text:
# Boris Wagner

Researcher
• E-mailBoris.Wagner@uib.no
Nygårdsgt. 5
Postboks 7800
5020 BERGEN
• 2019. Λc+ production in Pb–Pb collisions at √sNN = 5.02 TeV. Physics Letters B. 212-223.
• 2019. p−p, p−Λ, and Λ−Λ correlations studied via femtoscopy in pp reactions at √s=7 TeV. Physical Review C.
• 2019. Study of the Λ–Λ interaction with femtoscopy correlations in pp and p–Pb collisions at the LHC. Physics Letters B. 1-13.
• 2019. Study of J/ψ azimuthal anisotropy at forward rapidity in Pb-Pb collisions at √sNN=5.02 TeV. Journal of High Energy Physics (JHEP). 1-30.
• 2019. Production of the ρ(770)0 meson in pp and Pb-Pb collisions at √sNN = 2.76 TeV. Physical Review C. 1-20.
• 2019. Production of muons from heavy-flavour hadron decays in pp collisions at √s = 5.02 TeV. Journal of High Energy Physics (JHEP). 1-27.
• 2019. Measuring K0SK± interactions using pp collisions at √s=7 TeV. Physics Letters B. 22-34.
• 2019. Measurement of Υ(1S) elliptic flow at forward rapidity in Pb-Pb collisions at √sNN=5.02  TeV. Physical Review Letters. 1-13.
• 2019. Measurement of the inclusive isolated photon production cross section in p p collisions at √s=7 TeV. European Physical Journal C. 1-20.
• 2019. Measurement of jet radial profiles in Pb–Pb collisions at √sNN = 2.76 TeV. Physics Letters B. 204-219.
• 2019. Measurement of charged jet cross section in pp collisions at √s=5.02  TeV. Physical Review D. 1-22.
• 2019. Measurement of D0, D+, D∗+ and D+s production in pp collisions at √S = 5.02 TeV with ALICE. European Physical Journal C. 1-25.
• 2019. Inclusive J/ψ production at mid-rapidity in pp collisions at √s = 5.02 TeV. Journal of High Energy Physics (JHEP). 1-26.
• 2019. Energy dependence of exclusive J/ψ photoproduction off protons in ultra-peripheral p–Pb collisions at √sNN = 5.02 TeV. European Physical Journal C. 1-18.
• 2019. Design optimization of a pixel-based range telescope for proton computed tomography. Physica medica (Testo stampato). 87-97.
• 2019. Characterization of monolithic CMOS pixel sensor chip with ion beams for application in particle computed tomography. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. 1-4.
• 2019. Azimuthal Anisotropy of Heavy-Flavor Decay Electrons in p-Pb Collisions at √sNN=5.02  TeV. Physical Review Letters. 1-13.
• 2019. 3Λh and 3‾Λ‾h lifetime measurement in Pb–Pb collisions at √sNN = 5.02 TeV via two-body decay. Physics Letters B. 1-12.
• 2018. ϕ meson production at forward rapidity in Pb–Pb collisions at √sNN=2.76 TeV. European Physical Journal C. 1-18.
• 2018. Λ c + production in pp collisions at √s=7 TeV and in p-Pb collisions at √sNN=5.02 TeV. Journal of High Energy Physics (JHEP). 1-48.
• 2018. The ALICE Transition Radiation Detector: Construction, operation, and performance . Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. 88-127.
• 2018. Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at √sNN=2.76 TeV. Physical Review C. 1-23.
• 2018. Search for collectivity with azimuthal J/ψ-hadron correlations in high multiplicity p–Pb collisions at √sNN = 5.02 and 8.16 TeV. Physics Letters B. 7-20.
• 2018. Production of deuterons, tritons, 3He nuclei, and their antinuclei in pp collisions at √s=0.9, 2.76, and 7 TeV. Physical Review C.
• 2018. Neutral pion and η meson production at midrapidity in Pb-Pb collisions at √sNN=2.76 TeV. Physical Review C. 1-20.
• 2018. Measurements of low-pT electrons from semileptonic heavy-flavour hadron decays at mid-rapidity in pp and Pb-Pb collisions at √sN-N−=2.76 TeV. Journal of High Energy Physics (JHEP). 1-29.
• 2018. Measurement of D0, D+, D*+ and D s + production in Pb-Pb collisions at √sN-N−=5.02 TeV. Journal of High Energy Physics (JHEP). 1-34.
• 2018. J/ψ production as a function of charged-particle pseudorapidity density in p–Pb collisions at √sNN = 5.02 TeV. Physics Letters B. 91-104.
• 2018. Inclusive J/ψ production in Xe–Xe collisions at √sNN = 5.44 TeV. Physics Letters B. 419-428.
• 2018. Inclusive J/ψ production at forward and backward rapidity in p-Pb collisions at √sNN=8.16 TeV. Journal of High Energy Physics (JHEP). 1-27.
• 2018. First measurement of jet mass in Pb–Pb and p–Pb collisions at the LHC. Physics Letters B. 249-264.
• 2018. First measurement of Ξc0 production in pp collisions at √s = 7 TeV. Physics Letters B. 8-19.
• 2018. Dielectron production in proton-proton collisions at √s=7 TeV. Journal of High Energy Physics (JHEP). 1-47.
• 2018. D-meson azimuthal anisotropy in midcentral Pb-Pb collisions at √sNN=5.02  TeV. Physical Review Letters. 1-13.
• 2017. W and Z boson production in p-Pb collisions at √sNN = 5.02 TeV. Journal of High Energy Physics (JHEP). 1-26.
• 2017. The new Inner Tracking System of the ALICE experiment. Nuclear Physics A. 900-903.
• 2017. Searches for transverse momentum dependent flow vector fluctuations in Pb-Pb and p-Pb collisions at the LHC. Journal of High Energy Physics (JHEP). 1-32.
• 2017. Production of π0 and η mesons up to high transverse momentum in pp collisions at √s=2.76 TeV. European Physical Journal C. 1-25.
• 2017. Production of Σ(1385)± and Ξ(1530)0 in p–Pb collisions at √sNN=5.02 TeV. European Physical Journal C. 1-17.
• 2017. Probing non-linearity of higher order anisotropic flow in Pb-Pb collisions. Nuclear Physics A. 377-380.
• 2017. Measuring K0SK± interactions using Pb–Pb collisions at √sNN=2.76 TeV. Physics Letters B. 64-77.
• 2017. Measurement of the production of high-pT electrons from heavy-flavour hadron decays in Pb-Pb collisions at √sNN=2.76 TeV. Physics Letters B. 467-481.
• 2017. Measurement of electrons from beauty-hadron decays in p-Pb collisions at √sNN=5.02 TeV and Pb-Pb collisions at √sNN=2.76 TeV. Journal of High Energy Physics (JHEP). 1-39.
• 2017. K∗(892)0 and ϕ(1020) meson production at high transverse momentum in pp and Pb-Pb collisions at √sNN=2.76 TeV. Physical Review C. 1-18.
• 2017. J/ψ suppression at forward rapidity in Pb-Pb collisions at √sNN=5.02 TeV. Physics Letters B. 212-224.
• 2017. Investigations of anisotropic collectivity using multi-particle correlations in pp, p-Pb and Pb-Pb collisions. Nuclear Physics A. 437-440.
• 2017. Investigating the role of coherence effects on jet quenching in Pb-Pb collisions at √sNN = 2.76 TeV using jet substructure. Nuclear Physics A. 560-563.
• 2017. Enhanced production of multi-strange hadrons in high-multiplicity proton-proton collisions. Nature Physics. 535-539.
• 2017. Electroweak boson production in p–Pb and Pb–Pb collisions at sNN=5.02 TeV with ALICE. Nuclear Physics A. 309-312.
• 2017. Determination of the event collision time with the ALICE detector at the LHC. The European Physical Journal Plus. 1-17.
• 2017. Centrality dependence of the pseudorapidity density distribution for charged particles in Pb-Pb collisions at √sNN=5.02TeV. Physics Letters B. 567-577.
• 2017. Azimuthally differential pion femtoscopy relative to the second and thrid harmonic in Pb-Pb 2.76 TeV collisions from ALICE. Nuclear Physics A. 468-471.
• 2017. ALICE measurement of the J/ψ nuclear modification factor at mid-rapidity in Pb–Pb collisions at √sNN=5.02 TeV. Nuclear Physics A. 576-579.
• 2016. ϕ production at forward rapidity in pp, p–Pb and Pb–Pb collisions with ALICE. Nuclear Physics A. 453-456.
• 2016. Strangeness production as a function of charged particle multiplicity in proton-proton collisions. Nuclear Physics A. 777-780.
• 2016. Results from (anti-)(hyper-)nuclei production and searches for exotic bound states with ALICE at the LHC. Nuclear Physics A. 461-464.
• 2016. Multiplicity dependence of charged pion, kaon, and (anti)proton production at large transverse momentum in p–Pb collisions at √sNN=5.02 TeV. Physics Letters B. 720-735.
• 2016. Multipion Bose-Einstein correlations in pp,p -Pb, and Pb-Pb collisions at energies available at the CERN Large Hadron Collider. Physical Review C. Nuclear Physics.
• 2016. Measurements of heavy-flavour production in p–Pb collisions with ALICE. Nuclear Physics A. 493-496.
• 2016. Measurements of heavy-flavour nuclear modification factor and elliptic flow in Pb–Pb collisions at √sNN = 2.76 TeV with ALICE. Nuclear Physics A. 477-480.
• 2016. Measurement of an excess in the Yield of J/ψ at very low pT in Pb-Pb collisions at √sNN=2.76 TeV. Physical Review Letters.
• 2016. Measurement of D-meson production versus multiplicity in p-Pb collisions at √sNN=5.02 TeV. Journal of High Energy Physics (JHEP). 43 pages.
• 2016. Low-Mass Dielectron Production in pp, p–Pb and Pb–Pb Collisions with ALICE. Nuclear Physics A. 433-436.
• 2016. Light flavor results in p-Pb collisions with ALICE. Nuclear Physics A. 757-760.
• 2016. Inclusive quarkonium production at forward rapidity in pp collisions at √s = 8 TeV. European Physical Journal C.
• 2016. Heavy-flavor correlations and multiplicity dependence in pp and p–Pb collisions with ALICE. Nuclear Physics A. 479-500.
• 2016. Direct photon measurement in Pb-Pb collisions at √sNN = 2.76 TeV with ALICE. Nuclear Physics A. 421-424.
• 2016. Charge-dependent flow and the search for the chiral magnetic wave in Pb-Pb collisions at √sNN =2.76 TeV. Physical Review C. Nuclear Physics.
• 2016. Centrality dependence of the nuclear modification factor of charged pions, kaons, and protons in Pb-Pb collisions at √sNN =2.76 TeV. Physical Review C. Nuclear Physics.
• 2016. Centrality dependence of charged jet production in p–Pb collisions at √sNN = 5.02 TeV. European Physical Journal C.
• 2016. Centrality Dependence of the Charged-Particle Multiplicity Density at Midrapidity in Pb-Pb Collisions at √sNN =5.02 TeV. Physical Review Letters.
• 2016. Azimuthal anisotropy of charged jet production in √sNN=2.76 TeV Pb-Pb collisions. Physics Letters B. 511-525.
• 2016. Anisotropic flow of charged particles in Pb-Pb collisions at √sNN =5.02 TeV. Physical Review Letters.
• 2015. Production of inclusive Y(1S) and Y(2S) in p-Pb collisions at √sNN=5.02 TeV. Physics Letters B. 105-117.
• 2015. Measurement of jet suppression in central Pb-Pb collisions at √sNN=2.76 TeV. Physics Letters B. 1-14.
• 2015. Measurement of dijet kT in p-Pb collisions at √sNN=5.02 TeV. Physics Letters B. 385-395.
• 2015. Measurement of charged jet production cross sections and nuclear modification in p-Pb collisions at √sNN=5.02 TeV. Physics Letters B. 68-81.
• 2015. Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV. Journal of High Energy Physics (JHEP).
• 2015. Coherent ψ(2S) photo-production in ultra-peripheral PbPb collisions at √sNN=2.76 TeV. Physics Letters B. 358-370.
• 2015. Centrality dependence of inclusive J/ψ production in p-Pb collisions at √sNN = 5.02 TeV. Journal of High Energy Physics (JHEP). 1-33.
• 2015. Centrality dependence of high-pT D meson suppression in Pb-Pb collisions at √sNN = 2.76 TeV. Journal of High Energy Physics (JHEP). 1-24.
• 2014. Upgrade of the ALICE experiment: Letter of intent. Journal of Physics G: Nuclear and Particle Physics.
• 2014. Transverse momentum dependence of inclusive primary charged-particle production in p–Pb collisions at √sNN=5.02 TeV. European Physical Journal C.
• 2014. Technical design report for the upgrade of the ALICE inner tracking system. Journal of Physics G: Nuclear and Particle Physics.
• 2014. Production of light flavour hadrons at intermediate and high in pp, p-Pb and Pb-Pb collisions measured with ALICE. Nuclear Physics A. 309-314.
• 2014. Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at √sNN=2.76 TeV. Physics Letters B. 196-207.
• 2014. Neutral pion production at midrapidity in pp and Pb–Pb collisions at √ sNN TeV. European Physical Journal C. 1-20.
• 2014. Measurement of quarkonium production at forward rapidity in pp collisions at √s=7 TeV. European Physical Journal C. 22 pages.
• 2014. Measurement of prompt D -meson production in p-Pb collisions at sNN =5.02TeV. Physical Review Letters.
• 2014. Inclusive jet spectra in p–Pb collisions at ALICE. Nuclear Physics A. 1174-1178.
• 2014. Heavy-flavour production and nuclear modification factor in Pb–Pb collisions at √sNN = 2,76 TeV with ALICE. Nuclear Physics A. 514-519.
• 2014. Heavy-flavour elliptic flow measured in Pb–Pb collisions at √sNN = 2.76 TeV with ALICE. Nuclear Physics A. 530-534.
• 2014. Event-by-event mean pT fluctuations in pp and Pb–Pb collisions at the LHC. European Physical Journal C. 1-15.
• 2014. Centrality, rapidity and transverse momentum dependence of J/ψ suppression in Pb-Pb collisions at √sNN= 2.76TeV. Physics Letters B. 314-327.
• 2014. Beauty production in pp collisions at s=2.76 TeV measured via semi-electronic decays. Physics Letters B. 97-108.
• 2014. Azimuthally differential pion femtoscopy in Pb–Pb collisions at 2.76 TeV with ALICE at the LHC. Nuclear Physics A. 1088-1092.
• 2013. Upgrade of the ALICE experiment. Nuclear Physics A.
• 2013. Transverse Momentum Distribution and Nuclear Modification Factor of Charged Particles in p plus Pb Collisions at root(NN)-N-s=5.02 TeV. Physical Review Letters.
