrio, R.; Borwein, J.M.
2010-01-01
At the present time, IEEE 64-bit oating-point arithmetic is suficiently accurate for most scientic applications. However, for a rapidly growing body of important scientic computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion e ort. This pa- per presents a survey of recent applications of these techniques and provides someanalysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the one structure constant, scattering amplitudes of quarks, glu- ons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic at- tractors, Ising theory, quantum held theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable compo- nent of a modern large-scale scientic computing environment.
Earth's Rotation: A Challenging Problem in Mathematics and Physics
Ferrándiz, José M.; Navarro, Juan F.; Escapa, Alberto; Getino, Juan
2015-01-01
A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.
High-Precision Computation: Mathematical Physics and Dynamics
Energy Technology Data Exchange (ETDEWEB)
Bailey, D. H.; Barrio, R.; Borwein, J. M.
2010-04-01
At the present time, IEEE 64-bit oating-point arithmetic is suficiently accurate for most scientic applications. However, for a rapidly growing body of important scientic computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion e ort. This pa- per presents a survey of recent applications of these techniques and provides someanalysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the one structure constant, scattering amplitudes of quarks, glu- ons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic at- tractors, Ising theory, quantum held theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable compo- nent of a modern large-scale scientic computing environment.
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Rančić, Milica
2016-01-01
This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. In particular, it features mathematical methods and models of applied analysis, probability theory, differential equations, tensor analysis and computational modelling used in applications to important problems concerning electromagnetics, antenna technologies, fluid dynamics, material and continuum physics and financial engineering. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The ...
Baranovskaya T. P.; Loyko V. I.; Makarevich O. A.; Bogoslavskiy S. N.
2014-01-01
The article suggests a mathematical model of optimization of the volume of material flows: the model for the ideal conditions; the model for the working conditions; generalized model of determining the optimal input parameters. These models optimize such parameters of inventory management in technology-integrated grain production systems, as the number of cycles supply, the volume of the source material and financial flows. The study was carried out on the example of the integrated system of ...
Engineering Physics and Mathematics Division progress report for period ending March 31, 1991
Energy Technology Data Exchange (ETDEWEB)
1991-10-01
The primary purpose of this report is to provide an archival record of the activities of the Engineering Physics and Mathematics Division during the period September 1, 1989 through March 31, 1991. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research on the mathematical sciences prior to 1984 when those activities moved into the division. As in previous reports, our research is described through abstracts of journal articles, technical reports, and presentations. Summary lists of publications and presentations, staff additions and departures, scientific and professional activities of division staff, and technical conferences organized and sponsored by the division are included as appendices. The report is organized following the division of our research among four sections and information centers. These research areas are: Mathematical Sciences; Nuclear Data Measurement and Evaluations; Intelligent Systems; Nuclear Analysis and Shielding; and Engineering Physics Information Center.
Engineering Physics and Mathematics Division progress report for period ending September 30, 1987
Energy Technology Data Exchange (ETDEWEB)
1987-12-01
This report provides an archival record of the activities of the Engineering Physics and Mathematics Division during the period June 30, 1985 through September 30, 1987. Work in Mathematical Sciences continues to include applied mathematics research, statistics research, and computer science. Nuclear-data measurements and evaluations continue for fusion reactors, fission reactors, and other nuclear systems. Also discussed are long-standing studies of fission-reactor shields through experiments and related analysis, of accelerator shielding, and of fusion-reactor neutronics. Work in Machine Intelligence continues to feature the development of an autonomous robot. The last descriptive part of this report reflects the work in our Engineering Physics Information Center, which again concentrates primarily upon radiation-shielding methods and related data.
Engineering Physics and Mathematics Division progress report for period ending March 31, 1991
International Nuclear Information System (INIS)
1991-10-01
The primary purpose of this report is to provide an archival record of the activities of the Engineering Physics and Mathematics Division during the period September 1, 1989 through March 31, 1991. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research on the mathematical sciences prior to 1984 when those activities moved into the division. As in previous reports, our research is described through abstracts of journal articles, technical reports, and presentations. Summary lists of publications and presentations, staff additions and departures, scientific and professional activities of division staff, and technical conferences organized and sponsored by the division are included as appendices. The report is organized following the division of our research among four sections and information centers. These research areas are: Mathematical Sciences; Nuclear Data Measurement and Evaluations; Intelligent Systems; Nuclear Analysis and Shielding; and Engineering Physics Information Center
Engineering Physics and Mathematics Division progress report for period ending September 30, 1987
International Nuclear Information System (INIS)
1987-12-01
This report provides an archival record of the activities of the Engineering Physics and Mathematics Division during the period June 30, 1985 through September 30, 1987. Work in Mathematical Sciences continues to include applied mathematics research, statistics research, and computer science. Nuclear-data measurements and evaluations continue for fusion reactors, fission reactors, and other nuclear systems. Also discussed are long-standing studies of fission-reactor shields through experiments and related analysis, of accelerator shielding, and of fusion-reactor neutronics. Work in Machine Intelligence continues to feature the development of an autonomous robot. The last descriptive part of this report reflects the work in our Engineering Physics Information Center, which again concentrates primarily upon radiation-shielding methods and related data
Fundamentals of the Physics of Solids Volume 2: Electronic Properties
Sólyom, Jenő
2009-01-01
This book is the second of a single-authored, three-volume series that aims to deliver a comprehensive and self-contained account of the vast field of solid-state physics. It goes far beyond most classic texts in the presentation of the properties of solids and experimentally observed phenomena, along with the basic concepts and theoretical methods used to understand them and the essential features of various experimental techniques. The first volume deals with the atomic and magnetic structure and dynamics of solids, the second with those electronic properties that can be understood in the one-particle approximation, and the third with the effects due to interactions and correlations between electrons. This volume is devoted to the electronic properties of metals and semiconductors in the independent-electron approximation. After a brief discussion of the free-electron models by Drude and Sommerfeld, the methods for calculating and measuring the band structure of Bloch electrons moving in the periodic potent...
Energy Technology Data Exchange (ETDEWEB)
Niederle, J; Bednar, M; Bicak, J
1987-01-01
The conference, the fourth in the series of conferences on this subject, was held at the Bechyne castle (Czechoslovakia) on June 23-27, 1986, and was attended by about 100 theoreticians from 15 countries. The conference was organized by the Institute of Physics of the Czechoslovak Academy of Sciences in Prague together with the Faculties of Mathematics and Physics of the Charles University, Prague, and of the Comenius University, Bratislava, the Faculty of Nuclear Science and Physical Engineering of the Czech Techical University, Prague, with the Institute of Physics of the Electro-Physical Research Centre of the Slovak Academy of Sciences, Bratislava, and the Institute of Nuclear Physics of the Czechoslovak Academy of Sciences in Rez. It was sponsored by the International Union for Pure and Applied Physics, the International Association of Mathematical Physics and the Physical Scientific Section of the Union of Czechoslovak Mathematicians and Physicists. The main subjects discussed at the conference were: supersymmetries, supergravity and superstring theories; quantum field theory and in particular gauge theories, theories on lattices, renormalization; selected topics in non-linear equations, scattering theory and quantization. Details are given in the attached program. The proceedings include invited talks and contributions presented respectively at the morning and afternoon sessions of the conference. The main part of the proceedings will be published in the Czechoslovak Journal of Physics v. 37(1987), nos. 3,4 and 9.
International Nuclear Information System (INIS)
Niederle, J.; Bednar, M.; Bicak, J.
1987-01-01
The conference, the fourth in the series of conferences on this subject, was held at the Bechyne castle (Czechoslovakia) on June 23-27, 1986, and was attended by about 100 theoreticians from 15 countries. The conference was organized by the Institute of Physics of the Czechoslovak Academy of Sciences in Prague together with the Faculties of Mathematics and Physics of the Charles University, Prague, and of the Comenius University, Bratislava, the Faculty of Nuclear Science and Physical Engineering of the Czech Techical University, Prague, with the Institute of Physics of the Electro-Physical Research Centre of the Slovak Academy of Sciences, Bratislava, and the Institute of Nuclear Physics of the Czechoslovak Academy of Sciences in Rez. It was sponsored by the International Union for Pure and Applied Physics, the International Association of Mathematical Physics and the Physical Scientific Section of the Union of Czechoslovak Mathematicians and Physicists. The main subjects discussed at the conference were: supersymmetries, supergravity and superstring theories; quantum field theory and in particular gauge theories, theories on lattices, renormalization; selected topics in non-linear equations, scattering theory and quantization. Details are given in the attached program. The proceedings include invited talks and contributions presented respectively at the morning and afternoon sessions of the conference. The main part of the proceedings will be published in the Czechoslovak Journal of Physics v. 37(1987), nos. 3,4 and 9. (author)
Bogolyubov renormalization group and symmetry of solution in mathematical physics
International Nuclear Information System (INIS)
Shirkov, D.V.; Kovalev, V.F.
2000-01-01
Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparametrization one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of a new approach to solution for a problem of self-focusing laser beam in a nonlinear medium
FORMULATION OF MATHEMATICAL PROBLEM DESCRIBING PHYSICAL AND CHEMICAL PROCESSES AT CONCRETE CORROSION
Directory of Open Access Journals (Sweden)
Sergey V. Fedosov
2017-06-01
Full Text Available The article deals with the relevance of new scientific research focused on modeling of physical and chemical processes occurring in the cement concrete at their exploitation. The basic types of concrete corrosion are described. The problem of mass transfer processes in a flat reinforced concrete wall at concrete corrosion of the first and the second types has been mathematically formulated.
New Physical and Mathematical Model of Radiation Heat Transmission Inside Circular Furnace
Directory of Open Access Journals (Sweden)
V. I. Timoshpolsky
2004-01-01
Full Text Available Methods of solving problems concerning heat transmission by radiation are considered in the paper. The paper shows disadvantages of the existing techniques. A physical and mathematical model of a conjugate heat exchange has been developed to eliminate the above disadvantages.
Numerical methods for solution of some nonlinear problems of mathematical physics
International Nuclear Information System (INIS)
Zhidkov, E.P.
1981-01-01
The continuous analog of the Newton method and its application to some nonlinear problems of mathematical physics using a computer is considered. It is shown that the application of this method in JINR to the wide range of nonlinear problems has shown its universality and high efficiency [ru
The physics and mathematics of microstates in string theory: And a monstrous Farey tail
de Lange, P.
2016-01-01
A dissertation that delves into physical and mathematical aspects of string theory. In the first part of this work, microscopic properties string theoretic black holes are investigated. The second part is concerned with the moonshine phenomenon. The theory of generalized umbral moonshine is
Cusker, Jeremy; Rauh, Anne E.
2014-01-01
Discussions of the potential of open access publishing frequently must contend with the skepticism of research authors regarding the need to pay author fees (also known as publication fees). With that in mind, the authors undertook a survey of faculty, postdocs, and graduate students in physical science, mathematics, and engineering fields at two…
Mathematical, physical and numerical principles essential for models of turbulent mixing
Energy Technology Data Exchange (ETDEWEB)
Sharp, David Howland [Los Alamos National Laboratory; Lim, Hyunkyung [STONY BROOK UNIV; Yu, Yan [STONY BROOK UNIV; Glimm, James G [STONY BROOK UNIV
2009-01-01
We propose mathematical, physical and numerical principles which are important for the modeling of turbulent mixing, especially the classical and well studied Rayleigh-Taylor and Richtmyer-Meshkov instabilities which involve acceleration driven mixing of a fluid discontinuity layer, by a steady accerleration or an impulsive force.
Brekelmans, M.; van den Eeden, P.; Terwel, J.; Wubbels, Th.
1997-01-01
In two studies, one on secondary mathematics education, the other on secondary physics education, data were collected on students' cognitive achievement and characteristics of students and their learning environment. In this chapter the findings of the two studies are brought together in secondary
Motives and career barriers choosing studies in Physics and Mathematics: gender aspects
Directory of Open Access Journals (Sweden)
Aldona, Augustiene
2010-04-01
Full Text Available This article discusses the concepts of professional motivation and career barriers from the gender point of view. The research problem is expressed in the following questions: what personal and socio-cultural factors motivate young people to choose Physics and Mathematics study programmes? Are there significant differences in expression of motives and career barriers among male and female students? The sample consisted of 86 undergraduate students: 45 females and 41 male. Respondents were asked to write down their reflections as a free text answering the question why did they make such a professional choice choosing Physics and Mathematics studies. Motives that influenced the choice of Physics and Mathematics mostly expressed the dimension of self-realization and the dimension of material achievements. It was also found that both personality and social-cultural factors were important in choosing Physics and Mathematics, i.e. sensation of vocation and professional aptitude, as well as encouragement of relatives and good evaluation of future profession’s status. There were also found differences in expression of motives and career barriers among male and female students.
Assessing Student Learning in Gender Inclusive Tertiary Mathematics and Physics Education.
Wistedt, Inger
1998-01-01
The merits and limitations of an alternative assessment method implemented in an inclusive university education program are discussed based on data from a study in which 24 Swedish university students presented mathematics and physics project results. The study shows how an interdisciplinary approach to assessment can promote critical reflection…
[Professor Jules Gavarret (1809-1890) and the application of mathematics and physics to medicine].
Beyneix, A
2001-01-01
Professor Jules Gavarret has undertaken pretigious offices, has accumulated various titles and honours and has left an abundant bibliography about physics and chemistry of life phenomenon. To recount the career of one of the academics who were benefited the traditional medicine of the progress achieved in physical and mathematical sciences give us the opportunity of recalling one of the great Parisian personalities of 19th Century who had not been appreciated for too long.
Garnier, Helen E.; Lemmens, Meike; Druker, Stephen L.; Roth, Kathleen J.
2011-01-01
This second volume of the Third International Mathematics and Science Study (TIMSS) 1999 Video Study Technical Report focuses on every aspect of the planning, implementation, processing, analysis, and reporting of the science components of the TIMSS 1999 Video Study. The report is intended to serve as a record of the actions and documentation of…
Physics, mathematics and numerics of particle adsorption on fluid interfaces
Schmuck, Markus; Pavliotis, Grigorios A.; Kalliadasis, Serafim
2012-11-01
We study two arbitrary immiscible fuids where one phase contains small particles of the size of the interface and smaller. We primarily focus on charge-free particles with wetting characteristics described by the contact angle formed at the interface between the two phases and the particles. Based on the experimental observation that particles are adsorbed on the interface to reduce the interfacial energy and hence the surface tension as well, we formulate a free-energy functional that accounts for these physical effects. Using elements from calculus of variations and formal gradient flow theory, we derive partial differential equations describing the location of the interface and the density of the particles in the fluid phases. Via numerical experiments we analyse the time evolution of the surface tension, the particle concentration, and the free energy over time and reflect basic experimentally observed phenomena.
Tursucu, S.; Spandaw, J.G.; Flipse, S.M.; de Vries, M.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
Energy Technology Data Exchange (ETDEWEB)
Sommer, Elise Meister; Vargas, Jose Viriato Coelho [Universidade Federal do Parana (UFPR), Curitiba, PR (Brazil). Centro Politecnico. Setor de Tecnologia], Email: jvargas@demec.ufpr.br; Martins, Lauber de Souza; Ordonez, Juan Carlos [Florida State University, Tallahasse, FL (United States). Dept. of Mechanical Engineering and Center for Advanced Power Systems], Emails: martins@caps.fsu.edu, ordonez@eng.fsu.edu
2010-07-01
The Alkaline Membrane Fuel Cell (AMFC) is a recently developed fuel cell type, which has shown good experimental results in the laboratory. This paper introduces a mathematical model for the single AMFC with fixed volume and general square section. The main objective is to produce a reliable model (and computationally fast) to predict the response of the single AMFC according to variations of the physical properties of manufacturing materials and operating and design parameters. The model is based on mass, momentum, energy and species conservation, and electrochemical principles, and takes into account pressure drops in the gas channels and temperature gradients with respect to space in the flow direction. The simulation results comprise the AMFC temperature distribution, net power and polarization curves. It is shown that temperature spatial gradients and gas channels pressure drops significantly affect fuel cell performance. Such effects are not usually investigated in the models available in the literature, with most of them assuming uniform pressure and temperature operation. Therefore, the model is expected to be a useful tool for AMFC design and optimization. (author)
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.
International Nuclear Information System (INIS)
Sterba, F.
1983-01-01
Graduates of application oriented fields of all mathematics and physics specializations of Solid state physics and Nuclear physics work successfully in nuclear power. In the mathematics fields great attention is devoted to optimization, control, process modeling, etc. The subject Solid state physics is subdivided into the following specializations: physics of metals, magnetic properties of the solid state and structural analysis. These specializations educate specialists with a good knowledge of the structure and properties of metal materials. Great attention is devoted to the causes and development of defects, materials creep and the radiation damage of crystal lattices. The nuclear physics specialization Applied nuclear physics deals with the use of nuclear methods in diverse fields and provides basic knowledge in nuclear power generation and the operation of nuclear reactors. The Faculty of Mathematics and Physics of the Charles University in Prague also runs postgraduate study courses in nuclear physics measurement methods, solid state physics, etc. (E.S.)
