Justification of the coupled-mode approximation for a nonlinear elliptic problem with a periodic potential

Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions involving hyperbolic functions. We justify the use of the one-dimensional stationary coupled-mode system for a relevant elliptic problem by employing the method of Lyapunov--Schmidt reductions in Fourier space. In particular, existence of periodic/anti-periodic and decaying solutions is proved and the error terms are controlled in suitable norms. The use of multi-dimensional stationary coupled-mode systems is justified for analysis of bifurcations of periodic/anti-periodic solutions in a small multi-dimensional periodic potential.Comment: 18 pages, no figure

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Flavor changing Z-decays from scalar interactions at a Giga-Z Linear Collider

The flavor changing decay Z -> d_I \bar{d}_J is investigated with special emphasis on the b \bar{s} final state. Various models for flavor violation are considered: two Higgs doublet models (2HDM's), supersymmetry (SUSY) with flavor violation in the up and down-type squark mass matrices and SUSY with flavor violation mediated by R-parity-violating interaction. We find that, within the SUSY scenarios for flavor violation, the branching ratio for the decay Z -> b \bar{s} can reach 10^{-6} for large \tan\beta values, while the typical size for this branching ratio in the 2HDM's considered is about two orders of magnitudes smaller at best. Thus, flavor changing SUSY signatures in radiative Z decays such as Z -> b \bar{s} may be accessible to future ``Z factories'' such as a Giga-Z version of the TESLA design.Comment: 27 pages, 15 figures, REVTeX4. A new section added and a few minor corrections were made in the tex

Interpretation of Fracture Toughness and R-Curve Behavior by Direct Observation of Microfracture Process in Ti-Based Dendrite-Containing Amorphous Alloys

Fracture properties of Ti-based amorphous alloys containing ductile beta dendrites were explained by directly observing microfracture processes. Three Ti-based amorphous alloys were fabricated by adding Ti, Zr, V, Ni, Al, and Be into a Ti-6Al-4V alloy by a vacuum arc melting method. The effective sizes of dendrites varied from 63 to 104 mu m, while their volume fractions were almost constant within the range from 74 to 76 pct. The observation of the microfracture of the alloy containing coarse dendrites revealed that a microcrack initiated at the amorphous matrix of the notch tip and propagated along the amorphous matrix. In the alloy containing fine dendrites, the crack propagation was frequently blocked by dendrites, and many deformation bands were formed near or in front of the propagating crack, thereby resulting in a zig-zag fracture path. Crack initiation toughness was almost the same at 35 to 36 MPaaem within error ranges in the three alloys because it was heavily affected by the stress applied to the specimen at the time of crack initiation at the crack tip as well as strength levels of the alloys. According to the R-curve behavior, however, the best overall fracture properties in the alloy containing fine dendrites were explained by mechanisms of blocking of the crack growth and crack blunting and deformation band formation at dendrites. (C) The Minerals, Metals & Materials Society and ASM International 2015ope

Measurement of the total cross section and ρ -parameter from elastic scattering in pp collisions at √s=13 TeV with the ATLAS detector

In a special run of the LHC with β⋆=2.5 km, proton–proton elastic-scattering events were recorded at s√=13 TeV with an integrated luminosity of 340 μb−1 using the ALFA subdetector of ATLAS in 2016. The elastic cross section was measured differentially in the Mandelstam t variable in the range from −t=2.5⋅10−4 GeV2 to −t=0.46 GeV2 using 6.9 million elastic-scattering candidates. This paper presents measurements of the total cross section σtot, parameters of the nuclear slope, and the ρ-parameter defined as the ratio of the real part to the imaginary part of the elastic-scattering amplitude in the limit t→0. These parameters are determined from a fit to the differential elastic cross section using the optical theorem and different parameterizations of the t-dependence. The results for σtot and ρ are σtot(pp→X)=104.7±1.1 mb ,ρ=0.098±0.011. The uncertainty in σtot is dominated by the luminosity measurement, and in ρ by imperfect knowledge of the detector alignment and by modelling of the nuclear amplitude.publishedVersio

Riociguat treatment in patients with chronic thromboembolic pulmonary hypertension: Final safety data from the EXPERT registry

Objective: The soluble guanylate cyclase stimulator riociguat is approved for the treatment of adult patients with pulmonary arterial hypertension (PAH) and inoperable or persistent/recurrent chronic thromboembolic pulmonary hypertension (CTEPH) following Phase

Search for pair production of boosted Higgs bosons via vector-boson fusion in the bb¯bb¯ final state using pp collisions at √s = 13 TeV with the ATLAS detector

A search for Higgs boson pair production via vector-boson fusion is performed in the Lorentz-boosted regime, where a Higgs boson candidate is reconstructed as a single large-radius jet, using 140 fb−1 of proton–proton collision data at √s = 13 TeV recorded by the ATLAS detector at the Large Hadron Collider. Only Higgs boson decays into bottom quark pairs are considered. The search is particularly sensitive to the quartic coupling between two vector bosons and two Higgs bosons relative to its Standard Model prediction, K2V . This study constrains K2V to 0.55 < K2V < 1.49 at the 95% confidence level. The value K2V = 0 is excluded with a significance of 3.8 standard deviations with other Higgs boson couplings fixed to their Standard Model values. A search for new heavy spin-0 resonances that would mediate Higgs boson pair production via vector-boson fusion is carried out in the mass range of 1–5 TeV for the first time under several model and decay-width assumptions. No significant deviation from the Standard Model hypothesis is observed and exclusion limits at the 95% confidence level are derived

Charged-hadron production in pp, p+Pb, Pb+Pb, and Xe+Xe collisions at sNN−−−√ = 5 TeV with the ATLAS detector at the LHC

This paper presents measurements of charged-hadron spectra obtained in pp, p+Pb, and Pb+Pb collisions at s√ or sNN−−−√ = 5.02 TeV, and in Xe+Xe collisions at sNN−−−√ = 5.44 TeV. The data recorded by the ATLAS detector at the LHC have total integrated luminosities of 25 pb−1, 28 nb−1, 0.50 nb−1, and 3 μb−1, respectively. The nuclear modification factors RpPb and RAA are obtained by comparing the spectra in heavy-ion and pp collisions in a wide range of charged-particle transverse momenta and pseudorapidity. The nuclear modification factor RpPb shows a moderate enhancement above unity with a maximum at pT ≈ 3 GeV; the enhancement is stronger in the Pb-going direction. The nuclear modification factors in both Pb+Pb and Xe+Xe collisions feature a significant, centrality-dependent suppression. They show a similar distinct pT-dependence with a local maximum at pT ≈ 2 GeV and a local minimum at pT ≈ 7 GeV. This dependence is more distinguishable in more central collisions. No significant |η|-dependence is found. A comprehensive comparison with several theoretical predictions is also provided. They typically describe RAA better in central collisions and in the pT range from about 10 to 100 GeV