• 2013. Strange hadron and resonance production in Pb-Pb collisions at TeV with the ALICE experiment at LHC. Nuclear Physics A.
• 2013. Pseudorapidity Density of Charged Particles in p plus Pb Collisions at root s(NN)=5.02 TeV. Physical Review Letters.
• 2013. Production of pions, kaons and protons at high pT in TeV Pb-Pb collisions. Nuclear Physics A. 763c-766c.
• 2013. Overview of recent ALICE results, Nucl. Phys. A 904-905 (2013) 27c-34c. Nuclear Physics A. 27c-34c.
• 2013. Net-charge fluctuations in Pb-Pb collisions at root s(NN)=2.76 TeV. Physical Review Letters. 11 pages.
• 2013. Measurement of the D meson elliptic flow in Pb-Pb collisions at TeV with ALICE. Nuclear Physics A.
• 2013. Measurement of electrons from beauty hadron decays in pp collisions at root s=7 TeV. Physics Letters B. 13-23.
• 2013. Measurement of direct photons in pp and Pb-Pb collisions with ALICE. Nuclear Physics A.
• 2013. Long-range angular correlations on the near and away side in p-Pb collisions at root S-NN=5.02 TeV. Physics Letters B. 29-41.
• 2013. Long-range angular correlations of pi, K and p in p-Pb collisions at root s(NN)=5.02 TeV. Physics Letters B. 164-177.
• 2013. Jet structure in 2.76 TeV Pb-Pb collisions at ALICE. Nuclear Physics A.
• 2013. J/Ψ nuclear modification factor at mid-rapidity in Pb-Pb collisions at TeV. Nuclear Physics A.
• 2013. Isolated photon-hadron correlations in proton-proton collisions at = 7 TeV with the ALICE experiment. Nuclear Physics A.
• 2013. Exclusive J /ψ photoproduction off protons in ultraperipheral p -Pb collisions at sNN =5.02TeV. Physical Review Letters.
• 2013. Energy dependence of the transverse momentum distributions of charged particles in pp collisions measured by ALICE. European Physical Journal C.
• 2013. Coherent J/psi photoproduction in ultra-peripheral Pb-Pb collisions at root s(NN)=2.76 TeV. Physics Letters B. 1273-1283.
• 2013. Charge separation relative to the reaction plane in Pb-Pb collisions at root s(NN)=2.76 TeV. Physical Review Letters.
• 2013. Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at root S-NN=2.76 TeV. Physics Letters B. 18-28.
• 2013. Anisotropic flow measured from multi-particle azimuthal correlations for Pb-Pb collisions at 2.76 TeV by ALICE at the LHC. Nuclear Physics A.
• 2013. (Anti-)matter and hyper-matter production at the LHC with ALICE. Nuclear Physics A.
• 2012. Suppression of high transverse momentum D mesons in central Pb-Pb collisions at root s(NN)=2.76 TeV. Journal of High Energy Physics (JHEP).
• 2012. Production of K*(892)(0) and phi(1020) in pp collisions at root s=7 TeV. European Physical Journal C.
• 2012. Pion, kaon, and proton production in central Pb-Pb collisions at root s(NN)=2.76 TeV. Physical Review Letters.
• 2012. Particle-yield modification in jetlike azimuthal dihadron correlations in Pb-Pb collisions at root S-NN=2.76 TeV. Physical Review Letters.
• 2012. Multi-strange baryon production in pp collisions at root s=7 TeV with ALICE. Physics Letters B. 309-318.
• 2012. Measurement of the cross section for electromagnetic dissociation with neutron emission in Pb-Pb collisions at root s(NN)=2.76 TeV. Physical Review Letters.
• 2012. Measurement of prompt J/psi and beauty hadron production cross sections at mid-rapidity in pp collisions at root s=7 TeV. Journal of High Energy Physics (JHEP).
• 2012. Measurement of event background fluctuations for charged particle jet reconstruction in Pb-Pb collisions at root s(NN)=2.76 TeV. Journal of High Energy Physics (JHEP).
• 2012. Measurement of electrons from semileptonic heavy-flavor hadron decays in pp collisions at root s=7 TeV. Physical Review D. Particles and fields.
• 2012. Measurement of charm production at central rapidity in proton-proton collisions at root s=7 TeV. Journal of High Energy Physics (JHEP).
• 2012. Light vector meson production in pp collisions at root s=7 TeV ALICE Collaboration. Physics Letters B. 557-568.
• 2012. J/psi production as a function of charged particle multiplicity in pp collisions at root s=7 TeV. Physics Letters B. 165-175.
• 2012. J/psi Suppression at Forward Rapidity in Pb-Pb Collisions at root s(NN)=2.76 TeV. Physical Review Letters.
• 2012. J/psi Polarization in pp Collisions at root s=7 TeV. Physical Review Letters.
• 2012. Inclusive J/psi production in pp collisions at root s=2.76 TeV. Physics Letters B. 295-306.
• 2012. Heavy flavour decay muon production at forward rapidity in proton-proton collisions at root s=7 TeV. Physics Letters B. 265-275.
• 2012. D-S(+) meson production at central rapidity in proton-proton collisions at root s=7 TeV. Physics Letters B. 279-294.
• 2011. π0 and η measurement with photon conversions in ALICE in proton-proton collisions at sqrt(s) = 7 TeV. Nuclear Physics A. 281-284.
• 2011. pi0 measurement with ALICE electromagnetic calorimeters in p + p collisions at LHC. Journal of Physics: Conference Series. 4 pages.
• 2011. pi(0) and eta reconstruction from photon conversions in ALICE for first p-p collisions at the LHC. Journal of Physics: Conference Series. 4 pages.
• 2011. Vector meson production in pp collisions at s√=7 TeV, measured with the ALICE detector. Journal of Physics G: Nuclear and Particle Physics. 4 pages.
• 2011. Two-pion Bose-Einstein correlations in central Pb-Pb collisions at root(NN)-N-S=2.76 TeV. Physics Letters B. 328-337.
• 2011. Transverse energy measurements with ALICE. Nuclear Physics A. 249-252.
• 2011. The ALICE experiment at CERN LHC: Status and first results. International Journal of Modern Physics A. 517-522.
• 2011. Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at root s(NN)=2.76 TeV. Physics Letters B. 30-39.
• 2011. Studies of isolated photon production in simulated proton-proton collisions with ALICE-EMCal. Journal of Physics: Conference Series. 4 pages.
• 2011. Strange particle production in proton-proton collisions at root s=0.9 TeV with ALICE at the LHC. European Physical Journal C. 24 pages.
• 2011. Reaction plane determination by means of the ALICE zero degree calorimeters. Indian Journal of Physics. 1831-1835.
• 2011. Rapidity and transverse momentum dependence of inclusive J/psi production in pp collisions at root s=7 TeV. Physics Letters B. 442-455.
• 2011. Prospects for first heavy ion physics with the ALICE experiment. Nuclear Physics A. 522-525.
• 2011. Performance and First Physics Results of the ALICE Muon Spectrometer. Nuclear Physics A. 223-230.
• 2011. Neutral meson inclusive spectra measured with ALICE. Nuclear Physics A. 213-216.
• 2011. Multi-strange baryon measurements at LHC energies, with the ALICE experiment. Journal of Physics: Conference Series. 4 pages.
• 2011. Measurement of identified charged hadron spectra with ALICE using the ITS in proton-proton collisions at the LHC. Journal of Physics: Conference Series. 4 pages.
• 2011. Measurement of forward-rapidity heavy-flavour muons in proton-proton collisions at s**(1/2) = 7-TeV with ALICE. Nuclear Physics A. 323-326.
• 2011. Measurement of charged-particle pseudorapidity density with ALICE at LHC. Journal of Physics: Conference Series. 4 pages.
• 2011. Intrajet radiation study with the ALICE experiment at LHC. Journal of Physics: Conference Series. 4 pages.
• 2011. Inclusive electron spectrum from heavy-flavour decays in proton-proton collisions at s**(1/2) = 7-TeV measured with ALICE at LHC. Nuclear Physics A. 432-435.
• 2011. Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at root s(NN)=2.76 TeV. Physical Review Letters. 10 pages.
• 2011. High p(T) suppression of Lambda and K0(S) in Pb-Pb collisions at s(NN)**(1/2) = 2.76-TeV with ALICE. Journal of Physics G: Nuclear and Particle Physics. 4 pages.
• 2011. High \pt{} particle correlations in pp collisions at LHC/ALICE. Journal of Physics G: Nuclear and Particle Physics. 4 pages.
• 2011. Heavy quarkonium production in the ALICE experiment. Nuclear Physics A. 384-387.
• 2011. Heavy flavour production in the semi-muonic channel at forward rapidity in p p collisions at s**(1/2) = 7-TeV and Pb-Pb collisions at s(NN)**(1/2) = 2.76-TeV with ALICE. Journal of Physics G: Nuclear and Particle Physics. 4 pages.
• 2011. Femtoscopy of pp collisions at root s=0.9 and 7 TeV at the LHC with two-pion Bose-Einstein correlations. Physical Review D. Particles and fields. 22 pages.
• 2011. Emerging picture of hard scattering phenomena in p + p collisions at s**(1/2) = 7-TeV in ALICE. Nuclear Physics A. 461-464.
• 2011. D meson nuclear modification factors in Pb-Pb collisions at {\sqrt}sNN = 2.76 TeV, measured with the ALICE detector. Journal of Physics G: Nuclear and Particle Physics. 4 pages.
• 2011. Charm content in jets in proton-proton collisions with the ALICE experiment at CERN-LHC. Journal of Physics: Conference Series. 4 pages.
• 2011. Charged particle identification with PHOS and central tracking of ALICE. Indian Journal of Physics. 1197-1201.
• 2011. Charged Particle Production at Large Transverse Momentum in Pb−Pb Collisions at sNN−−−−√=2.76 TeV Measured with ALICE at the LHC. Journal of Physics G: Nuclear and Particle Physics. 4 pages.
• 2011. Can we observe the elliptic flow in pp collisions at LHC? Journal of Physics: Conference Series. 4 pages.
• 2011. Can we observe the elliptic flow in p p collisions at LHC? Journal of Physics: Conference Series. 4 pages.
• 2011. Baryon number transport at LHC energies with the ALICE experiment. Journal of Physics: Conference Series. 4 pages.
• 2011. Analysis of phi resonance in p p collisions at 900-GeV with the ALICE detector. Journal of Physics: Conference Series. 4 pages.
• 2011. ALICE results from p p collisions at the LHC. Nuclear Physics A. 7-14.
• 2011. ALICE potential for direct photon measurements in p-p and Pb-Pb collisions. Nuclear Physics A. 339-342.
• 2010. Two-pion Bose-Einstein correlations in pp collisions at root s=900 GeV. Physical Review D. Particles and fields. 14 pages.
• 2010. Transverse momentum spectra of charged particles in proton-proton collisions at root s=900 GeV with ALICE at the LHC. Physics Letters B. 53-68.
• 2010. The integration of the ALICE trigger system with sub-detectors. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. 335-336.
• 2010. The ALICE muon trigger system: Cosmic ray commissioning and first beam-induced events. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. 362-364.
• 2010. The ALICE electromagnetic calorimeter. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. 5-8.
• 2010. Strangeness and heavy flavours within the ALICE experiment. Journal of Physics G: Nuclear and Particle Physics. 7 pages.
• 2010. Readout upgrade, hardware and software, for the ALICE Data Acquisition program. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. 258-259.
• 2010. Potential physics measurement with ALICE electromagnetic calorimeters. Nuclear Physics A. 291-294.
• 2010. Midrapidity antiproton-to-proton ratio in pp collisons root s=0.9 and 7 TeV measured by the ALICE experiment. Physical Review Letters. 12 pages.
• 2010. Measurements of quarkonium production with ALICE at the LHC. Journal of Physics G: Nuclear and Particle Physics. 6 pages.
• 2010. First pp Collisions at the LHC as Seen by ALICE. Acta Physica Polonica B. 1669-1674.
• 2010. First physics measurements with ALICE at LHC: Charged-particle pseudorapidity density with the silicon pixel detector. Nuovo cimento. B. 481-488.
• 2010. Elliptic Flow of Charged Particles in Pb-Pb Collisions at \sqrt{s_{NN}} = 2.76 TeV. Physical Review Letters. 11 pages.
• 2010. Detection of atmospheric muons with ALICE detectors. Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers, Detectors and Associated Equipment. 57-61.
• 2010. Charged-particle multiplicity measurement in proton-proton collisions at root s=0.9 and 2.36 TeV with ALICE at LHC. European Physical Journal C. 89-108.
• 2010. Charged-Particle Multiplicity Density in Central Pb-Pb Collisions at sqrt{s_{NN}} = 2.76 TeV. Physical Review Letters. 11 pages.
• 2010. Alignment of the ALICE Inner Tracking System with cosmic-ray tracks. Journal of Instrumentation. 37 pages.
• 2008. The ALICE muon spectrometer and related physics. Journal of Physics G: Nuclear and Particle Physics. 1041454.
• 2008. The ALICE experiment at the CERN LHC. Journal of Instrumentation. 80002.
• 2008. Study of short-lived resonances in ALICE. Journal of Physics G: Nuclear and Particle Physics. 440526.
• 2008. Study of \Lambda(1520) production in pp simulated interactions at 14 TeV with the ALICE detector. Journal of Physics G: Nuclear and Particle Physics. 440597.
• 2008. Soft physics in ALICE. Journal of Physics G: Nuclear and Particle Physics. 440447.
• 2008. Jet and gamma-jet physics with ALICE. Journal of Physics G: Nuclear and Particle Physics. 1041674.
• 2008. Heavy flavour physics in ALICE. Journal of Physics G: Nuclear and Particle Physics. 1041444.
• 2008. Anisotropic flow measurements in ALICE. Journal of Physics G: Nuclear and Particle Physics. 1041654.


