The Moment Guided Monte Carlo method for the Boltzmann equation

In this work we propose a generalization of the Moment Guided Monte Carlo method developed in [11]. This approach permits to reduce the variance of the particle methods through a matching with a set of suitable macroscopic moment equations. In order to guarantee that the moment equations provide the correct solutions, they are coupled to the kinetic equation through a non equilibrium term. Here, at the contrary to the previous work in which we considered the simplified BGK operator, we deal with the full Boltzmann operator. Moreover, we introduce an hybrid setting which permits to entirely remove the resolution of the kinetic equation in the limit of infinite number of collisions and to consider only the solution of the compressible Euler equation. This modification additionally reduce the statistical error with respect to our previous work and permits to perform simulations of non equilibrium gases using only a few number of particles. We show at the end of the paper several numerical tests which prove the efficiency and the low level of numerical noise of the method.Comment: arXiv admin note: text overlap with arXiv:0908.026

A placebo-controlled, double-blind, randomized, multicenter study to assess the effects of dronedarone 400 mg twice daily for 12 weeks on atrial fibrillation burden in subjects with permanent pacemakers

Purpose Dronedarone is a benzofuran derivative with a pharmacological profile similar to amiodarone but has a more rapid onset of action and a much shorter half-life (13–19 h). Our goal was to evaluate the efficacy of dronedarone in atrial fibrillation (AF) patients using dual-chamber pacemakers capable of quantifying atrial fibrillation burden. Methods Pacemakers were adjusted to optimize AF detection. Patients with AF burden \u3e1 % were randomized to dronedarone 400 mg twice daily (BID) or placebo. Pacemakers were interrogated after 4 and 12 weeks of treatment. The primary endpoint was the change in AF burden from baseline over the 12-week treatment period. Patients with permanent AF, severe/recently decompensated heart failure, and current use of antiarrhythmic drugs were excluded. AF burden was assessed by a core laboratory blinded to treatment assignment. Results From 285 patients screened, 112 were randomized (mean age 76 years, 60 % male, 84 % hypertensive, 65 % with sick sinus syndrome, 26 % with diabetes mellitus type II, 15 % with heart failure). Baseline mean (SEM) AF burden was 8.77 % (0.16) for placebo and 10.14 % (0.17) for dronedarone. Over the 12-week study period, AF burden compared to baseline decreased by 54.4 % (0.22) (P = 0.0009) with dronedarone and trended higher by 12.8 % (0.16) (P = 0.450) with placebo. The absolute change in burden was decreased by 5.5 % in the dronedarone group and increased by 1.1 % in the placebo group. Heart rate during AF was reduced to approximately 4 beats/min with dronedarone (P = 0.285). Adverse events were higher with dronedarone compared to placebo (65 vs 56 %). Conclusions Dronedarone reduced pacemaker-assessed the relative AF burden compared to baseline and placebo by over 50 % during the 12-week observation period

Uncertainty quantification for kinetic models in socio-economic and life sciences

Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic and life sciences, where processes characterized by large groups of agents exhibit spontaneous emergence of social structures. Well-known examples are the formation of clusters in opinion dynamics, the appearance of inequalities in wealth distributions, flocking and milling behaviors in swarming models, synchronization phenomena in biological systems and lane formation in pedestrian traffic. The construction of kinetic models describing the above processes, however, has to face the difficulty of the lack of fundamental principles since physical forces are replaced by empirical social forces. These empirical forces are typically constructed with the aim to reproduce qualitatively the observed system behaviors, like the emergence of social structures, and are at best known in terms of statistical information of the modeling parameters. For this reason the presence of random inputs characterizing the parameters uncertainty should be considered as an essential feature in the modeling process. In this survey we introduce several examples of such kinetic models, that are mathematically described by nonlinear Vlasov and Fokker--Planck equations, and present different numerical approaches for uncertainty quantification which preserve the main features of the kinetic solution.Comment: To appear in "Uncertainty Quantification for Hyperbolic and Kinetic Equations

Searches For High-Frequency Variations In The B-8 Solar Neutrino Flux At The Sudbury Neutrino Observatory

We have performed three searches for high-frequency signals in the solar neutrino flux measured by the Sudbury Neutrino Observatory, motivated by the possibility that solar g-mode oscillations could affect the production or propagation of solar B-8 neutrinos. The first search looked for any significant peak in the frequency range 1-144 day(-1), with a sensitivity to sinusoidal signals with amplitudes of 12% or greater. The second search focused on regions in which g-mode signals have been claimed by experiments aboard the Solar and Heliospheric Observatory satellite, and was sensitive to signals with amplitudes of 10% or greater. The third search looked for extra power across the entire frequency band. No statistically significant signal was detected in any of the three searches.Natural Sciences and Engineering Research Council, CanadaIndustry Canada, CanadaNational Research Council, CanadaNorthern Ontario Heritage Fund, CanadaAtomic Energy of Canada, Ltd., CanadaOntario Power Generation, CanadaHigh Performance Computing Virtual Laboratory, CanadaCanada Foundation for InnovationDept. of Energy, USNational Energy Research Scientific Computing Center, USScience and Technologies Facilities Council, UKAstronom

A kinetic equation for economic value estimation with irrationality and herding

A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into account the interplay of the agents with sources of public information, herding phenomena, and irrationality of the individuals. In the formal grazing collision limit, a nonlinear nonlocal Fokker-Planck equation with anisotropic (or incomplete) diffusion is derived. The existence of global-in-time weak solutions to the Fokker-Planck initial-boundary-value problem is proved. Numerical experiments for the Boltzmann equation highlight the importance of the reliability of public information in the formation of bubbles and crashes. The use of Bollinger bands in the simulations shows how herding may lead to strong trends with low volatility of the asset prices, but eventually also to abrupt corrections

Progress on HL-LHC Nb3Sn Magnets

The high-luminosity Large Hadron Collider (HL-LHC) project aims at allowing to increase the collisions in the LHC by a factor of ten in the decade 2025-2035. One essential element is the superconducting magnet around the interaction region points, where the large aperture magnets will be installed to allow to further reduce the beam size in the interaction point. The core of this upgrade is the Nb Sn triplet, made up of 150-mm aperture quadrupoles in the range of 7-8 m. The project is being shared between the European Organization for Nuclear Research and the US Accelerator Upgrade Program, based on the same design, and on the two strand technologies. The project is ending the short model phase, and entering the prototype construction. We will report on the main results of the short model program, including the quench performance and field quality. A second important element is the 11 T dipole that replaces a standard dipole making space for additional collimators. The magnet is also ending the model development and entering the prototype phase. A critical point in the design of this magnet is the large current density, allowing increase of the field from 8 to 11 T with the same coil cross section as in the LHC dipoles. This is also the first two-in-one Nb Sn magnet developed so far. We will report the main results on the test and the critical aspects. 3