Abstract
The study deals with the complex systems in Nature by using of some specific numerical methods. First the method of the physical similarity is used for the characterization of the fluids flow regimes. Then, the method of the power laws and some of its multiple uses in Physics and another related fields are analyzed. The method of phenomenological universality, applied to the description of the growth processes is also discussed. The authors results presented in the paper were mainly obtained by computer simulations using the finite difference (FD) method and the classical gradient method (CGM).
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References
Gukhman, A.A.: Introduction to the Theory of Similarity. Academic Press, New York (1965)
Lyon, B.N.: Chem. Eng. Progr. 47, 2 (1951)
Petukhov, B.S.: Heat transfer and friction in turbulent pipe flow with variable physical properties. Adv. Heat Transf. 6, 503–564 (1970)
Landau, L., Lifshitz, E.M.: Mecanique des Fluides. MIR, Moscow (1971)
Iordache, D.A.: Selected Works of Numerical Physics. Printech, Bucuresti (2000)
Dobrescu, R., Iordache, D.: Complexity and Information. Romanian Academy Printing House, Bucharest (2010)
Kolmogorov, A.N.: A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high reynolds number. J. Fluid Mech. 13(1), 82–85 (1962)
Iordache, D.A., Iordache, V.: On the compatibility of the multi-fractal and similitude descriptions of the fracture parameters relative to the existing experimental data for concrete specimens. In: Proceedings of 1st South-East European Symposium on Interdisciplinary Approaches in Fractal Analysis (IAFA-3), Bucharest, 7–10 May, pp. 55–60 (2003)
Mandelbrot, B.B.: On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. J. Fluid Mech. 72(3), 401–416 (1975)
Witten Jr., T.A., Sander, L.M.: Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 47(19), 1400 (1981)
Bak, P., Tang, C., Wiesenfeld, K.: Self-organized criticality: an explanation of the 1/f noise. Phys. Rev. Lett. 59(4), 381 (1987)
Petrescu, A.D., Sterian, A.R., Sterian, P.E.: Solitons propagation in optical fibers computer experiments for students training. In: Gervasi, O., Gavrilova, M.L. (eds.) ICCSA 2007. LNCS, vol. 4705, pp. 450–461. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74472-6_36
Iordache, D.A., Pusca, S., Iordache, V.: Limit laws, frequency power laws and fractal scaling in technological series of ferrimagnetic materials. Rev. Non-conventional Technologies 4, 7–12 (2005)
Gompertz, B.: On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Phil. Trans. Roy. Soc. 115, 513 (1825)
Einstein, A.: Strahlungs-emission und –absorption nach der Quantentheorie. Deutsche Physikalische Gesellchaft 18, 318–323 (1916)
Steel, G.G.: Growth Kinetics of Tumors. Clarendon Press, Oxford (1974)
Weldom, T.E.: Mathematical model in Cancer Research. Adam Hilger, Briston (1988)
Delsanto, P.P., Griffa, M., Condat, C.A., Delsanto, S., Morra, L.: Phys. Rev. Lett. 94(14), 148105 (2005)
Guiot, C., Pugno, N., Delsanto, P.P.: Elasto-mechanical model of tumor-invasion. Appl. Phys. Lett. 89, 1 (2006)
Castorina, P., Delsanto, P.P., Guiot, C.: Phys. Rev. Lett. 96(18), 188701 (2006)
Royama, T.: Analytic Population Dynamics. Chapman & Hall, London (1992)
Brown, J.H., West, G.B. (eds.): Scaling in Biology. Oxford University Press, New York (2000)
West, G.B., Brown, J.H., Enquist, B.J.: A general model for ontogenetic growth. Nature 413(6856), 628 (2001)
West, G.B., Brown, J.H.: Life’s universal scaling laws. Phys. Today 57(9), 36–43 (2004)
Delsanto, P.P., Guiot, C., Degiorgis, P.G., Condat, C.A., Mansury, Y., Deisboeck, T.S.: Growth model for multicellular tumor spheroids. Appl. Phys. Lett. 85(18), 4225–4227 (2004)
Guiot, C., Delsanto, P.P., Carpinteri, A., Pugno, N., Mansury, Y., Deisboeck, T.S.: The dynamic evolution of the power exponent in a universal growth model of tumors. J. Theor. Biol. 240(3), 459–463 (2006)
Delsanto, P.P., Gliozzi, A.S., Guiot, C.: Scaling, growth and cyclicity in biology: a new computational approach. Theor. Biol. Med. Model. 5, 5 (2008)
Hartung, K.: Healthy Child. In: Venzmer, G. (ed.) New Health Book. Bertelsmann, Ratgeberverlag, Reinhard Mohn (1965;1969)
Guth, A.H.: Inflationary universe: a possible solution to the horizon and flatness problems. Phys. Rev. D. 23(2), 347 (1981)
