Probabilistic Approach to Time-Dependent Load-Transfer Models of Fracture

A probabilistic method for solving time-dependent load-transfer models of fracture is developed. It is applicable to any rule of load redistribution, i.e, local, hierarchical, etc. In the new method, the fluctuations are generated during the breaking process (annealed randomness) while in the usual method, the random lifetimes are fixed at the beginning (quenched disorder). Both approaches are equivalent.Comment: 13 pages, 4 figures. To appear in Phys.Rev.

Bounds for the time to failure of hierarchical systems of fracture

For years limited Monte Carlo simulations have led to the suspicion that the time to failure of hierarchically organized load-transfer models of fracture is non-zero for sets of infinite size. This fact could have a profound significance in engineering practice and also in geophysics. Here, we develop an exact algebraic iterative method to compute the successive time intervals for individual breaking in systems of height $n$ in terms of the information calculated in the previous height $n-1$. As a byproduct of this method, rigorous lower and higher bounds for the time to failure of very large systems are easily obtained. The asymptotic behavior of the resulting lower bound leads to the evidence that the above mentioned suspicion is actually true.Comment: Final version. To appear in Phys. Rev. E, Feb 199

Time dependence of breakdown in a global fiber-bundle model with continuous damage

A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled non-linear differential equations. A first integral of this set is analytically obtained. The time evolution of the system is studied by applying a discrete probabilistic method. Several results are discussed emphasizing their differences with the standard time-dependent model. The results obtained show that with this simple model a variety of experimental observations can be qualitatively reproduced.Comment: APS style, two columns, 4 figures. To appear in Phys. Rev.

Charged particle multiplicities in pp interactions at √s = 0.9, 2.36, and 7 TeV

Measurements of primary charged hadron multiplicity distributions are presented for non-single-diractive events in proton-proton collisions at centre-of-mass energies of √s = 0.9, 2.36, and 7 TeV, in five pseudorapidity ranges from |η| < 0.5 to |η| < 2.4. The data were collected with the minimum-bias trigger of the CMS experiment during the LHC commissioning runs in 2009 and the 7 TeV run in 2010. The multiplicity distribution at √s = 0.9 TeV is in agreement with previous measurements. At higher energies the increase of the mean multiplicity with √s is underestimated by most event generators. The average transverse momentum as a function of the multiplicity is also presented. The measurement of higher-order moments of the multiplicity distribution confirms the violation of Koba-Nielsen-Olesen scaling that has been observed at lower energies

First Measurement of Bose-Einstein Correlations in Proton-Proton Collisions at √s=0.9 and 2.36 TeV at the LHC

Bose-Einstein correlations have been measured using samples of proton-proton collisions at 0.9 and 2.36 TeV center-of-mass energies, recorded by the CMS experiment at the CERN Large Hadron Collider. The signal is observed in the form of an enhancement of pairs of same-sign charged particles with small relative four-momentum. The size of the correlated particle emission region is seen to increase significantly with the particle multiplicity of the event

Transverse-Momentum and Pseudorapidity Distributions of Charged Hadrons in pp Collisions at √s=7 TeV

Charged-hadron transverse-momentum and pseudorapidity distributions in proton-proton collisions at √s=7  TeV are measured with the inner tracking system of the CMS detector at the LHC. The charged-hadron yield is obtained by counting the number of reconstructed hits, hit pairs, and fully reconstructed charged-particle tracks. The combination of the three methods gives a charged-particle multiplicity per unit of pseudorapidity dN_(ch)/dη||η|<0.5=5.78±0.01(stat)±0.23(syst) for non-single-diffractive events, higher than predicted by commonly used models. The relative increase in charged-particle multiplicity from √s=0.9 to 7 TeV is [66.1±1.0(stat)±4.2(syst)]%. The mean transverse momentum is measured to be 0.545±0.005(stat)±0.015(syst)  GeV/c. The results are compared with similar measurements at lower energies

First measurement of hadronic event shapes in pp collisions at √s = 7 TeV

Hadronic event shapes have been measured in proton–proton collisions at √s = 7 TeV source, with a data sample collected with the CMS detector at the LHC. The sample corresponds to an integrated luminosity of 3.2 pb^(−1). Event-shape distributions, corrected for detector response, are compared with five models of QCD multijet production

Measurements of inclusive W and Z cross sections in pp collisions at √s=7 TeV

Measurements of inclusive W and Z boson production cross sections in pp collisions at √s = 7 TeV are presented, based on 2.9 pb^(-1) of data recorded by the CMS detector at the LHC. The measurements, performed in the electron and muon decay channels, are combined to give σ(pp → WX) x B (W → lv) = 9.95 ± 0.07 (stat.) ± 0.28 (syst.) ± 1.09 (lumi.) nb and σ(pp → ZX) x B (Z → ℓ+ℓ-) = 0.931 ± 0.026 (stat.) ± 0.023 (syst.) ± 0.102 (lumi.) nb, where ℓ stands for either e or µ. Theoretical predictions, calculated at the next-to-next-to-leading order in QCD using recent parton distribution functions, are in agreement with the measured cross sections. Ratios of cross sections, which incur an experimental systematic uncertainty of less than 4%, are also reported

Sustaining the Internet with Hyperbolic Mapping

The Internet infrastructure is severely stressed. Rapidly growing overheads associated with the primary function of the Internet---routing information packets between any two computers in the world---cause concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade. Here we present a method to map the Internet to a hyperbolic space. Guided with the constructed map, which we release with this paper, Internet routing exhibits scaling properties close to theoretically best possible, thus resolving serious scaling limitations that the Internet faces today. Besides this immediate practical viability, our network mapping method can provide a different perspective on the community structure in complex networks