By Sushanta Dattagupta
Within a unifying framework, Diffusion: Formalism and Applications covers either classical and quantum domain names, in addition to a number of purposes. the writer explores the greater than centuries-old historical past of diffusion, expertly weaving jointly various subject matters from physics, arithmetic, chemistry, and biology.
The ebook examines the 2 detailed paradigms of diffusion—physical and stochastic—introduced through Fourier and Laplace and later unified by way of Einstein in his groundbreaking paintings on Brownian movement. the writer describes the function of diffusion in chance concept and stochastic calculus and discusses themes in fabrics technological know-how and metallurgy, akin to defect-diffusion, radiation harm, and spinodal decomposition. additionally, he addresses the impression of translational/rotational diffusion on experimental facts and covers reaction-diffusion equations in biology. concentrating on diffusion within the quantum area, the ebook additionally investigates dissipative tunneling, Landau diamagnetism, coherence-to-decoherence transition, quantum details procedures, and electron localization.
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Additional info for Diffusion: Formalism and Applications
VIII 235, 5. N. 2010. Phys. Today. Narasimhan, T. N. 2009 (July). The dichotomous history of diffusion. Phys. Today. 48. Narasimhan, T. N. 2010. Current Sci. 98, 23. Pais, A. 2008. Subtle Is the Lord: The Science and Life of Albert Einstein. Oxford: Oxford University Press. Pearson, K. 1905. Nature 72, 294. Polya, G. 1920. 8, 171. Rayleigh, Lord. 1894. The Theory of Sound. London. Macmillan (reprinted 1929). , Ed. 1954. Selected papers. In Noise and Stochastic Processes. New York: Dover. Zwanzig, R.
1 Introduction At the beginning of Chapter 3, we questioned whether diffusion in the sense of Brownian motion discussed in Chapter 1 is a Gaussian–Markov process. 50) to the one-dimensional position coordinate x of the Brownian particle. The purpose of this chapter is to pursue this issue further by examining the mathematical structure of Brownian motion in detail (Chandrasekhar 1943) with the aid of Langevin equations (Langevin 1908). The simplest of these equations refers to the stochastic dynamics of a free particle under the fluctuating effects of its environment, much like Brown’s pollen grains undergoing incessant collisions with the surrounding water molecules.
Subtle Is the Lord: The Science and Life of Albert Einstein. Oxford: Oxford University Press. Pearson, K. 1905. Nature 72, 294. Polya, G. 1920. 8, 171. Rayleigh, Lord. 1894. The Theory of Sound. London. Macmillan (reprinted 1929). , Ed. 1954. Selected papers. In Noise and Stochastic Processes. New York: Dover. Zwanzig, R. 2001. Nonequlibrium Statistical Mechanics. New York: Oxford University Press. 1 Genesis of Markov Concept In a paper, Einstein (1906) provided a mathematical basis of his thesis work and went on to propound the idea of a Markovian stochastic process (Bharucha-Reid 1960, Gillespie 1991).
Diffusion: Formalism and Applications by Sushanta Dattagupta