Isoperimetric Inequalities for Minimal Submanifolds in Riemannian Manifolds: A Counterexample in Higher Codimension

For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small singular set. There is the natural question if a similar result is true for submanifolds of higher codimension. Specifically, B.White asked if the non-existence of an isoperimetric inequality for k-varifolds implies the existence of a nonzero, stationary, integral k-varifold. We present examples showing that this is not true in codimension greater than two. The key step is the construction of a Riemannian metric on the closed four-dimensional ball B with the following properties: (1) B has strictly convex boundary. (2) There exists a complete nonconstant geodesic. (3) There does not exist a closed geodesic in B.Comment: 11 pages, We changed the title and added a section that exhibits the relation between our example and the question posed by Brian White concerning isoperimetric inequalities for minimal submanifold

Insecurity for compact surfaces of positive genus

A pair of points in a riemannian manifold $M$ is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is insecure. A manifold is secure if all pairs of points in $M$ are secure. A manifold is insecure if there exists an insecure point pair, and totally insecure if all point pairs are insecure. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. We prove this for surfaces of genus greater than zero. We also prove that a closed surface of genus greater than one with any riemannian metric and a closed surface of genus one with generic metric are totally insecure.Comment: 37 pages, 11 figure

Convex domains of Finsler and Riemannian manifolds

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update

The type numbers of closed geodesics

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of variations in the large" by M. Mors

Atomic Configuration of Nitrogen Doped Single-Walled Carbon Nanotubes

Having access to the chemical environment at the atomic level of a dopant in a nanostructure is crucial for the understanding of its properties. We have performed atomically-resolved electron energy-loss spectroscopy to detect individual nitrogen dopants in single-walled carbon nanotubes and compared with first principles calculations. We demonstrate that nitrogen doping occurs as single atoms in different bonding configurations: graphitic-like and pyrrolic-like substitutional nitrogen neighbouring local lattice distortion such as Stone-Thrower-Wales defects. The stability under the electron beam of these nanotubes has been studied in two extreme cases of nitrogen incorporation content and configuration. These findings provide key information for the applications of these nanostructures.Comment: 25 pages, 13 figure

Photoluminescence investigations of 2D hole Landau levels in p-type single Al_{x}Ga_{1-x}As/GaAs heterostructures

We study the energy structure of two-dimensional holes in p-type single Al_{1-x}Ga_{x}As/GaAs heterojunctions under a perpendicular magnetic field. Photoluminescence measurments with low densities of excitation power reveal rich spectra containing both free and bound-carrier transitions. The experimental results are compared with energies of valence-subband Landau levels calculated using a new numerical procedure and a good agreement is achieved. Additional lines observed in the energy range of free-carrier recombinations are attributed to excitonic transitions. We also consider the role of many-body effects in photoluminescence spectra.Comment: 13 pages, 10 figures, accepted to Physical Review

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio

Spin Depolarization in Quantum Wires Polarized Spontaneously in a Zero Magnetic Field

The conditions for a spontaneous spin polarization in a quantum wire positioned in a zero magnetic field are analyzed under weak population of one-dimensional subbands that gives rise to the efficient quenching of the kinetic energy by the exchange energy of carriers. The critical linear concentration of carriers above which the quasi one-dimensional gas undergoes a complete spin depolarization is determined by the Hartree-Fock approximation. The dependence of the critical linear concentration on the concentration of carriers is defined to reveal the interplay of the spin depolarization with the evolution of the 0.7 (2e2/h) feature in the quantum conductance staircase from the e2/h to 3/2 (e2/h) values. This dependence is used to study the effect of the hole concentration on the 0.7 (2e2/h) feature in the quantum conductance staircase of the quantum wire prepared inside the p-type silicon quantum well using the split-gate technique. The 1D channel is demonstrated to be spin-polarized at the linear concentration of holes lower than the critical linear concentration, because the 0.7 (2e2/h) feature is close to the value of 0.5 (2e2/h) that indicates the spin degeneracy lifting for the first step of the quantum conductance staircase. The 0.7 (2e2/h) feature is found to take however its normal magnitude when the linear concentration of holes attains the critical value corresponding to the spin depolarization. The variations in the height of the 0.7 (2e2/h) feature observed in the hole quantum conductance staircase that is revealed by the p-type silicon quantum wire seem to be related to the evidences of the quantum conductance staircase obtained by varying the concentration of electrons in the 1D channel prepared inside the GaAs-AlGaAs heterojunction.Comment: 27 pages, 5 figure

Single hadron response measurement and calorimeter jet energy scale uncertainty with the ATLAS detector at the LHC

The uncertainty on the calorimeter energy response to jets of particles is derived for the ATLAS experiment at the Large Hadron Collider (LHC). First, the calorimeter response to single isolated charged hadrons is measured and compared to the Monte Carlo simulation using proton-proton collisions at centre-of-mass energies of sqrt(s) = 900 GeV and 7 TeV collected during 2009 and 2010. Then, using the decay of K_s and Lambda particles, the calorimeter response to specific types of particles (positively and negatively charged pions, protons, and anti-protons) is measured and compared to the Monte Carlo predictions. Finally, the jet energy scale uncertainty is determined by propagating the response uncertainty for single charged and neutral particles to jets. The response uncertainty is 2-5% for central isolated hadrons and 1-3% for the final calorimeter jet energy scale.Comment: 24 pages plus author list (36 pages total), 23 figures, 1 table, submitted to European Physical Journal

Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics

A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN