We study the existence, uniqueness and continuous dependence on initial data of the solution to a nonlocal Cahn-Hilliard equation on a bounded domain. The equation generates a gradient flow for a free energy functional with nonlocal interaction. Also we apply a nonlinear Poincaré inequality to show the existence of an absorbing set in each constant mass affine space.

We study the existence, uniqueness and continuous dependence on initial data of the solution for a nonlocal Cahn-Hilliard equation with Dirichlet boundary condition on a bounded domain. Under a nondegeneracy assumption the solutions are classical but when this is relaxed, the equation is satisfied in a weak sense. Also we prove that there exists a global attractor in some metric space.  2005 Elsevier Inc. All rights reserved.

The process pp → p + − p ( * ) , with + − a muon or an electron pair produced at midrapidity with mass larger than 110 GeV, has been observed for the first time at the LHC in pp collisions at √ s = 13 TeV. One of the two scattered protons is measured in the CMS-TOTEM precision proton spectrometer (CT-PPS), which operated for the first time in 2016. The second proton either remains intact or is excited and then dissociates into a low-mass state p * , which is undetected. The measurement is based on an integrated luminosity of 9.4 fb −1 collected during standard, high-luminosity LHC operation. A total of 12 µ + µ − and 8 e + e − pairs with m( + − ) > 110 GeV, and matching forward proton kinematics, are observed, with expected backgrounds of 1.49 ± 0.07 (stat) ± 0.53 (syst) and 2.36 ± 0.09 (stat) ± 0.47 (syst), respectively. This corresponds to an excess of more than five standard deviations over the expected background. The present result constitutes the first observation of proton-tagged γγ collisions at the electroweak scale. This measurement also demonstrates that CT-PPS performs according to the design specifications.

In a recent breakup-reaction experiment using a Be12 beam at 29  MeV/nucleon, the 0+ band head of the expected He4+He8 molecular rotation was clearly identified at about 10.3 MeV, from which a large monopole matrix element of 7.0±1.0  fm2 and a large cluster-decay width were determined for the first time. These findings support the picture of strong clustering in Be12, which has been a subject of intense investigations over the past decade. The results were obtained thanks to a specially arranged detection system around zero degrees, which is essential in determining the newly emphasized monopole strengths to signal the cluster formation in a nucleus.

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