Banagl, Markus
2011-01-01
The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested
The fundamentals of mathematical analysis
Fikhtengol'ts, G M
1965-01-01
The Fundamentals of Mathematical Analysis, Volume 1 is a textbook that provides a systematic and rigorous treatment of the fundamentals of mathematical analysis. Emphasis is placed on the concept of limit which plays a principal role in mathematical analysis. Examples of the application of mathematical analysis to geometry, mechanics, physics, and engineering are given. This volume is comprised of 14 chapters and begins with a discussion on real numbers, their properties and applications, and arithmetical operations over real numbers. The reader is then introduced to the concept of function, i
HISTORY OF THE ENGINEERING PHYSICS AND MATHEMATICS DIVISION 1955-1993
Energy Technology Data Exchange (ETDEWEB)
Maskewitz, B.F.
2001-09-14
A review of division progress reports noting significant events and findings of the Applied Nuclear Physics, Neutron Physics, Engineering Physics, and then Engineering Physics and Mathematics divisions from 1955 to 1993 was prepared for use in developing a history of the Oak Ridge National Laboratory in celebration of its 50th year. The research resulted in an accumulation of historic material and photographs covering 38 years of effort, and the decision was made to publish a brief history of the division. The history begins with a detailed account of the founding of the Applied Nuclear Physics Division in 1955 and continues through the name change to the Neutron Physics Division in the late 1950s. The material thereafter is presented in decades--the sixties, seventies, and eighties--and ends as we enter the nineties.
INTRA/Mod3.2. Manual and Code Description. Volume I - Physical Modelling
International Nuclear Information System (INIS)
Andersson, Jenny; Edlund, O.; Hermann, J.; Johansson, Lise-Lotte
1999-01-01
The INTRA Manual consists of two volumes. Volume I of the manual is a thorough description of the code INTRA, the Physical modelling of INTRA and the ruling numerical methods and volume II, the User's Manual is an input description. This document, the Physical modelling of INTRA, contains code characteristics, integration methods and applications
INTRA/Mod3.2. Manual and Code Description. Volume I - Physical Modelling
Energy Technology Data Exchange (ETDEWEB)
Andersson, Jenny; Edlund, O; Hermann, J; Johansson, Lise-Lotte
1999-01-01
The INTRA Manual consists of two volumes. Volume I of the manual is a thorough description of the code INTRA, the Physical modelling of INTRA and the ruling numerical methods and volume II, the User`s Manual is an input description. This document, the Physical modelling of INTRA, contains code characteristics, integration methods and applications
Are numbers real the uncanny relationship of mathematics and the physical world
Clegg, Brian
2016-01-01
Have you ever wondered what humans did before numbers existed? How they organized their lives, traded goods, or kept track of their treasures? What would your life be like without them? Numbers began as simple representations of everyday things, but mathematics rapidly took on a life of its own, occupying a parallel virtual world. In Are Numbers Real?, Brian Clegg explores the way that math has become more and more detached from reality, and yet despite this is driving the development of modern physics. From devising a new counting system based on goats, through the weird and wonderful mathematics of imaginary numbers and infinity, to the debate over whether mathematics has too much influence on the direction of science, this fascinating and accessible book opens the reader’s eyes to the hidden reality of the strange yet familiar entities that are numbers.
Teaching Secondary School Mathematics and Statistics: Evidence-Based Practice. Volume 1
Averill, Robin; Harvey, Roger
2009-01-01
"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…
Teaching Secondary School Mathematics and Statistics: Evidence-Based Practice. Volume 2
Averill, Robin; Harvey, Roger
2009-01-01
"We can never be sure that there is not some wild, untamed piece of mathematics ready to spring out on us... This is what keeps mathematics enchanting." This is how Jim Neyland, one of the contributing authors to this book, describes mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to…
2014-03-01
The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013. The Conference was attended by more than 280 participants and hosted about 400 oral, poster, and virtual presentations while counted more than 600 pre-registered authors. The second IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel sessions were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee. Further information on the editors, speakers and committees is available in the attached pdf.
PREFACE: 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare2015)
Vlachos, Dimitrios; Vagenas, Elias C.
2015-09-01
The 4th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place in Mykonos, Greece, from Friday 5th June to Monday 8th June 2015. The Conference was attended by more than 150 participants and hosted about 200 oral, poster, and virtual presentations. There were more than 600 pre-registered authors. The 4th IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather intense as after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with a high quality of talks creating an innovative and productive scientific environment for all attendees. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.
2015-01-01
The third International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Madrid, Spain, from Thursday 28 to Sunday 31 August 2014. The Conference was attended by more than 200 participants and hosted about 350 oral, poster, and virtual presentations. More than 600 pre-registered authors were also counted. The third IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral sessions and one poster session were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.
5th International Conference on Mathematical Modeling in Physical Sciences (IC-MSquare 2016)
International Nuclear Information System (INIS)
Vagenas, Elias C.; Vlachos, Dimitrios S.
2016-01-01
The 5th International Conference on Mathematical Modeling in Physical Sciences (IC- MSQUARE) took place at Athens, Greece, from Monday, 23"t"h of May, to Thursday, 26"t"h of May 2016. The Conference was attended by more than 130 participants and hosted about 170 oral, poster, and virtual presentations while counted more than 500 pre-registered authors. The 5"t"h IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics etc. The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel oral and one poster session were running every day. However, according to all attendees, the program was excellent with high level talks and the scientific environment was fruitful, thus all attendees had a creative time. We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee. (paper)
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis
2013-01-01
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.
Mathematical methods for physicists
Arfken, George B
2005-01-01
This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted
International Nuclear Information System (INIS)
1994-01-01
Traditional International Conference on programming and mathematical methods for solution of physical problems took place in Dubna in Jun, 14-19, 1993. More than 160 scientists from 14 countries participated in the Conference. They presented about 120 reports, the range of problems including computerized information complexes, experimental data acquisition and processing systems, mathematical simulation and calculation experiment in physics, analytical and numerical methods for solution of physical problems
FREE SOFTWARE IN ELECTRONIC LEARNING FUTURE TEACHERS OF MATHEMATICS, PHYSICS AND COMPUTER SCIENCE
Directory of Open Access Journals (Sweden)
Vladyslav Ye. Velychko
2016-05-01
Full Text Available Popularity of the use of free software in the IT industry is much higher than its popular use in educational activities. Disadvantages of free software and problems of its implementation in the educational process is a limiting factor for its use in the education system, however, openness, accessibility and functionality are the main factors for the introduction of free software in the educational process. Nevertheless, for future teachers of mathematics, physics and informatics free software is designed as well as possible because of the specificity of its creation, and therefore, there is a question of the system analysis of the possibilities of using open source software in e-learning for future teachers of mathematics, physics and computer science.
Modern mathematics for the engineer second series
1961-01-01
This volume and its predecessor were conceived to advance the level of mathematical sophistication in the engineering community. The books particularly focus on material relevant to solving the kinds of mathematical problems regularly confronted by engineers. Suitable as a text for advanced undergraduate and graduate courses as well as a reference for professionals, Volume Two's three-part treatment covers mathematical methods, statistical and scheduling studies, and physical phenomena. Contributions include chapters on chance processes and fluctuations by William Feller, Monte Carlo calculati
Engineering Physics and Mathematics Division progress report for period ending December 31, 1992
Energy Technology Data Exchange (ETDEWEB)
Ward, R.C.
1993-05-01
In this report, our research is described through abstracts of journal articles, technical reports, and presentations organized into sections following the five major operating units in the division: Mathematical Sciences, Intelligent Systems, Nuclear Data and Measurement Analysis, Nuclear Analysis and Shielding, and the Engineering Physics Information Centers. Each section begins with an introduction highlighting honors, awards, and significant research accomplishments in that unit during the reporting period.
The physical and mathematical model of dynamic economic analysis and assessment for NPP
International Nuclear Information System (INIS)
Xu Jiming
1992-01-01
A set physical and mathematical model of dynamic economic analysis referring to international general sub-item and account of investment and constant money levelized model and combining current economic analysis method in China for nuclear power plant was established. The model can be used in economic analysis not only for nuclear power plant but also for coal-fired power plant and can satisfy demand of doing economic analysis and assessment for nuclear power plant and conventional power plant
Engineering Physics and Mathematics Division progress report for period ending December 31, 1992
International Nuclear Information System (INIS)
Ward, R.C.
1993-05-01
In this report, our research is described through abstracts of journal articles, technical reports, and presentations organized into sections following the five major operating units in the division: Mathematical Sciences, Intelligent Systems, Nuclear Data and Measurement Analysis, Nuclear Analysis and Shielding, and the Engineering Physics Information Centers. Each section begins with an introduction highlighting honors, awards, and significant research accomplishments in that unit during the reporting period
One-dimensional chain of quantum molecule motors as a mathematical physics model for muscle fibers
International Nuclear Information System (INIS)
Si Tie-Yan
2015-01-01
A quantum chain model of multiple molecule motors is proposed as a mathematical physics theory for the microscopic modeling of classical force-velocity relation and tension transients in muscle fibers. The proposed model was a quantum many-particle Hamiltonian to predict the force-velocity relation for the slow release of muscle fibers, which has not yet been empirically defined and was much more complicated than the hyperbolic relationships. Using the same Hamiltonian model, a mathematical force-velocity relationship was proposed to explain the tension observed when the muscle was stimulated with an alternative electric current. The discrepancy between input electric frequency and the muscle oscillation frequency could be explained physically by the Doppler effect in this quantum chain model. Further more, quantum physics phenomena were applied to explore the tension time course of cardiac muscle and insect flight muscle. Most of the experimental tension transient curves were found to correspond to the theoretical output of quantum two- and three-level models. Mathematical modeling electric stimulus as photons exciting a quantum three-level particle reproduced most of the tension transient curves of water bug Lethocerus maximus. (special topic)
Physics, computer science and mathematics division. Annual report, 1 January - 31 December 1982
Energy Technology Data Exchange (ETDEWEB)
Jackson, J.D.
1983-08-01
Experimental physics research activities are described under the following headings: research on e/sup +/e/sup -/ annihilation; research at Fermilab; search for effects of a right-handed gauge boson; the particle data center; high energy astrophysics and interdisciplinary experiments; detector and other research and development; publications and reports of other research; computation and communication; and engineering, evaluation, and support operations. Theoretical particle physics research and heavy ion fusion research are described. Also, activities of the Computer Science and Mathematics Department are summarized. Publications are listed. (WHK)
Physics, computer science and mathematics division. Annual report, 1 January - 31 December 1982
International Nuclear Information System (INIS)
Jackson, J.D.
1983-08-01
Experimental physics research activities are described under the following headings: research on e + e - annihilation; research at Fermilab; search for effects of a right-handed gauge boson; the particle data center; high energy astrophysics and interdisciplinary experiments; detector and other research and development; publications and reports of other research; computation and communication; and engineering, evaluation, and support operations. Theoretical particle physics research and heavy ion fusion research are described. Also, activities of the Computer Science and Mathematics Department are summarized. Publications are listed
Fundamentals of Physics, Volume 1, (Chapters 1 - 21)
Walker, Jearl
2004-01-01
steam inside a railroad tank car cause the car to be crushed? 19-1 What Is Physics? 19-2 Avogadro's Number. 19-3 Ideal Gases. 19-4 Pressure, Temperature, and RMS Speed. 19-5 Translational Kinetic Energy. 19-6 Mean Free Path. 19-7 The Distribution of Molecular Speeds. 19-8 The Molar Speci.c Heats of an Ideal Gas. 19-9 Degrees of Freedom and Molar Speci.c Heats. 19-10 A Hint of Quantum Theory. 19-11 The Adiabatic Expansion of an Ideal Gas. Review & Summary. Questions. Problems. Chapter 20. Entropy and the Second Law of Thermodynamics. Why is the popping of popcorn irreversible? 20-1 What Is Physics? 20-2 Irreversible Processes and Entropy. 20-3 Change in Entropy. 20-4 The Second Law of Thermodynamics. 20-5 Entropy in the Real World: Engines. 20-6 Entropy in the Real World: Refrigerators. 20-7 The Ef.ciencies of Real Engines. 20-8 A Statistical View of Entropy. Review & Summary. Questions. Problems. Appendices. A The International System of Units (SI). B Some Fundamental Constants of Physics. C Some Astronomical Data. D Conversion Factors. E Mathematical Formulas. F Properties of the Elements. G Periodic Table of the Elements. Answers to Checkpoints and Odd-Numbered Questions and Problems. Index.
Progress in Computational Physics (PiCP) Volume 1 Wave Propagation in Periodic Media
Ehrhardt, Matthias
2010-01-01
Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures,
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
2000 Physical Acoustics Summer School (PASS 00). Volume II: Transparencies
National Research Council Canada - National Science Library
Bass, Henry
2001-01-01
.... Volume II of these proceedings contains copies of the transparencies used by the lecturers and Volume III contains background materials that were sent to student and discussion leader participants...
Lira, Matthew
This dissertation explores the Knowledge in Pieces (KiP) theory to account for how students learn to coordinate knowledge of mathematical and physical models in biology education. The KiP approach characterizes student knowledge as a fragmented collection of knowledge elements as opposed to stable and theory-like knowledge. This dissertation sought to use this theoretical lens to account for how students understand and learn with mathematical models and representations, such as equations. Cellular physiology provides a quantified discipline that leverages concepts from mathematics, physics, and chemistry to understand cellular functioning. Therefore, this discipline provides an exemplary context for assessing how biology students think and learn with mathematical models. In particular, the resting membrane potential provides an exemplary concept well defined by models of dynamic equilibrium borrowed from physics and chemistry. In brief, membrane potentials, or voltages, "rest" when the electrical and chemical driving forces for permeable ionic species are equal in magnitude but opposite in direction. To assess students' understandings of this concept, this dissertation employed three studies: the first study employed the cognitive clinical interview to assess student thinking in the absence and presence of equations. The second study employed an intervention to assess student learning and the affordances of an innovative assessment. The third student employed a human-computer-interaction paradigm to assess how students learn with a novel multi-representational technology. Study 1 revealed that students saw only one influence--the chemical gradient--and that students coordinated knowledge of only this gradient with the related equations. Study 2 revealed that students benefited from learning with the multi-representational technology and that the assessment detected performance gains across both calculation and explanation tasks. Last, Study 3 revealed how students
The International Linear Collider Technical Design Report - Volume 2: Physics
Barklow, Tim; Fujii, Keisuke; Gao, Yuanning; Hoang, Andre; Kanemura, Shinya; List, Jenny; Logan, Heather E; Nomerotski, Andrei; Perelstein, Maxim; Peskin, Michael E; Pöschl, Roman; Reuter, Jürgen; Riemann, Sabine; Savoy-Navarro, Aurore; Servant, Geraldine; Tait, Tim M P
2013-01-01
The International Linear Collider Technical Design Report (TDR) describes in four volumes the physics case and the design of a 500 GeV centre-of-mass energy linear electron-positron collider based on superconducting radio-frequency technology using Niobium cavities as the accelerating structures. The accelerator can be extended to 1 TeV and also run as a Higgs factory at around 250 GeV and on the Z0 pole. A comprehensive value estimate of the accelerator is give, together with associated uncertainties. It is shown that no significant technical issues remain to be solved. Once a site is selected and the necessary site-dependent engineering is carried out, construction can begin immediately. The TDR also gives baseline documentation for two high-performance detectors that can share the ILC luminosity by being moved into and out of the beam line in a "push-pull" configuration. These detectors, ILD and SiD, are described in detail. They form the basis for a world-class experimental programme that promises to incr...
The International Linear Collider Technical Design Report - Volume 2: Physics
Energy Technology Data Exchange (ETDEWEB)
Baer, Howard [Univ. of Oklahoma, Norman, OK (United States); Barklow, Tim [SLAC National Accelerator Lab., Menlo Park, CA (United States); Fujii, Keisuke [National Lab. for High Energy Physics (KEK), Tokai (Japan); Gao, Yuanning [Unlisted; Hoang, Andre [Univ. of Vienna (Austria); Kanemura, Shinya [Univ. of Toyama (Japan); List, Jenny [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Logan, Heather E. [Carleton Univ., Ottawa, ON (Canada); Nomerotski, Andrei [Univ. of Oxford (United Kingdom); Perelstein, Maxim [Cornell Univ., Ithaca, NY (United States); Peskin, Michael E. [SLAC National Accelerator Lab., Menlo Park, CA (United States); Pöschl, Roman [Univ. Paris-Sud, Orsay (France). Linear Accelerator Lab. (LAL); Reuter, Jürgen [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Riemann, Sabine [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Savoy-Navarro, Aurore [CNRS/IN2P3. Univ. Paris (France). Observatoire de Paris. AstroParticule et Cosmologie (APC); Servant, Geraldine [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Tait, Tim P. [Univ. of California, Los Angeles, CA (United States); Yu, Jaehoon [Univ. of Science and Technology of China, Hefei (China)
2013-06-26
The International Linear Collider Technical Design Report (TDR) describes in four volumes the physics case and the design of a 500 GeV centre-of-mass energy linear electron-positron collider based on superconducting radio-frequency technology using Niobium cavities as the accelerating structures. The accelerator can be extended to 1 TeV and also run as a Higgs factory at around 250 GeV and on the Z0 pole. A comprehensive value estimate of the accelerator is give, together with associated uncertainties. It is shown that no significant technical issues remain to be solved. Once a site is selected and the necessary site-dependent engineering is carried out, construction can begin immediately. The TDR also gives baseline documentation for two high-performance detectors that can share the ILC luminosity by being moved into and out of the beam line in a "push-pull" configuration. These detectors, ILD and SiD, are described in detail. They form the basis for a world-class experimental programme that promises to increase significantly our understanding of the fundamental processes that govern the evolution of the Universe.
