N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

Astrophysical magnetic fields and nonlinear dynamo theory

Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

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The phenomenology of small-scale turbulence

Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

Search for New Physics with Atoms and Molecules

The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

/pdf/the-structure-of-turbulent-shear-flow-2yf3szhaqb.pdf

The Structure of Turbulent Shear Flow

The saga of YIG: Spectra, thermodynamics, interaction and relaxation of magnons in a complex magnet

For a delta-correlated velocity field, simultaneous correlation functions of a passive scalar satisfy closed equations. We analyze the equation for the four-point function. To describe a solution completely, one has to solve the matching problems at the scale of the source and at the diffusion scale. We solve both the matching problems and thus find the dependence of the four-point correlation function on the diffusion and pumping scale for large space dimensionality $d$. It is shown that anomalous scaling appears in the first order of $1/d$ perturbation theory. Anomalous dimensions are found analytically both for the scalar field and for it's derivatives, in particular, for the dissipation field.

Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar.

Advection of a passive scalar θ in d = 2 by a large-scale velocity field rapidly changing in time is considered. The Gaussian feature of the passive scalar statistics in the convective interval was discovered in [1]. Here we examine deviations from the Gaussianity: we obtain analytically the simultaneous fourth-order correlation function of θ. Explicit expressions for fourth-order objects, like 〈(θ1 − θ2) 〉 are derived.

/pdf/fourth-order-correlation-function-of-a-randomly-advected-5d70ygof36.pdf

Fourth-order correlation function of a randomly advected passive scalar

We report a numerical study, supplemented by phenomenological explanations, of "energy condensation" in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to the emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard k{-5/3} one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to k{-1}. The fluctuations decay slowly as the coherent part grows.

/pdf/dynamics-of-energy-condensation-in-two-dimensional-3bnbpkkfq9.pdf

Dynamics of Energy Condensation in Two-Dimensional Turbulence

We describe the method for finding the non-Gaussian tails of the probability distribution function (PDF) for solutions of a stochastic differential equation, such as the convection equation for a passive scalar, the random driven Navier-Stokes equation, etc. The existence of such tails is generally regarded as a manifestation of the intermittency phenomenon. Our formalism is based on the WKB approximation in the functional integral for the conditional probability of large fluctuation. We argue that the main contribution to the functional integral is given by a coupled field-force configuration\char22{}the instanton. As an example, we examine the correlation functions of the passive scalar u advected by a large-scale velocity field \ensuremath{\delta} correlated in time. We find the instanton determining the tails of the generating functional, and show that it is different from the instanton that determines the probability distribution function of high powers of u. We discuss the simplest instantons for the Navier-Stokes equation. \textcopyright{} 1996 The American Physical Society.

/pdf/instantons-and-intermittency-17tnh1nv77.pdf

Igor Kolokolov

Papers

The saga of YIG: Spectra, thermodynamics, interaction and relaxation of magnons in a complex magnet

Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar.

Fourth-order correlation function of a randomly advected passive scalar

Dynamics of Energy Condensation in Two-Dimensional Turbulence

Instantons and Intermittency