Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

Dynamic Responsive Inguinal Scaffold Activates Myogenic Growth Factors Finalizing the Regeneration of the Herniated Groin

Background: Postoperative chronic pain caused by fixation and/or fibrotic incorporation of hernia meshes are the main concerns in inguinal herniorrhaphy. As inguinal hernia is a degenerative disease, logically the treatment should aim at stopping degeneration and activating regeneration. Unfortunately, in conventional prosthetic herniorrhaphy no relationship exists between pathogenesis and treatment. To overcome these incongruences, a 3D dynamic responsive multilamellar scaffold has been developed for fixation-free inguinal hernia repair. Made of polypropylene like conventional flat meshes, the dynamic behavior of the scaffold allows for the regeneration of all typical inguinal components: connective tissue, vessels, nerves, and myocytes. This investigation aims to demonstrate that, moving in tune with the groin, the 3D scaffold attracts myogenic growth factors activating the development of mature myocytes and, thus, re-establishing the herniated inguinal barrier. Methods: Biopsy samples excised from the 3D scaffold at different postoperative stages were stained with H&E and Azan–Mallory; immunohistochemistry for NGF and NGFR p75 was performed to verify the degree of involvement of muscular growth factors in the neomyogenesis. Results: Histological evidence of progressive muscle development and immunohistochemical proof of NFG and NFGRp75 contribution in neomyogenesis within the 3D scaffold was documented and statistically validated. Conclusion: The investigation appears to confirm that a 3D polypropylene scaffold designed to confer dynamic responsivity, unlike the fibrotic scar plate of static meshes, attracts myogenic growth factors turning the biological response into tissue regeneration. Newly developed muscles allow the scaffold to restore the integrity of the inguinal barrier

Feasibility Study of a Neutron Time Of Flight Facility at the CERN-PS

This report summarises the feasibility study of a neutron time-of-flight facility at the CERN-PS as described in Refs. [1] and [2]. The idea is to extract at 24 GeV/cproton bunches (r.m.s. length ~7 ns) on to a target. The neutrons produced by spallation are directed to an experimental area located 230 m downstream throughout a vacuum pipe (diameter ~80 cm) making use of the existing TT2A tunnel about 7 m below the ISR tunne

Bose-Einstein correlations of same-sign charged pions in the forward region in pp collisions at √s=7 TeV

Bose-Einstein correlations of same-sign charged pions, produced in protonproton collisions at a 7 TeV centre-of-mass energy, are studied using a data sample collected by the LHCb experiment. The signature for Bose-Einstein correlations is observed in the form of an enhancement of pairs of like-sign charged pions with small four-momentum difference squared. The charged-particle multiplicity dependence of the Bose-Einstein correlation parameters describing the correlation strength and the size of the emitting source is investigated, determining both the correlation radius and the chaoticity parameter. The measured correlation radius is found to increase as a function of increasing charged-particle multiplicity, while the chaoticity parameter is seen to decreas

Measurement of the mass and lifetime of the Ωb−\Omega_b^- baryon

A proton-proton collision data sample, corresponding to an integrated luminosity of 3 fb$^{-1}$ collected by LHCb at $\sqrt{s}=7$ and 8 TeV, is used to reconstruct $63\pm9$ $\Omega_b^-\to\Omega_c^0\pi^-$, $\Omega_c^0\to pK^-K^-\pi^+$ decays. Using the $\Xi_b^-\to\Xi_c^0\pi^-$, $\Xi_c^0\to pK^-K^-\pi^+$ decay mode for calibration, the lifetime ratio and absolute lifetime of the $\Omega_b^-$ baryon are measured to be \begin{align*} \frac{\tau_{\Omega_b^-}}{\tau_{\Xi_b^-}} &= 1.11\pm0.16\pm0.03, \\ \tau_{\Omega_b^-} &= 1.78\pm0.26\pm0.05\pm0.06~{\rm ps}, \end{align*} where the uncertainties are statistical, systematic and from the calibration mode (for $\tau_{\Omega_b^-}$ only). A measurement is also made of the mass difference, $m_{\Omega_b^-}-m_{\Xi_b^-}$, and the corresponding $\Omega_b^-$ mass, which yields \begin{align*} m_{\Omega_b^-}-m_{\Xi_b^-} &= 247.4\pm3.2\pm0.5~{\rm MeV}/c^2, \\ m_{\Omega_b^-} &= 6045.1\pm3.2\pm 0.5\pm0.6~{\rm MeV}/c^2. \end{align*} These results are consistent with previous measurements.Comment: 11 pages, 5 figures, All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-008.htm

