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Topic: Mathematical models in physics

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  20th WCP: Mathematical Models of Spacetime in Contemporary Physics and Essential Issues of the Ontology of Spacetime
Theories of spacetime in mathematical physics, while considering continua and metric manifolds, cannot explain the difference between time dimension and space dimensions, they are also unable to explain by means of geometry the unidirection of the passage of time, which can be comprehended only by means of thermodynamics.
The continuity and logic of evolution of physics of spacetime reconstructed by Heller is apparent, owing to the use of the language of contemporary mathematics.
Logical development of the physics of spacetime in Heller's view is exposed through the use of the theory of fibre bundle and the theory of differential manifolds.
www.bu.edu /wcp/Papers/Math/MathGos.htm   (2817 words)

 On the merits of mathematical models - Physics Today June 2006
Physicists have deployed mathematical models of interacting entities for two purposes: to establish the existence and properties of such entities—for example, quarks and other subatomic particles—by comparing precise calculations with precise measurements; and to predict and understand the properties of systems, such as doped semiconductors comprising known entities.
At one time, uncritical faith in mathematical modeling lent false plausibility to the notion that one might in fact measure the parameters, solve the equations, and thereby centrally control an economy.
The modeling of institutional process is as interesting for its limitations as for its successes, precisely because the regularities left unexplained by pure process models (which we have characterized as "zero-intelligence" models) are potential mathematical regularities of behavior.
www.physicstoday.org /vol-59/iss-6/p10.html   (964 words)

 Models [Internet Encyclopedia of Philosophy]
Physical models are used throughout the sciences, from immunoglobulin models of allergic reactions to macroeconomic models of the business cycle.
This is sometimes called a “mediating mathematical model” (Morton 1993) since it operates, in a sense, between the intractable Hamiltonian and the phenomenon it is thought to describe.
When this model is simulated on a computer, the resulting phase portrait is very similar to the one that was reconstructed from the data in the lab.
www.iep.utm.edu /m/models.htm   (3945 words)

 CUC - Academic Life - Physics
Physics is a science of immense scope: from the subnuclear world of elementary particles to the cosmos of the galaxies.
In studying the physical universe, the physicist must not only be able to make observations to collect data but must also be able to apply the mathematical models of the discipline.
The contribution of physics knowledge to the understanding of all aspects of the human environment both physical and philosophical is discussed.
www.cuc.edu /academic/departments/physics/index.html   (211 words)

 Mathematical physics Summary
Physics and mathematics have always enjoyed a close relationship, beginning in the Renaissance with Johannes Kepler's (1571-1630) 1609 discovery of the three laws of planetary orbits.
Mathematics became increasingly important to physicists during the latter half of the twentieth century, usually because the physical objects under investigation were inaccessible to experimental physics.
The term 'mathematical' physics is also sometimes used in a special sense, to distinguish research aimed at studying and solving problems inspired by physics within a mathematically rigorous framework.
www.bookrags.com /Mathematical_physics   (3520 words)

 Mathematical Physics - Research - Aplied Mathematical Physics
The thermohydraulic processes in the ground are governed by coupled partial differential equations, which are solved by means of analytical and numerical methods.
Several computer programs have been developed that deal with all aspects of the thermal processes, from fundamental particular processes to detailed three-dimensional simulation models with arbitrary time-dependent loading conditions.
Other problems that involve similar equations are also studied, e.g., groundwater movement around a nuclear waste repository and convective heat and moisture transport in building materials.
www.matfys.lth.se /app_math_phys.html   (132 words)

 Mathematical models in physics - Wikipedia, the free encyclopedia
Physical theories are almost invariably expressed using mathematical models, and the mathematics involved is generally more complicated than in the other sciences.
Different mathematical models use different geometries that are not necessarily entirely accurate descriptions of the geometry of the universe.
In engineering, physics models are often made by mathematical methods such as finite element analysis.
en.wikipedia.org /wiki/Mathematical_models_in_physics   (383 words)

 Mathematical model - Wikipedia, the free encyclopedia
models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.
Linear vs. nonlinear: Mathematical models are usually composed by variables, which are abstractions of quantities of interest in the described systems, and operators that act on these variables, which can be algebraic operators, functions, differential operators, etc. If all the operators in a mathematical model present linearity, the resulting mathematical model is defined as linear.
Mathematical modelling problems are often classified into fl box or white box models, according to how much a priori information is available of the system.
en.wikipedia.org /wiki/Mathematical_model   (1928 words)

 Myswizard » Theoretical physics
Theoretical physics employs mathematical models and abstractions, as opposed to experimental processes, in an attempt to understand Nature.
The proposed theories of physics are usually relatively new theories which deal with the study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory.
Note 1: Sometimes mathematical physics and theoretical physics are used synonymously to refer to the latter.
www.myswizard.com /2006/07/27/theoretical-physics   (1289 words)

