A One-Dimensional Model for Many-Electron Atoms in Extremely Strong Magnetic Fields: Maximum Negative Ionization

We consider a one-dimensional model for many-electron atoms in strong magnetic fields in which the Coulomb potential and interactions are replaced by one-dimensional regularizations associated with the lowest Landau level. For this model we show that the maximum number of electrons is bounded above by 2Z+1 + c sqrt{B}. We follow Lieb's strategy in which convexity plays a critical role. For the case of two electrons and fractional nuclear charge, we also discuss the critical value at which the nuclear charge becomes too weak to bind two electrons.Comment: 23 pages, 5 figures. J. Phys. A: Math and General (in press) 199

Equilibrium Shape of Crystals

This chapter discusses the equilibrium crystal shape (ECS) from a physical perspective, beginning with a historical introduction to the Wulff theorem. It takes advantage of excellent prior reviews, particularly in the late 1980's, recapping highlights from them. It contains many ideas and experiments subsequent to those reviews. Alternatives to Wulff constructions are presented. Controversies about the critical behavior near smooth edges on the ECS are recounted, including the eventual resolution. Particular attention is devoted to the origin of sharp edges on the ECS, to the impact of reconstructed or adsorbed surface phases coexisting with unadorned phases, and to the role and nature of possible attractive step-step interactions.Comment: Review from Handbook of Crystal Growth, Fundamentals, 2nd ed., T. Nishinaga, ed. (Elsevier, Amsterdam, 2015), vol. 1A (Thermodynamics and Kinetics), ch. 5, pp. 215-264; ISBN 9780444563699/eBook:9780444593764; http://www.sciencedirect.com/science/article/pii/B9780444563699000058. 26 figs., reformatted into Phys. Rev. style, 30 pages; slightly modified, alphabetized bibliography, inc. title