Exponential Runge-Kutta methods for stiff kinetic equations

We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation operators of BGK type. For Boltzmann type kinetic equations they work uniformly for a wide range of relaxation times and avoid the solution of nonlinear systems of equations even in stiff regimes. We give sufficient conditions in order that such methods are unconditionally asymptotically stable and asymptotic preserving. Such stability properties are essential to guarantee the correct asymptotic behavior for small relaxation times. The methods also offer favorable properties such as nonnegativity of the solution and entropy inequality. For this reason, as we will show, the methods are suitable both for deterministic as well as probabilistic numerical techniques

Weak decay processes in pre-supernova core evolution within the gross theory

The beta decay and electron capture rates are of fundamental importance in the evolution of massive stars in a pre-supernova core. The beta decay process gives its contribution by emitting electrons in the plasma of the stellar core, thereby increasing pressure, which in turn increases the temperature. From the other side, the electron capture removes free electrons from the plasma of the star core contributing to the reduction of pressure and temperature. In this work we calculate the beta decay and electron capture rates in stellar conditions for 63 nuclei of relevance in the pre-supernova stage, employing Gross Theory as the nuclear model. We use the abundances calculated with the Saha equations in the hypothesis of nuclear statistical equilibrium to evaluate the time derivative of the fraction of electrons. Our results are compared with other evaluations available in the literature. They have shown to be one order less or equal than the calculated within other models. Our results indicate that these differences may influence the evolution of the star in the later stages of pre-supernova. © 2014. The American Astronomical Society. All rights reserved..Fil: Ferreira, R. C.. Universidade Estadual Do Sudoeste Da Bahía; BrasilFil: Dimarco, A. J.. Universidade Estadual de Santa Cruz, Bahía, Brasil; BrasilFil: Samana, Arturo Rodolfo. Universidade Estadual de Santa Cruz, Bahía, Brasil; BrasilFil: Barbero, César Alberto. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

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 Narrow QRS Complex Tachycardia:

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73616/1/j.1540-8167.1999.tb00200.x.pd

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

Weak decay processes in pre-supernova core evolution within the gross theory

The beta decay and electron capture rates are of fundamental importance in the evolution of massive stars in a pre-supernova core. The beta decay process gives its contribution by emitting electrons in the plasma of the stellar core, thereby increasing pressure, which in turn increases the temperature. From the other side, the electron capture removes free electrons from the plasma of the star core contributing to the reduction of pressure and temperature. In this work we calculate the beta decay and electron capture rates in stellar conditions for 63 nuclei of relevance in the pre-supernova stage, employing Gross Theory as the nuclear model. We use the abundances calculated with the Saha equations in the hypothesis of nuclear statistical equilibrium to evaluate the time derivative of the fraction of electrons. Our results are compared with other evaluations available in the literature. They have shown to be one order less or equal than the calculated within other models. Our results indicate that these differences may influence the evolution of the star in the later stages of pre-supernova.Facultad de Ciencias ExactasInstituto de Física La Plat

Universality for Black Hole Heat Engines Near Critical Points

Johnson has shown [arXiv:1703.06119] that in the vicinity of a critical point the efficiency of a black hole heat engine can approach the Carnot efficiency while maintaining finite power. We characterize and extend this result in several ways, and we show how the rate of approach to the Carnot efficiency is governed by the critical exponents. We apply these results to several classes of black holes to illustrate their validity. Odd-order Lovelock black holes are known to have isolated critical points for which the critical exponents differ from the mean field theory values, providing a non-trivial test of the results. In this case, our results indicate the impossibility of even-order Lovelock black holes with isolated critical points in this class: their existence would constitute a violation of the second law of thermodynamics.Comment: 23 pages, 1 figur

Implications of different nitrogen input sources for potential production and carbon flux estimates in the coastal Gulf of Mexico (GOM) and Korean Peninsula coastal waters

The coastal Gulf of Mexico (GOM) and coastal sea off the Korean Peninsula (CSK) both suffer from human-induced eutrophication. We used a nitrogen (N) mass balance model in two different regions with different nitrogen input sources to estimate organic carbon fluxes and predict future carbon fluxes under different model scenarios. The coastal GOM receives nitrogen predominantly from the Mississippi and Atchafalaya rivers and atmospheric nitrogen deposition is only a minor component in this region. In the CSK, groundwater and atmospheric nitrogen deposition are more important controlling factors. Our model includes the fluxes of nitrogen to the ocean from the atmosphere, groundwater and rivers, based on observational and literature data, and identifies three zones (brown, green and blue waters) in the coastal GOM and CSK with different productivity and carbon fluxes. Based on our model results, the potential primary production rate in the inner (brown water) zone are over 2 gC m−2 d−1 (GOM) and 1.5 gC m−2 d−1 (CSK). In the middle (green water) zone, potential production is from 0.1 to 2 (GOM) and 0.3 to 1.5 gC m−2 d−1 (CSK). In the offshore (blue water) zone, productivity is less than 0.1 (GOM) and 0.3 (CSK) gC m−2 d−1. Through our model scenario results, overall oxygen demand in the GOM will increase approximately 21 % if we fail to reduce riverine N input, likely increasing considerably the area affected by hypoxia. Comparing the results from the USA with those from the Korean Peninsula shows the importance of considering both riverine and atmospheric inputs of nitrogen. This has direct implications for investigating how changes in energy technologies can lead to changes in the production of various atmospheric contaminants that affect air quality, climate and the health of local populations

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