Book summary
Summary of the book…
Title
English title
The continuous fields associated to the corpuscular systems
Original title (in Romanian)
Campurile continue asociate sistemelor corpusculare
Book cover
Author
C. Vamos
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy
Contents
Ch. I Derivation of Balance Equations
1. Continuous fields
2. Corpuscular systems
3. The derivation of the balance equations
4. Coarse-grained averages
5. The derivation of the Liouville equation
II. Applications of Balance Equations
6. The numerical modeling of diffusion
7. Granular flows
8. The continuous model of the lipidic bilayer
9. Financial hydrodynamics
10. The monotone trend estimation
Bibliography
Keywords
keyword1,
References
see the expanding block below
Cite this book as:
C. Vamos, The continuous fields associated to the corpuscular systems, Risoprint, 2007, Cluj-Napoca, Romania.
Book Title
Continuous fields associated to corpuscular systems,
Publisher
Editura Risoprint, Cluj-Napoca
Print ISBN
ISBN 978-973-751-557-5
Google scholar
The book on google scholar.
[1] A. Akhiezer et P. Pel´etminski, Les m´ethodes de la physique statistique, Mir, Moscou, 1980.
[2] E.L. Andreas and G. Trevino, Using wavelets to detect trends, Journal of Atmospheric and Oceanic Technology 14 (1996) 554-564.
[3] A. Aspect, P. Grangier, and G. Roger, Experimental realization of Eistein-Podolsky-Rosen-Bohm Gedankenexperiment: a new violation of Bell’s inequalities, Phys. Rev. Lett. 49 (1982) 91-94.
[4] R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, Wiley, New York, 1975.
[5] R.J. Bearman and J.G. Kirkwood, The Statistical Mechanical Theory of Transport Processes. XI. Equations of Transport in Multi-component Systems, J. Chem. Phys., 28 (1958) 136 (¸si ˆın [33], pag. 153).
[6] M. Bloom, E. Evans and O.G. Mouritsen, Physical properties of the fluid lipid-bilayer component of cell membranes: a perspective, Q. Rev. Biophys., 24 (1991) 293-307.
[7] D. Bohm, A suggested interpretation of the quantum theory in terms of hidden variables, Phys. Rev. 85 (1952) 166-179.
[8] F. Bonetto, J.L. Lebowitz and L. Rey-Bellet, Fourier’s law: a challenge to theorists, in Mathematical Physics 2000, edited by A. Fokas, A. Grigorian, T. Kibble and B. Zegarlinski, Imperial College Press, London, 2000.
[9] G.E.P. Box and G.M. Jenkins, Time Analysis: Forcasting and Control, 2nd ed., Holden Day, San Francisco, 1976.
[10] P.J. Brockwell and R.A. Davies, Time Series: Theory and Methods, 2nd ed., Springer-Verlag, New York, 1991.
[11] S. Chapman and Cowling, The Mathematical Theory of Non-uniform Gases, Cambridge University Press, Cambridge, 1953.
[12] C. Cercignani, Mathematical Methods in Kinetic Theory, Plenum, New York, 1990.
[13] E.G.D. Cohen, Fifty years of kinetic theory, Physica A, 194 (1993) 229-257.
[14] G. Cuniberti and L. Matassini, Liquid markets and market liquids. Collective and single-asset dynamics in financial markets, Eur. Phys. J. B 20 (2001) 561-564.
[15] L. Dragos, The Principles of the Continuum Mechanics, Ed. Tehnica, Bucuresti, 1983 (in Romanian).
[16] Y. Du, H. Li, and P. Kadanoff, Breakdown of Hydrodynamics in a OneDimansional System of Inelastic Particles, Phys. Rev. Lett. 78 (1995) 1269-1271.
[17] R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill Book Company, New York, 1965.
[18] C.W. Gardiner, Handbook of Stochastic Methods (for Physics, Chemistry and Natural Science), Springer-Verlag, Berlin, 1983.
[19] I.M. Gel’fand and A.M. Yaglom, Integration in Functional Spaces and its Applications in Quantum Physics, J. Math. Phys., 1 (1960) 48-69.
