Enzo Tonti

Enzo Tonti (30 October 1935 – 10 June 2021[1]) was an Italian physicist and mathematician, known for his contributions to engineering and mathematical physics.

Life

Enzo Tonti was born in Milan. He graduated in Mathematics and Physics at the University of Milan in 1961.[2] He began work there in 1962 as research assistant in the field of mathematical physics. In the year 1976, he accepted a professorship at the Engineering Faculty of the University of Trieste.

Scientific works

Tonti's contribution can be classified in three main fields. He worked on the variational formulations, showing that each differential equation, linear or not, can be expressed as an equation allowing for variational formulation[3][4][5][6]

He conducted researches on various physical theories, much different from each other, showing that they exhibit the same mathematical structure. The existence of analogies have been discovered, limited by now to the physics of macrocosm. This was possible by introducing a classification diagram containing the variables involved in physic theories, the so-called Tonti diagram.

In 2001 he presented a numerical method for the resolution of equations regulating physical fields starting from the algebraic formulation instead of using differential one. In other words, in the Cell Method[7] no discretization is required.

Applications

Several applications of Cell Method can be found through years.[8] For instance, Cell Method was extended to non-linear field (see[9]).

As is well known, the theories of different physical fields, exhibit analogies in their mathematical structure.[10] Enzo Tonti was interested in discovering the reason for these similarities by analyzing the role of the physical variables involved in each theory. This analysis made it possible to bring to light the reason for the existence of similarities between physical theories: the reason lies in the existence of the same mathematical structure that links the physical variables of each single theory to each other. This structure is highlighted by a classification diagram of the physical variables of each theory, a diagram known in the literature as Tonti diagram. The reason for the existence of analogies is limited, for now, to the classical and relativistic theories of the macrocosm[11]

Publications

Journal articles
  • Tonti E. A direct discrete formulation of field laws: The cell method. CMES- Computer Modeling in Engineering and Sciences. 2001 Jan 1;2(2):237-58. (Cited 277 times, according to Google Scholar [12])
  • Tonti, E., Finite formulation of the electromagnetic field. Progress in electromagnetics research, 2001. 32, pp. 1–44. (Cited 201 times, according to Google Scholar.[12])
  • Tonti E. Finite formulation of electromagnetic field.IEEE Transactions on Magnetics. 2002 Aug 7;38(2):333-6. (Cited 195 times, according to Google Scholar.[12])
  • Tonti E. The reason for analogies between physical theories. Applied Mathematical Modelling. 1976 Jun 1;1(1):37-50 . (Cited 139 times, according to Google Scholar.[12])
  • Tonti E. Variational formulation for every nonlinear problem. International Journal of Engineering Science. 1984 Jan 1;22(11-12):1343-71. (Cited 139 times, according to Google Scholar.[12])

Books
  • Tonti, Enzo. The Mathematical Structure of Classical and Relativistic Physics A General Classification Diagram. Springer . 2013. ISBN 9781461474227

References
  1. "Tonti Enzo". Il Piccolo (in Italian).
  2. "CV | Discrete Physics" (in Italian). Retrieved 2019-05-13.
  3. Tonti, Enzo (1984). "Variational formulation for every nonlinear problem". International Journal of Engineering Science. 22 (11–12): 1343–1371. doi:10.1016/0020-7225(84)90026-0.
  4. Filippov, V. M. "Variational Principles for Nonpotential Operators". Translations of Mathematical Monographs, American Mathematical Society, Providence, Rhode Island, 1989. 77.
  5. Carini, A.; Gelfi, P.; Marchina, E. (1995). "An energetic formulation for the linear viscoelastic problem. Part I: Theoretical results and first calculations". International Journal for Numerical Methods in Engineering. 38 (1): 37–62. Bibcode:1995IJNME..38...37C. doi:10.1002/nme.1620380104.
  6. Carini, A.; Mattei, O. (2015). "Variational formulations for the linear viscoelastic problem in the time domain". European Journal of Mechanics - A/Solids. 54: 146–159. Bibcode:2015EJMS...54..146C. doi:10.1016/j.euromechsol.2015.05.007.
  7. Tonti, Enzo (2001). "A direct discrete formulation of field laws: The cell method". Computer Modeling in Engineering and Sciences. 2 (2): 237–258. doi:10.3970/CMES.2001.002.237.
  8. Ferretti, E. (2014). The Cell Method: A Purely Algebraic Computational Method in Physics and Engineering Science. New York: Momentum Press.
  9. Freschi, C.; Delprete, F.; Repetto, M.; Rosso, C. (2013). "A Proposal of Nonlinear Formulation of Cell Method for Thermo-Elastostatic Problems". Computer Modeling in Engineering and Sciences. 94 (5): 395–418. doi:10.3970/CMES.2013.094.397.
  10. Branin, F. H. Jr. (1966). "The algebraic topological basis for network analogies and the vector calculus". Symposium on Generalized Networks. Polytechnic Institute of Brooklin, New York.
  11. Tonti, E. (2013). The Mathematical Structure of Classical and Relativistic Physics. Modeling and Simulation in Science, Engineering and Technology. New York: Springer Science+Business Media.
  12. Google Scholar Author page, Accessed Nov 24,. 2021
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.