Introduction

Abstract

In this book, our attention is concentrated mainly on the underlying phenomenon of the diffusive action of chaotic flows (turbulence). Indeed, we shall be concerned with the subject of passive scalar transport, where by “scalar” we mean something like small particle or chemical species concentration and by “passive” we mean that the added substance does not change the nature of fluid to the point where turbulence is appreciably affected.

Further Reading

1.1 Diffusion Concept

• S.G. Brush, The Kind of Motion We Call Heat (North Holland, Amsterdam, 1976)

• C. Cercignani, Ludwig Boltzmann. The Man Who Trusted Atoms (Oxford University Press, Oxford, 1998)

• H.U. Fuchs, The Dynamics of Heat (Springer, Berlin, 2010)

• C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1985)

• D. Kondepudi, Introduction to Modern Thermodynamics (Wiley, Chichester, 2008)

• G.M. Kremer, An Introduction to the Boltzmann Equation and Transport Processes in Gases (Springer, Berlin, 2010)

• J.C. Maxwell, The Scientific Papers (Cambridge University press, Cambridge, 1890)

• R.M. Mazo, Brownian Motion, Fluctuations, Dynamics and Applications (Clarendon Press, Oxford, 2002)

• F. Schweitzer, Brownian Agents and Active Particles (Springer, Berlin, 2003)

• N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 2007)

• B. Zeldovich Ya, A.A. Ruzmaikin, D.D. Sokoloff, The Almighty Chance (World Scientific, Singapore, 1990)

1.2 Diffusion Equation

• G.I. Barenblatt, Scaling Phenomena in Fluid Mechanics (Cambridge University Press, Cambridge, 1994)

• H.C. Berg, Random Walks in Biology (Princeton University Press, Princeton, NJ, 1969)

• R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena (Wiley, New York, 2002)

• J.M. Burgers, The Nonlinear Diffusion Equation (D. Reidel, Dordrecht, 1974)

• H. Carslaw, Mathematical Theory of Conduction of Heat in Solids (Macmillan, London, 1921)

• L. Dresner, Similarity Solutions of Nonlinear Partial Differential Equations (Longman, London, 1983)

• B. Perthame, Transport Equations in Biology (Birkhauser, Boston, MA, 2007)

• A.P.S. Selvadurai, Partial Differential Equations in Mechanics (Springer, Berlin, 2000)

• G.H. Weiss, Aspects and Applications of the Random Walk (Elsevier, Amsterdam, 1994)

• D.V. Widder, The Heat Equation (Academic, New York, 1975)

1.3 Anomalous Diffusion

• R. Balescu, Statistical Dynamics (Imperial College Press, London, 1977)

• D. Ben-Avraham, S. Havlin, Diffusion and Reactions in Fractals and Disordered Systems (Cambridge University Press, Cambridge, 1996)

• E.W. Montroll, M.F. Shlesinger, On the wonderful world of random walks, in Studies in Statistical Mechanics, ed. by J. Lebowitz, E.W. Montroll, vol. 11 (Elsevier Science Publishers, Amsterdam, 1984), p. 1

• E.W. Montroll, B.J. West, On an enriches collection of stochastic processes, in Fluctuation Phenomena, ed. by E.W. Montroll, J.L. Lebowitz (Elsevier, Amsterdam, 1979)

• A. Pekalski, K. Sznajd-Weron (eds.), Anomalous Diffusion. From Basics to Applications (Springer, Berlin, 1999)

• M.F. Shiesinger, G.M. Zaslavsky, Levy Flights and Related Topics in Physics (Springer, Berlin, 1995)

• D. Sornette, Critical Phenomena in Natural Sciences (Springer, Berlin, 2006)