We have published "Key Concepts of Science of Forms —Biological and Medical Fields" as a Special Issue of Forma, Vol. 27, 2012. It was composed of translations of some articles from the part of biology and medicine in the "Encyclopedia of Science of Forms" published in 2004 by Asakura Shoten Co. Ltd. This Encyclopedia has some other parts, such as physics, chemistry, geology, astronomy, mathematics and technology. In the present issue articles from physics and chemistry are picked up. However, the articles concerned to crystals are not included; a new issue for this field will be scheduled in future. Some translations are published as review articles because their contents are enriched by adding new topics.

Now, we hope that readers enjoy reading this special issue.

A large variety of polyhedral carbon forms, based on closed network of 5/6 rings of carbon, was discovered near the end of 20th century and named fullerenes. Typical forms of the members of fullerenes, including C₆₀, carbon nanotubes and carbon nano-onions are briefly introduced. In spite of unprecedented vigor in research and developmental activities into the properties and applications of fullerenes, the origin of exotic forms in fullerenes still remains unknown. We propose here that the fullerenes could be the results of crystallization of complex plasma of carbon. Close analogy between carbon nano-onions and mm-sized Coulomb balls is mentioned. The latters are nested spherical shells consisting of micron-sized plastic spheres and crystallized in spherical potential field.

Quasicrystals display diffraction patterns with symmetries forbidden in crystallography, and quasi-periodicity, have been found to be stable phases in several alloy systems. Thanks to their stability, one can grow single grained quasicrystals with large scale. In this article, we will first make a brief introduction to quasicrystals and describe the state of the art of structure for icosahedral quasicrystal. The morphologies of icosahedral quasicrystals are discussed in terms of atomic structures, surface structures and crystal growth mechanism.

Percolation model is one of the most foundamental models holding important concept such as phase transition, growth phenomena, universality, and also it provides clues for studies of transport coefficients of porous media, forest fire, epidemics in an orchard, networks and so on. There are mainly two types of percolation models, discrete percolation model and continuum percolation model. The former is based on a lattice structure, where some exact solutions are found, while the latter on continuum space, where more experimental investigations are expected.

Dynamics of vortices of filament type is introduced for the following three cases: deformation of a vortex filament by self-induction, entanglement of two vortex filaments by self-and mutual inductions and reconnection of two vortex filaments. The first two cases are treated by the use of vorticity equation without the viscous term, while the third one requires a treatment with the effect of viscosity.

In this work we review recent developments of experimental studies on chemically driven convection (CDC) emerging in a thin solution layer of the Belousov-Zhabotinsky reaction. Firstly, there are solitary waves due to convections and oscillatory or rotating convections accompanied by phase waves leading to global flow-pattern dynamics (called "flow waves"). The mechanism to realize the coherency and/or synchrony of such hydrodynamic patterns has not been established yet. Secondly, we summarize several models explaining some of these dynamics and show problems of the models. Especially, we emphasize the role of synchrony among nonlinear oscillators to establish hierarchical pattern dynamics of chemical wave trains and the flow waves. Thirdly, we demonstrate several examples of evolutionary pattern dynamics induced by CDCs in a batch reactor. In the reactor, the emerging phenomena show temporal development and evolutionary pattern dynamics. The direction of this development is from simple to complex, which looks like an evolution emerging in a real reaction-diffusion-convection system.

Self-induced vibration of drops of liquid nitrogen and oxygen placed on a plate with room temperature was observed, and some theoretical studies of this phenomenon are made. The drop became flat owing to the gravity, and its plane shape showed a certain kind of vibration, where its peripheral shape had a standing wave. Moreover, as the drop size decreased through evapolation, the number of waves around the periphery decreased after sudden transitions. Theoretical analysis is made to predict normal mode frequencies for wave numbers 2～6, which agree well with experimental values. A mechanism of self-induction is proposed, which is based on an assumption on vapor flow around the drop.