381 research outputs found

    Distribution of particles which produces a "smart" material

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    If Aq(ÎČ,α,k)A_q(\beta, \alpha, k) is the scattering amplitude, corresponding to a potential q∈L2(D)q\in L^2(D), where D⊂R3D\subset\R^3 is a bounded domain, and eikα⋅xe^{ik\alpha \cdot x} is the incident plane wave, then we call the radiation pattern the function A(ÎČ):=Aq(ÎČ,α,k)A(\beta):=A_q(\beta, \alpha, k), where the unit vector α\alpha, the incident direction, is fixed, and k>0k>0, the wavenumber, is fixed. It is shown that any function f(ÎČ)∈L2(S2)f(\beta)\in L^2(S^2), where S2S^2 is the unit sphere in R3\R^3, can be approximated with any desired accuracy by a radiation pattern: ∣∣f(ÎČ)−A(ÎČ)∣∣L2(S2)<Ï”||f(\beta)-A(\beta)||_{L^2(S^2)}<\epsilon, where Ï”>0\epsilon>0 is an arbitrary small fixed number. The potential qq, corresponding to A(ÎČ)A(\beta), depends on ff and Ï”\epsilon, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles Dm⊂DD_m\subset D, 1≀m≀M1\leq m\leq M, distributed in an a priori given bounded domain D⊂R3D\subset\R^3. The geometrical shape of a small particle DmD_m is arbitrary, the boundary SmS_m of DmD_m is Lipschitz uniformly with respect to mm. The wave number kk and the direction α\alpha of the incident upon DD plane wave are fixed.It is shown that a suitable distribution of the above particles in DD can produce the scattering amplitude A(αâ€Č,α)A(\alpha',\alpha), αâ€Č,α∈S2\alpha',\alpha\in S^2, at a fixed k>0k>0, arbitrarily close in the norm of L2(S2×S2)L^2(S^2\times S^2) to an arbitrary given scattering amplitude f(αâ€Č,α)f(\alpha',\alpha), corresponding to a real-valued potential q∈L2(D)q\in L^2(D).Comment: corrected typo

    Anomalous Power Law Distribution of Total Lifetimes of Branching Processes Relevant to Earthquakes

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    We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. Due to the large fluctuations of the number of aftershocks triggered directly by any earthquake (``productivity'' or ``fertility''), there is a large variability of the total number of aftershocks from one sequence to another, for the same mainshock magnitude. We study the regime where the distribution of fertilities ÎŒ\mu is characterized by a power law ∌1/ÎŒ1+Îł\sim 1/\mu^{1+\gamma} and the bare Omori law for the memory of previous triggering mothers decays slowly as ∌1/t1+Ξ\sim 1/t^{1+\theta}, with 0<Ξ<10 < \theta <1 relevant for earthquakes. Using the tool of generating probability functions and a quasistatic approximation which is shown to be exact asymptotically for large durations, we show that the density distribution of total aftershock lifetimes scales as ∌1/t1+Ξ/Îł\sim 1/t^{1+\theta/\gamma} when the average branching ratio is critical (n=1n=1). The coefficient 1<Îł=b/α<21<\gamma = b/\alpha<2 quantifies the interplay between the exponent b≈1b \approx 1 of the Gutenberg-Richter magnitude distribution ∌10−bm \sim 10^{-bm} and the increase ∌10αm\sim 10^{\alpha m} of the number of aftershocks with the mainshock magnitude mm (productivity) with α≈0.8\alpha \approx 0.8. More generally, our results apply to any stochastic branching process with a power-law distribution of offsprings per mother and a long memory.Comment: 16 pages + 4 figure

    Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}=2.76 TeV

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    The elliptic, v2v_2, triangular, v3v_3, and quadrangular, v4v_4, azimuthal anisotropic flow coefficients are measured for unidentified charged particles, pions and (anti-)protons in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}} = 2.76 TeV with the ALICE detector at the Large Hadron Collider. Results obtained with the event plane and four-particle cumulant methods are reported for the pseudo-rapidity range ∣η∣<0.8|\eta|<0.8 at different collision centralities and as a function of transverse momentum, pTp_{\rm T}, out to pT=20p_{\rm T}=20 GeV/cc. The observed non-zero elliptic and triangular flow depends only weakly on transverse momentum for pT>8p_{\rm T}>8 GeV/cc. The small pTp_{\rm T} dependence of the difference between elliptic flow results obtained from the event plane and four-particle cumulant methods suggests a common origin of flow fluctuations up to pT=8p_{\rm T}=8 GeV/cc. The magnitude of the (anti-)proton elliptic and triangular flow is larger than that of pions out to at least pT=8p_{\rm T}=8 GeV/cc indicating that the particle type dependence persists out to high pTp_{\rm T}.Comment: 16 pages, 5 captioned figures, authors from page 11, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/186

    Centrality dependence of charged particle production at large transverse momentum in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm{NN}}} = 2.76 TeV