text:
# Topological Quantum Field Theory Seminar

### $2$-Representation theory

The $2$-representation theory of $2$-categories is a categorical analogue of the representation theory of algebras. In my talk, I will recall its origins, its purposes, its basic features and explain some important examples. This talk is based on joint work with Mazorchuk, Miemietz, Tubbenhauer and Zhang.

format: plain


text:
# American Institute of Mathematical Sciences

June  2016, 21(4): 1149-1166. doi: 10.3934/dcdsb.2016.21.1149

## The 20-60-20 rule

 1 Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland 2 Institute of Mathematics, Jagiellonian University, S. Łojasiewicza 6, 30-348 Kraków, Poland

Received  June 2015 Published  March 2016

In this paper we discuss an empirical phenomena known as the 20-60-20 rule. It says that if we split the population into three groups, according to some arbitrary benchmark criterion, then this particular ratio often implies some sort of balance. From practical point of view, this feature leads to efficient management or control. We provide a mathematical illustration, justifying the occurrence of this rule in many real world situations. We show that for any population, which could be described using multivariate normal vector, this fixed ratio leads to a global equilibrium state, when dispersion and linear dependance measurement is considered.
Citation: Piotr Jaworski, Marcin Pitera. The 20-60-20 rule. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1149-1166. doi: 10.3934/dcdsb.2016.21.1149
##### References:

show all references

##### References:
 [1] Carlo Cercignani. The Boltzmann equation in the 20th century. Discrete & Continuous Dynamical Systems, 2009, 24 (1) : 83-94. doi: 10.3934/dcds.2009.24.83 [2] Sascha Kurz. The $[46, 9, 20]_2$ code is unique. Advances in Mathematics of Communications, 2021, 15 (3) : 415-422. doi: 10.3934/amc.2020074 [3] Peter E. Kloeden, Yuan Lou. Preface for the special issue "20 years of DCDS-B". Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : i-ii. doi: 10.3934/dcdsb.2020372 [4] Masaaki Harada. New doubly even self-dual codes having minimum weight 20. Advances in Mathematics of Communications, 2020, 14 (1) : 89-96. doi: 10.3934/amc.2020007 [5] Abraão D. C. Nascimento, Leandro C. Rêgo, Raphaela L. B. A. Nascimento. Compound truncated Poisson normal distribution: Mathematical properties and Moment estimation. Inverse Problems & Imaging, 2019, 13 (4) : 787-803. doi: 10.3934/ipi.2019036 [6] Zheng Yin, Ercai Chen. Conditional variational principle for the irregular set in some nonuniformly hyperbolic systems. Discrete & Continuous Dynamical Systems, 2016, 36 (11) : 6581-6597. doi: 10.3934/dcds.2016085 [7] Zheng Yin, Ercai Chen. The conditional variational principle for maps with the pseudo-orbit tracing property. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 463-481. doi: 10.3934/dcds.2019019 [8] Josef Hofbauer, Rida Laraki, Jérôme Renault. Preface: Special Issue in Honor of the 60th Birthday of Sylvain Sorin. Journal of Dynamics & Games, 2014, 1 (3) : i-iv. doi: 10.3934/jdg.2014.1.3i [9] Luis Alberto Fernández, Mariano Mateos, Cecilia Pola, Fredi Tröltzsch, Enrique Zuazua. Preface: A tribute to professor Eduardo Casas on his 60th birthday. Mathematical Control & Related Fields, 2018, 8 (1) : i-ii. doi: 10.3934/mcrf.201801i [10] Hongwei Lou, Qi Lü, Gengsheng Wang, Xu Zhang. Preface: A tribute to professor Jiongmin Yong on his 60th birthday. Mathematical Control & Related Fields, 2018, 8 (3&4) : i-i. doi: 10.3934/mcrf.201803i [11] Wenqing Hu, Chris Junchi Li. A convergence analysis of the perturbed compositional gradient flow: Averaging principle and normal deviations. Discrete & Continuous Dynamical Systems, 2018, 38 (10) : 4951-4977. doi: 10.3934/dcds.2018216 [12] Ricardo Almeida, Agnieszka B. Malinowska. Fractional variational principle of Herglotz. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2367-2381. doi: 10.3934/dcdsb.2014.19.2367 [13] H. O. Fattorini. The maximum principle in infinite dimension. Discrete & Continuous Dynamical Systems, 2000, 6 (3) : 557-574. doi: 10.3934/dcds.2000.6.557 [14] María J. Garrido-Atienza, José A. Langa, Pedro Marín Rubio, José Valero. Preface to the special issue in honor of Prof. Tomás Caraballo on occasion of his 60th birthday. Communications on Pure & Applied Analysis, 2020, 19 (4) : i-vi. doi: 10.3934/cpaa.2020080 [15] Hal L. Smith. Tribute to Horst R. Thieme on the occasion of his 60th birthday. Mathematical Biosciences & Engineering, 2010, 7 (1) : i-iii. doi: 10.3934/mbe.2010.7.1i [16] Chiun-Chuan Chen, Li-Chang Hung, Hsiao-Feng Liu. N-barrier maximum principle for degenerate elliptic systems and its application. Discrete & Continuous Dynamical Systems, 2018, 38 (2) : 791-821. doi: 10.3934/dcds.2018034 [17] Tomasz Komorowski, Adam Bobrowski. A quantitative Hopf-type maximum principle for subsolutions of elliptic PDEs. Discrete & Continuous Dynamical Systems - S, 2020, 13 (12) : 3495-3502. doi: 10.3934/dcdss.2020248 [18] Maria Francesca Betta, Rosaria Di Nardo, Anna Mercaldo, Adamaria Perrotta. Gradient estimates and comparison principle for some nonlinear elliptic equations. Communications on Pure & Applied Analysis, 2015, 14 (3) : 897-922. doi: 10.3934/cpaa.2015.14.897 [19] Giuseppe Capobianco, Tom Winandy, Simon R. Eugster. The principle of virtual work and Hamilton's principle on Galilean manifolds. Journal of Geometric Mechanics, 2021, 13 (2) : 167-193. doi: 10.3934/jgm.2021002 [20] Goro Akagi, Jun Kobayashi, Mitsuharu Ôtani. Principle of symmetric criticality and evolution equations. Conference Publications, 2003, 2003 (Special) : 1-10. doi: 10.3934/proc.2003.2003.1

2020 Impact Factor: 1.327


text:
# 2D linear plane strain elasticity¶

## General formulation of the problem¶

Consider a rectangular domain $$\Omega$$ with a circular hole of radius $$R$$ at its center (see the following figure). The body is fixed at the bottom boundary $$\Gamma_\mathrm{D}$$ and a constant linear loading $$\mathbf{g}$$ is applied to the upper edge of the plate $$\Gamma_\mathrm{N}$$. Moreover, the body is under volumetric loading $$\mathbf{b}$$. We are interested in the shape deformation of the circle and the concentration of stress around its circumference.

