Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$Comment: 34 page

An adaptive finite element method for the infinity Laplacian

We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem are well known to be singular in nature so we have taken the opportunity to conduct an a posteriori analysis of the method deriving residual based estimators to drive an adaptive algorithm. It is numerically shown that optimal convergence rates are regained using the adaptive procedure

Homogenization and enhancement for the G-equation

We consider the so-called G-equation, a level set Hamilton-Jacobi equation, used as a sharp interface model for flame propagation, perturbed by an oscillatory advection in a spatio-temporal periodic environment. Assuming that the advection has suitably small spatial divergence, we prove that, as the size of the oscillations diminishes, the solutions homogenize (average out) and converge to the solution of an effective anisotropic first-order (spatio-temporal homogeneous) level set equation. Moreover we obtain a rate of convergence and show that, under certain conditions, the averaging enhances the velocity of the underlying front. We also prove that, at scale one, the level sets of the solutions of the oscillatory problem converge, at long times, to the Wulff shape associated with the effective Hamiltonian. Finally we also consider advection depending on position at the integral scale

The ATLAS trigger system for LHC Run 3 and trigger performance in 2022

The ATLAS trigger system is a crucial component of the ATLAS experiment at the LHC. It is responsible for selecting events in line with the ATLAS physics programme. This paper presents an overview of the changes to the trigger and data acquisition system during the second long shutdown of the LHC, and shows the performance of the trigger system and its components in the proton-proton collisions during the 2022 commissioning period as well as its expected performance in proton-proton and heavy-ion collisions for the remainder of the third LHC data-taking period (2022–2025)

Search for the Zγ decay mode of new high-mass resonances in pp collisions at √s = 13 TeV with the ATLAS detector

This letter presents a search for narrow, high-mass resonances in the Zγ final state with the Z boson decaying into a pair of electrons or muons. The √s = 13 TeV pp collision data were recorded by the ATLAS detector at the CERN Large Hadron Collider and have an integrated luminosity of 140 fb−1. The data are found to be in agreement with the Standard Model background expectation. Upper limits are set on the resonance production cross section times the decay branching ratio into Zγ. For spin-0 resonances produced via gluon–gluon fusion, the observed limits at 95% confidence level vary between 65.5 fb and 0.6 fb, while for spin-2 resonances produced via gluon–gluon fusion (or quark–antiquark initial states) limits vary between 77.4 (76.1) fb and 0.6 (0.5) fb, for the mass range from 220 GeV to 3400 GeV

Study of Z → llγ decays at √s = 8 TeV with the ATLAS detector

This paper presents a study of Z → llγ decays with the ATLAS detector at the Large Hadron Collider. The analysis uses a proton–proton data sample corresponding to an integrated luminosity of 20.2 fb−1 collected at a centre-ofmass energy √s = 8 TeV. Integrated fiducial cross-sections together with normalised differential fiducial cross-sections, sensitive to the kinematics of final-state QED radiation, are obtained. The results are found to be in agreement with stateof-the-art predictions for final-state QED radiation. First measurements of Z → llγ γ decays are also reported

Search for heavy Higgs bosons with flavour-violating couplings in multi-lepton plus b-jets final states in pp collisions at 13 TeV with the ATLAS detector

A search for new heavy scalars with flavour-violating decays in final states with multiple leptons and b-tagged jets is presented. The results are interpreted in terms of a general two-Higgs-doublet model involving an additional scalar with couplings to the top-quark and the three up-type quarks (ρtt, ρtc, and ρtu). The targeted signals lead to final states with either a same-sign top-quark pair, three top-quarks, or four top-quarks. The search is based on a data sample of proton-proton collisions at √s = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 139 fb−1. Events are categorised depending on the multiplicity of light charged leptons (electrons or muons), total lepton charge, and a deep-neural-network output to enhance the purity of each of the signals. Masses of an additional scalar boson mH between 200 − 630 GeV with couplings ρtt = 0.4, ρtc = 0.2, and ρtu = 0.2 are excluded at 95% confidence level. Additional interpretations are provided in models of R-parity violating supersymmetry, motivated by the recent flavour and (g − 2)μ anomalies

Search for a new heavy scalar particle decaying into a Higgs boson and a new scalar singlet in final states with one or two light leptons and a pair of τ-leptons with the ATLAS detector

A search for a new heavy scalar particle X decaying into a Standard Model (SM) Higgs boson and a new singlet scalar particle S is presented. The search uses a proton-proton (pp) collision data sample with an integrated luminosity of 140 fb−1 recorded at a centre-of-mass energy of s√ = 13 TeV with the ATLAS detector at the Large Hadron Collider. The most sensitive mass parameter space is explored in X mass ranging from 500 to 1500 GeV, with the corresponding S mass in the range 200–500 GeV. The search selects events with two hadronically decaying τ-lepton candidates from H → τ+τ− decays and one or two light leptons (ℓ = e, μ) from S → VV (V = W, Z) decays while the remaining V boson decays hadronically or to neutrinos. A multivariate discriminant based on event kinematics is used to separate the signal from the background. No excess is observed beyond the expected SM background and 95% confidence level upper limits between 72 fb and 542 fb are derived on the cross-section σ(pp → X → SH) assuming the same SM-Higgs boson-like decay branching ratios for the S → VV decay. Upper limits on the visible cross-sections σ(pp → X → SH → WWττ) and σ(pp → X → SH → ZZττ) are also set in the ranges 3–26 fb and 6–33 fb, respectively