A random number generator for continuous random variables

A FORTRAN 4 routine is given which may be used to generate random observations of a continuous real valued random variable. Normal distribution of F(x), X, E(akimas), and E(linear) is presented in tabular form

Mineralogical and geochemical evidence of magma mingling/mixing in the Sierra de las Cruces volcanic range, Mexican Volcanic Belt

RESUMEN En la Sierra de las Cruces (SC), Cinturón Volcánico Mexicano (CVM), se encuentran expuestos flujos de lava, principalmente de composición dacítica, del Plioceno-Pleistoceno. Las rocas volcánicas de la SC son de textura porfirítica, conteniendo plagioclasa + anfibol + ortopiroxeno ± clinopiroxeno ± cuarzo ± óxidos de Fe-Ti. La mayor parte de ellas exhiben diversas características que indican un proceso de mezcla incompleta de magmas, con una cristalización fraccionada concomitante, en la que un pequeño volumen de un magma andesítico caliente es inyectado a un magma dacítico. Es probable que ambos tipos de roca se hayan generado por fusión parcial a diferentes niveles de la corteza continental. Las evidencias de la mezcla incompleta de magmas incluyen: (a) plagioclasas con texturas normal y anubarrada en la misma muestra, cristales redondeados y corroídos, y bordes de reacción en superficies de cristal disueltas; (b) enclaves magmáticos subredondeados y vesiculares, que ocurren en dimensiones de un pocos milímetros a ~20 centímetros de diámetro, con plagioclasa + ortopiroxeno + anfíbol + cuarzo ± olivino ± óxidos de Fe-Ti; (c) química de minerales, que incluye cristales con bordes de reacción o plagioclasas de composición heterogénea (zonación inversa y oscilatoria o cristales con zonación normal e inversa) en la misma muestra; y (d) variaciones geoquímicas de elementos y relaciones de elementos traza explicables por una mezcla de magmas y por un proceso de difusión. Los enclaves andesíticos podrían considerarse como porciones de magma intermedio que no se mezcló con los líquidos dacíticos receptores, lo que confirma la importancia de los procesos de mezcla incompleta de magmas en la evolución magmática del CVM. ABSTRACT Pliocene – Pleistocene lava flows, mainly of dacitic composition, are exposed in the Sierra de las Cruces (SC) volcanic range within the Mexican Volcanic Belt (MVB). SC volcanic rocks are porphyritic, generally containing an assemblage of plagioclase + amphibole + orthopyroxene ± clinopyroxene ± quartz ± Fe-Ti oxides. Most of them exhibit diverse mineralogical and geochemical features that attest a magma mixing and mingling processes with concomitant fractional crystallization in which a small volume of hot andesite magma injects into dacitic magma. Both rock types are probably derived from partial melting of continental crust at different levels. The evidences of magma mixing and mingling include: (a) normal and sieved plagioclases in the same sample, rounded and embayed crystals, and armoured rims over the dissolved crystal surfaces; (b) subrounded, vesicular magmatic enclaves, ranging from a few millimeters to ~20 centimeters in size, with plagioclase + orthopyroxene + amphibole + quartz ± olivine ± Fe-Ti-oxides assemblage; (c) mineral chemistry evidence such as crystals with reaction rims or heterogeneous plagioclase compositions (inverse and oscillatory zoning or normally and inversely zoned crystals) in the same sample; and (d) elemental geochemical variations and trace-element ratio more akin to magma mixing and to some extent diffusion process. These andesitic enclaves could be considered as portions of the intermediate magma that did not mix completely (mingling) with the felsic host lavas, confirming the major role of magma mixing and mingling processes in the overall evolution of the MV

Evidencias mineralógicas y geoquímicas de mezcla incompleta de magmas en la Sierra de las Cruces, Cinturón Volcánico Mexicano