Sierpinska, Anna
1994-01-01
The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.
Mathematical problems in image processing
International Nuclear Information System (INIS)
Chidume, C.E.
2000-01-01
This is the second volume of a new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics. This volume contains the lecture notes given by A. Chambolle during the School on Mathematical Problems in Image Processing. The school consisted of two weeks of lecture courses and one week of conference
Physical and mathematical modeling of diesel fuel liquid and vapor movement in porous media
International Nuclear Information System (INIS)
Johnson, T.E.; Kreamer, D.K.
1994-01-01
Two-dimensional physical modeling of diesel fuel leaks was conducted in sand tanks to determine liquid and vapor migration characteristics. Mathematical modeling provided estimation of vapor concentrations at discrete times and distances from the vapor source and was compared to the physical experiment. The mathematical gaseous diffusion model was analogous to the Theis equation for ground-water flow, accounted for sorptive effects of the media, and was calibrated using measured concentrations from the sand tank. Mathematically different positions of the vapor source were tested to better relate observed liquid flow rates and media configuration to gaseous concentrations. The calculated diffusion parameters were then used to estimate theoretical, three-dimensional vapor transport from a hypothetical liquid leak of 2.0 1/hr for 30 days. The associated three-dimensional vapor plume, which would be reasonably detectable by commercially available vadose zone monitors, was estimated to have a diameter of 8 m with a vapor concentration of 50 ppm at the outside edge of the vapor plume. A careful application of the method and values can be used to give a first approximation to the number of vapor monitors required at a field site as well as the optimal locations for the monitors
International Conference on $p$-Adic Mathematical Physics and its Applications
2015-01-01
Since 1987, there have been many interesting and promissing applications of p-adic (non-Archimedean, ultrametric) analysis to some problems of modern mathematical and theoretical physics, and also to some other related fields of sciences. As a result, it emerged a new field of research called p-adic mathematical physics. During this time, there has been permanent interest in investigation of relevant mathematical tools, as well as of possible applications -- from strings to the universe as a whole. In particular, there have been remarkable achievements in some complex biosystems with hierarchy. Enthusiastic researchers believe that application of p-adic analysis and ultrametric methods becomes one of scientific challenges of the 21st century. For the progress in this field in period 1987-2008 one can see review paper http://arxiv.org/abs/0904.4205. For an insight to investigations after 2008 one can look at publications of the journal p-Adic Numbers, Ultrametric Analysis and Applications. To promote this fiel...
Directory of Open Access Journals (Sweden)
Prokhorov V.B.,
2018-04-01
Full Text Available The important problem of developing the low-cost technologies that will be able to provide a deep decrease in the concentration of nitrogen oxides while maintaining fuel burn-up efficiency is considered. This paper presents the results of the aerodynamics study of the furnace of boiler TPP-210A on the base of the physical and mathematical models in the case when boiler retrofitting from liquid to solid slag removal with two to three times reduction of nitrogen oxide emissions and replacing the vortex burners with direct-flow burners. The need for these studies is due to the fact that the direct-flow burners are "collective action" burners, and efficient fuel combustion can be provided only by the interaction of fuel jets, secondary and tertiary air jets in the furnace volume. The new scheme of air staged combustion in a system of vertical vortexes of opposite rotation with direct-flow burners and nozzles and direct injection of Kuznetsky lean coal dust was developed. In order to test the functional ability and efficiency of the proposed combustion scheme, studies on the physical model of the boiler furnace and the mathematical model of the experimental furnace bench for the case of an isothermal fluid flow were carried out. Comparison showed an acceptable degree of coincidence of these results. In all studied regimes, pronounced vortices remain in both the vertical and horizontal planes, that indicates a high degree of mass exchange between jets and combustion products and the furnace aerodynamics stability to changes in regime factors.
Bureau of Naval Personnel, Washington, DC.
The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…
Nakahara, Tadao, Ed.; Koyama, Masataka, Ed.
The first volume of the 24th annual conference of the International Group for the Psychology of Mathematics Education includes plenary addresses, plenary panel discussions, research forum, project groups, discussion groups, short oral communications, and poster presentations. (ASK)
Fundamentals of university mathematics
McGregor, C M; Stothers, W W
2010-01-01
The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differe
Woo, Jeong-Ho, Ed.; Lew, Hee-Chan, Ed.; Park, Kyo-Sik Park, Ed.; Seo, Dong-Yeop, Ed.
2007-01-01
The first volume of the 31st annual proceedings of the International Group for the Psychology of Mathematics Education conference presents plenary lectures; research forums; discussion groups; working sessions; short oral communications; and posters from the meeting. Plenary lecture papers include: (1) On Humanistic Mathematics Education: A…
Pehkonen, Erkki, Ed.
The second volume of the proceedings of 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following papers: (1) "The Dilemma of Transparency: Seeing and Seeing through Talk in the Mathematics Classroom" (J. Adler); (2) "Abstraction is Hard in Computer-Science Too" (D.…
2017-01-01
This book presents beautiful photos of mathematical models of geometric surfaces made from a variety of materials including plaster, metal, paper, wood, and string. The construction of these models at the time (of Felix Klein and others) was not an end in itself, but was accompanied by mathematical research especially in the field of algebraic geometry. The models were used to illustrate the mathematical objects defined by abstract formulas, either as equations or parameterizations. In the second part of the book, the models are explained by experts in the field of geometry. This book is a reprint thirty years after the original publication in 1986 with a new preface by Gert-Martin Greuel. The models have a timeless appeal and a historical value. The Editor Prof. Dr. Gerd Fischer, Department of Mathematics, Technical University of Munich.
Mathematical and physical modeling of thermal stratification phenomena in steel ladles
Putan, V.; Vilceanu, L.; Socalici, A.; Putan, A.
2018-01-01
By means of CFD numerical modeling, a systematic analysis of the similarity between steel ladles and hot-water model regarding natural convection phenomena was studied. The key similarity criteria we found to be dependent on the dimensionless numbers Fr and βΔT. These similarity criteria suggested that hot-water models with scale in the range between 1/5 and 1/3 and using hot water with temperature of 45 °C or higher are appropriate for simulating natural convection in steel ladles. With this physical model, thermal stratification phenomena due to natural convection in steel ladles were investigated. By controlling the cooling intensity of water model to correspond to the heat loss rate of steel ladles, which is governed by Fr and βΔT, the temperature profiles measured in the water bath of the model were to deduce the extent of thermal stratification in liquid steel bath in the ladles. Comparisons between mathematically simulated temperature profiles in the prototype steel ladles and those physically simulated by scaling-up the measured temperatures profiles in the water model showed good agreement. This proved that it is feasible to use a 1/5 scale water model with 45 °C hot water to simulate natural convection in steel ladles. Therefore, besides mathematical CFD models, the physical hot-water model provided an additional means of studying fluid flow and heat transfer in steel ladles.
Mathematics for natural scientists II advanced methods
Kantorovich, Lev
2016-01-01
This book covers the advanced mathematical techniques useful for physics and engineering students, presented in a form accessible to physics students, avoiding precise mathematical jargon and laborious proofs. Instead, all proofs are given in a simplified form that is clear and convincing for a physicist. Examples, where appropriate, are given from physics contexts. Both solved and unsolved problems are provided in each chapter. Mathematics for Natural Scientists II: Advanced Methods is the second of two volumes. It follows the first volume on Fundamentals and Basics.
The Effect of Structured Exercise Intervention on Intensity and Volume of Total Physical Activity
Directory of Open Access Journals (Sweden)
Niko Wasenius
2014-12-01
Full Text Available This study aimed to investigate the effects of a 12-week structured exercise intervention on total physical activity and its subcategories. Twenty-three overweight or obese middle aged men with impaired glucose regulation were randomized into a 12-week Nordic walking group, a power-type resistance training group, and a non-exercise control group. Physical activity was measured with questionnaires before the intervention (1–4 weeks and during the intervention (1–12 weeks and was expressed in metabolic equivalents of task. No significant change in the volume of total physical activity between or within the groups was observed (p > 0.050. The volume of total leisure-time physical activity (structured exercises + non-structured leisure-time physical activity increased significantly in the Nordic walking group (p 0.050 compared to the control group. In both exercise groups increase in the weekly volume of total leisure-time physical activity was inversely associated with the volume of non-leisure-time physical activities. In conclusion, structured exercise intervention did not increase the volume of total physical activity. Albeit, endurance training can increase the volume of high intensity physical activities, however it is associated with compensatory decrease in lower intensity physical activities. To achieve effective personalized exercise program, individuality in compensatory behavior should be recognised.
Evaluation of an Integrated Curriculum in Physics, Mathematics, Engineering, and Chemistry
Beichner, Robert
1997-04-01
An experimental, student centered, introductory curriculum called IMPEC (for Integrated Mathematics, Physics, Engineering, and Chemistry curriculum) is in its third year of pilot-testing at NCSU. The curriculum is taught by a multidisciplinary team of professors using a combination of traditional lecturing and alternative instructional methods including cooperative learning, activity-based class sessions, and extensive use of computer modeling, simulations, and the world wide web. This talk will discuss the research basis for our design and implementation of the curriculum, the qualitative and quantitative methods we have been using to assess its effectiveness, and the educational outcomes we have noted so far.
Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2012-01-01
Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.
5th International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE 2016)
2016-01-01
The conference is to be held at Athens, Greece during May 23-26, 2016. The conference aims to promote the knowledge and the development of high-quality research in mathematical fields that have to do with the applications of other scientific fields and the modern technological trends that appear in them, these fields being those of Physics, Chemistry, Biology, Medicine, Economics, Sociology, Environmental sciences etc. All Conference related actions (submission, registration etc) are performed on-line by creating an account. After that, authors can login and have access to a number of tools for submitting a paper, proposing for a workshop, registering, send requests, manage their reviews etc.
Review of mathematical and physical basis of two-phase flow modelling
International Nuclear Information System (INIS)
Bottoni, M.; Sengpiel, W.
1992-08-01
Starting from a continuum-mechanical approach, this report gives a detailed overview of the deduction of conservation equations for the analytical description of two-phase flows by means of an adequate averaging process resulting in a two-fluid model and a homogeneous mixture model. The mathematical process of averaging leads to macroscopic formulations of stress terms and interfacial interaction terms. These terms depend on microscopic variables and thus give some helpful insight into the physical processes which have to be described by constitutive relations. (orig.) [de
Mathematics for natural scientists fundamentals and basics
Kantorovich, Lev
2016-01-01
This book, the first in a two part series, covers a course of mathematics tailored specifically for physics, engineering and chemistry students at the undergraduate level. It is unique in that it begins with logical concepts of mathematics first encountered at A-level and covers them in thorough detail, filling in the gaps in students' knowledge and reasoning. Then the book aids the leap between A-level and university-level mathematics, with complete proofs provided throughout and all complex mathematical concepts and techniques presented in a clear and transparent manner. Numerous examples and problems (with answers) are given for each section and, where appropriate, mathematical concepts are illustrated in a physics context. This text gives an invaluable foundation to students and a comprehensive aid to lecturers. Mathematics for Natural Scientists: Fundamentals and Basics is the first of two volumes. Advanced topics and their applications in physics are covered in the second volume.
Effects of physical activity and breaks on mathematics engagement in adolescents.
Owen, Katherine B; Parker, Philip D; Astell-Burt, Thomas; Lonsdale, Chris
2018-01-01
The purpose of this study was to determine whether physical activity has a positive relationship with school engagement regardless of the presence or absence of a recess or lunch break before the classroom lesson. Data were collected over three ten-week periods: January-April 2014 (Time 1), October-December 2014 (Time 2), and April-June 2015 (Time 3). A cohort of 2194 adolescents (mean age=13.40years, SD=.73) wore an accelerometer during the hour before a mathematics lesson and completed a questionnaire following the mathematics lesson to assess school engagement in that lesson. Linear mixed models indicated that moderate-intensity activity before a mathematics lesson had a positive linear relationship with cognitive engagement (β=.40, pmathematics lesson had a negative relationship with overall, behavioural, emotional, and cognitive engagement (β=-.18, pmathematics lessons could improve students' cognitive engagement. Educators should be aware that students tend to demonstrate the lowest levels of school engagement after recess breaks. Crown Copyright © 2017. Published by Elsevier Ltd. All rights reserved.
Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
International Nuclear Information System (INIS)
Carretero-González, R; Frantzeskakis, D J; Kevrekidis, P G
2008-01-01
The aim of this review is to introduce the reader to some of the physical notions and the mathematical methods that are relevant to the study of nonlinear waves in Bose–Einstein condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyse some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g. the linear or the nonlinear limit or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools. (invited article)
Research Data in Core Journals in Biology, Chemistry, Mathematics, and Physics.
Directory of Open Access Journals (Sweden)
Ryan P Womack
Full Text Available This study takes a stratified random sample of articles published in 2014 from the top 10 journals in the disciplines of biology, chemistry, mathematics, and physics, as ranked by impact factor. Sampled articles were examined for their reporting of original data or reuse of prior data, and were coded for whether the data was publicly shared or otherwise made available to readers. Other characteristics such as the sharing of software code used for analysis and use of data citation and DOIs for data were examined. The study finds that data sharing practices are still relatively rare in these disciplines' top journals, but that the disciplines have markedly different practices. Biology top journals share original data at the highest rate, and physics top journals share at the lowest rate. Overall, the study finds that within the top journals, only 13% of articles with original data published in 2014 make the data available to others.
International Nuclear Information System (INIS)
Aragones, J. M.; Ahnert, C.; Cabellos, O.
1999-01-01
The international conference on mathematics and computation, reactor physics and environmental analysis in nuclear applications in the biennial topical meeting of the mathematics and computation division of the American Nuclear Society. (Author)
Energy Technology Data Exchange (ETDEWEB)
Aragones, J. M.; Ahnert, C.; Cabellos, O.
1999-07-01
The international conference on mathematics and computation, reactor physics and environmental analysis in nuclear applications in the biennial topical meeting of the mathematics and computation division of the American Nuclear Society. (Author)
Directory of Open Access Journals (Sweden)
Rudolf Larenz
2017-09-01
Full Text Available The article aims at proposing a way of solution to the problem why mathematics is efficient in physics. Its strategy consists in, first, identifying servere reductionisms performed on physical processes in order to have them correspond to mathematics. As this makes it impossible to understand the real relationship between matter and mathematics, a necessary step on the way to an understanding is to abandon the reductionisms from the very outset. Consequently, one is faced with the need of searching for mathematical elements in nature, as if there never had been any successful mathematics in physics. And for this search, one has to rely on experience alone. To this end, the article takes its inspiration from two pillars of Aristotelian philosophy of nature, the notions of ‘substance’ and ‘dynamics’, together with a careful examination of the treasure of accumulated experience in physics. Upon this basis, the hylomorphic structure of elementary particles, which are considered to be at the basis of all material substances, is the source for the most common features of the dynamical order of material things in general. This dynamical order, in turn, is quite likely to be reflected in mathematical terms. This is a novel approach because, at present, the most common framework for dealing with the question of mathematics in physics is Scientific Realism. It addresses the question why the existent physico-mathematical theories are successful. In order to find an answer, it starts from these theories and some methodological considerations, but does not address the question of where these theories stem from. In particular, it does not consider the possibility that these theories might, at least in part, stem from the material things they are referring to. The latter approach is what is suggested here. It is that of Natural Realism, of which Aristotle is an eminent representative.
Dennery, Philippe
1967-01-01
""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo
Eren, Beytullah; Karadagli, Fatih
2012-03-06
Physical disintegration of representative toilet papers was investigated in this study to assess their disintegration potential in sewer systems. Characterization of toilet papers from different parts of the world indicated two main categories as premium and average quality. Physical disintegration experiments were conducted with representative products from each category according to standard protocols with improvements. The experimental results were simulated by mathematical model to estimate best-fit values of disintegration rate coefficients and fractional distribution ratios. Our results from mathematical modeling and experimental work show that premium products release more amounts of small fibers and disintegrate more slowly than average ones. Comparison of the toilet papers with the tampon applicators studied previously indicates that premium quality toilet papers present significant potential to persist in sewer pipes. Comparison of turbulence level in our experimental setup with those of partial flow conditions in sewer pipes indicates that drains and small sewer pipes are critical sections where disintegration of toilet papers will be limited. For improvement, requirements for minimum pipe slopes may be increased to sustain transport and disintegration of flushable products in small pipes. In parallel, toilet papers can be improved to disintegrate rapidly in sewer systems, while they meet consumer expectations.
Tutorium quantum mechanics. By an experienced tutor for students of physics and mathematics
International Nuclear Information System (INIS)
Schwindt, Jan-Markus
2013-01-01
Tutorium quantum mechanics is a book, written by an experiences tutor for all, who finally want to understand from the beginning physics and mathematics of quantum mechanics. The book treats the matter of the corresponding course in the framework of theoretical physics. The main topic lies in this book on the general postulates of quantum mechanics and the clarification of the fundamental terms. What is precisely a Hilbert space? What is an Hermitian operator? A tensor product? An entangled state? To what extend wave functions are vectors? The postulates raise until today also many questions concerning their interpretation. This is discussed in a separate chapter. This book is structured in such a way that each step and each new term is explained by means of simple examples. The author attaches great importance to the clarity of the applied mathematics - something, what he and many students in other textbooks had hitherto to miss. By this main topic is also very well suited for mathematicists, who want to deal with the issue. In the examination preparation the book is especially well suited for the clarification of terms and questions of understanding. The questions of understanding and the exercise problems interspersed in the text with solutions support additionally the learning and the preparation for examination.
