Computers, Mathematical Modeling, and Experimental Science

Authors

  • Pablo M. Jacovkis University of Buenos Aires

DOI:

https://doi.org/10.52712/issn.1850-0013-1014

Keywords:

mathematical modeling, numerical experimentation, experimental science

Abstract

In this article we argue that the computer not only works as a powerful tool for numerical modeling of problems in experimental science, but also in a certain sense applied mathematics may be considered an experimental science, whose laboratory is the computer, and therefore computer mathematical models are or may become tools to better know phenomena from different disciplines. In addition, one can observe how pure mathematics has also begun to use computers to calculate universal constants and to prove theorems.

Downloads

Download data is not yet available.

References

APPEL, K. y HAKEN, W. (1977): “Every planar map is four colorable. Part I. Discharging”, Illinois J. Math., 21, pp. 429-490.

APPEL, K.; HAKEN, W. y KOCH, J. (1977): “Every planar map is four colorable. Part II. Reducibility”, Illinois J. Math., 21, pp. 491-567.

ARNOLD, V. I. (1998): “Sur l’éducation mathématique”, Gazette de Mathématiciens, 78, Octobre (1998). Disponible en : http://www.ceremade.dauphine.fr/~msfr/articles/arnold/PRE_francais.tex.

ARNOLD, V. I. (1986): Catastrophe theory, Springer, Berlin.

BRADY, R.; BALL, R. C. (1984): “Fractal growth of copper electrodeposits”, Nature, 309, pp. 225-229.

BRENSTRUM, E. (1994): “The most important forecast in history”, New Zealand G e o g r a p h i c , 22, Apr-Jun. Disponible en: http://www.metservice.co.nz/learning/weather_d_day.asp.

CRICK, F. (1998): What mad pursuit, Nueva York, Basic Books.

DAWKINS, R. (1996): The blind watchmaker, 2da edición, Nueva York, W. W. Norton & Company.

DENGRA, S. (2004): “Estudios experimentales y teóricos del transporte iónico en electrodeposición en celdas delgadas”, Tesis de Doctorado, Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires.

DOMINGO, C.; VARSAVSKY, O. (1969): “Un modelo matemático de la Utopía de Moro”, Desarrollo Económico, 7, 3-36 (1967). Reproducido como Anexo II en: E. de Gortari, T. Garza H., C. Dagum, J. Hodara y O. Varsavsky, El problema de la predicción en ciencias sociales, México, D. F., Instituto de Investigaciones Sociales, Universidad Nacional Autónoma de México, pp. 191-225.

FEIGENBAUM, M. J. (1979): “The universal metric properties of nonlinear transformations”, J. Stat. Phys., 21, pp. 669-706.

FERMI, E.; PASTA, J.; ULAM, S. (1955): “Studies in nonlinear problems, I”. Los Alamos Report LA1940, (1955). Reproducido en: A. C. Newell (ed.), Nonlinear wave motion, Providence, RI, Ame. Math. Soc., 1974).

FORRESTER, J. (1971): World dynamics, Cambridge, MA, Wright-Allen Press.

GLEICK, J. (1986): Chaos, London, William Heinemann.

GRADOWCZYK, M. H. (1968): “Wave propagation and boundary instability in erodible-bed channels”, J. Fluid Mech, 33, pp. 93-112.

GRADOWCZYK, M. H.; MAGGIOLO, O. J.; FOLGUERA, H. C. (1968): “Localized scour in erodible-bed channels”, Journal of Hydraulic Research, 6, pp. 289-326.

HERRERA, A.; SCOLNIK, H. D.; CHICHILNISKY, G.; GALLOPIN, G.; HARDOY, J.; MOSOVICH, D.; OTEIZA, E.; de ROMERO BREST, G.; SUÁREZ C.; TALAVERA, L.(1977): ¿Catástrofe o nueva sociedad? Modelo Mundial Latinoamericano, Ottawa International Development Research Center.

JACOVKIS, P. M. (2004): “Reflexiones sobre la historia de la computación en Argentina”, Saber y Tiempo, 5 (17), pp. 127-146.

JACOVKIS, P. M. (1995): “Computación, azar y determinismo”, Ciencia Hoy, 5, Nro. 28, pp. 44-50.

JACOVKIS, P. M. (1995): “The hydrodynamic flow with a mobile bed: general and simplified approaches”, en: D. Bainov, Invited Lectures and Short Communications, Sixth International Colloquium on Differential Equations, Sofia, Bulgaria, Impulse, pp. 203-212.

