Vortex Molecular Crystal and Vortex Plastic Crystal States in Honeycomb and Kagome Pinning Arrays

Using numerical simulations, we investigate vortex configurations and pinning in superconductors with honeycomb and kagome pinning arrays. We find that a variety of novel vortex crystal states can be stabilized at integer and fractional matching field densities. The honeycomb and kagome pinning arrays produce considerably more pronounced commensuration peaks in the critical depinning force than triangular pinning arrays, and also cause additional peaks at noninteger matching fields where a portion of the vortices are located in the large interstitial regions of the pinning lattices. For the honeycomb pinning array, we find matching effects of equal strength at most fillings B/B_\phi=n/2 for n>2, where n is an integer, in agreement with recent experiments. For kagome pinning arrays, pronounced matching effects generally occur at B/B_\phi=n/3 for n>3, while for triangular pinning arrays pronounced matching effects are observed only at integer fillings B/B_\phi=n. At the noninteger matching field peaks in the honeycomb and kagome pinning arrays, the interstitial vortices are arranged in dimer, trimer, and higher order n-mer states that have an overall orientational order. We call these n-mer states "vortex molecular crystals" and "vortex plastic crystals" since they are similar to the states recently observed in colloidal molecular crystal systems. We argue that the vortex molecular crystals have properties in common with certain spin systems such as Ising and n-state Potts models. We show that kagome and honeycomb pinning arrays can be useful for increasing the critical current above that of purely triangular pinning arrays.Comment: 19 pages, 22 postscript figures. Version to appear in Phys. Rev.

Remote sensing of changes in morphology and physiology of trees under stress Annual progress report

Remote sensing of morphological and physiological changes in trees under stres

Jamming in Granular Polymers

We examine the jamming transition in a two-dimensional granular polymer system using compressional simulations. The jamming density \phi_c decreases with increasing length of the granular chain due to the formation of loop structures, in excellent agreement with recent experiments. The jamming density can be further reduced in mixtures of granular chains and granular rings, also as observed in experiment. We show that the nature of the jamming in granular polymer systems has pronounced differences from the jamming behavior observed for polydisperse two-dimensional disk systems at Point J. This result provides further evidence that there is more than one type of jamming transition.Comment: 5 pages, 7 postscript figures, version to appear in PR

On the Assouad dimension of self-similar sets with overlaps

It is known that, unlike the Hausdorff dimension, the Assouad dimension of a self-similar set can exceed the similarity dimension if there are overlaps in the construction. Our main result is the following precise dichotomy for self-similar sets in the line: either the \emph{weak separation property} is satisfied, in which case the Hausdorff and Assouad dimensions coincide; or the \emph{weak separation property} is not satisfied, in which case the Assouad dimension is maximal (equal to one). In the first case we prove that the self-similar set is Ahlfors regular, and in the second case we use the fact that if the \emph{weak separation property} is not satisfied, one can approximate the identity arbitrarily well in the group generated by the similarity mappings, and this allows us to build a \emph{weak tangent} that contains an interval. We also obtain results in higher dimensions and provide illustrative examples showing that the `equality/maximal' dichotomy does not extend to this setting.Comment: 24 pages, 2 figure

Multiscaling at Point J: Jamming is a Critical Phenomenon

We analyze the jamming transition that occurs as a function of increasing packing density in a disordered two-dimensional assembly of disks at zero temperature for ``Point J'' of the recently proposed jamming phase diagram. We measure the total number of moving disks and the transverse length of the moving region, and find a power law divergence as the packing density increases toward a critical jamming density. This provides evidence that the T = 0 jamming transition as a function of packing density is a {\it second order} phase transition. Additionally we find evidence for multiscaling, indicating the importance of long tails in the velocity fluctuations.Comment: 4 pages, 5 figures; extensive new numerical data; final version in press at PR

Silicon purification using a Cu-Si alloy source

Production of 99.9999% pure silicon from 98% pure metallurgical grade (MG) silicon by a vapor transport filtration process (VTP) is described. The VTF process is a cold wall version of an HCl chemical vapor transport technique using a Si:Cu3Si alloy as the silicon source. The concentration, origin, and behavior of the various impurities involved in the process were determined by chemically analyzing alloys of different purity, the slag formed during the alloying process, and the purified silicon. Atomic absorption, emission spectrometry, inductively coupled plasma, spark source mass spectrometry, and secondary ion mass spectroscopy were used for these analyses. The influence of the Cl/H ratio and the deposition temperature on the transport rate was also investigated