[2]:

%%tikz -l patterns -s 900,480
\input{formulation.tikz};

### Governing equations¶

This problem is governed by the same boundary value formulation as the first one, let us repeat it:

\begin{align} && -\mathrm{div}\boldsymbol{\sigma} &= \mathbf{b} && \text{in}\ \Omega, \\ && \boldsymbol{\sigma} \cdot \mathbf{n} &= \mathbf{g} && \text{on}\ \Gamma_\mathrm{N}, \\ && \mathbf{u} &= \bar{\mathbf{u}} && \text{on}\ \Gamma_\mathrm{D},\end{align}

where $$\mathbf{b}$$ denotes the volumetric loading, $$\mathbf{g}$$ is the surface loading ($$\Gamma_\mathrm{N}$$ beeing the upper part of the boundary where the Neumann boundary condition is prescribed), and the Dirichlet boundary is applied on the bottom part of the boundary $$\Gamma_\mathrm{D}$$. The Cauchy stress tensor $$\boldsymbol{\sigma}$$ is given by

\begin{align*} \boldsymbol{\sigma} =\lambda\mathrm{tr}(\boldsymbol{\varepsilon})\mathbf{I} + 2\mu\boldsymbol{\varepsilon} \end{align*}

where the strain tensor $$\boldsymbol{\varepsilon}$$ is the symmetric part of the gradient of deformation $$\nabla\mathbf{u}$$, i.e.

$$\boldsymbol{\varepsilon}=\frac{1}{2}\left(\nabla\mathbf{u}+ \left( \nabla\mathbf{u} \right)^{\top} \right)\,,$$

and $$\lambda$$ with $$\mu$$ are the Lame’s parametres that can be expressed in terms of the Young’s modulus $$E$$ and Poisson’s ratio $$\nu$$

$$\lambda = \frac{E \nu}{(1 + \nu) (1 - 2 \nu)}, \qquad \mu = \frac{E}{2(1 + \nu)}\,.$$

Multiplying the bulk equation by a test function $$\delta\mathbf{u}$$, integrating over the spatial domain $$\Omega$$, and integrating by parts yields the weak formulation of our problem: That is, find $$\mathbf{u}$$ such that $$\mathbf{u}-\bar{\mathbf{u}} \in \mathbf{V}$$ and

$$\int_{\Omega} \boldsymbol{\sigma} : \delta \boldsymbol{\varepsilon} \, \mathrm{d}V = \int_{\Omega} \mathbf{b}\cdot\delta\mathbf{u} \, \mathrm{d}V + \int_{\Gamma_N}\mathbf{g}\cdot\delta\mathbf{u} \, \mathrm{d}S, \qquad \forall \delta\mathbf{u} \in \mathbf{V}\,,$$

where $$\mathbf{V} = \{ \mathbf{v} \in H^1(\Omega; \mathbb{R}^2)| \mathbf{v} = 0\ \text{on}\ \Gamma_\mathrm{D}\}$$ is the function space for both the translated solution $$\mathbf{u}-\bar{\mathbf{u}}$$ and the test function $$\delta\mathbf{u}$$ and $$\delta\boldsymbol{\varepsilon}$$ is the symmetric part of the gradient $$\nabla \delta\mathbf{u}$$ and

\begin{align} \mathbf{u} = \bar{\mathbf{u}} & &\text{on}\ \Gamma_\mathrm{D}, \\ \delta\mathbf{u} = \mathbf{0} & &\text{on}\ \Gamma_\mathrm{D}. \end{align} **Remark:** The volumetric load is ussualy models effects of a constant gravity field :math:\tilde{\mathbf{b}}, i.e. .. math:: :nowrap: \begin{equation*} \mathbf{b}(\mathbf{x}) = \rho(\mathbf{x}) \tilde{\mathbf{b}} \end{equation*} where :math:\rho is the material's density. For cork we have .. math:: :nowrap: \begin{equation*} \rho = 200 \text{ kg}\,\text{m}^{-3}. \end{equation*} **Remark:** The 2D in-plane stress formulation (accounting for an eventual thickening or narrowing of the material in the 3rd dimension) is analogical to the 3D formulation, with a minor change of the constitutive equation, namely .. math:: :nowrap: $$\boldsymbol{\sigma} =\lambda^*\mathrm{tr}(\boldsymbol{\varepsilon})\mathbf{I} + 2\mu\boldsymbol{\varepsilon},$$ where .. math:: :nowrap: $$\lambda^* = \frac{2\lambda\mu}{\lambda + 2\mu}.$$ It should be emphasized that this model does not consider buckling of the material.

## Implementation¶

Let us first import the necessary libraries and mark the bottom boundary. For our convenience, we define the stress function $$\boldsymbol{\sigma}$$.

[3]:

import fenics as fe
import matplotlib.pyplot as plt
import numpy as np

# --------------------
# Functions and classes
# --------------------
# Bottom boundary
def bottom(x, on_boundary):
return (on_boundary and fe.near(x[1], 0.0))

# Strain function
def epsilon(u):

# Stress function
def sigma(u):
return lambda_*fe.div(u)*fe.Identity(2) + 2*mu*epsilon(u)
# lambda is a reserved python keyword, naming convention recommends using a single trailing underscore for such cases

The function bottom defines a set of points that constitute the bottom boundary. Here, x represents a vector of spatial coordinates, i.e. x[0] is the $$x$$ coordinate, and x[1] is the $$y$$ coordinate. Function sigma defines the stress tensors as a function of the displacement field $$\mathbf{u}$$. The UFL language offers implementations of the standart differential and tensor operators, including the divergence div, symmetric part of the gradient sym, and the identity tensor Identity. Here is a short table of other, frequently used operators:

FEniCS operators Description
grad(u) Gradient of function u
div(u) Divergence of function u
dot(u, v) Dot product between u and v
inner(u, v) Inner product between u and v
Identity(d) Identity tensor with dimension d
sym(A) Symmetric part of A
dev(A) Deviatoric part of A
A.T Transposition of the tensor A

For more, see the documentation of UFL (Unified Form Language, the language for expressing the weak forms).

### Problem parameters¶

Note that the vector loading $$\mathbf{b}$$ and $$\mathbf{g}$$ must be set as a tuple.

[4]:

# --------------------
# Parameters
# --------------------

# Density
rho = fe.Constant(200.0)

# Young's modulus and Poisson's ratio
E = 0.02e9
nu = 0.0

# Lame's constants
lambda_ = E*nu/(1+nu)/(1-2*nu)
mu = E/2/(1+nu)

l_x, l_y = 5.0, 5.0  # Domain dimensions
n_x, n_y = 20, 20  # Number of elements

g_z = -2.9575e5
b_z = -10.0
g = fe.Constant((0.0, g_z))
b = fe.Constant((0.0, b_z))

Moreover, we add the plane stress correction.

[5]:

model = "plane_strain"

if model == "plane_stress":
lambda_ = 2*mu*lambda_/(lambda_+2*mu)

### Geometry of the problem¶

The variable mesh points to the RectangleMesh object that contains the geometry of a rectangular mesh. We initialize the object specifying the lower left vertex and the upper right vertex (both in the form of the FEniCS object Point) followed by two integers denoting the discretization in the $$x$$ and $$y$$ direction respectively.

[6]:

# --------------------
# Geometry
# --------------------
mesh = fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y)

fe.plot(mesh)
plt.show()

By default, the mesh is discretized with the triangles oriented to the “right”. The orientation can be changed by adding the string "left" as the last (optional) argument.

[7]:

fe.plot(fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y, "left"))
plt.show()

Other types of mesh include "crossed", which makes each of the n_x*n_y squares crossed, and "left/right", which changes the orientation of the diagonal from one element to another.

[8]:

fe.plot(fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y, "crossed"))
plt.show()

[9]:

fe.plot(fe.RectangleMesh(fe.Point(0.0, 0.0), fe.Point(l_x, l_y), n_x, n_y, "left/right"))
plt.show()

Quadrilateral finite elements are also supported by FEniCS; a unit square mesh with quadrilateral discretization can be initialized by the create() method of the UnitSquareMesh object. We call it with the flag CellType.Type.quadrilateral.

[10]:

mesh_quad = fe.UnitSquareMesh.create(n_x, n_y, fe.CellType.Type.quadrilateral)

Nevertheless, quadrilateral elements are not fully implemented in FEniCS, e.g., plot() is not applicable to these meshes.

Other than elementary mesh geometries need to be imported into FEniCS. One possibility is to transfer the mesh from an external .xml file into the Mesh object.

[11]:

mesh = fe.Mesh("external_mesh.xml")
fe.plot(mesh)
plt.show()

The external .xml file can be generated for example using the Gmsh software. See this short tutorial on generating meshes with Gmsh and importing it into FEniCS, or the full documentation if necessary.

### Function spaces definition¶

In this example, the trial and test functions are vector valued, thus we work with a cartesian product of the space $$V$$ ($$V\times V$$ in 2D and $$V\times V\times V$$ in 3D). In FEniCS, the VectorFunctionSpace object implements such space.

[12]:

# --------------------
# Function spaces
# --------------------
V = fe.VectorFunctionSpace(mesh, "CG", 1)
u_tr = fe.TrialFunction(V)
u_test = fe.TestFunction(V)

We use the linear Lagrange elements again. Other types of elements, or approximation spaces, are summarized in the following table (more exhaustive list can be found here)

Keyword Description
"CG" Lagrange / Continous Galerkin
"DG" Discountinous Galerkin
"HER" Hermite elements - only partly supported
"B" Bubble functions

Vector function defined in this space must be defined using a tuple as

### Boundary conditions¶

#### Dirichlet boundary conditions¶

We repeat the initialization of the DirichletBC object representing the Dirichlet boundary conditions from the previous problem.

[13]:

# --------------------
# Boundary conditions
# --------------------
bc = fe.DirichletBC(V, fe.Constant((0.0, 0.0)), bottom)

Alternatively, we can restrict displacements in one direction only. In such case, the first argument of DirichletBC is a subspace V.sub(1) of the vector function space V. For example the following piece of code prescribes zero displacement in the $$y$$-direction

[14]:

bc = fe.DirichletBC(V.sub(1), 0.0, bottom)

#### Neumann boundary conditions¶

The top boundary can be created by the SubDomain object that is able to mark a subset of the domain specified by a given function. The function can be defined as a python class or as the compact lambda function.

[15]:

top = fe.AutoSubDomain(lambda x: fe.near(x[1], l_y))

We mark the top boundary using the MeshFunction object, which is a function evaluated on mesh entities defined by the topological dimension (third argument of the MeshFunction initialization). The topological dimension 1 returns function on facets out two dimensional problem.

[16]:

# Definition of Neumann boundary condition domain
boundaries = fe.MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
boundaries.set_all(0)

Finally, we can label the sub-domain top by integer 1.

[17]:

top.mark(boundaries, 1)
ds = fe.ds(subdomain_data=boundaries)

### Weak formulation¶

The weak form is implemented using pre-defined FEniCS operators as follows

[18]:

# --------------------
# Weak form
# --------------------
a = fe.inner(sigma(u_tr), epsilon(u_test))*fe.dx
l = rho*fe.dot(b, u_test)*fe.dx + fe.inner(g, u_test)*ds(1)

The objects dx and ds represent the integration domain. The following table gives the three basic implemented integration domains.

FEniCS object Description
dx Volume integration
ds Outer boundary integration
dS Internal boundary integration

Moreover, integration domain accepts the optional argument which defines only part of the domain. For example domain ds(1) represents part of the outer boundary labelled with 1.

To solve the problem, it is possible to use fe.solve(a==l, V, bc) again. However, we introduce another solution that is useful when we need to access the system matrices directly. For this purpose FEniCS provides a function assembly_system with three arguments: the left-hand side of the problem, the right-hand side, and the Dirichlet boundary conditions. This function returns assembled matrix A of the system and a vector L of the right-hand side of the linear system. Assembling is based on the selected type of function space. The variational continuous system is converted into an algebraic system $$\mathbf{A}\mathbf{x}=\mathbf{L}$$. The regularity of $$\mathbf{A}$$ is affected e.g. by the mesh degeneracy, an improper set of boundary conditions, or by the insuffuciency of the numerical integration.

