The cover art depicts Jeffery Kelly's pioneering development of Tafamidis as a clinical strategy to ameliorate transthyretin protein aggregation (in the center). Surrounding images highlight examples from this special issue of how his work has influenced other approaches to characterize and target the etiology of diverse protein misfolding diseases.
The cover image shows the logo of the 15th International Conference on Quasicrystals, held at Tel Aviv University in June 2023. The logo depicts the hexagonal Star of David. The background depicts a hexagonal quasiperiodic tiling, whose construction and characterization are the focus of the Review by Coates et al. in this volume. Such aperiodic yet perfectly ordered trigonal and hexagonal tilings served to study various experimental systems, such as the 3-fold surfaces of icosahedral quasicrystals and 6-fold bilayer graphene.
We provide an overview on the theory of topological quantum numbers from the point of view of non-commutative topology. Topological phases are described by K-groups of C*-algebras. The algebras are constructed from the set of positions of the nuclei of the materials we want to study. Topological quantum numbers are Chern numbers of K-group elements. Maps between K-groups which are of algebraic topological origin provide the means to obtain relations between different topological quantum numbers as, for instance, in the bulk edge correspondence. We present simple aperiodic examples related to quasicrystals to illustrate the theory.
The study of quasicrystals – materials that are characterized by their aperiodic yet long-range ordered structures1-5 – continues to evolve, offering new challenges and opportunities in understanding complex-ordered systems that transcend traditional crystallography. They have emerged as a rich interdisciplinary field, encompassing mathematics, physics, chemistry, and materials science. This introduces the additional challenge of bridging varied research communities, each with its distinct language and culture. Central to the investigation of quasicrystals are mathematical tools that describe their intricate geometric and topological properties, physical models that capture their unique electronic and other physical properties, as well as innovative experimental methods that can be employed to analyze their unique and complex nature. This special issue of the Israel Journal of Chemistry is dedicated to the latest advancements in quasicrystal research, presented at ICQ15 – the 15th International Conference on Quasicrystals – held on the campus of Tel Aviv University in June 2023 (see Fig. 1 for a group photo). It offers a valuable snapshot of the current state of quasicrystal research, highlighting the progress made in recent years and the challenges that lie ahead. The collection of Reviews and Research Articles, included here, spans a broad spectrum of topics, reflecting the diverse and interdisciplinary nature of quasicrystal research, providing a good entry point, as well as some deep insight, into the theoretical, experimental and practical underpinnings of aperiodic long-range order.
Liquid phase TEM has attracted widespread attention in recent years as a groundbreaking tool to address various fundamental problems in nanoscience. It has provided the opportunity to reveal many unseen dynamic phenomena of nanoscale materials in solution processes by direct imaging through liquids with high spatial and temporal resolution. After my earlier work on real-time imaging of the nucleation, growth, and dynamic motion of nanoparticles in liquids by developing high-resolution liquid phase transmission electron microscopy (TEM) down to the sub-nanometer level, I established my own research group at Lawrence Berkeley National Lab in 2010. My group focuses on developing and applying liquid phase TEM to investigate complex systems and reactions. We have studied a set of scientific problems centered on understanding how atomic level heterogeneity and fluctuations at solid-liquid interfaces impact nanoscale materials transformations using advanced liquid phase TEM. This article describes my personal journey in nanoscience, highlighting the main discoveries of my research group using liquid phase TEM as a unique tool. Some perspectives on the impacts of liquid phase TEM and the future opportunities in nanoscience and nanotechnology enabled by liquid phase TEM are also included.
Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and potentials. In this review, we present some generalisations of substitutions, with a focus on substitutions on compact alphabets, and with an outlook towards their spectral theory. Guided by two main examples, we will illustrate what changes when one moves from finite to compact (infinite) alphabets, and discuss under which assumptions do we recover the usual geometric and statistical properties which make them viable models of materials with almost periodic order. We also present a planar example (which is a two-dimensional generalisation of the Thue−Morse substitution), whose diffraction is purely singular continuous.