Tutorium quantum mechanics. By an experienced tutor for students of physics and mathematics. 2. ed.
International Nuclear Information System (INIS)
Schwindt, Jan-Markus
2016-01-01
The focus of this book lies on the general postulates of quantum mechanics (QM), their interpretation, their fundamental terms, and their mathematical formulation. The first and most comprehensive part of the book is dedicated to this thematics. In the second part an imported special case is treated: The QM of the wave functions in one, two, and three spatial dimensions under the condition, that the Hamiltonian operator consists only of the kinetic term and a timely independent potential. The most important examples hereby are the harmonic oscillator and the hydrogen atom. Also the scattering theory is discussed in this framework. The third part comprehends further themes, which belong to the canonical matter of a QM course: Combination of spin and angular momentum, QM with electromagnetism, perturbation theory, and systems with several particles. Rounded off is the whole by a short explanation of the path-integral term and by the relativistic theory of the electron (Dirac equation). Target group of this book are students of physics, who hear QM in the framework of theoretical physics. By the axiomatically deductive approach and the detailed discussion of the mathematical background it is also very well suited for mathematicians, who want to come to an understanding of QM in the subsidiary subject or in their leisure time.
Investigation of the blood behaviour and vascular diseases by using mathematical physic principles
Yardimci, Ahmet; Simsek, Buket
2017-07-01
In this paper we prepare a short survey for using of mathematical physic principles in blood flow and vascular diseases researches. The study of the behavior of blood flow in the blood vessels provides understanding on connection between flow and the development of dieseases such as atherosclerosis, thrombosis, aneurysms etc. and how the flow dynamics is changed under these conditions. Blood flow phenomena are often too complex that it would be possible to describe them entirely analytically, although simple models, such as Poiseuille model, can still provide some insight into blood flow. Blood is not an "ideal fluid" and energy is lost as flowing blood overcomes resistance. Resistance to blood flow is a function of viscosity, vessel radius, and vessel length. So, mathematical Physic principles are useful tools for blood flow research studies. Blood flow is a function of pressure gradient and resistance and resistance to flow can be estimates using Poiseuille's law. Reynold's number can be used to determine whether flow is laminar or turbulent.
New Editor-in-Chief for Journal of Physics A: Mathematical and Theoretical
Gillan, Rebecca
2014-04-01
We are delighted to announce that Professor Martin Evans of University of Edinburgh has been appointed as the new Editor-in-Chief of Journal of Physics A: Mathematical and Theoretical. Martin Evans has been Editor of the Statistical Physics section of the journal since 2009. Prior to this, he served as a Board Member for the journal. His areas of research include statistical mechanics of nonequilibrium systems, phase transitions and scaling regimes in nonequilibrium statistical physics, glassy dynamics, phase transitions and ordering in driven diffusive systems, mass transport models, condensation models, zero range processes and exclusion processes. We very much look forward to working with Martin to continue to improve the journal's quality and interest to the readership. We would like to thank our outgoing Editor-in-Chief, Professor Murray Batchelor. Murray has worked hard and provided excellent guidance in improving the quality of the journal and the service that the journal provides to authors, referees and readers. During the last five years, we have raised the quality threshold for acceptance in the journal and currently reject over 70% of submissions. As a result, papers published in Journal of Physics A: Mathematical and Theoretical are amongst the best in the field. We have also maintained and improved on our excellent receipt-to-first-decision times, which now average under 40 days for papers. With the help of Martin Evans and our distinguished Editorial Board, we will be working to further improve the quality of the journal whilst continuing to offer excellent services to our readers, authors and referees. We hope that you benefit from reading the journal. If you have any comments or questions, please do not hesitate to contact us at jphysa@iop.org. Rebecca Gillan Publisher
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.
Chick, Helen L., Ed.; Vincent, Jill L., Ed.
2005-01-01
The first volume of the 29th annual conference of the International Group for the Psychology of Mathematics Education contains plenary lecture and research forum papers as listed below. Short oral communications papers, poster presentations, brief summaries of discussion groups, and working sessions are also included in the volume. The plenary…
Olivier, Alwyn, Ed.; Newstead, Karen, Ed.
The fourth volume of this proceedings contains 29 full research reports continuing on from Volume 3, 84 short oral communications (abstracts only) and 34 poster presentations (abstracts only). The full papers include: (1) "Beliefs, Teacher Education and the History of Mathematics" (George N. Philippou and Constantinos Christou); (2) "Working Class…
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 125; Issue 4. Yoneda algebras of almost Koszul algebras. Zheng Lijing. Volume 125 Issue 4 November 2015 ... Author Affiliations. Zheng Lijing1. School of Mathematics and Physics, University of South China, Hengyang, Hunan, People's Republic of China ...
Directory of Open Access Journals (Sweden)
P. M. Shkapov
2015-01-01
Full Text Available The paper provides a mathematical model of thermo-gravity convection in a large volume vertical cylinder. The heat is removed from the product via the cooling jacket at the top of the cylinder. We suppose that a laminar fluid motion takes place. The model is based on the NavierStokes equation, the equation of heat transfer through the wall, and the heat transfer equation. The peculiarity of the process in large volume tanks was the distribution of the physical parameters of the coordinates that was taken into account when constructing the model. The model corresponds to a process of wort beer fermentation in the cylindrical-conical tanks (CCT. The CCT volume is divided into three zones and for each zone model equations was obtained. The first zone has an annular cross-section and it is limited to the height by the cooling jacket. In this zone the heat flow from the cooling jacket to the product is uppermost. Model equation of the first zone describes the process of heat transfer through the wall and is presented by linear inhomogeneous differential equation in partial derivatives that is solved analytically. For the second and third zones description there was a number of engineering assumptions. The fluid was considered Newtonian, viscous and incompressible. Convective motion considered in the Boussinesq approximation. The effect of viscous dissipation is not considered. The topology of fluid motion is similar to the cylindrical Poiseuille. The second zone model consists of the Navier-Stokes equations in cylindrical coordinates with the introduction of a simplified and the heat equation in the liquid layer. The volume that is occupied by an upward convective flow pertains to the third area. Convective flows do not mix and do not exchange heat. At the start of the process a medium has the same temperature and a zero initial velocity in the whole volume that allows us to specify the initial conditions for the process. The paper shows the
Averages, Areas and Volumes; Cambridge Conference on School Mathematics Feasibility Study No. 45.
Cambridge Conference on School Mathematics, Newton, MA.
Presented is an elementary approach to areas, columns and other mathematical concepts usually treated in calculus. The approach is based on the idea of average and this concept is utilized throughout the report. In the beginning the average (arithmetic mean) of a set of numbers is considered and two properties of the average which often simplify…
Measuring industrial energy efficiency: Physical volume versus economic value
Energy Technology Data Exchange (ETDEWEB)
Freeman, S.L.; Niefer, M.J.; Roop, J.M.
1996-12-01
This report examines several different measures of industrial output for use in constructing estimates of industrial energy efficiency and discusses some reasons for differences between the measures. Estimates of volume-based measures of output, as well as 3 value-based measures of output (value of production, value of shipments, and value added), are evaluated for 15 separate 4-digit industries. Volatility, simple growth rate, and trend growth rate estimates are made for each industry and each measure of output. Correlations are made between the volume- and value-based measures of output. Historical energy use data are collected for 5 of the industries for making energy- intensity estimates. Growth rates in energy use, energy intensity, and correlations between volume- and value-based measures of energy intensity are computed. There is large variability in growth trend estimates both long term and from year to year. While there is a high correlation between volume- and value-based measures of output for a few industries, typically the correlation is low, and this is exacerbated for estimates of energy intensity. Analysis revealed reasons for these low correlations. It appears that substantial work must be done before reliable measures of trends in the energy efficiency of industry can be accurately characterized.
Bárcenas, R. B.; Hernández, H. H. H.; Sabido, M.
2015-11-01
The collection of papers in this volume was presented during the X Mexican School on Gravitation and Mathematical Physics, which was held in Playa del Carmen, Quintana Roo, México, December 1-5, 2014. The Mexican School on Gravitation and Mathematical Physics is a series of conferences sponsored by the Mexican Physical Society that started in 1994 with the purposes of discussing and exchanging current ideas in gravitational physics. Each Mexican School has been devoted to a particular subject, and these have included supergravity, branes, black holes, the early Universe, observational cosmology, quantum gravity and numerical relativity. In this ocasion the theme of the school was Reaching a Century: Classical and Modified General Relativity's Attempts to explain the evolution of the Universe, which focused on the discussion of classical and modified aspects of general relativity. Following our previous Schools, world leaders in the field were invited to give courses and plenary lectures. More specialized talks were also presented in parallel sessions, and some of them have been included in these proceedings. The contributions in this volume have been reviewed and represent some of the courses, plenary talks and contributed talks presented during our X School. We are indebted to the contributors of these proceedings as well as to the rest of the participants in our Mexican School all for making of it a complete success. As for financial support we should mention the Mexican National Science and Technology Council (CONACyT), the Royal Society of London (UK), the Mexican Physical Society (SMF), as well as several Institutions including: Centro de Investigación y Estudios Avanzados (CINVESTAV), Universidad Autónoma Metropolitana Iztapalapa (UAM-I), Universidad de Guanajuato (UG), and Universidad Nacional Autónoma de México (UNAM).
Buckey, J. C.; Beattie, J. M.; Gaffney, F. A.; Nixon, J. V.; Blomqvist, C. G.
1984-01-01
Accurate, reproducible, and non-invasive means for ventricular volume determination are needed for evaluating cardiovascular function zero-gravity. Current echocardiographic methods, particularly for the right ventricle, suffer from a large standard error. A new mathematical approach, recently described by Watanabe et al., was tested on 1 normal formalin-fixed human hearts suspended in a mineral oil bath. Volumes are estimated from multiple two-dimensional echocardiographic views recorded from a single point at sequential angles. The product of sectional cavity area and center of mass for each view summed over the range of angles (using a trapezoidal rule) gives volume. Multiple (8-14) short axis right ventricle and left ventricle views at 5.0 deg intervals were videotaped. The images were digitized by two independent observers (leading-edge to leading-edge technique) and analyzed using a graphics tablet and microcomputer. Actual volumes were determined by filling the chambers with water. These data were compared to the mean of the two echo measurements.
Killgore, William D. S.; Olson, Elizabeth A.; Weber, Mareen
2013-12-01
Physical activity facilitates neurogenesis of dentate cells in the rodent hippocampus, a brain region critical for memory formation and spatial representation. Recent findings in humans also suggest that aerobic exercise can lead to increased hippocampal volume and enhanced cognitive functioning in children and elderly adults. However, the association between physical activity and hippocampal volume during the period from early adulthood through middle age has not been effectively explored. Here, we correlated the number of minutes of self-reported exercise per week with gray matter volume of the hippocampus using voxel-based morphometry (VBM) in 61 healthy adults ranging from 18 to 45 years of age. After controlling for age, gender, and total brain volume, total minutes of weekly exercise correlated significantly with volume of the right hippocampus. Findings highlight the relationship between regular physical exercise and brain structure during early to middle adulthood.
Physics for Scientists and Engineers, 5th edition - Volume 1
Tipler, Paul A.; Mosca, Gene P.
For nearly 30 years, Paul Tipler's Physics for Scientists and Engineers has set the standard in the introductory calculus-based physics course for clarity, accuracy, and precision. In this fifth edition, Paul has recruited Gene Mosca to bring his years of teaching experience to bear on the text, to scrutinize every explanation and example from the perspective of the freshman student. The result is a teaching tool that retains its precision and rigor, but offers struggling students the support they need to solve problems strategically and to gain real understanding of physical concepts.
Contributions to mathematical analysis and to numerical approximation in plasma physics
International Nuclear Information System (INIS)
Besse, N.
2009-01-01
The author's scientific works deal with numerical analysis and the simulation of the partial differential equations that intervene in the transport of charged particles and in plasma physics. In the chapters 2 and 3, a reduction of the Vlasov equation is presented, this method is based on the Liouville geometric invariants and it leads to a mathematical model named water-bag model that can be coupled with various equations of the electromagnetic field: the Poisson equation, the quasi-neutral equation or Maxwell equations. In the chapter 3 this reduction method is applied to the Vlasov gyro-kinetic equation to form the gyro-water-bag model. The mathematical analysis of this model produces interesting analytical results such as: threshold instabilities, instability growth rate, transport coefficient and non-linear turbulence mechanisms. Simulations have been performed to study turbulence in magnetized plasmas. In these plasmas occurred numerous instabilities due to the presence of high density and temperature gradients. These instabilities generate turbulence that deteriorates plasma confinement conditions required for thermonuclear fusion. The numerical calculation of turbulent thermal diffusivities is important since confinement time is determined by these transport coefficients. The chapter 4 gathers mathematical analysis issues like convergence or prior knowledge of errors concerning several high-order numerical methods used to solve Vlasov-Poisson or Vlasov-Einstein equation systems as well as the induction equation of an idealistic MHD system. The chapter 5 presents original numerical methods to solve several non-linear Vlasov equations such as Vlasov-Poisswell, Vlasov-Darwin, Vlasov-Maxwell and Vlasov-gyrokinetic that are involved either in inertial fusion or in magnetic confinement fusion
Handbook on the physics and chemistry of rare earths: Volume 17
International Nuclear Information System (INIS)
Gschneidner, K.A. Jr; Eyring, L.; Choppin, G.R.; Lander, G.H.
1993-10-01
This volume of the handbook is the first of a three volume set of reviews devoted to the interrelationships, similarities, differences and contrasts of the lanthanide and actinide series of elements. The volume contains eight chapters (numbered 110-117) concerned with some of the physical aspects of lanthanide and actinide series. The first three chapters are theoretical in nature and the last five are more heavily oriented towards experimental studies
Many-electron approaches in physics, chemistry and mathematics a multidisciplinary view
Site, Luigi
2014-01-01
This book provides a broad description of the development and (computational) application of many-electron approaches from a multidisciplinary perspective. In the context of studying many-electron systems Computer Science, Chemistry, Mathematics and Physics are all intimately interconnected. However, beyond a handful of communities working at the interface between these disciplines, there is still a marked separation of subjects. This book seeks to offer a common platform for possible exchanges between the various fields and to introduce the reader to perspectives for potential further developments across the disciplines. The rapid advances of modern technology will inevitably require substantial improvements in the approaches currently used, which will in turn make exchanges between disciplines indispensable. In essence this book is one of the very first attempts at an interdisciplinary approach to the many-electron problem.
International Nuclear Information System (INIS)
Lo Surdo, C.
2001-01-01
Hardly the role and the importance of Classical-Invariant Theory is the history of mathematics (say, between - 1850 and - 1920) can be fully appreciated by a nonspecialist. In this study, it was firstly purposed to provide a compact sketch of its foundations starting from (and keeping the framework of) some very basic ideas in the equation theory; and then, after reviewing a couple of classical examples, to illustrate a number of (presumably new) applications to physics, with special reference to constitutive relations in continuous material media. As a significant example of the latter type (amongst other ones), it shall be completely worked out the problem of the a priori structure of linear viscous-stress tensor in a magnetoplasma [it
Development of problem-based learning material for physics mathematics and its implementation
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Pujayanto Pujayanto
2017-02-01
Full Text Available The research aims to develop Problem Based Learning material teaching of Mathematics Physics and to know the effect on the cognitive capability of undergraduate students. The research uses development method of Borg and Gall. There are ten steps such as data collection, planning, product drafting, pretest, pretest revise 1, main test, main test revise 2, posttest, final revision, and dissemination and implementation. The data collection uses questionnaire and cognitive test which will support the qualitative data. The result shows that the criterion of developing problem-based learning teaching materials is 5 level category when 43.33% respondents rate 5 level category and the others give 4 level category. Furthermore, students which use the materials increased and the most of the students have acquired cognitive value exceeds the value of minimum completeness criteria.
In praise of simple physics the science and mathematics behind everyday questions
Nahin, Paul J
2016-01-01
Physics can explain many of the things that we commonly encounter. It can tell us why the night is dark, what causes the tides, and even how best to catch a baseball. With In Praise of Simple Physics, popular math and science writer Paul Nahin presents a plethora of situations that explore the science and math behind the wonders of everyday life. Roaming through a diverse range of puzzles, he illustrates how physics shows us ways to wring more energy from renewable sources, to measure the gravity in our car garages, to figure out which of three light switches in the basement controls the light bulb in the attic, and much, much more. How fast can you travel from London to Paris? How do scientists calculate the energy of an atomic bomb explosion? How do you kick a football so it stays in the air and goes a long way downfield? Nahin begins with simpler problems and progresses to more challenging questions, and his entertaining, accessible, and scientifically and mathematically informed explanations are all punc...
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1981
International Nuclear Information System (INIS)
Birge, R.W.
