Limit behaviour of focusing solutions to nonlinear diffusions

The paper is concerned with the behaviour of focusing solutions to nonlinear diffusion problems. These solutions describe the movement of a flow filling a hole and have consequences for the qualitative theory of degenerate nonlinear parabolic equations. The general equation under study is theso-called doubly nonlinear diffusion equation a²with parameters m > 0 and p > 1 such that m(p - 1) > 1 so that the finite propagation property holds and free boundaries occur. Well-known particular cases are the Porous Medium Equation and the evolutionary p-

Laplacian Equation. We study the behaviour of the families of selfsimilar focusing solutions as the parameters m and p tend to their limiting values and identify the limit problems these limits solve. In the case m(p - 1) -+ 1 we find as appropriate asymptotic problems a family of Hamilton-Jacobi equations. When we let m + ffi we obtain in the limit the Hele-Shaw problem. When p + cc we

obtain linear travelling waves with arbitrary speed, solutions of a certain ∞-Laplacian evolution problem.     

Nuclear modification of electron spectra and implications for heavy quark energy loss in Au+Au collisions at [FORMULA: SEE TEXT

The PHENIX experiment has measured midrapidity ([FORMULA: SEE TEXT]) transverse momentum spectra ([FORMULA: SEE TEXT]) of electrons as a function of centrality in Au+Au collisions at [FORMULA: SEE TEXT]. Contributions from photon conversions and from light hadron decays, mainly Dalitz decays of pi0 and eta mesons, were removed. The resulting nonphotonic electron spectra are primarily due to the semileptonic decays of hadrons carrying heavy quarks. Nuclear modification factors were determined by comparison to nonphotonic electrons in p+p collisions. A significant suppression of electrons at high pT is observed in central Au+Au collisions, indicating substantial energy loss of heavy quarks.     

Measurement of identified and inclusive photon second-harmonic parameter and implications for direct photon production in [FORMULA: SEE TEXT] Au+Au

The azimuthal distribution of identified pi0 and inclusive photons has been measured in [FORMULA: SEE TEXT] Au+Au collisions with the PHENIX experiment at the Relativistic Heavy-Ion Collider (RHIC). The second-harmonic parameter (nu2) was measured to describe the observed anisotropy of the azimuthal distribution. The measured inclusive photon is consistent with the value expected for the photons from hadron decay and is also consistent with the lack of direct photon signal over the measured pT range 1-6 GeV/c. An attempt is made to extract nu2 of direct photons.     

Measurement of high-pT single electrons from heavy-flavor decays in p + p collisions at square root of s = 200 GeV

The momentum distribution of electrons from decays of heavy flavor (charm and bottom) for midrapidity absolute value of y < 0.35 in p + p collisions at square root of s = 200 GeV has been measured by the PHENIX experiment at the BNL Relativistic Heavy Ion Collider over the transverse momentum range 0.3 < pT < 9 GeV/c. Two independent methods have been used to determine the heavy-flavor yields, and the results are in good agreement with each other. A fixed-order-plus-next-to-leading-log perturbative QCD calculation agrees with the data within the theoretical and experimental uncertainties, with the data/theory ratio of 1.71+/-0.02stat+/-0.18sys for 0.3 < pT < 9 GeV/c. The total charm production cross section at this energy has also been deduced to be sigma cc = 567+/-57stat+/-193sys microb.     

Net charge fluctuations in Au + Au interactions at sqrt[s(NN)]=130 GeV

Data from Au + Au interactions at sqrt[s(NN)]=130 GeV, obtained with the PHENIX detector at the Relativistic Heavy-Ion Collider, are used to investigate local net charge fluctuations among particles produced near midrapidity. According to recent suggestions, such fluctuations may carry information from the quark-gluon plasma. This analysis shows that the fluctuations are dominated by a stochastic distribution of particles, but are also sensitive to other effects, like global charge conservation and resonance decays.     

Centrality dependence of pi(+/-), K(+/-), p,and (-)p production from sqrt[s(NN)] = 130 GeV Au + Au collisions at RHIC

Identified pi(+/-), K(+/-), p, and (-)p transverse momentum spectra at midrapidity in sqrt[s(NN)] = 130 GeV Au+Au collisions were measured by the PHENIX experiment at RHIC as a function of collision centrality. Average transverse momenta increase with the number of participating nucleons in a similar way for all particle species. Within errors, all midrapidity particle yields per participant are found to be increasing with the number of participating nucleons. There is an indication that K(+/-), p, and (-)p yields per participant increase faster than the pi(+/-) yields. In central collisions at high transverse momenta (p(T) > or =2 GeV/c), (-)p and p yields are comparable to the pi(+/-) yields.     

Transverse-mass dependence of two-pion correlations in Au+Au collisions at square root[s(NN)] = 130 GeV

Two-pion correlations in square root[s(NN)] = 130 GeV Au+Au collisions at RHIC have been measured over a broad range of pair transverse momentum k(T) by the PHENIX experiment at RHIC. The k(T) dependent transverse radii are similar to results from heavy-ion collisions at square root[s(NN)] = 4.1, 4.9, and 17.3 GeV, whereas the longitudinal radius increases monotonically with beam energy. The ratio of the outwards to sidewards transverse radii (R(out)/R(side)) is consistent with unity and independent of k(T).     

Focusing of noncircular self-similar shock waves

We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.     

Interaction of the K0-K0 system with external fields

The energy-dependence of the $\text{K}{}^0\text{-}\text{K}{}^0$ parameters Δm, τ_S and η_+? suggested by Fermilab regeneration data is analyzed phenomenologically. Such variations with energy can arise from the interaction of the kaons with an external field or medium, and several specific examples are studied in detail.