[19]:

# --------------------
# Solver
# --------------------
u = fe.Function(V)
A, L = fe.assemble_system(a, l, bc)

FEniCS provides an overloaded function solve for solving linear systems that returns the vector of displacements $$\mathbf{u}$$. Therefore we must use u.vector(), which returns the Vector object, as the second argument.

[20]:

problem = fe.LinearVariationalProblem(a,l,u,bc)
solver = fe.LinearVariationalSolver(problem)

fe.solve(A, u.vector(), L)

[20]:

1

## Post-processing¶

Node values can be accessed by .vector() function. It returns an iterable PETScVector object which enables us to manipulate with nodal values. Since the displacement is a vector field, it cannot be plotted directly. We must specify scalar subspace for plotting of the results.

[21]:

fe.plot(u.sub(0))
plt.show()

A second option for visualization of the result is to call an optional argument mode with value "displacement" which plots the displaced domain

[22]:

fe.plot(u, mode="displacement")
plt.show()

Stress can be plotted similarly but since it is a second-order tensor we must specify a scalar subspace by two indices. For example stress $$\sigma_{yy}$$ is obtained by sigma(u)[1,1]

[23]:

stress = sigma(u)
fe.plot(stress[1, 1])
plt.show()

This procedure is sufficient for plotting the components of $$\boldsymbol{\sigma}$$ or for reusing $$\boldsymbol{\sigma}$$ in another weak form. However, if we need to access stress nodal values, we must first project it onto a suitable space. The displacement field “lives” in CG1, so the corresponding space for stress is the DG0 space. Moreover, since the stress is a second-order tensor we must define it as the TensorFunctionSpace object.

[24]:

V0 = fe.TensorFunctionSpace(mesh, "DG", 0)
stress_1 = fe.project(stress, V0)
fe.plot(stress_1[1, 1])
plt.show()

Projection of a function $u\in V$ onto a space $W$ means solving the following variational problem:
$$\text{Find}\,g\in W\,\text{s.t.}\,\int_\Omega uv\ \mathrm{d}V = \int_\Omega gv\ \mathrm{d}V,\ \forall v\in W.$$

Sometimes, it can be useful tool to convert a function into a non-corresponding space. However, the stress is obtained from the displacement by differentiation of the basis functions and thus the projection can be unnecessarily expensive. More effective way is to make the projection element-wise. Since we want to project the stress on the DG0 space, where no continuity at nodes is required, we can perform this local projection without loss of generality. It can be done by the following subroutine:

[25]:

def local_project(fce, space):
lp_trial, lp_test = fe.TrialFunction(space), fe.TestFunction(space)
lp_a = fe.inner(lp_trial, lp_test)*fe.dx
lp_L = fe.inner(fce, lp_test)*fe.dx
local_solver = fe.LocalSolver(lp_a, lp_L)
local_solver.factorize()
lp_f = fe.Function(space)
local_solver.solve_local_rhs(lp_f)
return lp_f
stress_2 = local_project(stress, V0)
fe.plot(stress_1[1, 1])
plt.show()

## Complete code¶

[ ]:

import fenics as fe
import matplotlib.pyplot as plt
import numpy as np

# --------------------
# Functions and classes
# --------------------
def bottom(x, on_boundary):
return (on_boundary and fe.near(x[1], 0.0))

# Strain function
def epsilon(u):

# Stress function
def sigma(u):
return lambda_*fe.div(u)*fe.Identity(2) + 2*mu*epsilon(u)

# --------------------
# Parameters
# --------------------

# Density
rho = fe.Constant(200.0)

# Young's modulus and Poisson's ratio
E = 0.02e9
nu = 0.0

# Lame's constants
lambda_ = E*nu/(1+nu)/(1-2*nu)
mu = E/2/(1+nu)

l_x, l_y = 5.0, 5.0  # Domain dimensions
n_x, n_y = 20, 20  # Number of elements

g_z = -2.9575e5
b_z = -10.0
g = fe.Constant((0.0, g_z))
b = fe.Constant((0.0, b_z))

# Model type
model = "plane_strain"
if model == "plane_stress":
lambda_ = 2*mu*lambda_/(lambda_+2*mu)

# --------------------
# Geometry
# --------------------
mesh = fe.Mesh("external_mesh.xml")

# Definition of Neumann condition domain
boundaries = fe.MeshFunction("size_t", mesh, mesh.topology().dim() - 1)
boundaries.set_all(0)

top = fe.AutoSubDomain(lambda x: fe.near(x[1], l_y))

top.mark(boundaries, 1)
ds = fe.ds(subdomain_data=boundaries)

# --------------------
# Function spaces
# --------------------
V = fe.VectorFunctionSpace(mesh, "CG", 1)
u_tr = fe.TrialFunction(V)
u_test = fe.TestFunction(V)

# --------------------
# Boundary conditions
# --------------------
bc = fe.DirichletBC(V, fe.Constant((0.0, 0.0)), bottom)

# --------------------
# Weak form
# --------------------
a = fe.inner(sigma(u_tr), epsilon(u_test))*fe.dx
l = rho*fe.dot(b, u_test)*fe.dx + fe.inner(g, u_test)*ds(1)

# --------------------
# Solver
# --------------------
u = fe.Function(V)
A_ass, L_ass = fe.assemble_system(a, l, bc)

fe.solve(A_ass, u.vector(), L_ass)

print(np.amax(u.vector()[:]))

# --------------------
# Post-process
# --------------------
fe.plot(u, mode="displacement")
plt.show()


text:
全文文献 工具书 数字 学术定义 翻译助手 学术趋势 更多

 因素 的翻译结果: 查询用时：1.929秒
 历史查询

 因素
 factors
 Studies on Granulosa Cell Apoptosis and Its Influencing Factors in the Pig 猪卵泡颗粒细胞凋亡及几种影响因素的研究 短句来源 Study on Zinc Absorption and Metabolism of Zinc Amino Acid Chelate and Effecting Factors 氨基酸螯合锌吸收、转运特点和影响因素的研究 短句来源 Study On Human Serum Leptin And Its Related Factors 人血清瘦素水平测定及其影响因素的研究 短句来源 The Study of The Insured and Uninsured Inpatient Expenses and The Influence Factors 医保与非医保患者住院费用及其影响因素的研究 短句来源 Study of Relative Factors of Acoustic Densitometry 声学密度定量的影响因素研究 短句来源 更多
 factor
 The clinic and experiment research on related factor of bone metastasis of bresat cancer 乳腺癌骨转移相关因素的实验与临床研究 短句来源 Expression of Apoptosis-related Antigens of HS in Relatively Resting Period and K and Effects of Related Factor 相对静息期增生性瘢痕、瘢痕疙瘩瘢痕凋亡相关抗原的表达及相关因素的影响 短句来源 Physiological Characteristics and Influence Factor of Nitrate-N Use of Winter Wheat 冬小麦硝态氮利用的生理特征及其影响因素 短句来源 Expeimental Study on Adenoviral-Mediated Exogenous Genes Expression in Spinal Cords and Peripheral Nerves and Influencing Factor on the Transgene Expression 腺病毒介导的外源性基因在脊髓和周围神经表达及其影响因素的实验研究 短句来源 An Initial Study of the Relationship between Infection,Psychologic Factor and Chronic Prostatitis 感染、心理因素和慢性前列腺炎关系的研究 短句来源 更多
 factors that
 The Analysis of the Factors that Influence the Culture Rate of Dysentery Bacilli 影响痢疾杆菌分离率的某些因素的分析与探討 短句来源 Some Factors that Influence Language Acquisition 影响儿童语言获得的几个因素 短句来源 Analysing the Factors that Affect the Achievement Cycle of Science Studies 影响科研成果周期的因素分析 短句来源 STUDIES ON THE MAIN REPRODUCTIVE CHARACTERISTICS OF HU-YANG AND THE FACTORS THAT INFLUENCE THEM 湖羊主要繁殖特性及其影响因素的研究 短句来源 Slaughter factors that affect pork quality in the USA 影响美国猪肉品质的屠宰因素 短句来源 更多
 factors which
 Other Factors Which Affect the Additional Bending Stresses in Web of Steel Crane Runway Girder 影响钢吊车梁腹板附加弯曲应力的其他因素 短句来源 THE FACTORS WHICH INFLUENCE THE SUGAR CONTENT AND WEIGHT OF GRAPE BERRY 葡萄果粒生长及影响果粒含糖量因素的研究 短句来源 Studies on the Factors which Affect Yoghurt Quality 影响酸奶质量因素的研究 短句来源 Study of Factors which Effect the Propagation of Human Umbilical Cord Vein Endofhelial Cell in Vitro 人脐静脉内皮细胞体外培养的影响因素 短句来源 A Study on the Factors which Influence the Activity in the Process of rIL-2 Purification 重组白细胞介素-2纯化过程中影响活性的因素探讨 短句来源 更多

我想查看译文中含有：的双语例句

 factors
 This paper studies intersection theory on the compactified moduli space ${\mbox{$\cal M$}} (n,d)$ of holomorphic bundles of rank n and degree d over a fixed compact Riemann surface $\Sigma$ of genus $g \geq 2$ where n and d may have common factors. We also determine all the composition factors of the symmetric tensors of the natural osp(2|2n)-module. The measure for uncertainty is a product of two factors evaluating the frequency selectivity in comparison with the ideal filter and the effective length of the filter in the digital domain, respectively. However, in the case of rational dilation factors, the wavelet literature is somewhat lacking in its treatment of this relationship. The paper examines the factors that are likely to influence the pharmaceutical industry in India in the new WTO regime and the preparedness of government, research organizations and firms to compete in this scenario. 更多
 factor
 Can one factor the classical adjoint of a generic matrix Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. Alcohol abuse is thought to be a risk factor for the cause of liver damage, hyperlipidemia and insulin resistance. PHENYLPYRUVIC ACID DERIVATIVES AS ENZYME INHIBITORS: THERAPEUTIC POTENTIAL ON MACROPHAGE MIGRATION INHIBITORY FACTOR 3D QSAR STUDIES OF INHIBITORS OF EPIDERMAL GROWTH FACTOR RECEPTOR [EGFR] USING CoMFA AND GFA METHODOLOGIES 更多
 factors that
 The paper examines the factors that are likely to influence the pharmaceutical industry in India in the new WTO regime and the preparedness of government, research organizations and firms to compete in this scenario. The factors that could affect the DNA yield were analyzed and the preparation technology and the experiment procedure were improved. Thrust ripple such as end force, slot force and normal force are key factors that affect the properties of permanent magnet linear synchronous motors (PMLSM). The ecological niche that roots occupy, their abundance and distribution, and the factors that affect them must be acknowledged. The application shows that it can solve the diverse problems of collaborative product development effectively, and help enterprises find out the critical factors that affect the collaboration. 更多
 factors which
 Yet we know little about the consequence of natural selection on the two reproductive modes and factors which control the balance of the two reproductive modes. The factors which affect the downstream relaxation rate of CO and lead to a decrease in carbon monoxide concentration at the channel exit are analyzed. The mechanisms of heat transfer in CaLa2S4- La2S3 samples in the investigated temperature range are discussed, as well as the factors which define the complex concentration dependence of thermal conductivity coefficient. This estimate depends on the rate of growth of factors which do not destroy the convergence of the series of squares of coefficients off(x) with respect to the orthonormal system under consideration. However, for stress corrosion, the factors which accelerate depassivation are dislocation piles-up at grain boundaries and hydrogen, which arises by corrosion reactions and weakens intergranular bonds. 更多
其他
 点击这里查询相关文摘
 相关查询

 CNKI小工具 在英文学术搜索中查有关因素的内容 在知识搜索中查有关因素的内容 在数字搜索中查有关因素的内容 在概念知识元中查有关因素的内容 在学术趋势中查有关因素的内容

 CNKI主页 |  设CNKI翻译助手为主页 | 收藏CNKI翻译助手 | 广告服务 | 英文学术搜索
2008 CNKI－中国知网

2008中国知网(cnki) 中国学术期刊(光盘版)电子杂志社


text:
occasional meanderings in physics' brave new world

Name:
Location: New Zealand

Marni D. Sheppeard

Monday, September 01, 2008

M Theory Lesson 220

A simple example of an adjunction between two 1-categories is a Galois connection. We are interested in the case of sets with a partial order, so there exists an arrow from $a$ to $b$ in a set $S$ whenever $a \leq b$. The natural functions (in this case functors) between such sets (here considered as categories) are monotone functions, so a Galois connection consists of two monotone functions $f: S \rightarrow T$ and $g: T \rightarrow S$ such that $f(a) \leq x$ iff $a \leq g(x)$. Observe that, at least when $g$ is onto, $fg$ is idempotent as a map from $T$ to $T$. This follows from $gfg (y) \geq g(y)$ (and $gfg (y) \leq g(y)$), which is true because the application of the one rule to $f(x) \leq f(x)$ gives $x \leq gf (x)$, and we can find a $y$ such that $x = g(y)$.

