The Mathematical Structure of Classical and Relativistic Physics (Modeling and Simulation in Science, Engineering and Technology) Sep 07, by Enzo. Enzo Tonti is on Facebook. Join Facebook to connect with Enzo Tonti and others you may know. Facebook gives people the power to share and makes the. The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram. Enzo Tonti. from: $ Top of Page. My Account · Billing.
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This article relies largely or entirely on a single source. Dispatched from the UK in 3 business days When will my order arrive? Istituto di matematica del Politecnico di Milano June Learn how and when to remove this template message. Journal of Computational Acoustics 9 04, Amazon Second Chance Pass it on, trade it in, give it a second life. This article may be too technical for most readers to understand.
Doing so, we have constructed a one-dimensional cell complex in time. Physical quantities can be divided into three main categories: Therefore, the temperature is said to be associated with a time interval T. Let us consider a subdivision of the time axis into many adjacent time intervals.
Tonti diagram – Wikipedia
Back cover copy The theories describing seemingly unrelated areas of physics have surprising analogies that have aroused the curiosity of scientists and motivated efforts to identify reasons for their existence.
The algebraic-topological structure of physical theories E Tonti Symmetry, similarity and group theoretic methods in mechanics, Integral variables are global variables, but there are also global variables which are associated with points, and which, therefore, cannot be considered integral variables. The equations linking the variables are contained in the rectangular boxes. The Best Books of Popularity Popularity Featured Price: This distinction leads to a classification of physical variables based on their association with space elements.
Every density is obtained by dividing a global variable by the extension of the associated space element. Therefore, a displacement is associated with a time interval Twhereas a position vector is associated with a time instant I.
Displacement and impulse are associated with time intervals, while momentum and position vector are associated with instants. Geometric Optics Antonio Romano. It is the case of field theories such as electromagnetism, gravitation, thermal conduction and irreversible thermodynamics. The same tontu association remains once we have performed the limit to obtain the field variables.
The Mathematical Structure of Classical and Relativistic Physics : A General Classification Diagram
To highlight the four space elements, it is expedient to divide a region of space into many cells, thus creating a cell complex. The first introduces the framework for the above-mentioned classification, methodically developing a geometric and topological formulation applicable to all physical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and tnoti.
Furthermore, if one considers that each space element and each time element can be endowed with two orientations, inner and outer, we must combine the 4×2 oriented space elements with the 2×2 oriented time elements, thus obtaining 32 possible space-time combinations.
Get fast, free shipping with Amazon Prime. A similar association exists between time-global variables and time elements. Please help improve it to make it understandable to non-expertswithout removing the technical details.
Written at a level accessible to graduate and advanced undergraduate students in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework. In electromagnetism, hence, vectors E and H are associated with lines, and vectors D and B are associated with surfaces. The following articles are merged in Scholar.
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There are two kinds of orientation: Are you an author? Journal of Computational Physics, Amazon Inspire Digital Educational Resources. Remarks on the Mathematical Classification of Physical Quantities. Space elements are naturally classified according to their dimension, from the smallest to the biggest, i.
ComiXology Thousands of Digital Comics. Mass density is given by the ratio of mass to volume, tontu being the global variable. Book ratings by Goodreads. Each field has its sources for example, electric charges are the source of electric fields, heat generators are the source of thermal fields and forces are the source of motion and deformation: Title Cited by Year A direct discrete formulation of field laws: This article is an orphanas no other articles link to it.
This “Cited by” count includes citations to the following articles in Scholar.
Tensor Calculus for Physicists. Amazon Drive Cloud storage from Amazon. This remark leads us to a distinction between vectors referred to lines and vectors referred to surfaces.
The first version associates the space elements endowed with inner orientation with the time elements endowed with inner orientation and vice versa: Particle dynamics, analytical mechanics and electric networks make use of space-global variables that depend only on the time variable. AmazonGlobal Ship Orders Internationally. Algebraic topology and computational electromagnetism E Tonti 4th Int.