Two Spheres PDF Download

Columnar structures, many of which are helical, refer to dense cylindrical packings of particles. They are ubiquitous, for example, they exist in the contexts of botany, foams, and nanoscience. There have been in-depth investigations of columnar structures of both hard spheres (e.g., ball bearings) and soft spheres (e.g., wet foams), through computer simulations, analytic derivations, or simple experiments. This monograph serves as a comprehensive guide for scientists, engineers, or artists who would like to have a good grasp of the fundamentals and applications of such aesthetically appealing structures for their own professional interests. The book begins with an introduction to the field of packing problems, where such problems are closely related not only to the columnar structures presented in the book but also to the structures of condensed matter systems in general. It then discusses about columnar structures of spheres and overviews their classifications and applications. It reviews the models and concepts employed in the authors’ studies on columnar structures of spheres. It also details the method of sequential deposition for generating columnar structures of hard spheres computationally or experimentally. Lastly, it presents some latest findings on the columnar structures of soft spheres and on the structures obtained from the longitudinal compression of a hard-sphere chain in a cylindrical harmonic potential.