Usually the sets $S$ and $T$ are quite different. Consider the original example for finite number fields. The finite field with $p^{n}$ elements, for $p$ prime, is an extension of the field with $p$ elements. Take the finite set of all fields in this large field which contain the field with $p$ elements. For any such field $K$, there is a map $K \mapsto \textrm{Gal}(K)$ which sends $K$ to its Galois group in the large field. The dual connection map takes any subgroup $H$ of the main Galois group to all elements of the large field that are fixed by $H$.

Now let $p = 3$ and $n = 3$. There are fields of 3, 9 and 27 elements that extend the field $F_{3}$. The main Galois group is all isomorphisms of the 27 element field that fix the field $F_{3}$. The dual connection map sends the trivial group inside this group to the full 27 element field, the whole Galois group to $F_{3}$ and an intermediary subgroup (bit from trit) to the 9 element field. All this is encoded in an elementary pair of arrows between the 2 kinds of three element set.

CarlBrannen said...

Let me make a pathetic effort to translate this into terms I can understand from the point of view of the stuff I'm doing.

"Partial Order" means the ordering of idempotents (or projection operators) by addition. That is, if p, q, and r are idempotents, and p+q = r, then
p less than or equal to r, and
q less than equal to r.

Strict inequality obtains when p and q are non zero.

"intermediary subgroup (bit from trit)" means the group of idempotents generated by products of the Pauli MUB? This is a group with 9 elements, provided you scale the elements appropriately. (And the scaling needed to make this a group is just where the pi/12 comes from in the neutrino spectrum.)

So how did I do?

September 02, 2008 7:30 AM
Kea said...

Gee, Carl, I still have to work this out myself, but yes, we should put all your idempotents into an adjunction, because mathematicians will like it, but it would be a 3 dimensional version. Note that each idempotent is made from the pieces of an adjunction here. What is nice is that the very idea of an adjunction in more general categories is also about little triangles (units and counits).

September 02, 2008 8:14 AM


text:
# Scale change on Quadratic

Consider the two functions $f(x)=ax^2$ and $g(x)=bx^2$. Using this transformation form $T(x,y)=(cx,cy)$, find a scale change that maps $f(x)$ onto $g(x)$

-

Temporarily, let $s=cx$ and $t=cy$. Then $x=\dfrac{s}{c}$ and $y=\dfrac{t}{c}$. Inserting in the equation $y=ax^2$ we get $$\frac{t}{c}=a\frac{s^2}{c^2}.$$ We want this to read $t=bs^2$. For that, we need $\dfrac{a}{c}=b$, or equivalently $c=\dfrac{a}{b}$.
So now our equation reads $t=bs^2$. Replace the letter $s$ by $x$, and $t$ by $y$.


text:
# Is 4x^2 + 24x + 12 a perfect square trinomial and how do you factor it?

No. The equation $4 {x}^{2} + 24 x + 12$ is not a perfect square trinomial because $12$ is not a perfect square. $\sqrt{12} = 2 \sqrt{3}$


text:
OESzybkiOptOptions¶

class OESzybkiOptOptions

This class represents optimization related options for szybki.

Constructors¶

OESzybkiOptOptions()
OESzybkiOptOptions(const OESzybkiOptOptions &)

Default and copy constructors.

operator=¶

OESzybkiOptOptions &operator=(const OESzybkiOptOptions &)

GetCalculateFrozenTerms¶

bool GetCalculateFrozenTerms() const

Returns the state of the calculate frozen terms flag. If true, OESzybki will include the constant energy terms in the final optimized energy.

double GetGradTolerance() const

Returns the optimizer gradient convergence criterion defined as RMS gradient in kcal/(mol Å).

GetMaxIter¶

unsigned int GetMaxIter() const

Returns the value of maximum number of optimizer iterations.

GetOptimizerType¶

unsigned int GetOptimizerType() const

Returns the optimiser type to be used, as as unsigned int from the OEOptType namespace.

SetCalculateFrozenTerms¶

void SetCalculateFrozenTerms(const bool)

Allows the omission of the energy calculation of the fixed terms at the end of the optimization. This situation occurs when adaptors are used. By default constant energy terms are calculated for the optimized structure and added to the total energy.

void SetGradTolerance(const double)

Sets the optimizer gradient convergence criterion defined as RMS gradient in kcal/(mol Å). If not set by the user a 0.1 value threshold for gradient norm $$\sqrt{\sum_i {g_ig_i} }$$, will be used as termination criteria for all optimization types but Newton-Raphson. In the case of the latter the default gradient tolerance is RMS gradient of 1e-5 kcal/(mol Å).

SetMaxIter¶

void SetMaxIter(const unsigned int)

Sets the value of maximum number of optimizer iterations. The default value is set to 1000.

SetOptimizerType¶

bool SetOptimizerType(const unsigned int)

Selects the type of the optimization which will be used for optimization. The available values are defined in the OEOptType namespace. Method returns false when the invalid selection is chosen, true otherwise.


text:
## Hiroshima Mathematical Journal

### Reaction-diffusion system approximation to the cross-diffusion competition system

#### Abstract

We study the stationary problem of a reaction-diffusion system with a small parameter $\varepsilon$, which approximates the cross-diffusion competition system proposed to study spatial segregation problem between two competing species. The convergence between two systems as $\varepsilon \downarrow 0$ is discussed from analytical and complementarily numerical point of views.

#### Article information

Source
Hiroshima Math. J., Volume 38, Number 2 (2008), 315-347.

Dates
First available in Project Euclid: 5 September 2008

https://projecteuclid.org/euclid.hmj/1220619462

Digital Object Identifier
doi:10.32917/hmj/1220619462

Mathematical Reviews number (MathSciNet)
MR2437576

Zentralblatt MATH identifier
1162.35387

#### Citation

Izuhara, Hirofumi; Mimura, Masayasu. Reaction-diffusion system approximation to the cross-diffusion competition system. Hiroshima Math. J. 38 (2008), no. 2, 315--347. doi:10.32917/hmj/1220619462. https://projecteuclid.org/euclid.hmj/1220619462


text:
# questions on convolutors on $L^p(G)$

Let $G$ be a locally compact group. Suppose $1<p<\infty$. We denote by $CV_p(G)$ the space of operators $T$ on $L^p(G)$ such that $T(f*g)=(Tf)*g$.

1) In the book "Amenable locally compact groups" of Pier, Proposition 9.2 (page 83), the author asserts that each operator of $CV_p(G)$ is a convolution operator with a measure on $G$. This proposition seems false to me. Does is it true?

2) (If the proposition 9.2 of Pier is false) Suppose that $G$ is a discrete group. Let $T\in CV_p(G)$. Does there exist a measure $\mu$ on $G$ such that $T(g)=\mu*g$ for any continuous function $g$ with compact support?

3) Let $G$ be an abelian locally compact group. We denote $\varepsilon_a$ the Dirac measure in the point $a\in G$. If $|\lambda|=1$, the operator $\lambda(\varepsilon_a*\cdot)$ is a extremal point of the closed unit ball of $CV_p(G)$.

Does there exist other known exemples of extremal points of this ball? Does there exist references on this subject?

-

This is a slightly rambling answer. If you have stated this right, then the book is false.

Take $p=2$. Then $CV_2(G)$ is simply the group von Neumann algebra $VN(G)$-- it's certainly not true that every member of $VN(G)$ is a measure, unless $G$ is finite. (I think this is not trivial to show. If $VN(G)=M(G)$ then as the map $M(G)\rightarrow VN(G)$ is always weak$^*$-continuous, we'd have that $A(G)=C_0(G)$, where $A(G)$ is the Fourier algebra. This is utterly false if, say, $G$ is abelian and infinite. I'm slightly embarrassed to say that I'll have to resort to Arens regularity-- from work of Young we know that $L^1(G)$ is not Arens regular when $G$ is infinite, and so neither is $M(G)$, but $VN(G)$ being a C$^*$-algebra is. Does anyone else know a nicer proof?)

When $p\not=2$, the same idea works-- $M(G)$ is not Arens regular unless $G$ is finite, but by construction $CV_p(G)$ is a closed subalgebra of $B(L^p(G))$, and by a result of mine, this algebra is Arens regular.

For (2), just argue by continuity-- both $T$ and left convolution by $\mu$ are continuous, so if $T(g)=\mu*g$ for all $g\in C_{00}(G)$, then the same will be true for all $g\in L^p(G)$. That is, in general, "no".

-
Just seen this, Matt. What Pier says (going from memory, I lent the book to a student) is that an operator in CV_p can be represented as convolution with some possibly infinite Radon measure on the group. Like you, I had an initial reaction of "that can't be right!" before eventually decoding terminology/notation. – user16299 Jun 15 '12 at 9:37
Ah, that sounds plausible. Indeed, if in (2) we're allow infinite measure, then the answer is easily seen to be "yes"-- evaluate $T$ at the point mass at the identity to get an $\ell^p$ function-- then convolution by this induces $T$. – Matthew Daws Jun 15 '12 at 9:41
BTW, I think M(X) can't be w*-isomorphic as a Banach space to any infinite-dimensional vN alg, because then this would give rise to an isomorphism of Banach spaces C_0(X) to predual of vN, hence by Akemann et al we have a weakly compact isomorphism, hence the identity on C_0 is weakly compact, hence C_0 is reflexive, which is only possible if X is finite. – user16299 Jun 15 '12 at 9:46

When Pier says, in his book, that every convolution operator on $L^p(G)$ can be regarded as convolution with some (Radon) measure, he is not demanding that this measure be finite. So the answer to your question 1) is "the proposition is correct".
I have not thought too deeply about your question 3), but I believe the answer should be "yes, there are other extreme points of the unit ball of $CV_p(G)$". For $p=2$ then you are essentially asking if every extreme point of $L^\infty(H)$, $H$ a LCA group, is the Fourier transform of a point mass, and I think that is highly unlikely. Probably Rudin's book on Fourier Analysis on Groups would have details that help you build a counter-example.


text:
# String functions and operators#

## String operators#

The || operator performs concatenation.

The LIKE statement can be used for pattern matching and is documented in Pattern comparison: LIKE.

## String functions#

Note

These functions assume that the input strings contain valid UTF-8 encoded Unicode code points. There are no explicit checks for valid UTF-8 and the functions may return incorrect results on invalid UTF-8. Invalid UTF-8 data can be corrected with from_utf8().

Additionally, the functions operate on Unicode code points and not user visible characters (or grapheme clusters). Some languages combine multiple code points into a single user-perceived character, the basic unit of a writing system for a language, but the functions will treat each code point as a separate unit.

