Nonlinear Evolution of the Kelvin–Helmholtz Instability of Supersonic Tangential Velocity Discontinuities

AbstractA nonlinear stability analysis using a multiple-scales perturbation procedure is performed for the instability of two layers of immiscible, inviscid, arbitrarily compressible fluids in relative motion. Such configurations are of relevance in a variety of astrophysical and space configurations. For modes ofallwavenumbers on, or in the stable neighborhood of, the linear neutral curve, the nonlinear evolution of the amplitude of the linear fields on the slow first-order scales is shown to be governed by a complicated nonlinear Klein–Gordon equation. Both the spatially dependent and space-independent versions of this equation are considered to obtain the regimes of physical parameter space where the linearly unstable solutions either evolve to final permanent envelope wave patterns resembling the ensembles of interacting vortices observed empirically, or are disrupted via nonlinear modulation instability

Measurement of the top quark mass using a profile likelihood approach with the lepton + jets final states in proton–proton collisions at s=13 TeV\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}

International audienceThe mass of the top quark is measured in 36.3$\,\text {fb}^{-1}$ of LHC proton–proton collision data collected with the CMS detector at $\sqrt{s}=13\,\text {Te}\hspace{-.08em}\text {V}$. The measurement uses a sample of top quark pair candidate events containing one isolated electron or muon and at least four jets in the final state. For each event, the mass is reconstructed from a kinematic fit of the decay products to a top quark pair hypothesis. A profile likelihood method is applied using up to four observables per event to extract the top quark mass. The top quark mass is measured to be $171.77\pm 0.37\,\text {Ge}\hspace{-.08em}\text {V}$. This approach significantly improves the precision over previous measurements