1982-12-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1981. During the year under review the Division devoted roughly half its effort to the final construction stages of the Time Projection Chamber and other equipment for the PEP-4 facility at SLAC. The year was marked by the successful passage of milestone after milestone - the two-sector test of the TPC with cosmic rays in July 1981, the full TPC test in November 1981, and the roll-in onto the PEP beam line on 6 January 1982. In other e + e - experiments, the Mark II detector continued its productive data-taking at PEP. In other areas, the final stages of data analysis, particularly for the structure functions, proceeded for the inelastic muon scattering experiment performed at Fermilab, a muon polarimeter experiment was developed and mounted at TRIUMF to probe for the presence of right-handed currents in muon decay, and the design and then construction began of fine-grained hadron calorimeters for the end caps of the Colliding Detector Facility at Fermilab. The Particle Data Group intensified its activities, despite financial constraints, as it proceeded toward production of a new edition of its authoritative Review of Particle Properties early in 1982. During 1981 the Theoretical Physics Group pursued a diverse spectrum of research in its own right and also interacted effectively with the experimental program. Research and development continued on the segmented mirror for the ten-meter telescope proposed by the University of California. Activities in the Computer Science and Mathematics Department encompassed networking, database management, software engineering, and computer graphics, as well as basic research in nonlinear phenomena in combustion and fluid flow
Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1981
Energy Technology Data Exchange (ETDEWEB)
Birge, R.W.
1982-12-01
This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1981. During the year under review the Division devoted roughly half its effort to the final construction stages of the Time Projection Chamber and other equipment for the PEP-4 facility at SLAC. The year was marked by the successful passage of milestone after milestone - the two-sector test of the TPC with cosmic rays in July 1981, the full TPC test in November 1981, and the roll-in onto the PEP beam line on 6 January 1982. In other e/sup +/e/sup -/ experiments, the Mark II detector continued its productive data-taking at PEP. In other areas, the final stages of data analysis, particularly for the structure functions, proceeded for the inelastic muon scattering experiment performed at Fermilab, a muon polarimeter experiment was developed and mounted at TRIUMF to probe for the presence of right-handed currents in muon decay, and the design and then construction began of fine-grained hadron calorimeters for the end caps of the Colliding Detector Facility at Fermilab. The Particle Data Group intensified its activities, despite financial constraints, as it proceeded toward production of a new edition of its authoritative Review of Particle Properties early in 1982. During 1981 the Theoretical Physics Group pursued a diverse spectrum of research in its own right and also interacted effectively with the experimental program. Research and development continued on the segmented mirror for the ten-meter telescope proposed by the University of California. Activities in the Computer Science and Mathematics Department encompassed networking, database management, software engineering, and computer graphics, as well as basic research in nonlinear phenomena in combustion and fluid flow.
From classical to quantum mechanics: ``How to translate physical ideas into mathematical language''
Bergeron, H.
2001-09-01
Following previous works by E. Prugovečki [Physica A 91A, 202 (1978) and Stochastic Quantum Mechanics and Quantum Space-time (Reidel, Dordrecht, 1986)] on common features of classical and quantum mechanics, we develop a unified mathematical framework for classical and quantum mechanics (based on L2-spaces over classical phase space), in order to investigate to what extent quantum mechanics can be obtained as a simple modification of classical mechanics (on both logical and analytical levels). To obtain this unified framework, we split quantum theory in two parts: (i) general quantum axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoints operators, and so on) and (ii) quantum mechanics proper that specifies the Hilbert space as L2(Rn); the Heisenberg rule [pi,qj]=-iℏδij with p=-iℏ∇, the free Hamiltonian H=-ℏ2Δ/2m and so on. We show that general quantum axiomatics (up to a supplementary "axiom of classicity") can be used as a nonstandard mathematical ground to formulate physical ideas and equations of ordinary classical statistical mechanics. So, the question of a "true quantization" with "ℏ" must be seen as an independent physical problem not directly related with quantum formalism. At this stage, we show that this nonstandard formulation of classical mechanics exhibits a new kind of operation that has no classical counterpart: this operation is related to the "quantization process," and we show why quantization physically depends on group theory (the Galilei group). This analytical procedure of quantization replaces the "correspondence principle" (or canonical quantization) and allows us to map classical mechanics into quantum mechanics, giving all operators of quantum dynamics and the Schrödinger equation. The great advantage of this point of view is that quantization is based on concrete physical arguments and not derived from some "pure algebraic rule" (we exhibit also some limit of the correspondence
Karam, E. H.; Srinivasan, R. S.; Charles, J. B.; Fortney, S. M.
1994-01-01
Different mathematical models of varying complexity have been proposed in recent years to study the cardiovascular (CV) system. However, only a few of them specifically address the response to lower body negative pressure (LBNP), a stress that can be applied in weightlessness to predict changes in orthostatic tolerance. Also, the simulated results produced by these models agree only partially with experimental observations. In contrast, the model proposed by Melchior et al., and modified by Karam et al. is a simple representation of the CV system capable of accurately reproducing observed LBNP responses up to presyncopal levels. There are significant changes in LBNP response due to a loss of blood volume and other alterations that occur in weightlessness and related one-g conditions such as bedrest. A few days of bedrest can cause up to 15% blood volume loss (BVL), with consequent decreases in both stroke volume and cardiac output, and increases in heart rate, mean arterial pressure, and total peripheral resistance. These changes are more pronounced at higher levels of LBNP. This paper presents the results of a simulation study using our CV model to examine the effect of BVL on LBNP response.
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.
Directory of Open Access Journals (Sweden)
Sidsel L Domazet
Full Text Available 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
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
Canuto, Claudio
2015-01-01
The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, ...
Some Aspects of Mathematical and Physical Approaches for Topological Quantum Computation
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V. Kantser
2011-10-01
Full Text Available A paradigm to build a quantum computer, based on topological invariants is highlighted. The identities in the ensemble of knots, links and braids originally discovered in relation to topological quantum field theory are shown: how they define Artin braid group -- the mathematical basis of topological quantum computation (TQC. Vector spaces of TQC correspond to associated strings of particle interactions, and TQC operates its calculations on braided strings of special physical quasiparticles -- anyons -- with non-Abelian statistics. The physical platform of TQC is to use the topological quantum numbers of such small groups of anyons as qubits and to perform operations on these qubits by exchanging the anyons, both within the groups that form the qubits and, for multi-qubit gates, between groups. By braiding two or more anyons, they acquire up a topological phase or Berry phase similar to that found in the Aharonov-Bohm effect. Topological matter such as fractional quantum Hall systems and novel discovered topological insulators open the way to form system of anyons -- Majorana fermions -- with the unique property of encoding and processing quantum information in a naturally fault-tolerant way. In the topological insulators, due to its fundamental attribute of topological surface state occurrence of the bound, Majorana fermions are generated at its heterocontact with superconductors. One of the key operations of TQC -- braiding of non-Abelian anyons: it is illustrated how it can be implemented in one-dimensional topological isolator wire networks.
Mathematical and numerical analysis of a few hydrodynamic and kinetic models of plasma physics
International Nuclear Information System (INIS)
Buet, C.
2005-01-01
My research work deals mainly with the mathematical modelling and the numerical simulation of plasma physics. This document is divided into 3 parts. The first one is a summary of the works done for the numerical solving of collision operators. The common thread of this part is obtaining numerical schemes preserving operators' properties namely physical invariants like mass, momentum and energy, equilibrium states and entropy decrease. These properties are generally checked formally for continuous operators, may give rise to some difficulties for discrete operators. In the second part I present a summary of the works regarding moments methods applied to radiative transfer and the numerical issues dealing with their discretization. The common thread of this part is how to get numerical schemes preserving asymptotic scattering and invariant domains for Lorentz models and also for non-linear telegraph-type equations involved in radiative transfer or electronic plasma. In the third part I present 2 themes linked to collision operators: multi-fluid ionization and the non-existence of linear monotone schemes for some linear parabolic equations
Böhm, Arno; Koizumi, Hiroyasu; Niu, Qian; Zwanziger, Joseph
2003-01-01
Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics) The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them
Dotson, Daniel S.; Franks, Tina P.
2015-01-01
More than 53,000 citations from 609 dissertations published at The Ohio State University between 1998-2012 representing four science disciplines--civil engineering, computer science, mathematics and physics--were examined to determine what, if any, preferences or trends exist. This case study seeks to identify whether or not researcher preferences…
DEFF Research Database (Denmark)
Domazet, Sidsel L; Tarp, Jakob; Huang, Tao
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 gra...
Butkovich, Nancy J.
2015-01-01
Doctoral candidates may request short-term embargoes on the release of their dissertations in order to apply for patents. This study examines how often inventions described in dissertations in chemical engineering, chemistry, physics, and mathematics are converted into U.S. patent applications, as well as the relationship between dissertation…
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…
International Nuclear Information System (INIS)
Mihai, Maria; Popescu, I.V.
2003-01-01
In this paper we report a physical-mathematical model for studying the organs and humans fluids by cybernetic principle. The input variables represent the trace elements which are determined by atomic and nuclear methods of elemental analysis. We have determined the health limits between which the organs might function. (authors)
1978-01-01
Colin B. Bull (1980) College of Mathematical and Physical Bruce A. Taft (1981) Science Department of Oceanography Ohio State University Washington...Gottschalk, Joseph Kestin (1981) and Richard W. Kline Division of Engineering Department of Energy Brown University (Engineering) Harold E. Bamford ...Research and Engineering (Climate dynamics, international Laboratory cooperation) (Arctic ecology, soil science) George Gryc (1981) Colin B. Bull (1980
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…
Computational physics and applied mathematics capability review June 8-10, 2010
Energy Technology Data Exchange (ETDEWEB)
Lee, Stephen R [Los Alamos National Laboratory
2010-01-01
Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the Laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled multi-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CPAM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections), as follows. Theme 1: Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the Laboratory. Theme 2: Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution
Mathematical simulation of water distillation column for decreasing volume of tritiated water
International Nuclear Information System (INIS)
Kinoshita, Masahiro; Naruse, Yuji
1981-12-01
Water distillation is an attractive method for decreasing volume of the tritiated water produced by operation of tritium facilities. The tritiated water is continuously fed to a column and it is separated into two streams. The top stream is discarded to the environment after addition of sufficient amount of uncontaminated water. The bottom stream is further treated for solidification and capsulation. The tridiagonal matrix method proved to provide surprisingly rapid convergences of the calculations. The concentration of deuterium naturally contained in the tritiated water is higher than the tritium concentration, but it was verified that presence of HDO can be ignored in the calculation. (author)
Impact of particle density and initial volume on mathematical compression models
DEFF Research Database (Denmark)
Sonnergaard, Jørn
2000-01-01
In the calculation of the coefficients of compression models for powders either the initial volume or the particle density is introduced as a normalising factor. The influence of these normalising factors is, however, widely different on coefficients derived from the Kawakita, Walker and Heckel...... equations. The problems are illustrated by investigations on compaction profiles of 17 materials with different molecular structures and particle densities. It is shown that the particle density of materials with covalent bonds in the Heckel model acts as a key parameter with a dominating influence...
Novotna, Jarmila, Ed.; Moraova, Hana, Ed.; Kratka, Magdalena, Ed.; Stehlikova, Nad'a, Ed.
2006-01-01
This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…
van den Heuvel-Panhuizen, Marja, Ed.
This document contains the proceedings of the 25th annual Conference of the International Group for the Psychology of Mathematics Education (PME). It features plenary lectures, research forums, discussion groups, working sessions, short oral communications, and poster presentations. Papers in Volume 1 include: (1) "The P in PME: Progress and…
Olivier, Alwyn, Ed.; Newstead, Karen, Ed.
The first volume of this proceedings contains an introduction and the plenary, research forum, working group, and discussion group papers. Papers include: (1) "Resources as a Verb: Recontextualizing Resources in and for School Mathematics" (Jill Adler); (2) "Markets and Standards: The Politics of Education in a Conservative Age" (Michael Apple);…
Puig, Luis, Ed.; Gutierrez, Angel, Ed.
The second volume of this proceedings contains full research articles. Papers include: (1) "Lave and Wenger's social practice theory and teaching and learning school mathematics" (J. Adler); (2) "Being a researcher and being a teacher" (J. Ainley); (3) "Procedural and conceptual aspects of standard algorithms in calculus" (M.B. Ali and D. Tall);…
A course of higher mathematics
Smirnov, Vladimir Ivanovich
1964-01-01
A Course of Higher Mathematics, Volume II: Advanced Calculus covers the theory of functions of real variable in advanced calculus. This volume is divided into seven chapters and begins with a full discussion of the solution of ordinary differential equations with many applications to the treatment of physical problems. This topic is followed by an account of the properties of multiple integrals and of line integrals, with a valuable section on the theory of measurable sets and of multiple integrals. The subsequent chapters deal with the mathematics necessary to the examination of problems in
DNA as information: at the crossroads between biology, mathematics, physics and chemistry.
Cartwright, Julyan H E; Giannerini, Simone; González, Diego L
2016-03-13
On the one hand, biology, chemistry and also physics tell us how the process of translating the genetic information into life could possibly work, but we are still very far from a complete understanding of this process. On the other hand, mathematics and statistics give us methods to describe such natural systems-or parts of them-within a theoretical framework. Also, they provide us with hints and predictions that can be tested at the experimental level. Furthermore, there are peculiar aspects of the management of genetic information that are intimately related to information theory and communication theory. This theme issue is aimed at fostering the discussion on the problem of genetic coding and information through the presentation of different innovative points of view. The aim of the editors is to stimulate discussions and scientific exchange that will lead to new research on why and how life can exist from the point of view of the coding and decoding of genetic information. The present introduction represents the point of view of the editors on the main aspects that could be the subject of future scientific debate. © 2016 The Author(s).
A course in mathematical physics 1 and 2 classical dynamical systems and classical field theory
Thirring, Walter
1992-01-01
The last decade has seen a considerable renaissance in the realm of classical dynamical systems, and many things that may have appeared mathematically overly sophisticated at the time of the first appearance of this textbook have since become the everyday tools of working physicists. This new edition is intended to take this development into account. I have also tried to make the book more readable and to eradicate errors. Since the first edition already contained plenty of material for a one semester course, new material was added only when some of the original could be dropped or simplified. Even so, it was necessary to expand the chap ter with the proof of the K-A-M Theorem to make allowances for the cur rent trend in physics. This involved not only the use of more refined mathe matical tools, but also a reevaluation of the word "fundamental. " What was earlier dismissed as a grubby calculation is now seen as the consequence of a deep principle. Even Kepler's laws, which determine the radii of the ...
Computer Hardware, Advanced Mathematics and Model Physics pilot project final report
International Nuclear Information System (INIS)
1992-05-01
The Computer Hardware, Advanced Mathematics and Model Physics (CHAMMP) Program was launched in January, 1990. A principal objective of the program has been to utilize the emerging capabilities of massively parallel scientific computers in the challenge of regional scale predictions of decade-to-century climate change. CHAMMP has already demonstrated the feasibility of achieving a 10,000 fold increase in computational throughput for climate modeling in this decade. What we have also recognized, however, is the need for new algorithms and computer software to capitalize on the radically new computing architectures. This report describes the pilot CHAMMP projects at the DOE National Laboratories and the National Center for Atmospheric Research (NCAR). The pilot projects were selected to identify the principal challenges to CHAMMP and to entrain new scientific computing expertise. The success of some of these projects has aided in the definition of the CHAMMP scientific plan. Many of the papers in this report have been or will be submitted for publication in the open literature. Readers are urged to consult with the authors directly for questions or comments about their papers
Schunicht, Shannon
2010-03-01
This WORLDY recognized mnemonic discovery resulted from this author' head injury (3 weeks unconsciousness). Beginning with some essential Brain Facts to explain how this remarkable discovery was devised: Right hemisphere => Spatial/musical Left hemisphere => Language/Logic This authors education: 2 ea BA degrees => language requirement A hole in the head (right hemisphere) may be spied on the WTVH DVD. The damaged right hemisphere accentuates this author's left hemisphere coupled with 2ea BA degrees that require a language ('83 BA a/Spanish & '94 BA w/Latin). Physical survival may be attributed to US Army RANGER training who Never say die! 10-82, 11-82, & 13 83. Recovery came having to learn EVERYTHING all over again, as I was reported having displayed upon awakening from the extended unconsciousness (19 days). Studies were difficult without a memory, but simple because I had always been forced to learn EVERYTHING MYSELF by mother who was a kindergarten teacher! The residual deficit continues to plague this author: Out of Sight is truly Out of mind! Even for a student whose memory is NOT disabled, memory is difficult. The ``nut's & bolts'' of this presentation are essentially having each Vowel represent a Mathematical operation. A: multiplication => @ O: division => Over I: subraction => mInus U: addition => plUs E: => Equals Most constants and variables are indeed consonants, e.g. c = speed of light z = altitude
Karadagli, Fatih; McAvoy, Drew C; Rittmann, Bruce E
2009-05-01
The processes that flushable solid products may undergo after discharge to wastewater systems are (1) physical disintegration of solids resulting from turbulence, (2) direct dissolution of water-soluble components, (3) hydrolysis of solids to form soluble components, and (4) biodegradation of soluble and insoluble components. We develop a mathematical model for physical disintegration of flushable solid consumer products and test it with two different flushable products--product A, which has 40% water soluble-content, and product B, which has no water-soluble components. We present our modeling analysis of experimental results, from which we computed disintegration rate constants and fractional distribution coefficients for the disintegration of larger solids. The rate constants for solids of product A in units of (hour(-1)) are 0.45 for > 8-mm, 2.25 x 10(-2) for 4- to 8-mm, 0.9 x 10(-2) for 2- to 4-mm, and 1.26 x 10(-2) for 1- to 2-mm solids. The rate constants for solids of product B in units of hour(-1) are 1.8 for > 8-mm, 1.8 for 4- to 8-mm, 3.6 x 10(-1) for 2- to 4-mm, and 2.25 x 10(-3) for 1- to 2-mm solids. As indicated by the rate constants, larger solids disintegrate at a faster rate than smaller solids. In addition, product B disintegrated much faster and went mostly to the smallest size range, while product A disintegrated more slowly and was transferred to a range of intermediate solid sizes.
