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

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

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

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

Centrality dependence of charged-particle pseudorapidity distributions from d+Au collisions at sqrt(s_{NN})=200 GeV

Charged-particle pseudorapidity densities are presented for the d+Au reaction at sqrt{s_{NN}}=200 GeV with -4.2 <= eta <= 4.2$. The results, from the BRAHMS experiment at RHIC, are shown for minimum-bias events and 0-30%, 30-60%, and 60-80% centrality classes. Models incorporating both soft physics and hard, perturbative QCD-based scattering physics agree well with the experimental results. The data do not support predictions based on strong-coupling, semi-classical QCD. In the deuteron-fragmentation region the central 200 GeV data show behavior similar to full-overlap d+Au results at sqrt{s_{NN}}=19.4 GeV.Comment: 4 pages, 3figures; expanded discussion of uncertainties; added 60-80% centrality range; added additional discussion on centrality selection bia

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

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

Superdeformed rotational bands in the Mercury region; A Cranked Skyrme-Hartree-Fock-Bogoliubov study

A study of rotational properties of the ground superdeformed bands in \Hg{0}, \Hg{2}, \Hg{4}, and \Pb{4} is presented. We use the cranked Hartree-Fock-Bogoliubov method with the {\skm} parametrization of the Skyrme force in the particle-hole channel and a seniority interaction in the pairing channel. An approximate particle number projection is performed by means of the Lipkin-Nogami prescription. We analyze the proton and neutron quasiparticle routhians in connection with the present information on about thirty presently observed superdeformed bands in nuclei close neighbours of \Hg{2}.Comment: 26 LaTeX pages, 14 uuencoded postscript figures included, Preprint IPN-TH 93-6

Recent Results from the BRAHMS Experiment

We present recent results obtained by the BRAHMS experiment at the Relativistic Heavy Ion Collider (RHIC) for the systems of Au + Au and Cu + Cu at \rootsnn{200} and at 62.4 GeV, and p + p at \rootsnn{200}. Nuclear modification factors for Au + Au and Cu + Cu collisions are presented. Analysis of anti-particle to particle ratios as a function of rapidity and collision energy reveal that particle populations at the chemical freeze-out stage for heavy-ion reactions at and above SPS energies are controlled by the baryon chemical potential. From the particle spectra we deduce significant radial expansion ($\beta \approx$ 0.75), as expected for systems created with a large initial energy density. We also measure the elliptic flow parameter $v_2$ versus rapidity and \ptn. We present rapidity dependent $p/\pi$ ratios within $0 < y < 3$ for Au + Au and Cu + Cu at \rootsnn{200}. \Raa is found to increase with decreasing collision energy, decreasing system size, and when going towards more peripheral collisions. However, \Raa shows only a very weak dependence on rapidity (for $0 < y < 3.2$), both for pions and protons.Comment: 16 pages and 14 figures, proceedings for plenary talk at Quark Matter 2005, Budapest, Hungar