On the stability of some isoperimetric inequalities for the fundamental tones of free plates

We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chasman adapting Weinberger's argument for the corresponding second order problem. Following a scheme introduced by Brasco and Pratelli for the second order case, we prove that a similar quantitative inequality holds also for the biharmonic operator. We also prove the sharpness of both such an inequality and the corresponding one for the biharmonic Steklov problem

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

Parametrization of the octupole degrees of freedom

A simple parametrization for the octupole collective variables is proposed and the symmetries of the wave functions are discussed in terms of the solutions corresponding to the vibrational limit. [PACS: 21.60Ev, 21.60.Fw, 21.10.Re]Comment: 14 page

High energy Coulomb-scattered electrons for relativistic particle beam diagnostics

A new system used for monitoring energetic Coulomb-scattered electrons as the main diagnostic for accurately aligning the electron and ion beams in the new Relativistic Heavy Ion Collider (RHIC) electron lenses is described in detail. The theory of electron scattering from relativistic ions is developed and applied to the design and implementation of the system used to achieve and maintain the alignment. Commissioning with gold and 3He beams is then described as well as the successful utilization of the new system during the 2015 RHIC polarized proton run. Systematic errors of the new method are then estimated. Finally, some possible future applications of Coulomb-scattered electrons for beam diagnostics are briefly discussed.Comment: 16 pages, 23 figure

Tri-axial Octupole Deformations and Shell Structure

Manifestations of pronounced shell effects are discovered when adding nonaxial octupole deformations to a harmonic oscillator model. The degeneracies of the quantum spectra are in a good agreement with the corresponding main periodic orbits and winding number ratios which are found by classical analysis.Comment: 10 pages, Latex, 4 postscript figures, to appear in JETP Letter

Spectral analysis of the biharmonic operator subject to Neumann boundary conditions on dumbbell domains

We consider the biharmonic operator subject to homogeneous boundary conditions of Neumann type on a planar dumbbell domain which consists of two disjoint domains connected by a thin channel. We analyse the spectral behaviour of the operator, characterizing the limit of the eigenvalues and of the eigenprojections as the thickness of the channel goes to zero. In applications to linear elasticity, the fourth order operator under consideration is related to the deformation of a free elastic plate, a part of which shrinks to a segment. In contrast to what happens with the classical second order case, it turns out that the limiting equation is here distorted by a strange factor depending on a parameter which plays the role of the Poisson coefficient of the represented plate.Comment: To appear in "Integral Equations and Operator Theory

Intrinsic vs. laboratory frame description of the deformed nucleus 48Cr

The collective yrast band of the nucleus $^{48}$Cr is studied using the spherical shell model and the HFB method. Both approaches produce basically the same axially symmetric intrinsic state up to the - accurately reproduced - observed backbending. Agreement between both calculations extends to most observables. The only significant discrepancy comes from the static moments of inertia and can be attributed to the need of a more refined treatment of pairing correlations in the HFB calculation.Comment: 4 pages, RevTeX 3.0 using psfig, 6 Postscript figures included using uufile

Genome-wide association study of relative Telomere Length.

Abstract Telomere function is essential to maintaining the physical integrity of linear chromosomes and healthy human aging. The probability of forming proper telomere structures depends on the length of the telomeric DNA tract. We attempted to identify common genetic variants associated with log relative telomere length using genome-wide genotyping data on 3,554 individuals from the Nurses' Health Study and the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial that took part in the National Cancer Institute Cancer Genetic Markers of Susceptibility initiative for breast and prostate cancer. After genotyping 64 independent SNPs selected for replication in additional Nurses' Health Study and Women's Genome Health Study participants, we did not identify genome-wide significant loci; however, we replicated the inverse association of log relative telomere length with the minor allele variant [C] of rs16847897 at the TERC locus (per allele b = 20.03, P = 0.003) identified by a previous genome-wide association study. We did not find evidence for an association with variants at the OBFC1 locus or other loci reported to be associated with telomere length. With this sample size we had .80% power to detect b estimates as small as 60.10 for SNPs with minor allele frequencies of $0.15 at genome-wide significance. However, power is greatly reduced for b estimates smaller than 60.10, such as those for variants at the TERC locus. In general, common genetic variants associated with telomere length homeostasis have been difficult to detect. Potential biological and technical issues are discussed

Rapidity dependence of deuteron production in Au+Au collisions at sNN\sqrt{s_{NN}} = 200 GeV

We have measured the distributions of protons and deuterons produced in high energy heavy ion Au+Au collisions at RHIC over a very wide range of transverse and longitudinal momentum. Near mid-rapidity we have also measured the distribution of anti-protons and anti-deuterons. We present our results in the context of coalescence models. In particular we extract the "volume of homogeneity" and the average phase-space density for protons and anti-protons. Near central rapidity the coalescence parameter $B_2(p_T)$ and the space averaged phase-space density $(p_T)$ are very similar for both protons and anti-protons. For protons we see little variation of either $B_2(p_T)$ or the space averaged phase-space density as the rapidity increases from 0 to 3. However both these quantities depend strongly on $p_T$ at all rapidities. These results are in contrast to lower energy data where the proton and anti-proton phase-space densities are different at $y$=0 and both $B_2$ and $f$ depend strongly on rapidity.Comment: Document updated after proofs received from PR