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    The inclusive transverse momentum (pTp_{\rm T}) distributions of primary charged particles are measured in the pseudo-rapidity range ∣η∣<0.8|\eta|<0.8 as a function of event centrality in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm{NN}}}=2.76 TeV with ALICE at the LHC. The data are presented in the pTp_{\rm T} range 0.15<pT<500.15<p_{\rm T}<50 GeV/cc for nine centrality intervals from 70-80% to 0-5%. The Pb-Pb spectra are presented in terms of the nuclear modification factor RAAR_{\rm{AA}} using a pp reference spectrum measured at the same collision energy. We observe that the suppression of high-pTp_{\rm T} particles strongly depends on event centrality. In central collisions (0-5%) the yield is most suppressed with RAA≈0.13R_{\rm{AA}}\approx0.13 at pT=6p_{\rm T}=6-7 GeV/cc. Above pT=7p_{\rm T}=7 GeV/cc, there is a significant rise in the nuclear modification factor, which reaches RAA≈0.4R_{\rm{AA}} \approx0.4 for pT>30p_{\rm T}>30 GeV/cc. In peripheral collisions (70-80%), the suppression is weaker with RAA≈0.7R_{\rm{AA}} \approx 0.7 almost independently of pTp_{\rm T}. The measured nuclear modification factors are compared to other measurements and model calculations.Comment: 17 pages, 4 captioned figures, 2 tables, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/284

    Measurement of charm production at central rapidity in proton-proton collisions at s=2.76\sqrt{s} = 2.76 TeV

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    The pTp_{\rm T}-differential production cross sections of the prompt (B feed-down subtracted) charmed mesons D0^0, D+^+, and D∗+^{*+} in the rapidity range ∣y∣<0.5|y|<0.5, and for transverse momentum 1<pT<121< p_{\rm T} <12 GeV/cc, were measured in proton-proton collisions at s=2.76\sqrt{s} = 2.76 TeV with the ALICE detector at the Large Hadron Collider. The analysis exploited the hadronic decays D0→^0 \rightarrow Kπ\pi, D+→^+ \rightarrow Kππ\pi\pi, D∗+→^{*+} \rightarrow D0π^0\pi, and their charge conjugates, and was performed on a Lint=1.1L_{\rm int} = 1.1 nb−1^{-1} event sample collected in 2011 with a minimum-bias trigger. The total charm production cross section at s=2.76\sqrt{s} = 2.76 TeV and at 7 TeV was evaluated by extrapolating to the full phase space the pTp_{\rm T}-differential production cross sections at s=2.76\sqrt{s} = 2.76 TeV and our previous measurements at s=7\sqrt{s} = 7 TeV. The results were compared to existing measurements and to perturbative-QCD calculations. The fraction of cdbar D mesons produced in a vector state was also determined.Comment: 20 pages, 5 captioned figures, 4 tables, authors from page 15, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/307

    Particle-yield modification in jet-like azimuthal di-hadron correlations in Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

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    The yield of charged particles associated with high-pTp_{\rm T} trigger particles (8<pT<158 < p_{\rm T} < 15 GeV/cc) is measured with the ALICE detector in Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV relative to proton-proton collisions at the same energy. The conditional per-trigger yields are extracted from the narrow jet-like correlation peaks in azimuthal di-hadron correlations. In the 5% most central collisions, we observe that the yield of associated charged particles with transverse momenta pT>3p_{\rm T}> 3 GeV/cc on the away-side drops to about 60% of that observed in pp collisions, while on the near-side a moderate enhancement of 20-30% is found.Comment: 15 pages, 2 captioned figures, 1 table, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/350

    ϒ production in p–Pb collisions at √sNN=8.16 TeV

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    ϒ production in p–Pb interactions is studied at the centre-of-mass energy per nucleon–nucleon collision √sNN = 8.16 TeV with the ALICE detector at the CERN LHC. The measurement is performed reconstructing bottomonium resonances via their dimuon decay channel, in the centre-of-mass rapidity intervals 2.03 < ycms < 3.53 and −4.46 < ycms < −2.96, down to zero transverse momentum. In this work, results on the ϒ(1S) production cross section as a function of rapidity and transverse momentum are presented. The corresponding nuclear modification factor shows a suppression of the ϒ(1S) yields with respect to pp collisions, both at forward and backward rapidity. This suppression is stronger in the low transverse momentum region and shows no significant dependence on the centrality of the interactions. Furthermore, the ϒ(2S) nuclear modification factor is evaluated, suggesting a suppression similar to that of the ϒ(1S). A first measurement of the ϒ(3S) has also been performed. Finally, results are compared with previous ALICE measurements in p–Pb collisions at √sNN = 5.02 TeV and with theoretical calculations.publishedVersio

    Centrality Dependence Of The Pseudorapidity Density Distribution For Charged Particles In Pb-pb Collisions At √snn=2.76tev

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    7264/Mai61062

    Long-range Angular Correlations On The Near And Away Side In P-pb Collisions At √snn=5.02 Tev

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    7191/Mar294
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