Cluster algebras in scattering amplitudes with special 2D kinematics

We study the cluster algebra of the kinematic configuration space $Conf_n(\mathbb{P}^3)$ of a n-particle scattering amplitude restricted to the special 2D kinematics. We found that the n-points two loop MHV remainder function found in special 2D kinematics depend on a selection of \XX-coordinates that are part of a special structure of the cluster algebra related to snake triangulations of polygons. This structure forms a necklace of hypercubes beads in the corresponding Stasheff polytope. Furthermore in $n = 12$, the cluster algebra and the selection of \XX-coordinates in special 2D kinematics replicates the cluster algebra and the selection of \XX-coordinates of $n=6$ two loop MHV amplitude in 4D kinematics.Comment: 22 page

How does breakup influence the total fusion of 6,7^{6,7}Li at the Coulomb barrier?

Total (complete + incomplete) fusion excitation functions of $^{6,7}$Li on $^{59}$Co and $^{209}$Bi targets around the Coulomb barrier are obtained using a new continuum discretized coupled channel (CDCC) method of calculating fusion. The relative importance of breakup and bound-state structure effects on total fusion is particularly investigated. The effect of breakup on fusion can be observed in the total fusion excitation function. The breakup enhances the total fusion at energies just around the barrier, whereas it hardly affects the total fusion at energies well above the barrier. The difference between the experimental total fusion cross sections for $^{6,7}$Li on $^{59}$Co is notably caused by breakup, but this is not the case for the $^{209}$Bi target.Comment: 9 pages, 9 figures, Submitted to Phys. Rev.

Synchronization in interacting Scale Free Networks

We study the fluctuations of the interface, in the steady state, of the Surface Relaxation Model (SRM) in two scale free interacting networks where a fraction $q$ of nodes in both networks interact one to one through external connections. We find that as $q$ increases the fluctuations on both networks decrease and thus the synchronization reaches an improvement of nearly $40\%$ when $q=1$. The decrease of the fluctuations on both networks is due mainly to the diffusion through external connections which allows to reducing the load in nodes by sending their excess mostly to low-degree nodes, which we report have the lowest heights. This effect enhances the matching of the heights of low-and high-degree nodes as $q$ increases reducing the fluctuations. This effect is almost independent of the degree distribution of the networks which means that the interconnection governs the behavior of the process over its topology.Comment: 13 pages, 7 figures. Added a relevant reference.Typos fixe

Differential Astrometry over 15 degrees

We observed the pair of radio sources 1150+812 and 1803+784 in November 1993 with a VLBI array, simultaneously recording at 8.4 and 2.3 GHz. We determined the angular separation between the two sources with submilliarcsecond accuracy by using differential techniques. This result demonstrates the feasibility of high precision differential astrometry for radio sources separated in the sky by almost 15 degrees, and opens the avenue to its application to larger samples of radio sources.Comment: 6 pages, latex2e, 2 figures, To appear in the proceedings of the EVN/JIVE Symposium No. 4, New Astronomy Reviews (eds. Garret, M. Campbell, R., and Gurvits, L.