Barontini, M., Dahia, P.L.: VHL disease. Best Pract. Res. Clin. Endocrinol. Metab. 24(3), 401–413 (2010)
Linde, A.: Inflation and quantum cosmology. Phys. Scr. 1991(T36), 30 (1991)
Iordache, D., Delsanto, P.P., Iordache, V.: Similitude models of some growth processes. In: Proceedings of 9th WSEAS International Mathematics and Computers in Biology and Chemistry (MCBC 2008), Bucharest, Romania, 54–59, 24 June 2008
Leibundgut, B., Sollerman, J.: A cosmological surprise: the universe accelerates. Europhys. News 32(4), 121–125 (2001)
Dobrescu, R., Iordache, D.: Complexity Modeling (in Romanian). Politehnica Press, Bucharest (2007)
Wilson, K.G.: Re-normalization group and critical phenomena. Phys. Rev. B 4, 3174–3184 (1971)
Majorana, E.: Il valore delle leggi statistiche nella fisica e nelle scienze sociali. Scientia, Febbraio-Marzo, p. 58 (1942)
Bodegom, E., Iordache, D.: Physics for Engineering students, vol. 1. Politehnica Press, Bucharest (2007)
Prigogine, I., Nicolis, G.: Self-Organization in Non-Equilibrium Systems: From Dissipative Structures to Order Through Fluctuations. Wiley, New York (1977)
Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(4), 623–656 (1948)
Mantegna, R.N.: The tenth article of Ettore Majorana. Europhy. News 37(4), 15–17 (2006)
Domb, C., Sykes, M.F.: On the susceptibility of a ferromagnetic above the Curie point. Proc. R. Soc. Lond. A 240(1221), 214–228 (1957)
Zinn-Justin, J.: Quantum Field Theory and critical Phenomena, 4th edn. Oxford University Press, New York (2002)
Iordache, D.: L’étude de la courbe dynamique d’aimantation d’un ferrite mixte de manganèse et zinc, de haute perméabilité. Bull. Polytech. Insts. Bucharest, 29(3) 25–41(1967)
Müller, G.: Rheological properties and velocity dispersion of a medium with power-law dependence of Q on frequency. J. Geophys. 54, 20–29 (1983)
Daniello, L., Iordache, D., et al.: Study of the frequency dependence of the viscosity coefficient of the bloch wall oscillations. Rev. Roum. Phys. 25(2), 193–198 (1980)
Stevens, S.S.: On the psychophysical law. Psychol. Rev. 64(3), 153 (1957)
Kolmogorov, A.N.: J. Fluid Mech. 13, 82 (1962)
Mandelbrot, B.B.: On the geometry of homogeneous turbulence, with stress on the fractal dimension of the iso-surfaces of scalars. J. Fluid Mech. 72(3), 401–416 (1975)
Iordache, D.A.: Contributions to the study of Numerical Phenomena intervening in the Computer Simulations of some Physical Processes. Credis Printing House, Bucharest, 118 p. (2004)
Courant, R., Hilbert, D.: Methods of Mathematical Physics. Wiley Interscience Publishers, New York, London (1962)
Hildebrand, F.B.: Methods of Applied Mathematics, pp. 36–122. Prentice-Hall, New Jersey (1965)
Delsanto, P.P., Chaskelis, H.H., Whitcombe, T., Mignogna, R.: Connection machine simulation of boundary effects in ultrasonic NDE. In: Ruud, C.O., Bussière, J.F., Green, R.E. (eds.) Nondestructive Characterization of Materials IV. Springer, Boston, MA (1991). https://doi.org/10.1007/978-1-4899-0670-0_26
Iordache, D.A., Sterian, P., Sterian, A.R., Pop, F.: Complex computer simulations, numerical artifacts, and numerical phenomena. Int. J. Comput. Commun. Control 5(5), 744–754 (2010)
Roşu, C., et al.: Mod. Phys. Lett. B 24(01), 65–73 (2010)
Levenberg, K.: Quart. Appl. Math. 164(1941)
Marquardt, D.W.: An algorithm for least-squares estimation of non-linear parameters. J. Soc. Industr. Appl. Math. 11, 431–441 (1963)
Mei, Z., Morris Jr., J.W.: Mössbauer spectrum curve fitting with a personal computer. Nucl. Instr. Meth. Phys. Res. Sect. B: Beam Interact. Mater. Atoms 47(2), 181–186 (1990)
Bodegom, E., Mcclure, D.W., Delsanto, P.P., Gliozzi, A., Iordache, D.A., Pop, F., Rosu, C., Widemhorn, R.: Computational Physics Guide (2009)
Iordache, D.A., Sterian, P., Tunaru, I.: Study of the gradient method aided dark current spectroscopy of CCDs. Annal. Rom. Sci. Ser. Sci. Technol. Inf. 6(2), 23–42 (2013)
Janesick, J.R.: Scientific charge-coupled devices. SPIE Press, Bellingham (2000). Appendices G1-G4, H1-H3
Widenhorn, R.: Charge Coupled Devices. VDM, Saarbruecken, Germany (2008)
Iordache, D.A., Sterian, P.E., Tunaru, I.: Charge coupled devices as particle detectors. Adv. High Energ. Phys. 2013, 12 (2013)
Widenhorn, R., Bodegom, E., Iordache, D., Tunaru, I.: Computational Approach to Dark Current Spectroscopy in CCDs as complex systems. I. Experimental part and choice of the uniqueness parameters. Print at the Scientific Bull. Univ. “Politehnica” Bucharest, 1 January 2010
