Chiral patterns arising from electrostatic growth models

Recently, unusual and strikingly beautiful seahorse-like growth patterns have been observed under conditions of quasi-two-dimensional growth. These `S'-shaped patterns strongly break two-dimensional inversion symmetry; however such broken symmetry occurs only at the level of overall morphology, as the clusters are formed from achiral molecules with an achiral unit cell. Here we describe a mechanism which gives rise to chiral growth morphologies without invoking microscopic chirality. This mechanism involves trapped electrostatic charge on the growing cluster, and the enhancement of growth in regions of large electric field. We illustrate the mechanism with a tree growth model, with a continuum model for the motion of the one-dimensional boundary, and with microscopic Monte Carlo simulations. Our most dramatic results are found using the continuum model, which strongly exhibits spontaneous chiral symmetry breaking, and in particular finned `S' shapes like those seen in the experiments.Comment: RevTeX, 12 pages, 9 figure

Status of Muon Collider Research and Development and Future Plans

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides continued work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (CoM) that could be a factory for the s-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay ($\pi \to \mu \nu_{\mu}$) channel, muon cooling, acceleration, storage in a collider ring and the collider detector. We also present theoretical and experimental R & D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the R & D since the Feasibility Study of Muon Colliders presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].Comment: 95 pages, 75 figures. Submitted to Physical Review Special Topics, Accelerators and Beam