Pliocene – Pleistocene lava flows, mainly of dacitic composition, are exposed in the Sierra de las Cruces (SC) volcanic range within the Mexican Volcanic Belt (MVB). SC volcanic rocks are porphyritic, generally containing an assemblage of plagioclase + amphibole + orthopyroxene ± clinopyroxene ± quartz ± Fe-Ti oxides. Most of them exhibit diverse mineralogical and geochemical features that attest a magma mixing and mingling processes with concomitant fractional crystallization in which a small volume of hot andesite magma injects into dacitic magma. Both rock types are probably derived from partial melting of continental crust at different levels. The evidences of magma mixing and mingling include: (a) normal and sieved plagioclases in the same sample, rounded and embayed crystals, and armoured rims over the dissolved crystal surfaces; (b) subrounded, vesicular magmatic enclaves, ranging from a few millimeters to ~20 centimeters in size, with plagioclase + orthopyroxene + amphibole + quartz ± olivine ± Fe-Ti-oxides assemblage; (c) mineral chemistry evidence such as crystals with reaction rims or heterogeneous plagioclase compositions (inverse and oscillatory zoning or normally and inversely zoned crystals) in the same sample; and (d) elemental geochemical variations and trace-element ratio more akin to magma mixing and to some extent diffusion process. These andesitic enclaves could be considered as portions of the intermediate magma that did not mix completely (mingling) with the felsic host lavas, confirming the major role of magma mixing and mingling processes in the overall evolution of the MVBEn la Sierra de las Cruces (SC), Cinturón Volcánico Mexicano (CVM), se encuentran expuestos flujos de lava, principalmente de composición dacítica, del Plioceno-Pleistoceno. Las rocas volcánicas de la SC son de textura porfirítica, conteniendo plagioclasa + anfibol + ortopiroxeno ± clinopiroxeno ± cuarzo ± óxidos de Fe-Ti. La mayor parte de ellas exhiben diversas características que indican un proceso de mezcla incompleta de magmas, con una cristalización fraccionada concomitante, en la que un pequeño volumen de un magma andesítico caliente es inyectado a un magma dacítico. Es probable que ambos tipos de roca se hayan generado por fusión parcial a diferentes niveles de la corteza continental. Las evidencias de la mezcla incompleta de magmas incluyen: (a) plagioclasas con texturas normal y anubarrada en la misma muestra, cristales redondeados y corroídos, y bordes de reacción en superficies de cristal disueltas; (b) enclaves magmáticos subredondeados y vesiculares, que ocurren en dimensiones de un pocos milímetros a ~20 centímetros de diámetro, con plagioclasa + ortopiroxeno + anfíbol + cuarzo ± olivino ± óxidos de Fe-Ti; (c) química de minerales, que incluye cristales con bordes de reacción o plagioclasas de composición heterogénea (zonación inversa y oscilatoria o cristales con zonación normal e inversa) en la misma muestra; y (d) variaciones geoquímicas de elementos y relaciones de elementos traza explicables por una mezcla de magmas y por un proceso de difusión. Los enclaves andesíticos podrían considerarse como porciones de magma intermedio que no se mezcló con los líquidos dacíticos receptores, lo que confirma la importancia de los procesos de mezcla incompleta de magmas en la evolución magmática del CV

Charge separation relative to the reaction plane in Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}}= 2.76 TeV

Measurements of charge dependent azimuthal correlations with the ALICE detector at the LHC are reported for Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV. Two- and three-particle charge-dependent azimuthal correlations in the pseudo-rapidity range $|\eta| < 0.8$ are presented as a function of the collision centrality, particle separation in pseudo-rapidity, and transverse momentum. A clear signal compatible with a charge-dependent separation relative to the reaction plane is observed, which shows little or no collision energy dependence when compared to measurements at RHIC energies. This provides a new insight for understanding the nature of the charge dependent azimuthal correlations observed at RHIC and LHC energies.Comment: 12 pages, 3 captioned figures, authors from page 2 to 6, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/286

A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at s=0.9\sqrt{s}=0.9, 2.76 and 7 TeV

Measurements of the sphericity of primary charged particles in minimum bias proton--proton collisions at $\sqrt{s}=0.9$, 2.76 and 7 TeV with the ALICE detector at the LHC are presented. The observable is linearized to be collinear safe and is measured in the plane perpendicular to the beam direction using primary charged tracks with $p_{\rm T}\geq0.5$ GeV/c in $|\eta|\leq0.8$. The mean sphericity as a function of the charged particle multiplicity at mid-rapidity ($N_{\rm ch}$) is reported for events with different $p_{\rm T}$ scales ("soft" and "hard") defined by the transverse momentum of the leading particle. In addition, the mean charged particle transverse momentum versus multiplicity is presented for the different event classes, and the sphericity distributions in bins of multiplicity are presented. The data are compared with calculations of standard Monte Carlo event generators. The transverse sphericity is found to grow with multiplicity at all collision energies, with a steeper rise at low $N_{\rm ch}$, whereas the event generators show the opposite tendency. The combined study of the sphericity and the mean $p_{\rm T}$ with multiplicity indicates that most of the tested event generators produce events with higher multiplicity by generating more back-to-back jets resulting in decreased sphericity (and isotropy). The PYTHIA6 generator with tune PERUGIA-2011 exhibits a noticeable improvement in describing the data, compared to the other tested generators.Comment: 21 pages, 9 captioned figures, 3 tables, authors from page 16, published version, figures from http://aliceinfo.cern.ch/ArtSubmission/node/308

