Titlebook: Distributions in the Physical and Engineering Sciences, Volume 3; Random and Anomalous Alexander I. Saichev,Wojbor A. woyczyński Textbook 2

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Jan Lies,Christian Schicha,Falk Tennertel equations with anomalous diffusion. In the case when . is the Laplacian and the nonlinear term, .(.) is quadratic, the equation boils down to the classical Burgers equation that has been studied in Volume 2, and Chapter . of the present volume where it has been analyzed in the context of passive tracer transport in Burgers turbulence.

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https://doi.org/10.1007/978-3-319-92586-8Theory of Distributions; Anomalous fractional random dynamics; Generalized stochastic processes and fi

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Basic Distributional Tools for Probability Theorylds. The aim of this chapter is to introduce the basic definitions and ideas of probability theory, and show how the simple distribution-theoretic concepts of the Dirac delta, its derivatives, and other related distributions can constructively be used to streamline statistical calculations. This app

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Random Distributions: Generalized Stochastic Processescomplex numbers, but random quantities. Such random distributions can be thought of as generalized stochastic processes, or generalized stochastic fields, depending on whether we are discussing distributions on one-dimensional, or multi-dimensional spaces. The origins of the theory can be traced bac

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Dynamical and Statistical Characteristics of Random Fields and Waveslizations. In this chapter we discuss this phenomenon employing the tool of lognormal distributions. A preliminary analysis of parametric stochastic resonance, dynamical and statistical energy localization for wavefields in randomly layered media, wave-beam propagation in random parabolic waveguides

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Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows . along with the force . are known and random. Additionally we will study how statistical properties of passive tracers suspended in Burgers flows evolve in time. The first problem is often referred to as “Burgers turbulence” because Burgers equation, discussed in detail in Chapter 14 of Volume 2 o

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Probability Distributions of Passive Tracers in Randomly Moving Mediaium with random velocity field .. Both, the case of compressible, and of incompressible . media will be considered. The material is based on the authors’ paper [1]. In the previous chapter, we have investigated the passive tracer transport in randomly moving media governed by a simplified hydrodynam

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Linear Anomalous Fractional Dynamics in Continuous Medianal diffusion equations. The model reflects the asymptotic behavior of a jump (anomalous random walk) process with random jump sizes and random inter-jump time intervals with infinite means (and variances) which do not satisfy the law of large numbers. In the case when these intervals have a fractio

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Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Mediael equations with anomalous diffusion. In the case when . is the Laplacian and the nonlinear term, .(.) is quadratic, the equation boils down to the classical Burgers equation that has been studied in Volume 2, and Chapter . of the present volume where it has been analyzed in the context of passive