[20] S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge, Turbulent cascades in foreign exchange markets, Nature 381 (1996) 767-770.
[21] O. Gherman and L. Saliu, Statistical Physics, Ed. Tehnica, Bucuresti, 1976 (in Romanian).
[22] P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations, Wiley, London, 1971.
[23] I. Goldhirsh and G. Zanetti, Clustering instability in dissipative gases,Phys. Rev. Lett., 70 (1993) 1619-1622.
[24] P.K. Haff, Grain flow as a fluid-mechanical phenomenon, J. Fluid Mech.134 (1983) 401-430.
[25] R.C. Haskel, D.C. Petersen and M.W. Johnson, Light-scattering technique for the study of dynamic thickness fluctuations in liquid films, Phys. Rev. E, 47 (1993) 439-451.
[26] W. Helfrich, Steric interaction of fluid membranes in multilayer systems, Z. Naturforsch., 33a (1978) 305-315.
[27] J.H. Irving and J.G. Kirkwood, The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodinamics, J. Chem. Phys., 18 (1950) 817 (¸si ˆın [33], pag. 52).
[28] J.T. Jenkins and S.B. Savage, A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles, J. Fluid Mech. 130 (1983) 187-202.
[29] P.D. Jones and M.E. Mann, Climate over past millennia, Reviews of Geophysics 42 (2002) RG2002.
[30] J.B. Keller, Bohm’s interpretetion of the quantum theory in terms of ”hidden” variables, Phys. Rev 89 (1953) 1040-41.
[31] C. Kipnis and C. Landim, Scaling limits of interacting particles systems, Springer, Berlin, 1999.
[32] J.G. Kirkwood, The statistical mechanical theory of transport processes. I. General theory, J. Phys. Chem., 14 (1946) 180-201 (¸si ˆın [33], pag. 1).
[33] J.G. Kirkwood, Selected Topics in Statistical Mechanics, Edited by R.W. Zwanzig, Gordon and Breach, New York, 1967.
[34] A. Kolmogorov et S. Fomine, El´ements de la th´eorie des fonctions et de l’analyse fonctionelle, Mir, Moscou, 1974.
[35] J. Koplik and J.R. Banavar, Continuum deductions from molecular hydrodynamics, Annu. Rev. Fluid Mech., 27 (1995) 257-292.
[36] L. Laloux, P. Cizeau, J. Bouchaud and M. Potters, Noise Dressing of Financial Correlation Matrices, Phys. Rev. Lett. 83 (1999) 1467-1470.
[37] R. Lipowsky, The conformation of membranes, Nature, 349 (1991) 475-481.
[38] L. Landau et E. Lifchitz, Physique theorique, tome I, Mecanique, Mir, Moscou, 1969.
[39] L. Landau et E. Lifchitz, Physique theorique, tome I, Mecanique quantique. Theorie non relativiste, Mir, Moscou, 1974.
[40] L. Landau and E. Lifchitz, Statistical Physics, Ed. Tehnica, Bucuresti, 1988 (in Romanian).
[41] L. Landau et E. Lifchitz, Physique theorique, tome VI, Mecanique des fluides, Mir, Moscou, 1971.
[42] B.B. Mandelbrot, Fractals and Scaling in Finance. Discontinuity, Concentration, Risk, Springer, New York, 1997.
[43] R.N. Mantegna and H.E. Stanley, Scaling behaviour in the dynamics of an economic index, Nature 376 (1995) 46-49.
[44] R.N. Mantegna and H.E. Stanley, An Introduction to Econophysics, Cambridge University Press, Cambridge, 2001.
[45] J.W. Moffat, A dynamical model of the capital markets, Physica A 264 (1999) 532-542.
[46] I. Muller, Thermodynamics, Pitman, Boston, 1985.
[47] A.J. Murdoch, The motivation of continuum concepts and relations from discrete considerations, Q. J. Mech. Appl. Math., 36 (1983) 163-187.
[48] A.J. Murdoch, A corpuscular approach to continuum mechanics: basic considerations, Arch. Rational Mech. Anal., 88 (1985) 291-321.