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

The inclusive transverse momentum ($p_{\rm T}$) distributions of primary charged particles are measured in the pseudo-rapidity range $|\eta|<0.8$ as a function of event centrality in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}=2.76$ TeV with ALICE at the LHC. The data are presented in the $p_{\rm T}$ range $0.15<p_{\rm T}<50$ GeV/$c$ for nine centrality intervals from 70-80% to 0-5%. The Pb-Pb spectra are presented in terms of the nuclear modification factor $R_{\rm{AA}}$ using a pp reference spectrum measured at the same collision energy. We observe that the suppression of high-$p_{\rm T}$ particles strongly depends on event centrality. In central collisions (0-5%) the yield is most suppressed with $R_{\rm{AA}}\approx0.13$ at $p_{\rm T}=6$-7 GeV/$c$. Above $p_{\rm T}=7$ GeV/$c$, there is a significant rise in the nuclear modification factor, which reaches $R_{\rm{AA}} \approx0.4$ for $p_{\rm T}>30$ GeV/$c$. In peripheral collisions (70-80%), the suppression is weaker with $R_{\rm{AA}} \approx 0.7$ almost independently of $p_{\rm T}$. 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

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

The elliptic, $v_2$, triangular, $v_3$, and quadrangular, $v_4$, azimuthal anisotropic flow coefficients are measured for unidentified charged particles, pions and (anti-)protons in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ 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 $|\eta|<0.8$ at different collision centralities and as a function of transverse momentum, $p_{\rm T}$, out to $p_{\rm T}=20$ GeV/$c$. The observed non-zero elliptic and triangular flow depends only weakly on transverse momentum for $p_{\rm T}>8$ GeV/$c$. The small $p_{\rm T}$ 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 $p_{\rm T}=8$ GeV/$c$. The magnitude of the (anti-)proton elliptic and triangular flow is larger than that of pions out to at least $p_{\rm T}=8$ GeV/$c$ indicating that the particle type dependence persists out to high $p_{\rm T}$.Comment: 16 pages, 5 captioned figures, authors from page 11, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/186

Strange particle production in proton-proton collisions at s=0.9\sqrt{s}=0.9 TeV with ALICE at the LHC

The production of mesons containing strange quarks (K$^0_s$, $\phi$) and both singly and doubly strange baryons ($\Lambda$, Anti-$\Lambda$, and $\Xi$+Anti-$\Xi$) are measured at central rapidity in pp collisions at $\sqrt{s}$ = 0.9 TeV with the ALICE experiment at the LHC. The results are obtained from the analysis of about 250 k minimum bias events recorded in 2009. Measurements of yields (dN/dy) and transverse momentum spectra at central rapidities for inelastic pp collisions are presented. For mesons, we report yields () of 0.184 $\pm$ 0.002 stat. $\pm$ 0.006 syst. for K$^0_s$ and 0.021 $\pm$ 0.004 stat. $\pm$ 0.003 syst. for $\phi$. For baryons, we find = 0.048 $\pm$ 0.001 stat. $\pm$ 0.004 syst. for $\Lambda$, 0.047 $\pm$ 0.002 stat. $\pm$ 0.005 syst. for Anti-$\Lambda$ and 0.0101 $\pm$ 0.0020 stat. $\pm$ 0.0009 syst. for $\Xi$+Anti-$\Xi$. The results are also compared with predictions for identified particle spectra from QCD-inspired models and provide a baseline for comparisons with both future pp measurements at higher energies and heavy-ion collisions.Comment: 33 pages, 21 captioned figures, 10 tables, authors from page 28, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/387

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

The $p_{\rm T}$-differential production cross sections of the prompt (B feed-down subtracted) charmed mesons D$^0$, D$^+$, and D$^{*+}$ in the rapidity range $|y|<0.5$, and for transverse momentum $1< p_{\rm T} <12$ GeV/$c$, were measured in proton-proton collisions at $\sqrt{s} = 2.76$ TeV with the ALICE detector at the Large Hadron Collider. The analysis exploited the hadronic decays D$^0 \rightarrow$K$\pi$, D$^+ \rightarrow$K$\pi\pi$, D$^{*+} \rightarrow$D$^0\pi$, and their charge conjugates, and was performed on a $L_{\rm int} = 1.1$ nb$^{-1}$ event sample collected in 2011 with a minimum-bias trigger. The total charm production cross section at $\sqrt{s} = 2.76$ TeV and at 7 TeV was evaluated by extrapolating to the full phase space the $p_{\rm T}$-differential production cross sections at $\sqrt{s} = 2.76$ TeV and our previous measurements at $\sqrt{s} = 7$ 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