Hall, R.N.: Electron-hole recombination in germanium. Phys. Rev. 87(2), 387 (1952)
Shockley, W., Read Jr., W.T.: Statistics of the recombinations of holes and electrons. Phys. Rev. 87(5), 835 (1952)
Sze, S.M., Ng, K.K.: Physics of Semiconductor Devices. Willey, Hoboken (1981)
Widenhorn, R., Blouke, M.M., Weber, A., Rest, A., Bodegom, E.: Temperature dependence of dark current in a CCD. In: Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications III, vol. 4669, pp. 193–202, 24 April 2002
Widenhorn, R., Blouke, M.M., Weber, A., Rest, A., Bodegom, E.: Temperature dependence of dark current in a CCD. In: Sensors and Camera Systems for Scientific, Industrial, and Digital Photography Applications III, vol. 4669, pp. 193–202, 24 April 2002
Rogojan, R., Sterian, P.E., Sterian, A.R., Elisa, M.: Spectral behavior and nonlinear optical properties of aluminophosphate semiconductor-doped glasses. In: 11th International School on Quantum Electronics: Laser Physics and Applications, vol. 4397, pp. 358–362, 9 April 2001
Landau, R.H., Paez, R.H.: Computational Physics: Problem Solving with Computers. Wiley, New York, Chichester (1997)
Dima M, et al.: The QUANTGRID project (RO)—quantum security in GRID computing applications. In: AIP Conference Proceedings, AIP, vol. 1203(1) (2010)
Iliescu, F.S., Sterian, A.P., Barbarini, E., Avram, M., Iliescu, C.: Continuous separation of white blood cell from blood in a microfluidic device. UPB Sci. Bull. Ser. A. 71(4), 21–30 (2009)
Maciuc, F.C., Stere, C.I., Sterian, A.R.: Rate equations for an erbium laser system: a numerical approach. In: Sixth Conference on Optics, ROMOPTO 2000, 29 Jun, vol. 4430, pp. 136–147 (2001)
Lazar, B., et al.: Simulating delayed pulses in organic materials. Comput. Sci. Appl. 2006, 779–784 (2006)
Sterian, A., Sterian, P.: Mathematical models of dissipative systems in quantum engineering. Math. Prob. Eng. 2012, 12 (2012). Article ID 347674
Ninulescu, V., Sterian, A.-R.: Dynamics of a two-level medium under the action of short optical pulses. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Laganà, A., Lee, H.P., Mun, Y., Taniar, D., Tan, Chih Jeng Kenneth (eds.) ICCSA 2005. LNCS, vol. 3482, pp. 635–642. Springer, Heidelberg (2005). https://doi.org/10.1007/11424857_70
Sterian, A., Ninulescu, V.: Nonlinear phenomena in erbium-doped lasers. In: Gervasi, O., Gavrilova, M.L., Kumar, V., Laganà, A., Lee, H.P., Mun, Y., Taniar, D., Tan, C.J.K. (eds.) ICCSA 2005. LNCS, vol. 3482, pp. 643–650. Springer, Heidelberg (2005). https://doi.org/10.1007/11424857_71
Dănilă, O., et al.: Perspectives on entangled nuclear particle pairs generation and manipulation in quantum communication and cryptography systems. Adv. High Energ. Phys. 2012, 10 (2012)
Dima, M., et al.: Classical and quantum communications in grid computing. Optoelectron. Adv. Mater. Rapid Commun. 4(1), 1840–1843 (2010)
Stefanescu, E., et al.: Study on the fermion systems coupled by electric dipol interaction with the free electromagnetic field. In: Proceedings of SPIE 5850, Advanced Laser Technologies 2004, 160 (2005)
Sterian, A.R.: Computer modeling of the coherent optical amplifier and laser systems. In: Gervasi, O., Gavrilova, M.L. (eds.) ICCSA 2007. LNCS, vol. 4705, pp. 436–449. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74472-6_35
Anghel, D.A., et al.: Modeling quantum well lasers. Math. Prob. Eng. 2012, 11 (2012)
Urquhart, P. (ed.): Advances in Optical Amplifiers. InTech, Rijeka, Croatia (2011)
Acknowledgements
The authors thank very much to Professor Pier Paolo Delsanto and to Dr. Marco Scalerandi from Dipartimento di Fisica di Politecnico di Torino for their valuable cooperation concerning the Finite Differences and LISA methods, as well as to Professors Erik Bodegom and Ralf Widenhorn from the Physics Department of the Portland State University for their important awarded information and suggestions concerning the field of Charge Coupled Devices.
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Iordache, D.A., Sterian, P.E. (2018). Study of Some Complex Systems by Using Numerical Methods. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2018. ICCSA 2018. Lecture Notes in Computer Science(), vol 10961. Springer, Cham. https://doi.org/10.1007/978-3-319-95165-2_38
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