Reversible stretching of homopolymers and random heteropolymers

We have analyzed the equilibrium response of chain molecules to stretching. For a homogeneous sequence of monomers, the induced transition from compact globule to extended coil below the $\theta$-temperature is predicted to be sharp. For random sequences, however, the transition may be smoothed by a prevalence of necklace-like structures, in which globular regions and coil regions coexist in a single chain. As we show in the context of a random copolymer, preferential solvation of one monomer type lends stability to such structures. The range of stretching forces over which necklaces are stable is sensitive to chain length as well as sequence statistics.Comment: 14 pages, 4 figure

Steiner t-designs for large t

One of the most central and long-standing open questions in combinatorial design theory concerns the existence of Steiner t-designs for large values of t. Although in his classical 1987 paper, L. Teirlinck has shown that non-trivial t-designs exist for all values of t, no non-trivial Steiner t-design with t > 5 has been constructed until now. Understandingly, the case t = 6 has received considerable attention. There has been recent progress concerning the existence of highly symmetric Steiner 6-designs: It is shown in [M. Huber, J. Algebr. Comb. 26 (2007), pp. 453-476] that no non-trivial flag-transitive Steiner 6-design can exist. In this paper, we announce that essentially also no block-transitive Steiner 6-design can exist.Comment: 9 pages; to appear in: Mathematical Methods in Computer Science 2008, ed. by J.Calmet, W.Geiselmann, J.Mueller-Quade, Springer Lecture Notes in Computer Scienc

Anomalous Dynamics of Forced Translocation

We consider the passage of long polymers of length N through a hole in a membrane. If the process is slow, it is in principle possible to focus on the dynamics of the number of monomers s on one side of the membrane, assuming that the two segments are in equilibrium. The dynamics of s(t) in such a limit would be diffusive, with a mean translocation time scaling as N^2 in the absence of a force, and proportional to N when a force is applied. We demonstrate that the assumption of equilibrium must break down for sufficiently long polymers (more easily when forced), and provide lower bounds for the translocation time by comparison to unimpeded motion of the polymer. These lower bounds exceed the time scales calculated on the basis of equilibrium, and point to anomalous (sub-diffusive) character of translocation dynamics. This is explicitly verified by numerical simulations of the unforced translocation of a self-avoiding polymer. Forced translocation times are shown to strongly depend on the method by which the force is applied. In particular, pulling the polymer by the end leads to much longer times than when a chemical potential difference is applied across the membrane. The bounds in these cases grow as N^2 and N^{1+\nu}, respectively, where \nu is the exponent that relates the scaling of the radius of gyration to N. Our simulations demonstrate that the actual translocation times scale in the same manner as the bounds, although influenced by strong finite size effects which persist even for the longest polymers that we considered (N=512).Comment: 13 pages, RevTeX4, 16 eps figure

Large Synoptic Survey Telescope: From science drivers to reference design

In the history of astronomy, major advances in our understanding of the Universe have come from dramatic improvements in our ability to accurately measure astronomical quantities. Aided by rapid progress in information technology, current sky surveys are changing the way we view and study the Universe. Next- generation surveys will maintain this revolutionary progress. We focus here on the most ambitious survey currently planned in the visible band, the Large Synoptic Survey Telescope (LSST). LSST will have unique survey capability in the faint time domain. The LSST design is driven by four main science themes: constraining dark energy and dark matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. It will be a large, wide-field ground-based system designed to obtain multiple images covering the sky that is visible from Cerro Pachon in Northern Chile. The current baseline design, with an 8.4 m (6.5 m effective) primary mirror, a 9.6 deg2 field of view, and a 3,200 Megapixel camera, will allow about 10,000 square degrees of sky to be covered using pairs of 15-second exposures in two photometric bands every three nights on average. The system is designed to yield high image quality, as well as superb astrometric and photometric accuracy. The survey area will include 30,000 deg2 with δ < +34.5◦ , and will be imaged multiple times in six bands, ugrizy, covering the wavelength range 320-1050 nm. About 90% of the observing time will be devoted to a deep- wide-fast survey mode which will observe a 20,000 deg2 region about 1000 times in the six bands during the anticipated 10 years of operation. These data will result in databases including 10 billion galaxies and a similar number of stars, and will serve the majority of science programs. The remaining 10% of the observing time will be allocated to special programs such as Very Deep and Very Fast time domain surveys. We describe how the LSST science drivers led to these choices of system parameters