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# APPLICATIONS OF STATISTICAL MATHEMATICS

**A. Gadomski, J. Kertész, H.E. Stanley, N. Vandewalle**

ISBN **0444504095**

Pages **389**

Description

The field of statistical physics has undergone a spectacular development in recent years. The fundamentals of the subject have advanced dynamically with multidisciplinary approaches involving physicists, chemists and mathematicians. Equally spectacular has been the development of applications of statistical mechanics to shed light on a wide range of problems, many of them arising in fields quite distant from traditional physics disciplines. Recent applications range from such topics as oil recovery from porous rock to protein folding, DNA structure, morphogenesis and the cooperative behavior of living creatures. Concepts and methods of statistical physics have been applied successfully to 'exotic' problems that seem to be far from physics, such as vehicular and pedestrial traffic, or economy and finance.

This book presents not only the keynote invited talks, but a number of high quality, interesting, contributed communications from senior scientists and young students active in the field. Topics covered include DNA migration, wetting, chemical waves, granular media, molecular motors, biological pattern formation and motion, as well as practical problems such as heart diagnosis, internet traffic jamming, oil recovery and econophysics.

Contents

Preface. Keynote Invited Talks. Problems of DNA entry into a cell (P.-G. de Gennes). Charge inversion in DNA-amphiphile complexes: possible application to gene therapy (P.S. Kuhn, Y. Levin, M.C. Barbosa). Application of statistical mechanics to the wetting of complex liquids (F. Fondecave, F. Brochard-Wyart). Rotating chemical waves: theory and experiments (A. Volford et al. ). Formation of Liesegang patterns (Z. Ráz). Applications of statistical mechanics to non-brownian random motion (P. Kutner, K. Wysocki). Population dynamics and Burgers' equation (D.R. Nelson). Statistical physics model of an evolving population (K. Sznajd-Weron, A. Pekalski). Application of statistical physics to heartbeat diagnosis (S. Havlin et al. ). 'Sausage-string' deformations of blood vessels at high blood pressures (P. Alstrøm et al. ). Fractality, chaos, and reactions in imperfectly mixed open hydrodynamical flows (A. Pétek et al. ). Application of statistical physics to politics (S. Galam). Application of statistical physics to the Internet traffics (M. Takayasu, K. Fukuda, H. Takayasu). Applications of statistical mechanics in number theory (M. Wolf). Computational test of kinetic theory of granular media (M.D. Shattuck et al. ). Granular flow, collisional cooling and charged grains (D.E. Wolf, T. Scheffler, J. Schäfer). Application of statistical mechanics to collective motion in biology (T. Vicsek et al. ). Formation of colony patterns by a bacterial cell population (T. Matsushita et al. ). Application of statistical mechanics to stochastic transport (J. Luczka). Applications of statistical physics to economic and financial topics (M. Ausloos et al. ). Molecular motors and the forces they exert (M.E. Fisher, A.B. Kolomeisky). Application of braid statistics to particle dynamics (A.T. Skjeltorp, S. Clausen, G. Helgesen). Applications of statistical mechanics in subcontinuum fluid dynamics (M. Cieplak et al. ). Applications of statistical mechanics to natural hazards and landforms (D.L. Turcotte). Application of statistical physics to impact fragmentation (H. Inaoka, H. Takayasu). Equations of granular materials (S.F. Edwards). Contributed Communications. Phase separation in a weak first-order phase transition (H. Arkin et al. ). Fractal-type relations and extensions suitable for systems of evolving polycrystalline microstructures (A. Gadomski). On the application of statistical physics for the description of nonequilibrium effects in chemical systems (J. Gorecki, J.N. Gorecka). Strong motion duration effects on base isolated systems (R. Greco, G.C. Marano, D. Foti). Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking (K. Ivanova, M. Ausloos). Mean-field-type equations for spread of epidemics: the 'small world' model (A. Kleczkowski, B.T. Grenfell). Gaussian-logarithmic distribution of relaxation times in relaxor materials (R. Skulski). The effect of vibrational degrees of freedom on the phase transition in a 2D Ising model (S.V. Stroganova, M.I. Vasilevskiy, O.V. Vikhrova). Aging and self-organization of shear bands in granular materials (J. Török et al. ). Markov and non-Markov processes in complex systems by the dynamical information entropy (R.M. Yulmetyev, F.M. Gafarov).