Kaon production in S+nucleus and Pb+Pb collisions at CERN SPS

Charged and neutral kaon production in S-nucleus and Pb-Pb collisions has been measured at CERN in the NA35 and NA49 experiments, close to mid-rapidity. The production ofK ^± in S+S, Ag, Au at 200 GeV/nucleon was measured via their one-prong (kink) topology inside a Time Projection Chamber (TPC). The resulting charged kaon yields are in agreement with other measurements done in the same experiment. TheK ⁺/K ^? ratio was found to be 1.30±0.15 in central S+Au interactions. The production ofK _S ⁰ in Pb+Pb collisions was measured using the NA49’s large (Main) TPCs outside the magnetic field. The resulting yields are compatible with other measurements performed in the same experiment, within the quoted systematic errors. The preliminary rapidity distribution in Pb+Pb scales with the number of participants if compared to S+S collisions. From this we conclude that no further strangeness enhancement (relative to nucleon-nucleon collisions) is observed in going from S+S to Pb+Pb.     

From crystal steps to continuum laws: Behavior near large facets in one dimension

The passage from discrete schemes for surface line defects (steps) to nonlinear macroscopic laws for crystals is studied via formal asymptotics in one space dimension. Our goal is to illustrate by explicit computations the emergence from step motion laws of continuum-scale power series expansions for the slope near the edges of large, flat surface regions (facets). We consider surface diffusion kinetics via the Burton, Cabrera and Frank (BCF) model by which adsorbed atoms diffuse on terraces and attach-detach at steps. Nearest-neighbor step interactions are included. The setting is a monotone train of N steps separating two semi-infinite facets at fixed heights. We show how boundary conditions for the continuum slope and flux, and expansions in the height variable near facets, may emerge from the algebraic structure of discrete schemes as N→∞. Our technique relies on the use of self-similar discrete slopes, conversion of discrete schemes to sum equations, and their reduction to nonlinear integral equations for the continuum-scale slope. Approximate solutions to the continuum equations near facet edges are constructed formally by direct iterations. For elastic-dipole and multipole step interactions, the continuum slope is found in agreement with a previous hypothesis of ‘local equilibrium’.     

Generalized Iteration Method for First-Kind Integral Equations

An iteration method is described to solve one-dimensional, first-kind integral equations with finite integration limits and difference kernel, K ( x − x '), that decays exponentially. The method relies on deriving via the Wiener–Hopf factorization and solving by suitable iterations in the Fourier complex plane a pair of integral relations, where each iteration accounts for all end point singularities in x of the exact solution. For even and odd kernels, this pair reduces to decoupled, 2nd-kind Fredholm equations, and the iteration yields Neumann series subject to known convergence criteria. This formulation is applied to a classic problem of steady advection-diffusion in the two-dimensional (2D) potential flow of concentrated fluid. The remarkable overlap of recently derived asymptotic expansions for the flux in this case is shown to be intimately related to the analyticity of the kernel Fourier transform.     

On the Wiener–Hopf Method for Surface Plasmons: Diffraction from Semiinfinite Metamaterial Sheet

By formally invoking the Wiener–Hopf method, we explicitly solve a one‐dimensional, singular integral equation for the excitation of a slowly decaying electromagnetic wave, called surface plasmon‐polariton (SPP), of small wavelength on a semiinfinite, flat conducting sheet irradiated by a plane wave in two spatial dimensions. This setting is germane to wave diffraction by edges of large sheets of single‐layer graphene. Our analytical approach includes (i) formulation of a functional equation in the Fourier domain; (ii) evaluation of a split function, which is expressed by a contour integral and is a key ingredient of the Wiener–Hopf factorization; and (iii) extraction of the SPP as a simple‐pole residue of a Fourier integral. Our analytical solution is in good agreement with a finite‐element numerical computation.     

Light emission efficiency and imaging performance of Y3Al5O12: Ce (YAG: Ce) powder screens under diagnostic radiology conditions

In this study Y₃Al₅O₁₂: Ce powder scintillator was evaluated for use in X-ray imaging detectors. This phosphor, also known as YAG: Ce scintillator or P-46 phosphor, is a non-hygroscopic, emitting green light with very short decay time. These properties are very attractive for X-ray imaging. Y₃Al₅O₁₂: Ce powder was used to prepare various test screens (33–166 mg/cm²). Absolute luminescence efficiency measurements were performed for various X-ray tube voltages (50–130 kVp). In addition parameters related to image quality such as the modulation transfer function and the detective quantum efficiency were examined. A theoretical model, describing radiation and light transfer, was employed to fit experimental data and to estimate values of optical parameters. Absolute efficiency was found to decrease with X-ray tube voltage. Highest efficiency was obtained for the 107 mg/cm² screen. Light attenuation coefficients were close to those of green emitting rare earth scintillators. At low spatial frequencies the detective quantum efficiency was high for the 107–166 mg/cm² screens. The light emission efficiency and imaging performance of Y₃Al₅O₁₂: Ce was not better than currently employed scintillators. However due to its very fast response and high spectral compatibility to optical sensors it may be considered for use in digital imaging detectors.     

Event-by-event fluctuations of the Kaon-to-Pion ratio in central Pb+Pb collisions at 158 GeV per nucleon

We present the first measurement of fluctuations from event to event in the production of strange particles in collisions of heavy nuclei. The ratio of charged kaons to charged pions is determined for individual central Pb+Pb collisions. After accounting for the fluctuations due to detector resolution and finite number statistics we derive an upper limit on genuine nonstatistical fluctuations, which could be related to a first- or second-order QCD phase transition. Such fluctuations are shown to be very small.     

Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons. I.

Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schrödinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential ${v(x)= \epsilon \chi(x) |x|^{-1}}Inspired by the works of Rodnianski and Schlein [31] and Wu [34,35], we derive a new nonlinear Schr?dinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential v(x) = ec(x) |x|^-1{v(x)= \epsilon \chi(x) |x|^{-1}}, where e{\epsilon} is sufficiently small and c ? C₀^￥{\chi \in C_0^{\infty}} even, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (Part II) of this paper.     

Second-order corrections to mean field evolution of weakly interacting Bosons. II

We study the evolution of an N-body weakly interacting system of Bosons. Our work forms an extension of our previous paper Grillakis, Machedon, and Margetis (2010) [13], in which we derived a second-order correction to a mean-field evolution law for coherent states in the presence of small interaction potential. Here, we remove the assumption of smallness of the interaction potential and prove global existence of solutions to the equation for the second-order correction. This implies an improved Fock-space estimate for our approximation of the N-body state.