Mathematical Physics Framework SustainingNatural Anticipation and Selection of Attention
Directory of Open Access Journals (Sweden)
Alfons Salden
2005-04-01
Full Text Available An ambient intelligent environment is definitely a prerequisite for anticipating the needs and catching the attention of systems. But how to endow such an environment with natural anticipatory and attentive features is still a hardly ever properly addressed question. Before providing a roadmap towards such an ambient intelligent environment we first give cognitive-ergonomic accounts for how natural anticipation and selection of attention (NASA emerge in living organisms. In particular, we describe why, when and how exploratory and goal-directed acts by living organisms are controlled while optimizing their changing and limited structural and functional capabilities of multimodal sensor, cognitive and actuator systems. Next, we describe how NASA can be embedded and embodied in sustainable intelligent multimodal systems (SIMS. Such systems allow an ambient intelligent environment to (self- interact taking its contexts into account. In addition, collective intelligent agents (CIA distribute, store, extend, maintain, optimize, diversify and sustain the NASA embedded and embodied in the ambient intelligent environment. Finally, we present the basic ingredients of a mathematical-physical framework for empirically modeling and sustaining NASA within SIMS by CIA in an ambient intelligent environment. An environment which is modeled this way, robustly and reliably over time aligns multi-sensor detection and fusion; multimodal fusion, dialogue planning and fission; multi actuator fission, rendering and presentation schemes. NASA residing in such an environment are then active within every phase of perception-decision-action cycles, and are gauged and renormalized to its physics. After determining and assessing across several evolutionary dynamic scales appropriate fitness, utility and measures, NASA can be realized by reinforcement learning and self-organization.
VOLUME OF PHYSICAL ACTIVITY AND INJURY OCCURRENCE IN YOUNG BASKETBALL PLAYERS
Directory of Open Access Journals (Sweden)
Jenny Gianoudis
2008-03-01
Full Text Available Participation in organised, competitive physical activity by young athletes is increasing rapidly. This is concurrent with an increase in sporting injuries in the young population. This pilot study aimed to compare the weekly volume and types of physical activity in young basketball players injured and not injured during the season. Detailed physical activity and injury data were prospectively collected in 46 school-level basketball players aged 14 to 18 years. Participants completed physical activity logs which documented the type of physical activity undertaken, what the activity consisted of (i.e. training, competition and the level at which it was played on a daily basis. Allied health staff completed a weekly injury form. Results showed that injured and uninjured athletes participated in a similar volume of total weekly physical activity over the season. However, injured athletes (p = 0.04 and athletes who specifically sustained overuse injuries (p = 0.01 participated in a greater amount of basketball refereeing than uninjured athletes. Based on these findings it was concluded that greater participation in running-type physical activity such as refereeing, as an addition to training and competition, may predispose the young basketball player to increased injury risk. Future research using larger sample sizes are required to further investigate the role of participation volume and type on injury occurrence in adolescent athletes
Underhill, Robert G., Ed.
This document, presented in two volumes, reports on a psychology of mathematics education conference, the theme of which was "Theoretical and Conceptual Frameworks in Mathematics Education." The two volumes include 58 papers, descriptions of 4 poster and 2 video presentations, and reports of and reactions to 2 plenary sessions presented…
Chen, B B; Shih, T T F; Hsu, C Y; Yu, C W; Wei, S Y; Chen, C Y; Wu, C H; Chen, C Y
2011-06-01
(1) to correlate thigh muscle volume measured by magnetic resonance image (MRI) with anthropometric measurements and physical function in elderly subjects; (2) to predict MRI-measured thigh muscle volume using anthropometric measurements and physical functional status in elderly subjects. Cross-sectional, nonrandomized study. Outpatient clinic in Taiwan. Sixty-nine elderly subjects (33 men and 36 women) aged 65 and older. The anthropometric data (including body height, body weight, waist size, and thigh circumference), physical activity and function (including grip strength, bilateral quadriceps muscle power, the up and go test, chair rise, and five meters walk time) and bioelectrical impedance analysis data (including total body fat mass, fat-free mass, and predictive muscle size) were measured. MRI-measured muscle volume of both thighs was used as the reference standard. The MRI-measured thigh volume was positively correlated with all anthropometric data, quadriceps muscle power and the up and go test as well as fat-free mass and predictive muscle mass, whereas it was negatively associated with age and walk time. In predicting thigh muscle volume, the variables of age, gender, body weight, and thigh circumference were significant predictors in the linear regression model: Muscle volume (cm3) =4226.3－42.5 × Age (year)－955.7 × gender (male=1, female=2) + 45.9 × body weight(kg) + 60.0 × thigh circumference (cm) (r2 = 0.745, P estimate = 581.6 cm3). The current work provides evidence of a strong relationship between thigh muscle volume and physical function in the elderly. We also developed a prediction equation model using anthropometric measurements. This model is a simple and noninvasive method for everyday clinical practice and follow-up.
International Conference on Applied Mathematics and Informatics
Vasilieva, Olga
2015-01-01
This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applications to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues—as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.
Proceedings of the 1992 topical meeting on advances in reactor physics. Volume 2
Energy Technology Data Exchange (ETDEWEB)
1992-04-01
This document, Volume 2, presents proceedings of the 1992 Topical Meeting on Advances in Reactor Physics on March 8--11, 1992 at Charleston, SC. Session topics were as follows: Transport Theory; Fast Reactors; Plant Analyzers; Integral Experiments/Measurements & Analysis; Core Computational Systems; Reactor Physics; Monte Carlo; Safety Aspects of Heavy Water Reactors; and Space-Time Core Kinetics. The individual reports have been cataloged separately. (FI)
2011-11-01
What causes an ice skater to accelerate? Hugh Fricker Note on the definitions of weight Nenad Stojilovic A-level physics is mathematical enough Helen Hare Correction to 'Confusion over the physics of circular motion'
Winkel, Brian
2012-01-01
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)
Pappas, Theoni
1997-01-01
In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions
Stroud, K A
2013-01-01
A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.
Fusion Engineering Device. Volume IV. Physics basis and physics R and D requirements
International Nuclear Information System (INIS)
1981-10-01
This volume covers the following issues: (1) confinement scaling, (2) cross section shaping, limits on B and q, (3) ion cyclotron heating, (4) neutral beam heating, (5) mechanical pump limiter, (6) poloidal divertor, and (7) non-divertor active impurity control
Weight, Volume, and Physical Properties of Major Hardwood Species in the Upland-South
Alexander Clark; Douglas R. Phillips; Douglas J. Frederick
1986-01-01
The weight, volume, and physical properties oftrees1 to 20 inchesd.b.h.were determined for sweetgum, yellow-poplar, hickory, post oak, scarlet oak, southern red oak, and white oakin northern Alabama and Mississippi, eastern Arkansas, southern Kentucky and Tennessee. Hard hardwoods, soft hardwoods, and individual species equations are presented for predicting green and...
Weight, Volume, and Physical Properties of Major Hardwood Species in the Piedmont
Alexander Clark; Douglas R. Phillips; Douglas J. Frederick
1986-01-01
Weight, volume, and physical properties of trees 1 to 20 inches d.b.h.were determined for red maple, sweetgum, sycamore, yellow-poplar, elm, hickory, chestnut oak, scarlet oak, southern red oak, and white oak in the Piedmont of the Southeastern United States. A total of 772 trees were destructively sampled at 16 locations from Viryinia to Alabama. Hard hardwoods, soft...
P.J. Radtke; D.M. Walker; A.R. Weiskittel; J. Frank; J.W. Coulston; J.A. Westfall
2015-01-01
Forest mensurationists in the United States have expended considerable effort over the past century making detailed observations of treesâ dimensions. In recent decades efforts have focused increasingly on weights and physical properties. Work is underway to compile original measurements from past volume, taper, and weight or biomass studies for North American tree...
The influences of the physical-chemical factors on the free-volume relations in polymers
International Nuclear Information System (INIS)
Bartos, J.; Kristiak, J.; Kristiakova, K.; Sausa, O.; Bandzuch, P.
1995-01-01
The positron annihilation spectroscopy was used to the study of different physical-chemical factors on the free-volume microstructure of the model polymeric systems [amorphous 1,4-cis-poly(butadiene), amorphous a-tactic and semi-crystal iso-tactic poly(propylene), polycarbonate
Bone mineral density across a range of physical activity volumes: NHANES 2007-2010.
Whitfield, Geoffrey P; Kohrt, Wendy M; Pettee Gabriel, Kelley K; Rahbar, Mohammad H; Kohl, Harold W
2015-02-01
The association between aerobic physical activity volume and bone mineral density (BMD) is not completely understood. The purpose of this study was to clarify the association between BMD and aerobic activity across a broad range of activity volumes, particularly volumes between those recommended in the 2008 Physical Activity Guidelines for Americans and those of trained endurance athletes. Data from the 2007-2010 National Health and Nutrition Examination Survey were used to quantify the association between reported physical activity and BMD at the lumbar spine and proximal femur across the entire range of activity volumes reported by US adults. Participants were categorized into multiples of the minimum guideline-recommended volume based on reported moderate- and vigorous-intensity leisure activity. Lumbar and proximal femur BMD were assessed with dual-energy x-ray absorptiometry. Among women, multivariable-adjusted linear regression analyses revealed no significant differences in lumbar BMD across activity categories, whereas proximal femur BMD was significantly higher among those who exceeded the guidelines by 2-4 times than those who reported no activity. Among men, multivariable-adjusted BMD at both sites neared its highest values among those who exceeded the guidelines by at least 4 times and was not progressively higher with additional activity. Logistic regression estimating the odds of low BMD generally echoed the linear regression results. The association between physical activity volume and BMD is complex. Among women, exceeding guidelines by 2-4 times may be important for maximizing BMD at the proximal femur, whereas among men, exceeding guidelines by ≥4 times may be beneficial for lumbar and proximal femur BMD.
Energy Technology Data Exchange (ETDEWEB)
Belloni, M., E-mail: mabelloni@davidson.edu [Physics Department, Davidson College, Davidson, NC 28035 (United States); Robinett, R.W., E-mail: rick@phys.psu.edu [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States)
2014-07-01
The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems.
Medina, L; Ley Koo, E
2008-01-01
This article illustrates a practical way to connect and coordinate the teaching and learning of physics and mathematics. The starting point is the electrostatic potential, which is obtained in any introductory course of electromagnetism from the Coulomb potential and the superposition principle for any charge distribution. The necessity to develop solutions to the Laplace and Poisson differential equations is also recognized, identifying the Coulomb potential as the generating function of har...
International Nuclear Information System (INIS)
Machado, Alessandra S.; Lima, Inaya; Lopes, Ricardo T.
2013-01-01
X-ray transmission micro-computed tomography technique is a reality for characterization of pores spaces and fractures. Imaging rocks in three-dimensions this technique enables routine visualization of structures in samples, which can be spatially resolved down to the sub-micron scale. The image of micro-computed tomography is a mapping of the linear attenuation coefficient of one cross section of the sample in study. The main objective of this work is to describe the importance of using mathematical filters in the volume measurement of a travertine sample as, well as to evaluate the relevance of the filters, which were: Gaussian Blur, Unsharp Mask, Median, Uniform and Kuwahara. The results showed interesting differences both among the different filters and, mainly, in the same filter when using different radius and, also, for analysis of 2D space, as well as the resulting histograms. However the study showed that even with the evolution of the 'upgrades' of the image there is not a technique capable of solving 100% of the problems that a digital image might present and that the choice of filters must always determine the characteristics of the image emphasizing them within a specific application, always taking into consideration the image processing time. (author)
Jamil, Norazaliza Mohd; Wang, Qi
2017-09-01
Renewable energy or biofuel from lignocellulosic biomass is an alternative way to replace the depleting fossil fuels. The production cost can be reduced by increasing the concentration of biomass particles. However, lignocellulosic biomass is a suspension of natural fibres, and processing at high solid concentration is a challenging task. Thus, understanding the factors that affect the rheology of biomass suspension is crucial in order to maximize the production at a minimum cost. Our aim was to develop a mathematical model for enzymatic hydrolysis of cellulose by combining three scales: the macroscopic flow field, the mesoscopic particle orientation, and the microscopic reactive kinetics. The governing equations for the flow field, particle stress, kinetic equations, and particle orientation were coupled and were simultaneously solved using a finite element method based software, COMSOL. One of the main results was the changes in rheology of biomass suspension were not only due to the decrease in volume fraction of particles, but also due the types of fibres. The results from the simulation model agreed qualitatively with the experimental findings. This approach has enables us to obtain better predictive capabilities, hence increasing our understanding on the behaviour of biomass suspension.
Study of the asymptotic expansion of multiple integrals in mathematical physics
International Nuclear Information System (INIS)
Chako, N.
1968-01-01
We have applied the method of stationary phase to evaluate double and multiple integrals of the type: (A) U(k) = g(x)e ikφ(x) d(x), (x)=(x 1 ,..., x n ) for large values of the parameter k. In the first part we have established in a rigorous manner the stationary phase method to double and multiple integrals of type (A). Furthermore we have obtained an asymptotic expansion of (A), if the amplitude and phase functions can be developed in a canonical form near the vicinity of critical or stationary points of the integral. This development contains as particular cases all those which are important in physical applications, especially, to diffraction and scattering of electromagnetic and corpuscular waves by optical systems, diffracting bodies and potential scatterers. In the second part we have considered the problem of convergence of the expansion of the principal contribution to the integral in the asymptotic sense of Poincare. The proof is based on the increasing method used in mathematical analysis. The third part is devoted to the derivation of various asymptotic series due to different types of critical or stationary points associated with the amplitude and phase functions. In the fourth part we have generalized the method to multiple integrals and to the case where the parameter k enter implicitly in the phase function The latter type of integrals extend the scope of the former type to a number of important physical problems; for instance, to the propagation of waves in dispersive and absorbing media. In the last chapter we have made a study and compared the results obtained by the application of the stationary phase method to the integrals (double) of diffraction and the results derived by using the Young-Rubinowicz method. Result of our analysis shows the equivalence of the two methods of approach to the problems of diffraction based, on one hand, on the Fresnel-Kirchhoff theory and, on the other hand, the Young-Rubinowicz theory, provided one interprets in
Directory of Open Access Journals (Sweden)
Luis Rojas-Torres
2014-09-01
Full Text Available This paper summarizes a study conducted in 2013 with the purpose of predicting the failure rate of math courses taken by Pharmacy, Mathematics, Actuarial Science, Physics and Meteorology students at Universidad de Costa Rica (UCR. Using the Logistics Regression statistical techniques applied to the 2010 cohort, failure rates were predicted of students in the aforementioned programs in one of their Math introductory courses (Calculus 101 for Physics and Meteorology, Math Principles for Mathematics and Actuarial Science and Applied Differential Equations for Pharmacy. For these models, the UCR admission average, the student’s genre, and the average correct answers in the Quantitative Skills Test were used as predictor variables. The most important variable for all models was the Quantitative Skills Test, and the model with the highest correct classification rate was the Logistics Regression. For the estimated Physics-Meteorology, Pharmacy and Mathematics-Actuarial Science models, correct classifications were 89.8%, 73.6%, and 93.9%, respectively.
International Nuclear Information System (INIS)
Wit, B. de; Morier-Genoud, S.; Ovsienko, V.; Lopes Cardoso, G.; Mahapatra, S.; Sundell, P.; Boulanger, N.; Gava, E.; Karndumri, P.; Narain, K.S.; Theis, U.; Tomasiello, A.; Slizovskiy, S.; Roytenberg, D.; Voronov, T.
2011-01-01
This workshop was dedicated to supersymmetry, supergravity, topological field theories and their mathematical formulations. This document is composed of a large part of the slides presented at the workshop
Churilla, James R; Fitzhugh, Eugene C
2012-02-01
This study examined the association of total physical activity volume (TPAV) and physical activity (PA) from three domains [leisure-time physical activity (LTPA), domestic, transportation] with metabolic syndrome. We also investigated the relationship between LTPA intensity and metabolic syndrome risk. Sample included adults who participated in the 1999-2004 National Health and Nutrition Examination Survey. Physical activity measures were created for TPAV, LTPA, domestic PA, and transportational PA. For each, a six-level measure based upon no PA (level 1) and quintiles (levels 2-6) of metabolic equivalents (MET)·min·wk(-1) was created. A three-level variable associated with the current Department of Health and Human Services (DHHS) PA recommendation was also created. SAS and SUDAAN were used for the statistical analysis. Adults reporting the greatest volume of TPAV and LTPA were found to be 36% [odds ratio (OR) 0.64; 95% confidence interval (CI) 0.49-0.83] and 42% (OR 0.58; 95% CI 0.43-0.77), respectively, less likely to have metabolic syndrome. Domestic and transportational PA provided no specific level of protection from metabolic syndrome. Those reporting a TPAV that met the DHHS PA recommendation were found to be 33% (OR 0.67; 95%; CI 0.55-0.83) less likely to have metabolic syndrome compared to their sedentary counterparts. Adults reporting engaging in only vigorous-intensity LTPA were found to be 37% (OR 0.63; 95 CI 0.42-0.96) to 56% (OR 0.44; 95% CI 0.29-0.67) less likely to have metabolic syndrome. Volume, intensity, and domain of PA may all play important roles in reducing the prevalence and risk of metabolic syndrome.
