Table of contents

Some specific structures in which a growing quantity reaches record high values typically arise for instabilities in random media. Despite the rarity of these concentrations, they dominate the integral characteristics of the growing quantity (the mean value, the mean square value, etc.). The appearance of such structures is called "intermittency".The geometric properties of intermittent structures depend strongly on whether the growing quantity is a scalar or a vector. The scalar case is illustrated here by the example of an instability which arises in problems of chemical kinetics. The vector case is illustrated by the problem of the selfexcitation of a magnetic field in a random flow of a conducting fluid.

Topological solitons that polarize the Dirac vacuum can assume fractional fermion (and electric) charge. The effect is investigated in detail in low-dimensional [(1 + 1)- and (2 + 1 )-dimensional space-time] quantum field theory models. A review is given of phenomena associated with fractional charges found experimentally in quasi-one-dimensional (spin-charge anomaly in lightly doped polyacetylene) and two-dimensional systems (quantum Hall effect). Topics covered include: (1) fractional charge in one-dimensional quantum field theory models, (2) anomalous quantum numbers in the Peierls-Fröhlich system, and (3) twodimensional models of quantum field theory and the quantum Hall effect.

Contemporary transmission electron microscopes have resolutions down to 1.5–2 Å, and this enables one to observe atoms directly. A theory is presented of the formation of electronmicroscope images at atomic resolution, the influence of aberrations, the properties of the transfer function, and the methods of processing, calculating, and interpreting images. The relation is examined between electron microscopy and electron diffraction. Examples are given of electron-microscope studies of the atomic structure of various objects—molecules, crystals, various organic and inorganic compounds, including minerals and semiconductors, and of studies of defects of crystal-structure and of its formation during crystal growth.

CONTENTS 1. Introduction 420 2. Production of aerogels 420 3. Properties of aerogels 422 4. Sol-gel conversion 426 5. Applications of aerogels 427 6. Aerogels and ball lightning 428 7. Conclusion 431 References 432