Two particle correlation measurements at PHENIX

Measurements of two particle azimuthal correlations in relativistic heavy ion collisions are useful tools to dissect the interplay between hard-scattered partons and hot dense medium. Correlations with trigger particle selection relative to second order event plane are sensitive to the path-length dependence of parton energy loss and to the influence of the medium on jet for high and intermediate transverse momenta pairs, respectively. To study the parton-medium coupling, it is also crucial to obtain correlations with rejection of contributions from higher harmonic flow. We present current results of second order event plane dependent correlations as well as correlations in which contributions from higher harmonic flow have been excluded in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV measured by PHENIX.Comment: 4 pages, 3 figures, Hard Probes 2012 Proceeding

String operations on rational Gorenstein spaces

F\'{e}lix and Thomas developed string topology of Chas and Sullivan on simply-connected Gorenstein spaces. In this paper, we prove that the degree shifted homology of the free loop space of a simply-connected ${\mathbb Q}$-Gorenstein space with rational coefficient is a non-unital and non-counital Frobenius algebra by solving the up to constant problem. We also investigate triviality or non-triviality of the loop product and coproduct of particular Gorenstein spaces.Comment: 27page

Global Strong Well-posedness of the Three Dimensional Primitive equations in LpL^p-spaces

In this article, an $L^p$-approach to the primitive equations is developed. In particular, it is shown that the three dimensional primitive equations admit a unique, global strong solution for all initial data $a \in [X_p,D(A_p)]_{1/p}$ provided $p \in [6/5,\infty)$. To this end, the hydrostatic Stokes operator $A_p$ defined on $X_p$, the subspace of $L^p$ associated with the hydrostatic Helmholtz projection, is introduced and investigated. Choosing $p$ large, one obtains global well-posedness of the primitive equations for strong solutions for initial data $a$ having less differentiability properties than $H^1$, hereby generalizing in particular a result by Cao and Titi (Ann. Math. 166 (2007), pp. 245-267) to the case of non-smooth initial data.Comment: 26 page

Effects of additive noise on the stability of glacial cycles

It is well acknowledged that the sequence of glacial-interglacial cycles is paced by the astronomical forcing. However, how much is the sequence robust against natural fluctuations associated, for example, with the chaotic motions of atmosphere and oceans? In this article, the stability of the glacial-interglacial cycles is investigated on the basis of simple conceptual models. Specifically, we study the influence of additive white Gaussian noise on the sequence of the glacial cycles generated by stochastic versions of several low-order dynamical system models proposed in the literature. In the original deterministic case, the models exhibit different types of attractors: a quasiperiodic attractor, a piecewise continuous attractor, strange nonchaotic attractors, and a chaotic attractor. We show that the combination of the quasiperiodic astronomical forcing and additive fluctuations induce a form of temporarily quantised instability. More precisely, climate trajectories corresponding to different noise realizations generally cluster around a small number of stable or transiently stable trajectories present in the deterministic system. Furthermore, these stochastic trajectories may show sensitive dependence on very small amounts of perturbations at key times. Consistently with the complexity of each attractor, the number of trajectories leaking from the clusters may range from almost zero (the model with a quasiperiodic attractor) to a significant fraction of the total (the model with a chaotic attractor), the models with strange nonchaotic attractors being intermediate. Finally, we discuss the implications of this investigation for research programmes based on numerical simulators. }Comment: Parlty based on a lecture given by M. Crucifix at workshop held in Rome in 2013 as a part of Mathematics of Planet Earth 201