[49] V. Plerou, P. Gopikrishnan, B. Rosenow, L.N. Amaral and H.E. Stanley, Universal and nonuniversal properties of cross correlations in financial time series, Phys Rev Lett. 83 (1999) 1471-1474.
[50] L.Z. Rumshiski, Mathematical Processing of the Experimental Data, Ed. Tehnica, Bucure¸sti, 1974 (in Romanian).
[51] M. Shinbrot, Lectures on Fluid Mechanics, Gordon and Breach, London, 1973.
[52] H. Spohn, Large Scale Dynamics of Interacting Particles, Springer, Berlin, 1991.
[53] L. Peliti and S. Leibler, Effects of thermal fluctuations on systems with small surface tension, Phys. Rev. Lett., 54 (1985) 1690-1693.
[54] D.B. Percival and A.T. Walden, Wavelet Methods for Time Series Analysis, Cambridge University Press, 2000.
[55] H. Poincare, Science and Hypothesis, Ed. Stiintifica ¸si enciclopedica, Bucuresti, 1986 (in Romanian).
[56] A. Sveshnikov and A. Tikhonov, The Theory of Functions of a Complex Variable, Mir Publishers, Moscow, 1978.
[57] T. Takabayasi, On the Formulation of Quantum Mechanics associated with Classical Pictures, Progr. Theor. Phys. 8 (1952) 143-182.
[58] M. Tarek, D.J. Tobias and M.L. Klein, Molecular dynamics simulation of tetradecyltrimethylammonium bromide monolayers at the air/water interface, J. Phys. Chem., 90 (1995) 1393-1402.
[59] C. Truesdell and R. Toupin, The Classical Field Theories, in Handbuch der Physik, III/1, Springer, Berlin, 1960.
[60] C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics, in Handbuch der Physik, III/3, Springer, Berlin, 1965.
[61] C. Vamos, Automatic algorithm for monotone trend removal, Phys. Rev. E 75 (2007) 036705.
[62] C. Vamos, A. Georgescu, and N. Suciu, Balance equations for the vector fields defined on orientable manifolds, Tensor N.S. 54 (1993) 63-67.
[63] C. Vamos, A. Georgescu, N. Suciu and I. Turcu, Balance equations for physical systems with corpuscular structure, Physica A, 227 (1996) 81-92.
[64] C. Vamos, A. Georgescu and N. Suciu, Balance equations for a finite number of particles, St. Cerc. Mat., 48 (1996) 115-127.
[65] C. Vamos and T. Petrila, Velocity balance equation for a fluid mixture, Rev. Roum. Sci. Techn.-Mec. Appl. 38 (1993) 277-282.
[66] C. Vamos, N. Suciu and W. Blaj, Derivation of one-dimensional hydrodynamic model for stock price evolution, Physica A, 287 (2000) 461-467.
[67] C. Vamos, N. Suciu and A. Georgescu, Hydrodynamic equations for one-dimensional systems of inelastic particles, Phys. Rev. E, 55, (1997) 6277-6280.
[68] C. Vamo¸s, N. Suciu, and M. Peculea, Numerical Modelling of OneDimensional Diffusion by Random Walk, Revue d’Analyse Numerique et de Theorie de l’Approximation, Tome XXVI, Nr. 1-2, (1997) 237 247.
[69] C. Vamo¸s, N. Suciu, and H. Vereecken, Generalized random walk algorithm for the numerical modeling of complex diffusion processes, J. Comp. Phys., 186 (2003) 527-544.
[70] J. Voit, The Statistical Mechanics of Financial Markets, Springer, Heidelberg, 2001.
[71] J. von Neumann, Mathematical Foundations of Quantum Mechanics, University Press, Princeton, 1955.
[72] T. Xiang and B.D. Anderson, Molecular distributions in interphases: statistical mechanical theory combined with molecular dynamics simulation of a model lipid bilayer, Biophys. J., 66 (1994) 561-573.
[73] S. Zhao and G.W. Wei, Jump process for the trend estimation of time series, Computational Statistics & Data Analysis 42 (2003) 219-241.