The lower() and upper() functions do not perform locale-sensitive, context-sensitive, or one-to-many mappings required for some languages. Specifically, this will return incorrect results for Lithuanian, Turkish and Azeri.

chr(n) → varchar#

Returns the Unicode code point n as a single character string.

codepoint(string) → integer#

Returns the Unicode code point of the only character of string.

concat(string1, ..., stringN) → varchar#

Returns the concatenation of string1, string2, ..., stringN. This function provides the same functionality as the SQL-standard concatenation operator (||).

concat_ws(string0, string1, ..., stringN) → varchar#

Returns the concatenation of string1, string2, ..., stringN using string0 as a separator. If string0 is null, then the return value is null. Any null values provided in the arguments after the separator are skipped.

concat_ws(string0, array(varchar)) → varchar

Returns the concatenation of elements in the array using string0 as a separator. If string0 is null, then the return value is null. Any null values in the array are skipped.

format(format, args...) → varchar
hamming_distance(string1, string2) → bigint#

Returns the Hamming distance of string1 and string2, i.e. the number of positions at which the corresponding characters are different. Note that the two strings must have the same length.

length(string) → bigint#

Returns the length of string in characters.

levenshtein_distance(string1, string2) → bigint#

Returns the Levenshtein edit distance of string1 and string2, i.e. the minimum number of single-character edits (insertions, deletions or substitutions) needed to change string1 into string2.

lower(string) → varchar#

Converts string to lowercase.

lpad(string, size, padstring) → varchar#

Left pads string to size characters with padstring. If size is less than the length of string, the result is truncated to size characters. size must not be negative and padstring must be non-empty.

ltrim(string) → varchar#

Removes leading whitespace from string.

luhn_check(string) → boolean#

Tests whether a string of digits is valid according to the Luhn algorithm.

This checksum function, also known as modulo 10 or mod 10, is widely applied on credit card numbers and government identification numbers to distinguish valid numbers from mistyped, incorrect numbers.

Valid identification number:

select luhn_check('79927398713');
-- true

Invalid identification number:

select luhn_check('79927398714');
-- false

position(substring IN string) → bigint#

Returns the starting position of the first instance of substring in string. Positions start with 1. If not found, 0 is returned.

Note

This SQL-standard function has special syntax and uses the IN keyword for the arguments. See also strpos().

replace(string, search) → varchar#

Removes all instances of search from string.

replace(string, search, replace) → varchar

Replaces all instances of search with replace in string.

reverse(string) → varchar#

Returns string with the characters in reverse order.

rpad(string, size, padstring) → varchar#

Right pads string to size characters with padstring. If size is less than the length of string, the result is truncated to size characters. size must not be negative and padstring must be non-empty.

rtrim(string) → varchar#

Removes trailing whitespace from string.

soundex(char) → string#
soundex returns a character string containing the phonetic representation of char.

It is typically used to evaluate the similarity of two expressions phonetically, that is how the string sounds when spoken:

SELECT name
FROM nation
WHERE SOUNDEX(name)  = SOUNDEX('CHYNA');

name  |
-------+----
CHINA |
(1 row)

split(string, delimiter)#

Splits string on delimiter and returns an array.

split(string, delimiter, limit)

Splits string on delimiter and returns an array of size at most limit. The last element in the array always contain everything left in the string. limit must be a positive number.

split_part(string, delimiter, index) → varchar#

Splits string on delimiter and returns the field index. Field indexes start with 1. If the index is larger than the number of fields, then null is returned.

split_to_map(string, entryDelimiter, keyValueDelimiter) → map<varchar, varchar>#

Splits string by entryDelimiter and keyValueDelimiter and returns a map. entryDelimiter splits string into key-value pairs. keyValueDelimiter splits each pair into key and value.

split_to_multimap(string, entryDelimiter, keyValueDelimiter)#

Splits string by entryDelimiter and keyValueDelimiter and returns a map containing an array of values for each unique key. entryDelimiter splits string into key-value pairs. keyValueDelimiter splits each pair into key and value. The values for each key will be in the same order as they appeared in string.

strpos(string, substring) → bigint#

Returns the starting position of the first instance of substring in string. Positions start with 1. If not found, 0 is returned.

strpos(string, substring, instance) → bigint

Returns the position of the N-th instance of substring in string. When instance is a negative number the search will start from the end of string. Positions start with 1. If not found, 0 is returned.

starts_with(string, substring) → boolean#

Tests whether substring is a prefix of string.

substr(string, start) → varchar#

This is an alias for substring().

substring(string, start) → varchar#

Returns the rest of string from the starting position start. Positions start with 1. A negative starting position is interpreted as being relative to the end of the string.

substr(string, start, length) → varchar

This is an alias for substring().

substring(string, start, length) → varchar

Returns a substring from string of length length from the starting position start. Positions start with 1. A negative starting position is interpreted as being relative to the end of the string.

translate(source, from, to) → varchar#

Returns the source string translated by replacing characters found in the from string with the corresponding characters in the to string. If the from string contains duplicates, only the first is used. If the source character does not exist in the from string, the source character will be copied without translation. If the index of the matching character in the from string is beyond the length of the to string, the source character will be omitted from the resulting string.

Here are some examples illustrating the translate function:

SELECT translate('abcd', '', ''); -- 'abcd'
SELECT translate('abcd', 'a', 'z'); -- 'zbcd'
SELECT translate('abcda', 'a', 'z'); -- 'zbcdz'
SELECT translate('Palhoça', 'ç','c'); -- 'Palhoca'
SELECT translate('abcd', 'b', U&'\+01F600'); -- a😀cd
SELECT translate('abcd', 'a', ''); -- 'bcd'
SELECT translate('abcd', 'a', 'zy'); -- 'zbcd'
SELECT translate('abcd', 'ac', 'z'); -- 'zbd'
SELECT translate('abcd', 'aac', 'zq'); -- 'zbd'

trim(string) → varchar

Removes leading and trailing whitespace from string.

trim([ [ specification ] [ string ] FROM ] source ) → varchar#

Removes any leading and/or trailing characters as specified up to and including string from source:

SELECT trim('!' FROM '!foo!'); -- 'foo'
SELECT trim(LEADING FROM '  abcd');  -- 'abcd'
SELECT trim(BOTH '$' FROM '$var\$'); -- 'var'
SELECT trim(TRAILING 'ER' FROM upper('worker')); -- 'WORK'

upper(string) → varchar#

Converts string to uppercase.

word_stem(word) → varchar#

Returns the stem of word in the English language.

word_stem(word, lang) → varchar

Returns the stem of word in the lang language.

## Unicode functions#

normalize(string) → varchar#

Transforms string with NFC normalization form.

normalize(string, form) → varchar

Transforms string with the specified normalization form. form must be one of the following keywords:

Form

Description

NFD

Canonical Decomposition

NFC

Canonical Decomposition, followed by Canonical Composition

NFKD

Compatibility Decomposition

NFKC

Compatibility Decomposition, followed by Canonical Composition

Note

This SQL-standard function has special syntax and requires specifying form as a keyword, not as a string.

to_utf8(string) → varbinary#

Encodes string into a UTF-8 varbinary representation.

from_utf8(binary) → varchar#

Decodes a UTF-8 encoded string from binary. Invalid UTF-8 sequences are replaced with the Unicode replacement character U+FFFD.

from_utf8(binary, replace) → varchar

Decodes a UTF-8 encoded string from binary. Invalid UTF-8 sequences are replaced with replace. The replacement string replace must either be a single character or empty (in which case invalid characters are removed).


text:
Merging black holes in young star clusters

@article{DiCarlo2019MergingBH,
title={Merging black holes in young star clusters},
author={Ugo N Di Carlo and Nicola Giacobbo and Michela Mapelli and Mario Pasquato and Mario Spera and Long Wang and Francesco Haardt},
journal={Monthly Notices of the Royal Astronomical Society},
year={2019}
}
Searching for distinctive signatures, which characterize different formation channels of binary black holes (BBHs), is a crucial step towards the interpretation of current and future gravitational wave detections. Here, we investigate the demography of merging BBHs in young star clusters (SCs), which are the nursery of massive stars. We performed $4\times{} 10^3$ N-body simulations of SCs with metallicity $Z=0.002$, initial binary fraction $0.4$ and fractal initial conditions, to mimic the… Expand

Paper Mentions

Unexpectedly high formation rate of merging binary black holes in open clusters
• Physics
• Proceedings of the International Astronomical Union
• 2019
Abstract Gravitational wave direct detections suggest that 30 M⊙ binary black holes (BBHs) commonly exist in the universe. One possible formation scenario of such BBHs is dynamical three-bodyExpand
Mass and Rate of Hierarchical Black Hole Mergers in Young, Globular and Nuclear Star Clusters
• Computer Science, Physics
• Symmetry
• 2021
This work presents a fast semi-analytic approach to simulate hierarchical mergers in nuclear star clusters, globular clusters (GCs) and young star clusters (YSCs), finding that multiple formation channels are favored to reproduce the observed BBH population. Expand
Intermediate-mass black holes from stellar mergers in young star clusters
Intermediate-mass black holes (IMBHs) in the mass range $10^2\!-\!10^5\, \mathrm{M_{\odot }}$ bridge the gap between stellar black holes (BHs) and supermassive BHs. Here, we investigate theExpand
Effect of distant encounters on black hole binaries in globular clusters: Systematic increase of in-cluster mergers in the LISA band
• Physics
• Physical Review D
• 2019
We present the first systematic study on how distant weak interactions impact the dynamical evolution of merging binary black holes (BBHs) in dense stellar clusters. Recent studies indicate thatExpand
Black holes: The next generation—repeated mergers in dense star clusters and their gravitational-wave properties
When two black holes merge in a dense star cluster, they form a new black hole with a well-defined mass and spin. If that "second-generation" black hole remains in the cluster, it will continue toExpand
New insights on binary black hole formation channels after GWTC-2: young star clusters versus isolated binaries
With the recent release of the Second Gravitational Wave Transient Catalog (GWTC-2), which introduced dozens of new detections, we are at a turning point of gravitational wave astronomy, as we areExpand
Hierarchical black hole mergers in young, globular and nuclear star clusters: the effect of metallicity, spin and cluster properties
We explore hierarchical black hole (BH) mergers in nuclear star clusters (NSCs), globular clusters (GCs) and young star clusters (YSCs), accounting for both original and dynamically assembled binaryExpand
Constraining the Fraction of Binary Black Holes Formed in Isolation and Young Star Clusters with Gravitational-wave Data
Ten binary black-hole mergers have already been detected during the first two observing runs of advanced LIGO and Virgo, and many more are expected to be observed in the near future. This opens theExpand
Dynamics of binary black holes in low-mass young star clusters
Young star clusters are dynamically active stellar systems and are a common birthplace for massive stars. Low-mass star clusters (∼300–103 M⊙) are more numerous than massive systems and areExpand
Implications of Eccentric Observations on Binary Black Hole Formation Channels
• Physics
• The Astrophysical Journal Letters
• 2021
Orbital eccentricity is one of the most robust discriminators for distinguishing between dynamical and isolated formation scenarios of binary black hole mergers using gravitational-wave observatoriesExpand