LANFORD III, O. E. (1984): “A shorter proof of the existence of the Feigenbum fixed point”, Commun. Math. Phys., 96, pp. 521-538.

LANFORD III, O. E. (1982): “Acomputer-assisted proof of the Feigenbaum conjectures”, Bull. Amer. Math. Soc., 6, pp. 427-431.

LORENZ, N. (1963): “Deterministic nonperiodic flow”, J. Atmos. Sci. 20, pp. 130-141.

MACRAE, N. (1992): John von Neumann, Nueva York, Pantheon Books. Reimpreso por American Mathematical Society (1999).

MACKENZIE, D. (2004): “Mathematical modeling and cancer”, SIAM News, 37:1, pp. 1-3.

MATSUSHITA, M.; SANO, M.; HAYAKAWA, Y.; HONJO, H. y SAWADA, Y. (1984): “Fractal structures of zinc metal leaves grown by electrodeposition”, Phys. Rev. Lett., 53, pp. 286-289.

MAY, R. M. (1976): “Simple mathematical models with very complicated dynamics”, Nature, 261, pp. 459-467.

MEADOWS, D. H.; MEADOWS, D. C.; RANDERS, J. y BEHRENS, W. W. (1972): The limits of growth, Nueva York, Universe Books.

MESAROVIC, M. (1979): “Practical application of global modeling”, en: B. Lazarevic (ed.), Global and large scale system models, Lecture Notes in Control and Information Science, Berlin, Springer, pp. 42-57.

METROPOLIS, N. y ULAM, S. (1949): “The Monte Carlo method”, Journal of the American Statistical Association, 44, pp. 335-341.

RICHARDSON, L.F. (1956): Weather prediction by numerical process, Cambridge University Press, Cambridge, UK, (1922). Reeditado por Dover, Nueva York.

ROBERTSON, N.; SANDERS, D. P.; SEYMOUR, P. D. y THOMAS, R. (1997): “The four color theorem”, J. Combin. Theory Ser. B, 70, pp. 2-44.

SADOSKY, M. (1972): “Cinco años del Instituto de Cálculo de la Universidad de Buenos Aires”, entrevista, Ciencia Nueva, 3, Nro. 17, pp. 13-18.

SCOLNIK, H. D. (1979): “A critical review of some global models”, en: B. Lazarevic (ed.), Global and large scale system models, Lecture Notes in Control and Information Sciences, Berlin, Springer, pp. 58-80.

STAUFFER, D. (1985): Introduction to percolation theory, Londres, Taylor & Francis.

STROGATZ, S. (2003): “The real scientific hero of 1953”, The New York Times, March 4.

SUSSMANN, H. J. (1975): “Catastrophe theory”, Synthèse, 31, pp. 229-270.

SUSSMANN, H. J. y ZAHLER, R. (1978): “Catastrophe theory as applied to the social and biological sciences: a critique”, Synthèse, 37, pp. 117-216.

THOM, R. (1972): Stabilité structurelle et morphogénèse, París, Benjamin.

VARSAVSKY, O. (1970): “Modelos matemáticos y experimentación numérica”, en: O. Varsavsky y A. E. Calcagno (eds.) América Latina. Modelos matemáticos, Santiago de Chile, Editorial Universitaria.

VARSAVSKY, O. (1969): “Los modelos matemáticos y la predicción en ciencias sociales”, en: E. de Gortari, T. Garza H., C. Dagum, J. Hodara y O. Varsavsky, El problema de la predicción en ciencias sociales, México D.F., Instituto de Investigaciones Sociales, Universidad Nacional Autónoma de México, pp. 97-114.

VARSAVSKY, O. (1963): “La experimentación numérica”, Ciencia e Investigación, 19, pp. 340-347.

WITTEN, T. A. Jr. y SANDER, L. M. (1981): “Diffusion-limited aggregation: a kinetic critical phenomenon”, Phys. Rev. Lett., 47, pp. 1400-1403.

Downloads

Published

2005-06-30

How to Cite

Jacovkis, P. M. (2005). Computers, Mathematical Modeling, and Experimental Science. Revista Iberoamericana De Ciencia, Tecnología Y Sociedad - CTS (Ibero-American Science, Technology and Society Journal), 2(5), 51–63. https://doi.org/10.52712/issn.1850-0013-1014

Issue

Section

Articles