Measurement of the ratio of branching fractions BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma)

The ratio of branching fractions of the radiative B decays B0 -> K*0 gamma and Bs0 -> phi gamma has been measured using 0.37 fb-1 of pp collisions at a centre of mass energy of sqrt(s) = 7 TeV, collected by the LHCb experiment. The value obtained is BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) = 1.12 +/- 0.08 ^{+0.06}_{-0.04} ^{+0.09}_{-0.08}, where the first uncertainty is statistical, the second systematic and the third is associated to the ratio of fragmentation fractions fs/fd. Using the world average for BR(B0 -> K*0 gamma) = (4.33 +/- 0.15) x 10^{-5}, the branching fraction BR(Bs0 -> phi gamma) is measured to be (3.9 +/- 0.5) x 10^{-5}, which is the most precise measurement to date.Comment: 15 pages, 1 figure, 2 table

Constraints on the unitarity triangle angle γ\gamma from Dalitz plot analysis of B0→DK+π−B^0 \to D K^+ \pi^- decays

The first study is presented of CP violation with an amplitude analysis of the Dalitz plot of $B^0 \to D K^+ \pi^-$ decays, with $D \to K^+ \pi^-$, $K^+ K^-$ and $\pi^+ \pi^-$. The analysis is based on a data sample corresponding to $3.0\,{\rm fb}^{-1}$ of $pp$ collisions collected with the LHCb detector. No significant CP violation effect is seen, and constraints are placed on the angle $\gamma$ of the unitarity triangle formed from elements of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. Hadronic parameters associated with the $B^0 \to D K^*(892)^0$ decay are determined for the first time. These measurements can be used to improve the sensitivity to $\gamma$ of existing and future studies of the $B^0 \to D K^*(892)^0$ decay.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-059.html; updated to correct figure 9 (numerical results unchanged

Measurement of the CKM angle γ from a combination of B±→Dh± analyses

A combination of three LHCb measurements of the CKM angle γ is presented. The decays B±→D K± and B±→Dπ± are used, where D denotes an admixture of D0 and D0 mesons, decaying into K+K−, π+π−, K±π∓, K±π∓π±π∓, K0Sπ+π−, or K0S K+K− final states. All measurements use a dataset corresponding to 1.0 fb−1 of integrated luminosity. Combining results from B±→D K± decays alone a best-fit value of γ =72.0◦ is found, and confidence intervals are set γ ∈ [56.4,86.7]◦ at 68% CL, γ ∈ [42.6,99.6]◦ at 95% CL. The best-fit value of γ found from a combination of results from B±→Dπ± decays alone, is γ =18.9◦, and the confidence intervals γ ∈ [7.4,99.2]◦ ∪ [167.9,176.4]◦ at 68% CL are set, without constraint at 95% CL. The combination of results from B± → D K± and B± → Dπ± decays gives a best-fit value of γ =72.6◦ and the confidence intervals γ ∈ [55.4,82.3]◦ at 68% CL, γ ∈ [40.2,92.7]◦ at 95% CL are set. All values are expressed modulo 180◦, and are obtained taking into account the effect of D0–D0 mixing

Measurement of the Bs0→J/ψηB_{s}^{0} \rightarrow J/\psi \eta lifetime

Using a data set corresponding to an integrated luminosity of $3 fb^{-1}$, collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV, the effective lifetime in the $B^0_s \rightarrow J/\psi \eta$ decay mode, $\tau_{\textrm{eff}}$, is measured to be $\tau_{\textrm{eff}} = 1.479 \pm 0.034~\textrm{(stat)} \pm 0.011 ~\textrm{(syst)}$ ps. Assuming $CP$ conservation, $\tau_{\textrm{eff}}$ corresponds to the lifetime of the light $B_s^0$ mass eigenstate. This is the first measurement of the effective lifetime in this decay mode.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2016-017.htm