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 ยท Billing.

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Since in each field of physics the global variables are associated with a space and a time element, the association of the corresponding densities and the rates with the space and time element of the corresponding global variable is spontaneous.

Doing so, we have constructed a one-dimensional cell complex in time. The reason for analogies between physical theories E Tonti Applied Mathematical Modelling 1 1, At first glance, the notions of inner and outer orientation of a time element may appear strange, certainly unusual. The starting point of this classification stems from a remark by Maxwell. The third category, that of energy variablesis created by multiplying a configuration variable by a source variable.

The fact that physical variables are associated with space and time elements endowed with inner or outer orientation and that space and time elements of a primal and a dual cell complex can be classified as shown on the right-hand side of Figs.

Tonti diagram

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 system can’t perform the operation now. Progress in electromagnetics research 32, Remarks on the Mathematical Classification of Physical Quantities.


Every density is obtained by dividing a global variable by the extension of the associated space element. Wikipedia articles that are too technical from February All articles that are too technical Articles needing expert attention from February All articles needing expert attention Wikipedia articles with possible conflicts of interest from December Articles needing additional references from December All articles needing additional references Orphaned articles from November All orphaned articles Articles needing cleanup from June All pages needing cleanup Cleanup tagged articles with a reason field from June Wikipedia pages needing cleanup from June Articles with multiple maintenance issues.

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The first complex is called primal and the second dual. 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: Dual complex, outer orientation: Amazon Inspire Digital Educational Resources. The term time-global variables is used to indicate variables that are not tontl of other variables.

New articles by this author. Figures 3 and 4 show how the space elements of the primal complex, which are endowed with inner orientation, induce an outer orientation on the elements of the dual complex. Visit our Beautiful Books page and find lovely books for kids, photography lovers and more. Please help improve it to make it understandable to non-expertswithout removing the technical details.

The physical variables, both global variables and densities, in turn, can be divided into three classes: Title Cited by Year A direct discrete formulation of field laws: The space-time diagrams show clearly which phenomenological equations describe irreversible phenomena: This article has multiple issues.


Enzo Tonti (Author of The Mathematical Structure of Classical and Relativistic Physics)

Suitable for a diverse audience of physicists, engineers, and mathematicians, The Mathematical Structure of Classical and Relativistic Physics offers a valuable resource for studying the physical world. Referring here to particle dynamics, we see that configuration variables are geometrical and kinematic variables, while source variables are static and dynamic variables.

The Mathematical Structure of Classical and Relativistic Physics is the first book to analyze this structure in depth, thereby exposing the relationship between a global physical variables and b space and time elements such as points, lines, surfaces, instants, and intervals.

Mass density is given by the ratio of mass to volume, mass being the global variable. Pressure is the ratio of the normal force on an element of plane surface to the surface area, therefore the normal force is the global variable and the pressure is its surface density.

This article may be too technical for most readers to understand. Istituto di matematica del Politecnico di Milano Description 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.

Enzo Tonti – Google Scholar Citations

To highlight fnzo four space elements, it is expedient to divide a region of space into many cells, thus creating a cell complex. Email address for updates. December Learn how and when to remove this template message.