Electromagnetic Casimir Forces of Parabolic Cylinder and Knife-Edge Geometries

An exact calculation of electromagnetic scattering from a perfectly conducting parabolic cylinder is employed to compute Casimir forces in several configurations. These include interactions between a parabolic cylinder and a plane, two parabolic cylinders, and a parabolic cylinder and an ordinary cylinder. To elucidate the effect of boundaries, special attention is focused on the "knife-edge" limit in which the parabolic cylinder becomes a half-plane. Geometrical effects are illustrated by considering arbitrary rotations of a parabolic cylinder around its focal axis, and arbitrary translations perpendicular to this axis. A quite different geometrical arrangement is explored for the case of an ordinary cylinder placed in the interior of a parabolic cylinder. All of these results extend simply to nonzero temperatures.Comment: 17 pages, 10 figures, uses RevTeX

Casimir Force at a Knife's Edge

The Casimir force has been computed exactly for only a few simple geometries, such as infinite plates, cylinders, and spheres. We show that a parabolic cylinder, for which analytic solutions to the Helmholtz equation are available, is another case where such a calculation is possible. We compute the interaction energy of a parabolic cylinder and an infinite plate (both perfect mirrors), as a function of their separation and inclination, $H$ and $\theta$, and the cylinder's parabolic radius $R$. As $H/R\to 0$, the proximity force approximation becomes exact. The opposite limit of $R/H\to 0$ corresponds to a semi-infinite plate, where the effects of edge and inclination can be probed.Comment: 5 pages, 3 figures, uses RevTeX; v2: expanded conclusions; v3: fixed missing factor in Eq. (3) and incorrect diagram label (no changes to results); v4: fix similar factor in Eq. (16) (again no changes to results

Typical Peak Sidelobe Level of Binary Sequences

For a binary sequence Sn = {si: i=1,2,...,n} E [epsilon] {±1}n [superscript n] , n > 1, the peak sidelobe level (PSL) is defined as M(Sn [subscript n])= max [subscript k=1,2,...,n-1| [divided by] E [epsilon superscript n-k subscript i=1 s [subscript 1] S [subscript 1 = k]. It is shown that the distribution of M(Sn) is strongly concentrated, and asymptotically almost surely y [gamma] {S [subscript n])=M(Sn [subscript n] [divided by] [square root of] n 1n n E [epsilon] [1-o(1), [square root of] 2]. Explicit bounds for the number of sequences outside this range are provided. This improves on the best earlier known result due to Moon and Moser that the typical Y [gamma] (Sn {subscript n]) E [epsilon] [o(1 [divided by] [square root of] 1n n).2], and settles to the affirmative the conjecture of Dmitriev and Jedwab on the growth rate of the typical peak sidelobe. Finally, it is shown that modulo some natural conjecture, the typical Y [gamma](Sn [subscript n]) equals [square root of] 2 .United States-Israel Binational Science FoundationEuropean Research CouncilIsrael Science Foundation (Grant 1177/06)Massachusetts Institute of Technology. Di Capua Graduate Fellowshi

Assigning spectrum-specific P-values to protein identifications by mass spectrometry

Motivation: Although many methods and statistical approaches have been developed for protein identification by mass spectrometry, the problem of accurate assessment of statistical significance of protein identifications remains an open question. The main issues are as follows: (i) statistical significance of inferring peptide from experimental mass spectra must be platform independent and spectrum specific and (ii) individual spectrum matches at the peptide level must be combined into a single statistical measure at the protein level