Kaski, K.; Salomaa, M.
1990-01-01
These are Proceedings of the Third Nordic Symposium on Computer Simulation in Physics, Chemistry, Biology, and Mathematics, held August 25-26, 1989, at Lahti (Finland). The Symposium belongs to an annual series of Meetings, the first one of which was arranged in 1987 at Lund (Sweden) and the second one in 1988 at Kolle-Kolle near Copenhagen (Denmark). Although these Symposia have thus far been essentially Nordic events, their international character has increased significantly; the trend is vividly reflected through contributions in the present Topical Issue. The interdisciplinary nature of Computational Science is central to the activity; this fundamental aspect is also responsible, in an essential way, for its rapidly increasing impact. Crucially important to a wide spectrum of superficially disparate fields is the common need for extensive - and often quite demanding - computational modelling. For such theoretical models, no closed-form (analytical) solutions are available or they would be extremely difficult to find; hence one must rather resort to the Art of performing computational investigations. Among the unifying features in the computational research are the methods of simulation employed; methods which frequently are quite closely related with each other even for faculties of science that are quite unrelated. Computer simulation in Natural Sciences is presently apprehended as a discipline on its own right, occupying a broad region somewhere between the experimental and theoretical methods, but also partially overlapping with and complementing them. - Whichever its proper definition may be, the computational approach serves as a novel and an extremely versatile tool with which one can equally well perform "pure" experimental modelling and conduct "computational theory". Computational studies that have earlier been made possible only through supercomputers have opened unexpected, as well as exciting, novel frontiers equally in mathematics (e.g., fractals
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…
Barton, Bill, Ed.; Irwin, Kathryn C., Ed.; Pfannkuch, Maxine, Ed.; Thomas, Michael O. J., Ed.
This document contains the proceedings of the 25th annual conference of the Mathematics Education Research Group of Australia (MERGA) held at the University of Auckland, New Zealand. The focus of this meeting is mathematics education in the South Pacific. Presentations are centered around the topic of numeracy in primary or elementary school.…
International Conference on Mathematical Sciences and Statistics 2013 : Selected Papers
Leong, Wah; Eshkuvatov, Zainidin
2014-01-01
This volume is devoted to the most recent discoveries in mathematics and statistics. It also serves as a platform for knowledge and information exchange between experts from industrial and academic sectors. The book covers a wide range of topics, including mathematical analyses, probability, statistics, algebra, geometry, mathematical physics, wave propagation, stochastic processes, ordinary and partial differential equations, boundary value problems, linear operators, cybernetics and number and functional theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists.
Representative volume size: A comparison of statistical continuum mechanics and statistical physics
Energy Technology Data Exchange (ETDEWEB)
AIDUN,JOHN B.; TRUCANO,TIMOTHY G.; LO,CHI S.; FYE,RICHARD M.
1999-05-01
In this combination background and position paper, the authors argue that careful work is needed to develop accurate methods for relating the results of fine-scale numerical simulations of material processes to meaningful values of macroscopic properties for use in constitutive models suitable for finite element solid mechanics simulations. To provide a definite context for this discussion, the problem is couched in terms of the lack of general objective criteria for identifying the size of the representative volume (RV) of a material. The objective of this report is to lay out at least the beginnings of an approach for applying results and methods from statistical physics to develop concepts and tools necessary for determining the RV size, as well as alternatives to RV volume-averaging for situations in which the RV is unmanageably large. The background necessary to understand the pertinent issues and statistical physics concepts is presented.
Catalog of physical protection equipment. Book 1: Volume I. Barriers and structural components
International Nuclear Information System (INIS)
Haberman, W.
1977-06-01
A catalog of commercially available physical protection equipment has been prepared for use by the U.S. Nuclear Regulatory Commission (NRC). Included is information on barrier structures and equipment, interior and exterior intrusion detection sensors, entry (access) control devices, surveillance and alarm assessment equipment, contraband detection sensors, automated response equipment, general purpose displays and general purpose communications, with one volume devoted to each of these eight areas. For each item of equipment the information included consists of performance, physical, cost and supply/logistics data. The entire catalog is contained in three notebooks for ease in its use by licensing and inspection staff at NRC
Catalog of physical protection equipment. Book 3: Volume VII. General purpose display components
International Nuclear Information System (INIS)
1977-06-01
A catalog of commercially available physical protection equipment has been prepared under MITRE contract AT(49-24)-0376 for use by the U. S. Nuclear Regulatory Commission (NRC). Included is information on barrier structures and equipment, interior and exterior intrusion detection sensors, entry (access) control devices, surveillance and alarm assessment equipment, contraband detection sensors, automated response equipment, general purpose displays and general purpose communications, with one volume devoted to each of these eight areas. For each item of equipment the information included consists of performance, physical, cost and supply/logistics data. The entire catalog is contained in three notebooks for ease in its use by licensing and inspection staff at NRC
The physics benchmark processes for the detector performance studies used in CLIC CDR Volume 3
Allanach, B.J.; Desch, K.; Ellis, J.; Giudice, G.; Grefe, C.; Kraml, S.; Lastovicka, T.; Linssen, L.; Marschall, J.; Martin, S.P.; Muennich, A.; Poss, S.; Roloff, P.; Simon, F.; Strube, J.; Thomson, M.; Wells, J.D.
2012-01-01
This note describes the detector benchmark processes used in volume 3 of the CLIC conceptual design report (CDR), which explores a staged construction and operation of the CLIC accelerator. The goal of the detector benchmark studies is to assess the performance of the CLIC ILD and CLIC SiD detector concepts for different physics processes and at a few CLIC centre-of-mass energies.
Chowdhury, Mohammad Mahfuz; Fujii, Teruo; Sakai, Yasuyuki
2013-07-01
In our previous studies, we observed that cell-secreted BMP4 had a prominent influence on mouse embryonic stem cell (mESC) behaviors in a membrane-based two-chambered microbioreactor (MB), but not in a macro-scale culture (6-well plate/6WP). In this study, we investigated how the physical aspects of these cultures regulated BMP4 signaling by developing mathematical models of the cultures. The models estimated signaling activity in the cultures by considering size of the undifferentiated mESC colonies and their growth, diffusion of BMP4, and BMP4 trafficking process in the colonies. The models successfully depicted measured profile of BMP4 concentration in the culture medium which was two times higher in the MB than that in the 6WP during 5-day culture. The models estimated that, owing to the small volume and the membrane, cells were exposed to a higher BMP4 concentration in the top chamber of the MB than that in the 6WP culture. The higher concentration of BMP4 induced a higher concentration of BMP4-bound receptor in the colony in the MB than in the 6WP, thereby leading to the higher activation of BMP4 signaling in the MB. The models also predicted that the size of the MB, but not that of the 6WP, was suitable for maximizing BMP4 accumulation and upregulating its signaling. This study will be helpful in analyzing culture systems, designing microfluidic devices for controlling ESC or other cell behavior. Copyright © 2013 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
On the Ability To Infer Deficiency in Mathematics From Performance in Physics Using Hierarchies
Riban, David M.
1971-01-01
Presents the procedures, results, and conclusions of a study designed to see if mathematical deficiencies can be inferred from PSSC students' performance by using a hierarchical model of requisite skills. Assuming inferences were possible, remediation was given. No effect due to remediation was observed but analysis indicated incidental learning…
International Nuclear Information System (INIS)
Huang, J H; Wang, X J; Wang, J
2016-01-01
The primary purpose of this paper is to propose a mathematical model of PLZT ceramic with coupled multi-physics fields, e.g. thermal, electric, mechanical and light field. To this end, the coupling relationships of multi-physics fields and the mechanism of some effects resulting in the photostrictive effect are analyzed theoretically, based on which a mathematical model considering coupled multi-physics fields is established. According to the analysis and experimental results, the mathematical model can explain the hysteresis phenomenon and the variation trend of the photo-induced voltage very well and is in agreement with the experimental curves. In addition, the PLZT bimorph is applied as an energy transducer for a photovoltaic–electrostatic hybrid actuated micromirror, and the relation of the rotation angle and the photo-induced voltage is discussed based on the novel photostrictive mathematical model. (paper)
Exceptional structures in mathematics and physics and the role of the octonions
International Nuclear Information System (INIS)
Toppan, Francesco
2003-12-01
There is a growing interest in the logical possibility that exceptional mathematical structures (exceptional Lie and super Lie algebras, the exceptional Jordan algebra, etc.) could be linked to an ultimate 'exceptional' formulation for a Theory Of Everything (TOE). The maximal division algebra of the octonions can be held as the mathematical responsible for the existence of the exceptional structures mentioned above. In this context it is quite motivating to systematically investigate the properties of octonionic spinors and the octonionic realizations of supersymmetry. In particular the M-algebra can be consistently defined for two structures only, a real structure, leading to the standard M-algebra, and an octonionic structure. The octonionic version of the M-algebra admits striking properties induced by octonionic p-forms identities. (author)
Exceptional structures in mathematics and physics and the role of the octonions
Energy Technology Data Exchange (ETDEWEB)
Toppan, Francesco
2003-12-15
There is a growing interest in the logical possibility that exceptional mathematical structures (exceptional Lie and super Lie algebras, the exceptional Jordan algebra, etc.) could be linked to an ultimate 'exceptional' formulation for a Theory Of Everything (TOE). The maximal division algebra of the octonions can be held as the mathematical responsible for the existence of the exceptional structures mentioned above. In this context it is quite motivating to systematically investigate the properties of octonionic spinors and the octonionic realizations of supersymmetry. In particular the M-algebra can be consistently defined for two structures only, a real structure, leading to the standard M-algebra, and an octonionic structure. The octonionic version of the M-algebra admits striking properties induced by octonionic p-forms identities. (author)
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…
Michaluk, Lynnette; Stoiko, Rachel; Stewart, Gay; Stewart, John
2018-04-01
Elementary teachers often hold inaccurate beliefs about the Nature of Science (NoS) and have negative attitudes toward science and mathematics. Using a pre-post design, the current study examined beliefs about the NoS, attitudes toward science and mathematics, and beliefs about the teaching of mathematics and science in a large sample study ( N = 343) of pre-service teachers receiving a curriculum-wide intervention to improve these factors in comparison with Science, Technology, Engineering, and Mathematics (STEM) and non-STEM majors in other physics courses ( N = 6697) who did not receive the intervention, over a 10-year period. Pre-service teachers evidenced initially more negative attitudes about mathematics and science than STEM majors and slightly more positive attitudes than non-STEM majors. Their attitudes toward mathematics and science and beliefs about the NoS were more similar to non-STEM than STEM majors. Pre-service teachers initially evidenced more positive beliefs about the teaching of mathematics and science, and their beliefs even increased slightly over the course of the semester, while these beliefs in other groups remained the same. Beliefs about the NoS and the teaching of mathematics and science were significantly negatively correlated for STEM and non-STEM majors, but were not significantly correlated for pre-service teachers. Beliefs about the NoS and attitudes toward mathematics and science were significantly positively correlated for both pre-service teachers and STEM students pursing the most mathematically demanding STEM majors. Attitudes toward science and mathematics were significantly positively correlated with accurate beliefs about the teaching of mathematics and science for all student groups.
Directory of Open Access Journals (Sweden)
Yohan Godoy
2018-01-01
Full Text Available For this work, a constructivist didactic proposal was designed in which the students of the third year of General Media Education can acquire a significant learning in the use of Scientific Notation. The type of research used is among feasible projects with a non-experimental field design. For data collection, the survey technique was used, which was applied to 43 students of the Physics subject of the third year of the Liceo Rosario Almarza Trujillo-Venezuela. The analysis of the results indicated that they present deficiencies in terms of significant numbers and order magnitude, which are essential mathematical aspects for the understanding and use of Scientific Notation in the area of Physics, as well as highlighting the need for Implement other teaching and learning strategies, such as a series of complementary activities for the teacher in the classroom or the student. In view of these results, a didactic guide was carried out using the known mathematical aspects and various ludic activities to extend the notion and use of scientific notation.
Physics of laser fusion. Volume II. Diagnostics of experiments on laser fusion targets at LLNL
Energy Technology Data Exchange (ETDEWEB)
Ahlstrom, H.G.
1982-01-01
These notes present the experimental basis and status for laser fusion as developed at LLNL. There are two other volumes in this series: Vol. I, by C.E. Max, presents the theoretical laser-plasma interaction physics; Vol. III, by J.F. Holzrichter et al., presents the theory and design of high-power pulsed lasers. A fourth volume will present the theoretical implosion physics. The notes consist of six sections. The first, an introductory section, provides some of the history of inertial fusion and a simple explanation of the concepts involved. The second section presents an extensive discussion of diagnostic instrumentation used in the LLNL Laser Fusion Program. The third section is a presentation of laser facilities and capabilities at LLNL. The purpose here is to define capability, not to derive how it was obtained. The fourth and fifth sections present the experimental data on laser-plasma interaction and implosion physics. The last chapter is a short projection of the future.
Physics of laser fusion. Volume II. Diagnostics of experiments on laser fusion targets at LLNL
International Nuclear Information System (INIS)
Ahlstrom, H.G.
1982-01-01
These notes present the experimental basis and status for laser fusion as developed at LLNL. There are two other volumes in this series: Vol. I, by C.E. Max, presents the theoretical laser-plasma interaction physics; Vol. III, by J.F. Holzrichter et al., presents the theory and design of high-power pulsed lasers. A fourth volume will present the theoretical implosion physics. The notes consist of six sections. The first, an introductory section, provides some of the history of inertial fusion and a simple explanation of the concepts involved. The second section presents an extensive discussion of diagnostic instrumentation used in the LLNL Laser Fusion Program. The third section is a presentation of laser facilities and capabilities at LLNL. The purpose here is to define capability, not to derive how it was obtained. The fourth and fifth sections present the experimental data on laser-plasma interaction and implosion physics. The last chapter is a short projection of the future
Inverting seismic data for rock physical properties; Mathematical background and application
Energy Technology Data Exchange (ETDEWEB)
Farfour, Mohammed; Yoon, Wang Jung; Kim, Jinmo [Geophysical Prospecting Lab, Energy & Resources Eng., Dept., Chonnam National University, Gwangju (Korea, Republic of); Lee, Jeong-Hwan [Petroleum Engineering & Reservoir Simulation Lab, Energy & Resources Eng., Dept., Chonnam National University, Gwangju (Korea, Republic of)
2016-06-08
The basic concept behind seismic inversion is that mathematical assumptions can be established to relate seismic to geological formation properties that caused their seismic responses. In this presentation we address some widely used seismic inversion method in hydrocarbon reservoirs identification and characterization. A successful use of the inversion in real example from gas sand reservoir in Boonsville field, Noth Central Texas is presented. Seismic data was not unambiguous indicator of reservoir facies distribution. The use of the inversion led to remove the ambiguity and reveal clear information about the target.
Technical area status report for chemical/physical treatment. Volume 2, Appendices
Energy Technology Data Exchange (ETDEWEB)
Brown, C.H. Jr. [Oak Ridge National Lab., TN (United States); Schwinkendorf, W.E. [BDM Federal, Inc., Arlington, VA (United States)
1993-08-01
These Appendices describe various technologies that may be applicable to the Mixed Waste Treatment Plant (MWTP) Chemical/Physical Treatment System (CPTS). These technologies were identified by the CPTS Technical Support Group (TSG) as potentially applicable to a variety of separation, volume reduction, and decontamination requirements. The purpose was to identify all available and developing technologies, and their characteristics, for subsequent evaluation for specific requirements identified for the CPTS. However, the technologies described herein are not necessarily all inclusive, nor are they necessarily all applicable.
Theoretical physics 8 statistical physics
Nolting, Wolfgang
2018-01-01
This textbook offers a clear and comprehensive introduction to statistical physics, one of the core components of advanced undergraduate physics courses. It follows on naturally from the previous volumes in this series, using methods of probability theory and statistics to solve physical problems. The first part of the book gives a detailed overview on classical statistical physics and introduces all mathematical tools needed. The second part of the book covers topics related to quantized states, gives a thorough introduction to quantum statistics, followed by a concise treatment of quantum gases. Ideally suited to undergraduate students with some grounding in quantum mechanics, the book is enhanced throughout with learning features such as boxed inserts and chapter summaries, with key mathematical derivations highlighted to aid understanding. The text is supported by numerous worked examples and end of chapter problem sets. About the Theoretical Physics series Translated from the renowned and highly successf...
Sneyd, James
2009-01-01
There has been a long history of interaction between mathematics and physiology. This book looks in detail at a wide selection of mathematical models in physiology, showing how physiological problems can be formulated and studied mathematically, and how such models give rise to interesting and challenging mathematical questions. With its coverage of many recent models it gives an overview of the field, while many older models are also discussed, to put the modern work in context. In this second edition the coverage of basic principles has been expanded to include such topics as stochastic differential equations, Markov models and Gibbs free energy, and the selection of models has also been expanded to include some of the basic models of fluid transport, respiration/perfusion, blood diseases, molecular motors, smooth muscle, neuroendrocine cells, the baroreceptor loop, turboglomerular oscillations, blood clotting and the retina. Owing to this extensive coverage, the second edition is published in two volumes. ...
