Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Magnetic and structural properties of barium hexaferrite BaFe12O19 from various growth techniques

Barium hexaferrite powder samples with grains in the m-range were obtained from solid-state sintering, and crystals with sizes up to 5 mm grown from PbO, Na2CO3, and BaB2O4 fluxes, respectively. Carbonate and borate fluxes provide the largest and structurally best crystals at significantly lower growth temperatures of 1533 K compared to flux-free synthesis (1623 K). The maximum synthesis temperature can be further reduced by the application of PbO-containing fluxes (down to 1223 K upon use of 80 at % PbO), however, Pb-substituted crystals Ba1-xPbxFe12O19 with Pb contents in the range of 0.23(2) x 0.80(2) form, depending on growth temperature and flux PbO content. The degree of Pb-substitution has only a minor influence on unit cell and magnetic parameters, although the values for Curie temperature, saturation magnetization, as well as the coercivity of these samples are significantly reduced in comparison with those from samples obtained from the other fluxes. Due to the lowest level of impurities, the samples from carbonate flux show superior quality compared to materials obtained using other methods

Measurement of nuclear modification factors of gamma(1S)), gamma(2S), and gamma(3S) mesons in PbPb collisions at root s(NN)=5.02 TeV

The cross sections for ϒ(1S), ϒ(2S), and ϒ(3S) production in lead-lead (PbPb) and proton-proton (pp) collisions at √sNN = 5.02 TeV have been measured using the CMS detector at the LHC. The nuclear modification factors, RAA, derived from the PbPb-to-pp ratio of yields for each state, are studied as functions of meson rapidity and transverse momentum, as well as PbPb collision centrality. The yields of all three states are found to be significantly suppressed, and compatible with a sequential ordering of the suppression, RAA(ϒ(1S)) > RAA(ϒ(2S)) > RAA(ϒ(3S)). The suppression of ϒ(1S) is larger than that seen at √sNN = 2.76 TeV, although the two are compatible within uncertainties. The upper limit on the RAA of ϒ(3S) integrated over pT, rapidity and centrality is 0.096 at 95% confidence level, which is the strongest suppression observed for a quarkonium state in heavy ion collisions to date. © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.Peer reviewe

Development and validation of HERWIG 7 tunes from CMS underlying-event measurements

This paper presents new sets of parameters (“tunes”) for the underlying-event model of the HERWIG7 event generator. These parameters control the description of multiple-parton interactions (MPI) and colour reconnection in HERWIG7, and are obtained from a fit to minimum-bias data collected by the CMS experiment at s=0.9, 7, and 13Te. The tunes are based on the NNPDF 3.1 next-to-next-to-leading-order parton distribution function (PDF) set for the parton shower, and either a leading-order or next-to-next-to-leading-order PDF set for the simulation of MPI and the beam remnants. Predictions utilizing the tunes are produced for event shape observables in electron-positron collisions, and for minimum-bias, inclusive jet, top quark pair, and Z and W boson events in proton-proton collisions, and are compared with data. Each of the new tunes describes the data at a reasonable level, and the tunes using a leading-order PDF for the simulation of MPI provide the best description of the dat

Azimuthal separation in nearly back-to-back jet topologies in inclusive 2-and 3-jet events in pp collisions at root s=13TeV

A measurement for inclusive 2- and 3-jet events of the azimuthal correlation between the two jets with the largest transverse momenta, Delta phi(12), is presented. The measurement considers events where the two leading jets are nearly collinear ("back-to-back") in the transverse plane and is performed for several ranges of the leading jet transverse momentum. Proton-proton collision data collected with the CMS experiment at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 35.9 fb(-1) are used. Predictions based on calculations using matrix elements at leading-order and next-to-leading-order accuracy in perturbative quantum chromodynamics supplemented with leading-log parton showers and hadronization are generally in agreement with themeasurements. Discrepancies between the measurement and theoretical predictions are as large as 15%, mainly in the region 177 degrees <Delta phi(12) <180 degrees. The 2- and 3-jet measurements are not simultaneously described by any of models.Peer reviewe

MUSiC : a model-unspecific search for new physics in proton-proton collisions at root s=13TeV

Results of the Model Unspecific Search in CMS (MUSiC), using proton-proton collision data recorded at the LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1), are presented. The MUSiC analysis searches for anomalies that could be signatures of physics beyond the standard model. The analysis is based on the comparison of observed data with the standard model prediction, as determined from simulation, in several hundred final states and multiple kinematic distributions. Events containing at least one electron or muon are classified based on their final state topology, and an automated search algorithm surveys the observed data for deviations from the prediction. The sensitivity of the search is validated using multiple methods. No significant deviations from the predictions have been observed. For a wide range of final state topologies, agreement is found between the data and the standard model simulation. This analysis complements dedicated search analyses by significantly expanding the range of final states covered using a model independent approach with the largest data set to date to probe phase space regions beyond the reach of previous general searches.Peer reviewe

Measurement of the top quark Yukawa coupling from t(t)over-bar kinematic distributions in the dilepton final state in proton-proton collisions at root s=13 TeV

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