References

SHOWING 1-10 OF 205 REFERENCES
The Detection Rates of Merging Binary Black Holes Originating from Star Clusters and Their Mass Function
• Physics
• 2017
Advanced LIGO achieved the first detection of the gravitational wave, which was from a merging binary black hole (BBH). In the near future, more merger events will be observed, and the massExpand
Gravitational-wave emission from binary black holes formed in open clusters
• Physics
• Monthly Notices of the Royal Astronomical Society
• 2019
In order to investigate the formation rate of binary black holes (BBHs) in stellar clusters with a mass comparable to open clusters, we performed a series of direct $N$-body simulations of openExpand
Stellar black hole binary mergers in open clusters
• Physics
• Monthly Notices of the Royal Astronomical Society
• 2018
In this paper we study the evolution of a primordial black hole binary (BHB) in a sample of over 1500 direct-summation $N-$body simulations of small-and intermediate-size isolated star clusters asExpand
Eccentric Black Hole Mergers Forming in Globular Clusters
We derive the probability for a newly formed binary black hole (BBH) to undergo an eccentric gravitational wave (GW) merger during binary-single interactions inside a stellar cluster. By integratingExpand
Dynamical Formation of Low-Mass Merging Black Hole Binaries like GW151226
• Physics
• 2016
Using numerical models for star clusters spanning a wide range in ages and metallicities (Z) we study the masses of binary black holes (BBHs) produced dynamically and merging in the local universeExpand
Binary Mergers and Growth of Black Holes in Dense Star Clusters
• Physics
• 2006
We model the dynamical evolution of primordial black holes (BHs) in dense star clusters using a simplified treatment of stellar dynamics in which the BHs are assumed to remain concentrated in anExpand
MOCCA-SURVEY Database - I. Coalescing binary black holes originating from globular clusters
• Physics
• 2017
In this first of a series of papers, we utilize results for around two thousand star cluster models simulated using the MOCCA code for star cluster evolution (Survey Database I) to determine theExpand
A new route towards merging massive black holes
• Physics
• 2016
Recent advances in gravitational-wave astronomy make the direct detection of gravitational waves from the merger of two stellar-mass compact objects a realistic prospect. Evolutionary scenariosExpand
Post-Newtonian Dynamics in Dense Star Clusters: Highly Eccentric, Highly Spinning, and Repeated Binary Black Hole Mergers.
• Physics, Medicine
• Physical review letters
• 2018
Modelling the relativistic accelerations and gravitational-wave emission in isolated binaries and during three- and four-body encounters finds that nearly half of all binary black hole mergers occur inside the cluster, with about 10% of those mergers entering the LIGO/Virgo band with eccentricities greater than 0.1. Expand
Binary Black Hole Mergers from Globular Clusters: Masses, Merger Rates, and the Impact of Stellar Evolution
• Physics
• 2016
The recent discovery of GW150914, the binary black hole merger detected by Advanced LIGO, has the potential to revolutionize observational astrophysics. But to fully utilize this new window into theExpand


text:
# AB-011 : Electrical Techniques for Using Different Power Sources

### Overview

As vibration motors have a wide variety of applications, they are often integrated into systems which have different power sources. A common concern, in terms of power supply, is adjusting the source power supply voltage to a suitable level for the vibration motor or drive circuitry. This protects the motor and can ensure a constant level of performance for uses like haptic feedback.

Our vibration motors are all DC powered and have rated voltages ranging from 1.5V to 24V, with most operating in the lower end of the spectrum. This is often less than the system’s power supply voltage and further steps are required to reduce the supply voltage to the vibration motor to avoid damaging it.

For applications which are powered by batteries, such as handheld equipment, the voltage supply may not be constant. Although batteries are often specified by a nominal voltage, almost all battery chemistries fluctuate depending on their level of charge. This can impact on the performance of the vibration motor.

Therefore this Application Bulletin is aimed at discussing popular techniques for powering vibration motors from different, and in some cases fluctuating power sources. We’ve already covered how motors are driven in mobile phones, and in this bulletin, we have assumed that the output of the power circuit would be connected directly to the motor via a discrete driver or h-bridge.

Should you have any questions, or are unsure about what is the best approach for your application and choice of the vibration motor, please contact us for advice.

### Potential Divider

Potential Divider Circuit

The potential divider is a very simple and cheap method for reducing a voltage and can be calculated using Ohm’s Law. It is created by placing a resistor in series with the motor, then some of the supply voltage appears across the new resistor, R1, and the rest falls across the motor.

Analysis of the circuit is not completely straightforward because of the motor’s ‘back electromotive force’, or EMF. This is created by the rotation of the motor through its internal magnetic field and appears as a voltage source in the opposite direction to the supply voltage. See the equivalent circuit for DC operation below. Unfortunately accounting for the EMF is difficult because it varies with the speed of the motor.

Potential Divider Equivalent Circuit

Thankfully with the information supplied in our comprehensive datasheets and a simple reduction in the circuit, you are able to find a value for the series resistor for each of our vibration motors.

The value of $$R_{1}$$ must be low enough that the motor’s voltage is above the Certified Start Voltage, but high enough so it does not exceed the Maximum Operating Voltage. We can also remove the EMF from the equation. For the maximum value of $$R_{1}$$ (ensuring the motor reaches the Certified Start Voltage), we consider the circuit when the motor has not yet started turning, which means the EMF is zero. In addition, for the minimum value of $$R_{1}$$ (ensuring the motor does not exceed the Maximum Operating Voltage), we consider the worst case, which is when the motor operates at its maximum resistance. This is also when the EMF equals zero.

We can then reduce the circuit to a simple voltage divider equation, where the upper and lower values of $$R_{1}$$ are bound by the following:

$$R_{M} \frac{V_{s}-V_{max}}{V_{max}} \leq R_{1} \leq R_{M} \frac{V_{s}-V_{start}}{V_{start}}$$

Where:

$$R_{1}$$ is the series resistor

$$R_{M}$$ is the value Typical Maximum Terminal Resistance (in vibration motor’s datasheet)

$$V_{s}$$ is the supply voltage

$$V_{start}$$ is the value Certified Start Voltage (in vibration motor’s datasheet)

$$V_{max}$$ is the value Maximum Operating Voltage (in vibration motor’s datasheet)

Please note: These are theoretical limits and are based on typical values. You should always test your system thoroughly and work well within these limits using an appropriate safety factor.

As an example, if we were trying to drive the 304-103 SMD vibration motor from a 15V supply, we could use the equation above to calculate the minimum and maximum values of $$R_{1}$$.

$$R_{1}$$ Maximum

$$R_{1}\leq R_{M} \frac{V_{s}-V_{start}}{V_{start}}$$

$$R_{1}\leq 34\Omega \frac {15V – 1.8V}{1.8V}$$

$$R_{1}\leq 249 \Omega$$

$$R_{1}$$ Minimum

$$R_{1} \geq R_{M} \frac{V_{s}-V_{max}}{V_{max}}$$

$$R_{1} \geq 34 \Omega \frac{15 V-3.2V}{3.2V}$$

$$R_{1} \geq 125 \Omega$$

It is also important to calculate the power dissipated through the series resistor, to ensure it is of a suitable power rating. The calculation is straightforward, as the Maximum Operating Current for the selected motor is also found in the datasheet.

Continuing with the example of the 304-103, using the maximum value for $$R_{1}$$ allowed:

$$P_{R1} = i^2 R_{1}$$

$$P_{R1} = (75mA)^2 \times 249\Omega$$

$$P_{R1} = 1.4W$$

Determining the power rating of the resistor required to handle this level of power dissipation is beyond the scope of this article, but there are plenty of articles on the web that can help. We can also see from the equation above that choosing a smaller value for $$R_{1}$$ can decrease the minimum power rating.

### Series Diode

The diode in Series with Vibration Motor

This is possibly the simplest method for reducing the supply voltage by a fixed amount. It works by placing a silicon diode in series with the power supply and motor, which causes the diode to work in its normal forward biased region.

In this operation, the diode has a voltage drop of 0.6V – 0.7V, regardless of supply voltage. This is a great solution if the supply voltage is just above the Maximum Operating Voltage of the vibration motor, or within 0.6V.

This may seem like a rare occurrence, however many of our motors are rated at 3V with a Maximum Operating Voltage of ~3.6V. These vibrating motors are often used in handheld and mobility applications, where lithium-ion batteries are a popular choice of power source. These are mainly in the 3.6V – 4.2V range (depending on charge), making the series diode method a perfect low cost, low footprint solution.

Power dissipation in the diode is also an issue, but for example, a typical motor might take 100mA, with 0.6v across the diode, leading to a 60mW power dissipation, which should be within the scope of many small footprint diodes.

### Zener Diode

The ideal diode does not allow any current to pass when a voltage is applied in the reverse direction, acting as an open circuit. In reality, diodes have a “breakdown region”. This is when the reverse voltage is large enough that the diode breaks down and allows current to flow. Zener diodes are designed to operate in this region where they have a near constant voltage drop, which is known as the breakdown voltage or Zener voltage.

Some simpler circuits use a Zener diode in series with the load. The required breakdown voltage of the diode would be equal to the supply voltage minus the desired voltage across the load. For vibration motors, this design may not be desirable as the diode could become hot as there is a large current passing through it.

A preferred method is to use a load connected in parallel with the diode, whereupon the Zener will ‘clamp’ the voltage across the load. This means that even under a variable power source, as long as the source voltage is greater than the Zener diode’s breakdown voltage, the load will have a steady voltage supply. Note that the Zener voltage is dependant upon the current flowing through the device, and therefore the voltage supplied to the load can also fluctuate a little.

Power dissipation in the Zener is something to be considered and generally, there’s a graph on the Zener datasheet that can be used to determine the power dissipation based on current.

Zener Diode Voltage Regulator

A schematic of a typical Zener diode regulation circuit is shown to the right. As Zener diodes are designed to operate in the breakdown region, they point in the opposite direction to normal diodes in schematics, with the anode connected to the ground or negative terminal.

To limit the current and dissipate excess voltage, a resistor is placed in series with the power supply. The value of the resistor $$R_{1}$$ is calculated as follows:

$$R_{1} = \frac{V_{S} – V_{Z}}{I_{Z} + I_{L}}$$

Where:

$$V_{S}$$ is the supply voltage

$$R_{1}$$ is the Zener diode’s breakdown voltage

$$I_{Z}$$ is the current through the Zener diode (taken from diode’s datasheet)

$$I_{L}$$ is the current drawn by the motor, the value Typical Operating Current

We saw this technique used in Application Bulletin 008: Vibration Motor Best Practices from the Mobile/Cell Phone Industry.

### LDO Voltage Regulators

Low drop-out (LDO) voltage regulators are widely packaged as integrated circuits. Many of them can accept a range of input voltages and output a reduced constant voltage. The value of the output voltage depends on the specific regulator, but there are many that are designed to be adjusted with a couple of external components.

LDO regulators can be used to ensure a constant vibration alerting amplitude in battery-powered applications, where the varying charge levels of the battery would otherwise cause a varying vibration motor performance.

Voltage Regulator IC

This example is based around an LT3060. A potential divider is used to adjust the output voltage, values used will be dependant on the specific regulator. Linear regulators tend to be based on a Zener diode/transistor design with a feedback loop to adjust the output voltage.

Most regulators also included a shutdown (SHDN) pin, which can be used to shutdown the regulator (saving power) and by inference, turn the motor on and off.

An alternative to linear regulators is switching mode power stepping designs which are more power efficient than linear regulators. However given that the vibration motor is not often driven continuously, they are rarely worth the additional expense or PCB real-estate.

### Dedicated Motor Driver ICs

Motor drive integrated circuits are often the easiest way to drive a motor, though not the cheapest. They can accept a range of input voltages, output different voltage levels, accept a variety of control signals, and are often very well documented.  Information on the IC’s conformity limits will be detailed in their datasheets, and they also often include application notes for customisations.

In Application Bulletin 003 we looked at certain chips aimed driving Linear Resonant Actuators. Many of these devices also supported ERM vibration motors and included application notes for extra customisation.

DRV8601 Vibration Motor Driver (ERM or LRA)

### Conclusion

Powering a vibration motor’s drive circuitry directly from a power source is not always possible, as often the motor’s maximum rated voltage is below that of many power supplies. Even if a DC voltage bus is readily available, there may be other circuitry in the application that uses a significantly higher voltage than the vibration motor. Problems can also arise from battery voltage sources, as the supply voltage may fluctuate and lead to reduced performance.

Fortunately, it is much easier to regulate the voltage down than to boost it up, and we have demonstrated some of the popular circuit techniques for connecting higher voltage fluctuating power sources to vibration motors.

Reducing and stabilising the supply voltage can be performed using discrete components or integrated circuits. Above we have provided example circuits and formulae for calculating important component values. We have also discussed popular ICs and linked to separate Application Bulletins which further expand on the topic.