 The end of time | Ask MetaFilter
Mathematics is, at its purest, the exploration of an abstract mathematical universe.
Newtonian physics were fine for describing things of speeds that we observe everyday, but when applied to things that were very close the speed of light relative to the observer, Newtonian physical models broke down.
The physics community, as a rule, is relentlessly realist and in so being are inclined to a sort of Platonism, an idealism complementary to their realism.
ask.metafilter.com /mefi/28356   (3445 words)

 Models as Mediators - Cambridge University Press   (Site not responding. Last check: 2007-11-06)
Models as Mediators discusses the ways in which models function in modern science, particularly in the fields of physics and economics.
Models play a variety of roles in the sciences: they are used in the development, exploration and application of theories and in measurement methods.
Models and the limits of theory: quantum Hamiltonians and the BCS model of superconductivity Nancy Cartwright; 10.
www.cambridge.org /catalogue/catalogue.asp?ISBN=0521650976   (351 words)

 IUPAP: C18: Report 2002
All physics is mathematical, in the sense that physics is a quantitative subject and mathematics is the language of physics.
The mathematical study of mirror symmetry, and algebraic geometry in general, Algebraic geometry is expected to be even more useful and to benefit enormously from the supergravity-string theory-M-theory perspective and profusion of concrete and unexpected features.
This development is of particular significance for physics, because it brings some relatively sophisticated mathematical methods into practical use for the solution of a wide range of physical problems in the quantization of complex systems with dynamical symmetries.
www.iupap.org /commissions/c18/reports/ga-02.html   (2586 words)

 Pacific Union College | Physics
Physics is the search for the fundamental physical laws of nature.
In particular, physics is the study of forces and motion of physical entities, seeking to find basic relations that synthesize these phenomena.
To achieve this goal involves observation and experimentation from which physical and mathematical models are developed that suggest concepts and theories.
www.puc.edu /PUC/academics/Academic_Departments/Physics_Dept   (169 words)

 Mathematical Physics :: Physics : Gourt
Mathematical physics is the scientific discipline concerned with "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories"
Euclidean Geometric Transforms for Physics - A new method of correlating physics formulas to derive one formula from a related formula using Euclidean geometry to represent the inter-relationship of physics formulas.
Homological Methods in Mathematical Physics - These lecture notes by Joseph Krasil'shchik and Alexander Verbovetsky are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations.
science.gourt.com /Physics/Mathematical-Physics.html   (939 words)

 Predictions from Mathematical models
> temperature in the model is 1 degree.
> > temperature in the model is 1 degree.
Instead, only what is measured from\nandgt; within the mathematical model itself, by an observer who exists and\nandgt; functions purely within the mathematical model, is comparable to the\nandgt; outcome of our measurements.\nandgt;\nandgt; It is a very simple idea, but it is very very different from anything\nandgt; physics has attempted so far.
www.physicsforums.com /showthread.php?t=61845   (3472 words)

 IUPAP: C18: Report 2005
The mandate of the C18 commission covers the mathematical studies of problems originating in, or relevant to physics, including mathematical models of physical systems, mathematical aspects of physical theories, and computational techniques.
We have communicated with the main professional society in the area, the International Association of Mathematical Physicists (IAMP) which was made easy due to the fact that the vicepresident of the IAMP is a C18 member, and vice versa, the chair of C18 belongs to the executive committee of the IAMP.
The first one should distinguish a person who enriched and impacted the field of mathematical physics, the second one a person who achieved a significant result within the last ten years with preference to individuals from an environment without a strong mathematical physics tradition.
www.iupap.org /commissions/c18/reports/ga-05.html   (589 words)

 Theoretical Physics - Search Results - MSN Encarta
Theoretical Physics, physics employing mathematical models and abstractions rather than experimental processes.
Physics: If you want to find…, Reality: Einstein's space is no closer…
Water : chemistry and physics of water : atomic structure: Water Molecule
encarta.msn.com /Theoretical_Physics.html   (136 words)

 block mathematical physics   (Site not responding. Last check: 2007-11-06)
In this course trainees are introduced to mathematical modeling from a Mathematical Physics and Continuum Mechanics point of view for practical, industrial problems.
The physical models are from such diverse fields as: elasticity, hydrodynamics, viscoelasticity, electromagnetism, heat conduction, mixtures and porous media, and chemical processes.
The practical problem (including its technical, industrial background) is explained in words and a first set-up to the modeling and the techniques to be used for this is given.
www.win.tue.nl /oowi/courses/block_physics.html   (436 words)

