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 Multilevel Monte Carlo Asymptotic-Preserving Particle Method for Kinetic Equations in the Diffusion Limit

We propose a multilevel Monte Carlo method for a particle-based asymptotic-preserving scheme for kinetic equations. Kinetic equations model transport and collision of particles in a position-velocity phase-space. With a diffusive scaling, the kinetic equation converges to an advection-diffusion equation in the limit of zero mean free path. Classical particle-based techniques suffer from a strict time-step restriction to maintain stability in this limit. Asymptotic-preserving schemes provide a solution to this time step restriction, but introduce a first-order error in the time step size. We demonstrate how the multilevel Monte Carlo method can be used as a bias reduction technique to perform accurate simulations in the diffusive regime, while leveraging the reduced simulation cost given by the asymptotic-preserving scheme. We describe how to achieve the necessary correlation between simulation paths at different levels and demonstrate the potential of the approach via numerical experiments.Comment: 20 pages, 7 figures, published in Monte Carlo and Quasi-Monte Carlo Methods 2018, correction of minor typographical error

An Exercise in Forecasting Loop Current and Eddy Frontal Positions in the Gulf of Mexico

As part of a model-evaluation exercise to forecast Loop Current and Loop Current eddy frontal positions in the Gulf of Mexico, the Princeton Regional Ocean Forecast System (PROFS) is tested to forecast 14 4-week periods Aug/25/99- Sep/20/00, during which a powerful eddy, Eddy Juggernaut (Eddy-J) separated from the Loop Current and propagated southwestward. To initialize each forecast, PROFS assimilates satellite sea surface height (SSH) anomaly and temperature (SST) by projecting them into subsurface density using a surface/subsurface correlation that is a function of the satellite SSH anomaly. The closest distances of the forecast fronts from seven fixed stations in the northern Gulf over a 4-week forecast horizon are then compared against frontal observations derived primarily from drifters. Model forecasts beat persistence and the major source of error is found to be due to the initial hindcast fields

Influence of Menopausal Status on Lipids and Lipoproteins and Fat Mass Distribution: The Pioneer Project

Following menopause, fat redistribution and increased risk for dyslipidemia are common. The influence of menopause; however, on the associations between total and regional fat mass with lipids and lipoproteins remains unclear. PURPOSE: The purpose of this investigation was to determine the influence of menopausal status on associations between total and regional fat mass and lipids and lipoproteins. METHODS: Sedentary, non-smoking women (n=209) were grouped based on current menstrual status: premenopausal (n=143, mean±SD; age=42.7±7.7 yr, BMI=24.5±4.0 kg•m -2, WC=77.4±9.9 cm) or postmenopausal (n=66, mean±SD; age=52.9±5.3 yr, BMI= 24.9±4.2 kg•m -2, WC=78.8±9.9 cm). Fasting (12 hr) serum samples were analyzed for total cholesterol (TC), triglyceride (Tg), LDL-C, HDL-C, HDL2-C, and HDL3-C concentrations. Total (TF), abdominal (AF), hip (HF) and mid-thigh (MTF) fat mass were quantified by DXA. A MANCOVA was used to determine differences between groups for total and regional fat mass and lipids and lipoproteins controlling for HRT status. Stepwise multiple regression analysis was used to determine if menopausal status influenced the association of total and regional fat mass with lipids and lipoproteins. The criterion reference for statistical significance was set at a P \u3c 0.05. RESULTS: Postmenopausal women had significantly greater TC, HDL-C, LDL-C and HDL3-C concentrations than premenopausal women. No significant differences were observed between groups for total and regional fat mass. In premenopausal women, AF predicted TC, but no associations were observed in postmenopausal women. In premenopausal women, AF+HF and AF+TF were significant predictors of Tg and LDL-C, respectively. In contrast, only AF predicted Tg and LDL-C in postmenopausal women. AF+MTF best predicted HDL-C in premenopausal women; however, TF+MTF best predicted HDL-C in postmenopausal women. In premenopausal women, no associations were observed with HDL2-C or HDL3-C. TF and TF+MTF were best predictors of HDL2-C and HDL3-C, respectively in postmenopausal women. CONCLUSION: Menopausal status has an effect on lipid and lipoprotein-cholesterol concentrations, but not on total and regional fat mass. In addition, menopausal status had an influence on the associations of total and regional fat mass with lipids and lipoproteins

