Neutrino wave function and oscillation suppression

We consider a thought experiment, in which a neutrino is produced by an electron on a nucleus in a crystal. The wave function of the oscillating neutrino is calculated assuming that the electron is described by a wave packet. If the electron is relativistic and the spatial size of its wave packet is much larger than the size of the crystal cell, then the wave packet of the produced neutrino has essentially the same size as the wave packet of the electron. We investigate the suppression of neutrino oscillations at large distances caused by two mechanisms: 1) spatial separation of wave packets corresponding to different neutrino masses; 2) neutrino energy dispersion for given neutrino mass eigenstates. We resolve contributions of these two mechanisms.Comment: 7 page

Experience in Developing Early Warning System for Financial Crises and the Forecast of Russian Banking Sector Dynamic in 2012

The article summarizes the key results of researches in the field of early warning systems for financial crises, conducted by the Center for Macroeconomic Analysis and Short-Term Forecasting (CMASF) since 2005. The proposed early warning system consists of three major blocks: the leading indicators of certain types of risks and the composite leading indicator of a systemic banking crisis; the medium-term scenario forecasting of key macroeconomic and financial indicators; stress testing of credit and liquidity risks of banks. On the basis of this early warning system we estimate the risks of financial crisis and some kinds of systemic risks in the different scenarios for the Russian economy in 2012. The analysis, in particular, revealed a sensitivity threshold of the domestic financial sector to changes in the world oil prices. Furthermore, it was found that the greatest destabilizing effect on the Russian financial sector may be caused by systemic credit risk.systemic financial crises, credit risks, liquidity risks, currency risks, early warning system, leading indicators, stress testing

Analysis of a tensor POD-ROM for parameter dependent parabolic problems

A space-time-parameters structure of the parametric parabolic PDEs motivates the application of tensor methods to define reduced order models (ROMs). Within a tensor-based ROM framework, the matrix SVD -- a traditional dimension reduction technique -- yields to a low-rank tensor decomposition (LRTD). Such tensor extension of the Galerkin proper orthogonal decomposition ROMs (POD-ROMs) benefits both the practical efficiency of the ROM and its amenability for the rigorous error analysis when applied to parametric PDEs. The paper addresses the error analysis of the Galerkin LRTD-ROM for an abstract linear parabolic problem that depends on multiple physical parameters. An error estimate for the LRTD-ROM solution is proved, which is uniform with respect to problem parameters and extends to parameter values not in a sampling/training set. The estimate is given in terms of discretization and sampling mesh properties, and LRTD accuracy. The estimate depends on the smoothness rather than on the Kolmogorov n-widths of the parameterized manifold of solutions. Theoretical results are illustrated with several numerical experiments

Multiplicity dependence of jet-like two-particle correlations in p-Pb collisions at sNN\sqrt{s_{NN}} = 5.02 TeV

Two-particle angular correlations between unidentified charged trigger and associated particles are measured by the ALICE detector in p-Pb collisions at a nucleon-nucleon centre-of-mass energy of 5.02 TeV. The transverse-momentum range 0.7 $< p_{\rm{T}, assoc} < p_{\rm{T}, trig} <$ 5.0 GeV/$c$ is examined, to include correlations induced by jets originating from low momen\-tum-transfer scatterings (minijets). The correlations expressed as associated yield per trigger particle are obtained in the pseudorapidity range $|\eta|<0.9$. The near-side long-range pseudorapidity correlations observed in high-multiplicity p-Pb collisions are subtracted from both near-side short-range and away-side correlations in order to remove the non-jet-like components. The yields in the jet-like peaks are found to be invariant with event multiplicity with the exception of events with low multiplicity. This invariance is consistent with the particles being produced via the incoherent fragmentation of multiple parton--parton scatterings, while the yield related to the previously observed ridge structures is not jet-related. The number of uncorrelated sources of particle production is found to increase linearly with multiplicity, suggesting no saturation of the number of multi-parton interactions even in the highest multiplicity p-Pb collisions. Further, the number scales in the intermediate multiplicity region with the number of binary nucleon-nucleon collisions estimated with a Glauber Monte-Carlo simulation.Comment: 23 pages, 6 captioned figures, 1 table, authors from page 17, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/161

Effective Rheology of Bubbles Moving in a Capillary Tube

We calculate the average volumetric flux versus pressure drop of bubbles moving in a single capillary tube with varying diameter, finding a square-root relation from mapping the flow equations onto that of a driven overdamped pendulum. The calculation is based on a derivation of the equation of motion of a bubble train from considering the capillary forces and the entropy production associated with the viscous flow. We also calculate the configurational probability of the positions of the bubbles.Comment: 4 pages, 1 figur

Tensorial parametric model order reduction of nonlinear dynamical systems

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper orthogonal decomposition (POD) combined with the discrete empirical interpolation method (DEIM). For parametric systems, TROM employs low-rank tensor approximations in place of truncated SVD, a key dimension-reduction technique in POD with DEIM. Three popular low-rank tensor compression formats are considered for this purpose: canonical polyadic, Tucker, and tensor train. The use of multilinear algebra tools allows the incorporation of information about the parameter dependence of the system into the reduced model and leads to a POD-DEIM type ROM that (i) is parameter-specific (localized) and predicts the system dynamics for out-of-training set (unseen) parameter values, (ii) mitigates the adverse effects of high parameter space dimension, (iii) has online computational costs that depend only on tensor compression ranks but not on the full-order model size, and (iv) achieves lower reduced space dimensions compared to the conventional POD-DEIM ROM. The paper explains the method, analyzes its prediction power, and assesses its performance for two specific parameter-dependent nonlinear dynamical systems

Interpolatory tensorial reduced order models for parametric dynamical systems

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent and parameter-specific. The ROM exploits compressed tensor formats to find a low rank representation for a sample of high-fidelity snapshots of the system state. This tensorial representation provides ROM with an orthogonal basis in a universal space of all snapshots and encodes information about the state variation in parameter domain. During the online phase and for any incoming parameter, this information is used to find a reduced basis that spans a parameter-specific subspace in the universal space. The computational cost of the online phase then depends only on tensor compression ranks, but not on space or time resolution of high-fidelity computations. Moreover, certain compressed tensor formats enable to avoid the adverse effect of parameter space dimension on the online costs (known as the curse of dimension). The analysis of the approach includes an estimate for the representation power of the acquired ROM basis. We illustrate the performance and prediction properties of the ROM with several numerical experiments, where tensorial ROM's complexity and accuracy is compared to those of conventional POD-ROM

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

Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider

Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the presence of global azimuthal correlations. The Pb-Pb values are higher than the p-Pb values at similar multiplicities. In both systems, the second harmonic four-particle cumulants exhibit a transition from positive to negative values when the multiplicity increases. The negative values allow for a measurement of $v_{2}\{4\}$ to be made, which is found to be higher in Pb-Pb collisions at similar multiplicities. The second harmonic six-particle cumulants are also found to be higher in Pb-Pb collisions. In Pb-Pb collisions, we generally find $v_{2}\{4\} \simeq v_{2}\{6\}\neq 0$ which is indicative of a Bessel-Gaussian function for the $v_{2}$ distribution. For very high-multiplicity Pb-Pb collisions, we observe that the four- and six-particle cumulants become consistent with 0. Finally, third harmonic two-particle cumulants in p-Pb and Pb-Pb are measured. These are found to be similar for overlapping multiplicities, when a $|\Delta\eta| > 1.4$ gap is placed.Comment: 25 pages, 11 captioned figures, 3 tables, authors from page 20, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/87