Alexandrov meets Lott-Villani-Sturm

Here I show the compatibility of two definitions of generalized curvature bounds: the lower bound for sectional curvature in the sense of Alexandrov and the lower bound for Ricci curvature in the sense of Lott-Villani-Sturm

Crystal Undulator As A Novel Compact Source Of Radiation

A crystalline undulator (CU) with periodically deformed crystallographic planes is capable of deflecting charged particles with the same strength as an equivalent magnetic field of 1000 T and could provide quite a short period L in the sub-millimeter range. We present an idea for creation of a CU and report its first realization. One face of a silicon crystal was given periodic micro-scratches (grooves), with a period of 1 mm, by means of a diamond blade. The X-ray tests of the crystal deformation have shown that a sinusoidal-like shape of crystalline planes goes through the bulk of the crystal. This opens up the possibility for experiments with high-energy particles channeled in CU, a novel compact source of radiation. The first experiment on photon emission in CU has been started at LNF with 800 MeV positrons aiming to produce 50 keV undulator photons.Comment: Presented at PAC 2003 (Portland, May 12-16

Telescopic actions

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold

First observation of proton reflection from bent crystals

We recently suggested using short bent crystals as primary collimators in a two stage cleaning system for hadron colliders, with the aim of providing larger impact parameters in the secondary bulk absorber, through coherent beam-halo deflection [1]. Tests with crystals a few mm long, performed with 70 GeV proton beams at IEHP in Protvino, showed a channeling efficiency exceeding 85 %. We also observed disturbing phenomena such as dechannelling at large impact angle, insufficient bending induced by volume capture inside the crystal, multiple scattering of non-channeled protons and, for the first time, a proton flux reflected by the crystalline planes. Indeed, protons with a tangent path to the curved planes somewhere inside the crystal itself are deflected in the opposite direction with respect to the channeled particles, with an angle almost twice as large as the critical angle. This effect, up to now only predicted by computer simulations [2], produces a flux of particles in the wrong direction with respect to the absorber, which may hamper the collimation efficiency if neglected

Electron affinity of Li: A state-selective measurement

We have investigated the threshold of photodetachment of Li^- leading to the formation of the residual Li atom in the $2p ^2P$ state. The excited residual atom was selectively photoionized via an intermediate Rydberg state and the resulting Li^+ ion was detected. A collinear laser-ion beam geometry enabled both high resolution and sensitivity to be attained. We have demonstrated the potential of this state selective photodetachment spectroscopic method by improving the accuracy of Li electron affinity measurements an order of magnitude. From a fit to the Wigner law in the threshold region, we obtained a Li electron affinity of 0.618 049(20) eV.Comment: 5 pages,6 figures,22 reference

A simple proof of Perelman's collapsing theorem for 3-manifolds

We will simplify earlier proofs of Perelman's collapsing theorem for 3-manifolds given by Shioya-Yamaguchi and Morgan-Tian. Among other things, we use Perelman's critical point theory (e.g., multiple conic singularity theory and his fibration theory) for Alexandrov spaces to construct the desired local Seifert fibration structure on collapsed 3-manifolds. The verification of Perelman's collapsing theorem is the last step of Perelman's proof of Thurston's Geometrization Conjecture on the classification of 3-manifolds. Our proof of Perelman's collapsing theorem is almost self-contained, accessible to non-experts and advanced graduate students. Perelman's collapsing theorem for 3-manifolds can be viewed as an extension of implicit function theoremComment: v1: 9 Figures. In this version, we improve the exposition of our arguments in the earlier arXiv version. v2: added one more grap

Manifolds with 1/4-pinched flag curvature

We say that a nonnegatively curved manifold $(M,g)$ has quarter pinched flag curvature if for any two planes which intersect in a line the ratio of their sectional curvature is bounded above by 4. We show that these manifolds have nonnegative complex sectional curvature. By combining with a theorem of Brendle and Schoen it follows that any positively curved manifold with strictly quarter pinched flag curvature must be a space form. This in turn generalizes a result of Andrews and Nguyen in dimension 4. For odd dimensional manifolds we obtain results for the case that the flag curvature is pinched with some constant below one quarter, one of which generalizes a recent work of Petersen and Tao

Asymptotically Extrinsic Tamed Submanifolds

We study, from the extrinsic point of view, the structure at infinity of open submanifolds, ϕ : Mm → Mn(κ) isometrically immersed in the real space forms of constant sectional curvature κ ≤ 0.We shall use the decay of the second fundamental form of the so-called tamed immersions to obtain a description at infinity of the submanifold in the line of the structural results in Greene et al. (Int Math Res Not 1994:364–377, 1994) and Petrunin and Tuschmann (Math Ann 321:775–788, 2001) and an estimation from below of the number of its ends in terms of the volume growth of a special class of extrinsic domains, the extrinsic balls.Vicent Gimeno: Work partially supported by the Research Program of University Jaume I Project UJI-B2016-07, and DGI -MINECO Grant (FEDER) MTM2013-48371-C2-2-P. Vicente Palmer: Work partially supported by the Research Program of University Jaume I Project UJI-B2016-07, DGI -MINECO Grant (FEDER) MTM2013-48371-C2-2-P, and Generalitat Valenciana Grant PrometeoII/2014/064. G. Pacelli Bessa: Work partially supported by CNPq- Brazil grant # 301581/2013-4

Volume reflection of a proton beam in a bent crystal

Volume reflection of 70 GeV proton beam from bent (111) atomic planes of silicon was observed in experiment devoted to the study of channeling in very short bent crystals. This phenomenon was predicted by A.M.Taratin and S.A.Vorobiev in 1987. Volume reflection is resulted from coherent interaction of incident protons with crystal lattice in tangency point of proton trajectories with bent atomic planes and has the same nature as channeling. Average deflection angle of reflected protons was found to be equal to 1.6 times the critical angle for channeling. The study fulfilled makes possible to develop new approach to crystal deflectors for high energy particle beams based on volume reflection phenomenon