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

Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at √(s_NN) = 2.76 TeV

Measurements are presented by the CMS Collaboration at the Large Hadron Collider (LHC) of the higher-order harmonic coefficients that describe the azimuthal anisotropy of charged particles emitted in √(s_NN)=2.76 TeV PbPb collisions. Expressed in terms of the Fourier components of the azimuthal distribution, the n=3–6 harmonic coefficients are presented for charged particles as a function of their transverse momentum (0.3<p_T<8.0GeV/c), collision centrality (0%–70%), and pseudorapidity (|η|<2.0). The data are analyzed using the event plane, multiparticle cumulant, and Lee-Yang zeros methods, which provide different sensitivities to initial-state fluctuations. Taken together with earlier LHC measurements of elliptic flow (n=2), the results on higher-order harmonic coefficients develop a more complete picture of the collective motion in high-energy heavy-ion collisions and shed light on the properties of the produced medium

Rapid Quantification of Dynamic and Spall Strength of Metals Across Strain Rates

The response of metals and their microstructures under extreme dynamic conditions can be markedly different from that under quasistatic conditions. Traditionally, high strain rates and shock stresses are measured using cumbersome and expensive methods such as the Kolsky bar or large spall experiments. These methods are low throughput and do not facilitate high-fidelity microstructure-property linkages. In this work, we combine two powerful small-scale testing methods, custom nanoindentation, and laser-driven micro-flyer shock, to measure the dynamic and spall strength of metals. The nanoindentation system is configured to test samples from quasistatic to dynamic strain rate regimes (10$^{-3}$ s$^{-1}$ to 10$^{+4}$ s$^{-1}$). The laser-driven micro-flyer shock system can test samples through impact loading between 10$^{+5}$ s$^{-1}$ to 10$^{+7}$ s$^{-1}$ strain rates, triggering spall failure. The model material used for testing is Magnesium alloys, which are lightweight, possess high-specific strengths and have historically been challenging to design and strengthen due to their mechanical anisotropy. Here, we modulate their microstructure by adding or removing precipitates to demonstrate interesting upticks in strain rate sensitivity and evolution of dynamic strength. At high shock loading rates, we unravel an interesting paradigm where the spall strength of these materials converges, but the failure mechanisms are markedly different. Peak aging, considered to be a standard method to strengthen metallic alloys, causes catastrophic failure, faring much worse than solutionized alloys. Our high throughput testing framework not only quantifies strength but also teases out unexplored failure mechanisms at extreme strain rates, providing valuable insights for the rapid design and improvement of metals for extreme environments

Ocean forests: breakthrough yields for macroalgae

The US Department of Energy Advanced Research Projects Agency - Energy (ARPA-E) MacroAlgae Research Inspiring Novel Energy Research (MARINER) program is encouraging technologies for the sustainable harvest of large funding research of macroalgae for biofuels at less than $80 per dry metric ton (DMT). The Ocean Forests team, led by the University of Southern Mississippi, is developing a complete managed ecosystem where nutrients are transformed and recycled. The team’s designs address major bottlenecks in profitability of offshore aquaculture systems including economical moored structures that can withstand storms, efficient planting, managing and harvesting systems, and sustainable nutrient supply. The work is inspired by Lapointe who reported yields of Gracilaria tikvahiae equivalent to 127 DMT per hectare per year (compared with standard aquaculture systems in the range of 20 to 40 DMT/ha/yr). This approach offers the potential for breakthrough yields for many macroalgae species. Moreover, mini-ecosystems in offshore waters create communities of macroalgae, shellfish, and penned finfish, supplemented by visiting free-range fish that can increase productivity, produce quality products, and create jobs and income for aquafarmers. Additional benefits include reduced disease in fish pens, cleaning contaminated coastal waters, and maximizing nutrient recycling. Cost projections for a successful, intensive, scaled system are competitive with current prices for fossil fuels

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 Search for Neutrinos from the Solar hep Reaction and the Diffuse Supernova Neutrino Background with the Sudbury Neutrino Observatory

A search has been made for neutrinos from the hep reaction in the Sun and from the diffus