Continuous and discrete transformations of a one-dimensional porous medium equation

We consider the one-dimensional porous medium equation $u_t=\left (u^nu_x \right )_x+\frac{\mu}{x}u^nu_x$. We derive point transformations of a general class that map this equation into itself or into equations of a similar class. In some cases this porous medium equation is connected with well known equations. With the introduction of a new dependent variable this partial differential equation can be equivalently written as a system of two equations. Point transformations are also sought for this auxiliary system. It turns out that in addition to the continuous point transformations that may be derived by Lie's method, a number of discrete transformations are obtained. In some cases the point transformations which are presented here for the single equation and for the auxiliary system form cyclic groups of finite order

Symmetry classification of third-order nonlinear evolution equations. Part I: Semi-simple algebras

We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and extensions of these semi-simple Lie algebras by solvable Lie algebras. The methods we employ are extensions and refinements of previous techniques which have been used in such classifications.Comment: 53 page

Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source

A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential equations, generated by families of point transformations. A class of variable coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the general form $f(x)u_t=(g(x)u_x)_x+h(x)u^m$ ($m\ne0,1$) is studied from the symmetry point of view in the framework of the approach proposed. The singular subclass of the equations with $m=2$ is singled out. The group classifications of the entire class, the singular subclass and their images are performed with respect to both the corresponding (generalized extended) equivalence groups and all point transformations. The set of admissible transformations of the imaged class is exhaustively described in the general case $m\ne2$. The procedure of classification of nonclassical symmetries, which involves mappings between classes of differential equations, is discussed. Wide families of new exact solutions are also constructed for equations from the classes under consideration by the classical method of Lie reductions and by generation of new solutions from known ones for other equations with point transformations of different kinds (such as additional equivalence transformations and mappings between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica

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

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

Measurement of the cross-sections of the electroweak and total production of a Zγ pair in association with two jets in pp collisions at √s = 13 TeV with the ATLAS detector

This Letter presents the measurement of the fiducial and differential cross-sections of the electroweak production of a Zγ pair in association with two jets. The analysis uses 140 fb−1 of LHC proton–proton collision data taken at √s = 13 TeV recorded by the ATLAS detector during the years 2015–2018. Events with a Z boson candidate decaying into either an e+e− or μ+μ− pair, a photon and two jets are selected. The electroweak component is extracted by requiring a large dijet invariant mass and by using the information about the centrality of the system and is measured with an observed and expected significance well above five standard deviations. The fiducial pp → Zγ jj cross-section for the electroweak production is measured to be 3.6 ± 0.5 fb. The total fiducial cross-section that also includes contributions where the jets arise from strong interactions is measured to be 16.8+2.0 −1.8 fb. The results are consistent with the Standard Model predictions. Differential cross-sections are also measured using the same events and are compared with parton-shower Monte Carlo simulations. Good agreement is observed between data and predictions

Combination of searches for heavy spin-1 resonances using 139 fb−1 of proton-proton collision data at √s = 13 TeV with the ATLAS detector

A combination of searches for new heavy spin-1 resonances decaying into diferent pairings of W, Z, or Higgs bosons, as well as directly into leptons or quarks, is presented. The data sample used corresponds to 139 fb−1 of proton-proton collisions at √s = 13 TeV collected during 2015–2018 with the ATLAS detector at the CERN Large Hadron Collider. Analyses selecting quark pairs (qq, bb, tt¯, and tb) or third-generation leptons (τν and τ τ ) are included in this kind of combination for the frst time. A simplifed model predicting a spin-1 heavy vector-boson triplet is used. Cross-section limits are set at the 95% confdence level and are compared with predictions for the benchmark model. These limits are also expressed in terms of constraints on couplings of the heavy vector-boson triplet to quarks, leptons, and the Higgs boson. The complementarity of the various analyses increases the sensitivity to new physics, and the resulting constraints are stronger than those from any individual analysis considered. The data exclude a heavy vector-boson triplet with mass below 5.8 TeV in a weakly coupled scenario, below 4.4 TeV in a strongly coupled scenario, and up to 1.5 TeV in the case of production via vector-boson fusion

Measurement of vector boson production cross sections and their ratios using pp collisions at √s = 13.6 TeV with the ATLAS detector

Abstract available from publisher's website