Columnar Structures of Spheres

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.

"The study of quasi-one-dimensional systems has undergone a renaissance of sort over the last decade. Novel computational and analytical tools have been developed and new soft-matter experimental systems have been investigated to enrich these findings. This book collates and reworks a series of reprints by the two authors and their coworkers that capture some of the most important advances in that field. The clear pedagogical effort of this book, supported by beautiful figures, is sure to stimulate further advances in this area."

~Prof. Patrick Charbonneau, Duke University, USA

"This monograph contains the joint research efforts of Winkelmann, Chan, and some of their colleagues on the packing problems of quasi-one-dimensional columnar structures. Based on the results from multiple numerical techniques, analytical calculations, and carefully designed experiments, some of the new advances in this field are beautifully presented. The materials are laid out in a very accessible and appealing way, which nonetheless does not diminish its scientific depth and value."

~Prof. Yujie Wang, Shanghai Jiaotong University, China

"This is the very first book addressing the topic of columnar packings of spheres, i.e., arrangements of spheres confined within a narrow cylindrical geometry. Using a comprehensive language, it encompasses the fundamentals of the problem with its applications in disciplines as diverse as botany and nanoscience."

~Prof. Iker Zuriguel, University of Navarra, Spain

"Winkelmann and Chan have thoroughly explained and beautifully illustrated the essence of packings in cylindrical confinement. Scientists, engineers, and artists alike will find this monograph fascinating, whether for the fundamentals of packing science or the elegance of aesthetic packing structures."

~Prof. Zexin Zhang, Soochow University, China