Mathematical systems are, of course, the substance of physical theory and so that is not exactly a trivial result in terms of physics.
The notion of "an infinitude" is a physically transcendental and theological fabrication, and it is a standard denizen of the world of science, most especially because science that relies heavily on mathematics.
That is not really a question of physics, but one of metaphysics: physics is concerned with finding out how nature behaves, what the fundamental rules are, and stating the answer in a precise mathematical language, while metaphysics concerns itself with how or why the rules have the form that they do.
graham.main.nc.us /~bhammel/PHYS/sho.html   (13359 words)

 The Role Of Models: From Anthropology To Particle Physics   (Site not responding. Last check: 2007-11-06)
"Scientific theories are models of one part of nature, and all models initially have a limited range of validity," said Kane in a presentation at the American Association for the Advancement of Science meeting in Philadelphia this week.
His mistake was that he accepted the model as truth without comparing it to events in the real world.
As an example, Kane cites the Standard Model of particle physics---the basic theory that defines the particles in an atom and the forces which hold those particles together.
www.eurekalert.org /pub_releases/1998-02/UoM-TROM-150298.php   (259 words)

 Flow and Transport Models, Soil Physics, Oklahoma State University
From this understanding they create mathematical models that help to extend this knowledge to new areas and new conditions.
Models are generally made for a specific purpose.
The model user must select a model which is consistent with the system of interest, the answers required, and the data available.
soilphysics.okstate.edu /models.html   (172 words)

 Physics: Graduate Catalog, University of Connecticut
The committee and the student jointly plan a curriculum that is designed to provide the general knowledge of physics appropriate for the Ph.D. and also the specialized expertise necessary to conduct dissertation research.
These include atomic, molecular and optical physics (experimental and theoretical), condensed matter physics (experimental and theoretical), nuclear physics (experimental and theoretical), particle and field theory (including relativity and cosmology) and quantum optics (experimental and theoretical).
Experimental methods used in modern research are applied to experiments from various fields of physics, including: low temperature conductivity of metals, x-ray diffraction, acoustic attenuation, optical constants of metals, color centers in alkali halides, nuclear beta decay, Zeeman effects and others.
catalog.grad.uconn.edu /physics.html   (1496 words)

These topics include controversies of global warming, renewable energy sources, the transport of pollutants and percolation, acoustic and seismic detection for weapons of mass destruction as well as hydrocarbon exploration, the physics of earthquakes and volcanoes, and the atomic and molecular basis of environmental spectroscopy.
The course is open to all engineering, physical science and biological science majors and other interested students.
Recommended pre-requisites are first year physics and chemistry as well as introductory calculus.
www.physics.purdue.edu /academic_programs/courses/phys270E   (100 words)

 biomath reu   (Site not responding. Last check: 2007-11-06)
In a PDE model, physical quantities are assumed to be continuous and differentiable functions depending on several variables such as the time, spatial coordinates.
An important class of models is the reaction-diffusion equations based on the diffusion mechanism and reaction/interacting of different species.
PDE and Mathematical Biology as a training course on the basic knowledge on reaction-diffusion equations.
www.math.wm.edu /~shij/reu.html   (611 words)

 Graduate Research in Mathematical Physics - Department of Physics and Astronomy - The University of Iowa
Mathematical physics is an interdisciplinary subject where theoretical physics and mathematics intersect.
Our program in Mathematical Physics is one of the few in the U.S. that is fully interdisciplinary, combining both physicists and mathematicians in a working relationship.
The Department of Physics and Astronomy is a part of the College of Liberal Arts and Sciences.
www.physics.uiowa.edu /graduate/math.html   (539 words)

 Review, buy Mathematical Physics: M Kdv Solitons on the Background of Quasi-Periodic Finite-Gap Solutions (Mkdv ...   (Site not responding. Last check: 2007-11-06)
This is an updated and expanded second edition of a successful and well-reviewed text presenting a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory.
The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities.
This book is intended for graduate students and researchers interested in the modelling of periodic phenomena in physics and biology and will provide a second knowledge of the application of the theory of nonlinear oscillations to a particular class of problems.
booksall.net /mathematical-physics1/110.html   (3056 words)

 V.E.1. Mathematical Sciences
Mathematical system theory and control theory: control in the presence of uncertainties, robust and adaptive control for multi-variable and nonlinear systems, system identification and its relation to adaptive control, hybrid control, H-infinity control, nonholonomic control.
Mathematical modeling is a major factor in assuring that a system is well designed and that it will work once built.
Advances in modeling and computational capabilities are needed to support stochastic modeling and simulation of combat to assess changes in doctrine and tactics and to determine the cost effectiveness of new systems on the battlefield (see Figure V-6).
www.fas.org /man/dod-101/army/docs/astmp/c5/P5E1.htm   (691 words)

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