The mathematics of geometrical and physical optics. The k-funktion and its ramifications
Energy Technology Data Exchange (ETDEWEB)
Stavroudis, O.N. [Centro de Investigaciones en Optica, Leon, Guanajuato (Mexico)
2006-07-01
In this sequel to his book, 'The Optics of Rays, Wavefronts, and Caustics', Stavroudis not only covers his own research results, but also includes more recent developments. The book is divided into three parts, starting with basic mathematical concepts that are further applied in the book. Surface geometry is treated with classical mathematics, while the second part covers the k-function, discussing and solving the eikonal equation as well as Maxwell equations in this context. A final part on applications consists of conclusions drawn or developed in the first two parts of the book, discussing such topics as the Cartesian oval, the modern Schiefspiegler, Huygen's principle, and Maxwell's model of Gauss' perfect lens. From the contents: Part I: Preliminaries - Calculus of variations - Calculus of variations: differential geometry of space curves (helix and ellipse) - Fermat's principle and the ray equation for inhomogeneous isotropic media - Hilbert integral, the derivation of the Hamilton-Jacobi theory, and the eikonal equation - First-order partial differential equations. Part II: The k-Function - Calculation of surface differential geometry parameters - Ray tracing - Refraction of wavefronts at surfaces - Solution of the Maxwell equation in the context of the k-function. Part III: Applications - Pseudo Maxwell equations - Derivation and discussion of the Cartesian oval - The modern Schiefspiegler - Huygen's principle - Maxwell's model of Gauss' perfect lens. (orig.)
Guide for the evaluation of physical protection equipment. Book 1: Volumes I--III
International Nuclear Information System (INIS)
Haberman, W.
1977-06-01
A guide for evaluating the performance of commercially available physical protection equipment has been prepared in partial fulfillment of Task 2 of MITRE contract AT(49-24)-0376 for use by the U.S. Nuclear Regulatory Commission (NRC). Separate evaluation procedures are provided for each generic type of equipment contained in the companion document, Catalog of Physical Protection Equipment. Among the equipment parameters evaluated, as appropriate, are sensitivity, area/volume of coverage, false/nuisance alarm rate, resistance to countermeasures, environmental requirements, installation parameters and maintenance. Four evaluation techniques are employed (inspections, analyses, demonstrations and tests); standard test equipment (both commercially available as well as developmental) to be used in the evaluation are listed
Guide for the evaluation of physical protection equipment. Book 2: Volumes IV--VIII
International Nuclear Information System (INIS)
Haberman, W.
1977-06-01
A guide for evaluating the performance of commercially available physical protection equipment has been prepared for use by U.S. NRC. Separate evaluation procedures are provided for each generic type of equipment contained in the companion document, Catalog of Physical Protection Equipment (NUREG-0274). Among the equipment parameters evaluated are sensitivity, area/volume of coverage, false/nuisance alarm rate, resistance to countermeasures, environmental requirements, installation parameters and maintenance. Four evaluation techniques are employed (inspections, analyses, demonstrations and tests); standard test equipment (both commercially available as well as developmental) to be used in the evaluation is listed. The following categories of equipment are covered: surveillance and alarm assessment components, contraband detection components, automated response components, general purpose display components, and general purpose communication components
Canuto, Claudio
2015-01-01
The purpose of the volume is to provide a support for a first course in Mathematics. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level requires the additional study of ...
Target Volume Delineation in Oropharyngeal Cancer: Impact of PET, MRI, and Physical Examination
International Nuclear Information System (INIS)
Thiagarajan, Anuradha; Caria, Nicola; Schöder, Heiko; Iyer, N. Gopalakrishna; Wolden, Suzanne; Wong, Richard J.; Sherman, Eric; Fury, Matthew G.; Lee, Nancy
2012-01-01
Introduction: Sole utilization of computed tomography (CT) scans in gross tumor volume (GTV) delineation for head-and-neck cancers is subject to inaccuracies. This study aims to evaluate contributions of magnetic resonance imaging (MRI), positron emission tomography (PET), and physical examination (PE) to GTV delineation in oropharyngeal cancer (OPC). Methods: Forty-one patients with OPC were studied. All underwent contrast-enhanced CT simulation scans (CECTs) that were registered with pretreatment PETs and MRIs. For each patient, three sets of primary and nodal GTV were contoured. First, reference GTVs (GTVref) were contoured by the treating radiation oncologist (RO) using CT, MRI, PET, and PE findings. Additional GTVs were created using fused CT/PET scans (GTVctpet) and CT/MRI scans (GTVctmr) by two other ROs blinded to GTVref. To compare GTVs, concordance indices (CI) were calculated by dividing the respective overlap volumes by overall volumes. To evaluate the contribution of PE, composite GTVs derived from CT, MRI, and PET (GTVctpetmr) were compared with GTVref. Results: For primary tumors, GTVref was significantly larger than GTVctpet and GTVctmr (p 0.75), indicating that although the modalities were complementary, the added benefit was small in the context of CECTs. In addition, PE did not aid greatly in nodal GTV delineation. Conclusion: PET and MRI are complementary and combined use is ideal. However, the low CI (ctpetmr vs. ref) particularly for primary tumors underscores the limitations of defining GTVs using imaging alone. PE is invaluable and must be incorporated.
Mathematics and quantum mechanics
International Nuclear Information System (INIS)
Santander, M.
2000-01-01
Several episodes in the relation between Mathematics and Quantum Mechanics are discussed; and the emphasis is put in the existence of multiple and sometimes unexpected connections between ideas originating in Mathematics and in Quantum Physics. The question of the unresasonable effectiveness of Mathematics in Physics is also presented in the same light. (Author) 3 refs
Kalanov, Temur Z.
2014-03-01
A critical analysis of the foundations of standard vector calculus is proposed. The methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is proved that the vector calculus is incorrect theory because: (a) it is not based on a correct methodological basis - the unity of formal logic and of rational dialectics; (b) it does not contain the correct definitions of ``movement,'' ``direction'' and ``vector'' (c) it does not take into consideration the dimensions of physical quantities (i.e., number names, denominate numbers, concrete numbers), characterizing the concept of ''physical vector,'' and, therefore, it has no natural-scientific meaning; (d) operations on ``physical vectors'' and the vector calculus propositions relating to the ''physical vectors'' are contrary to formal logic.
Peng, Xiaoguang; McKenna, Gregory B.
2016-04-01
Three important kinetic phenomena have been cataloged by Kovacs in the investigation of molecular glasses during structural recovery or physical aging. These are responses to temperature-jump histories referred to as intrinsic isotherms, asymmetry of approach, and memory effect. Here we use a thermosensitive polystyrene-poly (N -isopropylacrylamide)-poly (acrylic acid) core-shell particle-based dispersion as a colloidal model and by working at a constant number concentration of particles we use temperature changes to create volume-fraction changes. This imposes conditions similar to those defined by Kovacs on the colloidal system. We use creep experiments to probe the physical aging and structural recovery behavior of colloidal glasses in the Kovacs-type histories and compare the results with those seen in molecular glasses. We find that there are similarities in aging dynamics between molecular glasses and colloidal glasses, but differences also persist. For the intrinsic isotherms, the times teq needed for relaxing or evolving into the equilibrium (or stationary) state are relatively insensitive to the volume fraction and the values of teq are longer than the α -relaxation time τα at the same volume fraction. On the other hand, both of these times grow at least exponentially with decreasing temperature in molecular glasses. For the asymmetry of approach, similar nonlinear behavior is observed for both colloidal and molecular glasses. However, the equilibration time teq is the same for both volume-fraction up-jump and down-jump experiments, different from the finding in molecular glasses that it takes longer for the structure to evolve into equilibrium for the temperature up-jump condition than for the temperature down-jump condition. For the two-step volume-fraction jumps, a memory response is observed that is different from observations of structural recovery in two-step temperature histories in molecular glasses. The concentration dependence of the dynamics
Niels Bohr collected works, volume 9: Nuclear physics (1929-1952)
International Nuclear Information System (INIS)
Peierls, R.
1985-01-01
This volume deals with Bohr's work on nuclear physics which began in the pre-1932 days with his thinking deeply, but inconclusively about the seeming contradictions then presented by the evidence about the nucleus. In 1936 Bohr recognized and described the insights provided by neutron scattering experiments and the excitement of this new understanding and its extension and consolidation occupied much of the subsequent years. In 1939 he was again first in understanding the essential features of the newly discovered phenomenon of fission, applying successfully the point of view of nuclear reactions which he had developed over the past three years. Later, in 1949-50, he was impressed by the success of the nuclear shell model, which on the face of it seemed hard to reconcile with the picture of the closely interacting nucleons which he had pioneered in 1936 and he put much effort into clarifying this paradox. As in earlier volumes the published papers are supported by appropriate selections from unpublished notes and drafts, and by relevant correspondence. CONTENTS: Foreword. Part I: Papers and Manuscripts Related to Nuclear Physics. Part II: Selected Correspondence (1929-1949). Inventory of Relevant Manuscripts in the Niels Bohr Archive. Index
Belloni, M.; Robinett, R. W.
2014-07-01
The infinite square well and the attractive Dirac delta function potentials are arguably two of the most widely used models of one-dimensional bound-state systems in quantum mechanics. These models frequently appear in the research literature and are staples in the teaching of quantum theory on all levels. We review the history, mathematical properties, and visualization of these models, their many variations, and their applications to physical systems. quote>For the ISW and the attractive DDF potentials, Eq. (4) implies, as expected, that energy eigenfunctions will have a kink-a discontinuous first derivative at the location of the infinite jump(s) in the potentials. However, the large |p| behavior of the momentum-space energy eigenfunction given by Eq. (5) will be |ϕ(p)|∝1/p2. Therefore for the ISW and the attractive DDF potentials, expectation value of p will be finite, but even powers of p higher than 2 will not lead to convergent integrals. This analysis proves that despite the kinks in the ISW and attractive DDF eigenfunctions, is finite, and therefore yield appropriate solutions to the Schrödinger equation.The existence of power-law ‘tails’ of a momentum distribution as indicated in Eq. (5) in the case of ‘less than perfect’ potentials [41], including a 1/p2 power-law dependence for a singular potential (such as the DDF form) may seem a mathematical artifact, but we note two explicit realizations of exactly this type of behavior in well-studied quantum systems.As noted below (in Section 6.2) the momentum-space energy eigenfunction of the ground state of one of the most familiar (and singular) potentials, namely that of the Coulomb problem, is given by ϕ1,0,0(p)=√{8p0/π}p0/2 where p0=ħ/a0 with a0 the Bohr radius. This prediction for the p-dependence of the hydrogen ground state momentum-space distribution was verified by Weigold [42] and collaborators with measurements taken out to p-values beyond 1.4p0; well out onto the power-law
Mathematical and numerical study of nonlinear boundary problems related to plasma physics
International Nuclear Information System (INIS)
Sermange, M.
1982-06-01
After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr
Physical and mathematical models for diffusion of thermal pollutants in water
International Nuclear Information System (INIS)
Pires, E.C.; Giorgetti, M.F.; Carajilescov, P.
1983-01-01
Mathematical models, such as the Fickian model and the model at PAILY and SAYRE, have been used in the analysis of thermal pollution. In the present work, experimental simulations of thermal dispersion were made using an artificial channel with injection of hat water and measurements of the temperature field were taken. The results were compared with the results given by the mentioned models, applying the image sources method. Due to the limitations of the model of PAILY and SAYRE, it was generalized for thermal sources posicioned at any place in the channel. The model of PAILY and SAYRE proved to be more satisfactory than the Fickian model and the image sources method was considered adequate. (Author) [pt
Directory of Open Access Journals (Sweden)
Juana Teresa Suárez Sarria
2013-12-01
Full Text Available Mathematical modelling constitutes a very useful tool for the planning and administration of the forest ecosystems. With the objective of predicting the behavior of volume by hectare of Pinus caribaea Moreletvar. caribaea. Barret y Golfari plantations at the «Jazmines» Silvicultural Unit, Viñales, seven non-lineal regression models were evaluated. The best goodness of fit model was the volume per hectare was the one designed by Hossfeld I, with a determining coefficient of 63, 9 % with a high significance parameter (P <0.001. The description curves for the annual mean increment with the time (IMA and the annual periodical increment (ICA of this variables were provided.
Blessing of dimensionality: mathematical foundations of the statistical physics of data.
Gorban, A N; Tyukin, I Y
2018-04-28
The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.This article is part of the theme issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Blessing of dimensionality: mathematical foundations of the statistical physics of data
Gorban, A. N.; Tyukin, I. Y.
2018-04-01
The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction. This article is part of the theme issue `Hilbert's sixth problem'.
Energy Technology Data Exchange (ETDEWEB)
Almeida, N. A.; Benilov, M. S. [Departamento de Fisica, CCCEE, Universidade da Madeira Largo do Municipio, 9000 Funchal (Portugal)
2012-07-15
A transformation of the ion momentum equation simplifies a mathematical description of the transition layer between a quasi-neutral plasma and a collisionless sheath and clearly reveals the physics involved. Balance of forces acting on the ion fluid is delicate in the vicinity of the sonic point and weak effects come into play. For this reason, the passage of the ion fluid through the sonic point, which occurs in the transition layer, is governed not only by inertia and electrostatic force but also by space charge and ion-atom collisions and/or ionization. Occurrence of different scenarios of asymptotic matching in the plasma-sheath transition is analyzed by means of simple mathematical examples, asymptotic estimates, and numerical calculations. In the case of a collisionless sheath, the ion speed distribution plotted on the logarithmic scale reveals a plateau in the intermediate region between the sheath and the presheath. The value corresponding to this plateau has the meaning of speed with which ions leave the presheath and enter the sheath; the Bohm speed. The plateau is pronounced reasonably well provided that the ratio of the Debye length to the ion mean free path is of the order of 10{sup -3} or smaller. There is no such plateau if the sheath is collisional and hence no sense in talking of a speed with which ions enter the sheath.
Mathematical Modeling in Combustion Science
Takeno, Tadao
1988-01-01
An important new area of current research in combustion science is reviewed in the contributions to this volume. The complicated phenomena of combustion, such as chemical reactions, heat and mass transfer, and gaseous flows, have so far been studied predominantly by experiment and by phenomenological approaches. But asymptotic analysis and other recent developments are rapidly changing this situation. The contributions in this volume are devoted to mathematical modeling in three areas: high Mach number combustion, complex chemistry and physics, and flame modeling in small scale turbulent flow combustion.
Energy Technology Data Exchange (ETDEWEB)
1980-02-01
Volume 1 of the conference proceedings contains sessions on neutrino physics and weak interactions, e/sup +/e/sup -/ physics, and theory. Five of the papers have already been cited in ERA, and can be found by reference to the entry CONF-790642-- in the Report Number Index. The remaining 30 will be processed as they are received on the Atomindex tape. (RWR)
Plumpton, C
1968-01-01
Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-level is assumed and the subject is developed by a concentric treatment in which each new topic is used to illustrate ideas already treated. The major topics of Algebra, Calculus, Coordinate Geometry, and Trigonometry are developed together. This volume covers most of the Pure Mathematics required for t
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard; Gray, Jeremy
Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO.......Volume 1 in Theme on "History of Mathematics", in "Encyclopedia of Life Support Systems (EOLSS), developed under the auspices of the UNESCO....
Beta decay of hyperons. Lectures in mathematics and physics at the University of Texas at Austin
Energy Technology Data Exchange (ETDEWEB)
Bohm, A.; Garcia, A.; Kielanowski, P.
1985-01-01
This book is an introduction to the physics of the semileptonic decay of hyperons. After a general introduction and a description of the experimental results the Cabibbo theory is introduced for the theoretical description of these results. Then radiative and other corrections are discussed. Finally this decay is considered in the framework of broken SU(3). This book applies to graduate students and other ''non-specialists'' who want to get some insight into the physics of weak interactions. (HSI).
Bartocci, Claudio; Guerraggio, Angelo; Lucchetti, Roberto; Williams, Kim
2011-01-01
Steps forward in mathematics often reverberate in other scientific disciplines, and give rise to innovative conceptual developments or find surprising technological applications. This volume brings to the forefront some of the proponents of the mathematics of the twentieth century, who have put at our disposal new and powerful instruments for investigating the reality around us. The portraits present people who have impressive charisma and wide-ranging cultural interests, who are passionate about defending the importance of their own research, are sensitive to beauty, and attentive to the soci
Mones, Enys; Stopczynski, Arkadiusz; Pentland, Alex 'Sandy'; Hupert, Nathaniel; Lehmann, Sune
2018-01-01
Targeted vaccination, whether to minimize the forward transmission of infectious diseases or their clinical impact, is one of the 'holy grails' of modern infectious disease outbreak response, yet it is difficult to achieve in practice due to the challenge of identifying optimal targets in real time. If interruption of disease transmission is the goal, targeting requires knowledge of underlying person-to-person contact networks. Digital communication networks may reflect not only virtual but also physical interactions that could result in disease transmission, but the precise overlap between these cyber and physical networks has never been empirically explored in real-life settings. Here, we study the digital communication activity of more than 500 individuals along with their person-to-person contacts at a 5-min temporal resolution. We then simulate different disease transmission scenarios on the person-to-person physical contact network to determine whether cyber communication networks can be harnessed to advance the goal of targeted vaccination for a disease spreading on the network of physical proximity. We show that individuals selected on the basis of their closeness centrality within cyber networks (what we call 'cyber-directed vaccination') can enhance vaccination campaigns against diseases with short-range (but not full-range) modes of transmission. © 2018 The Author(s).
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A.; Bell, Ellis
2013-01-01
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry,…