Convective Instability Of The Solar Corona: Why The Solar Wind Blows

Chapman's (1957) conductive model of the solar corona is characterized by a temperature varying as r**(-2/7) with heliocentric distance r. The density distribution in this non-isothermal hydrostatic model has a minimum value at 123 RS, and increases with r above that altitude. It is shown that this hydrostatic model becomes convectively unstable above r = 35 RS, where the temperature lapse rate becomes superadiabatic. Beyond this radial distance heat conduction fails to be efficient enough to keep the temperature gradient smaller than the adiabatic lapse rate. We report the results obtained by Lemaire (1968) who showed that an additional mechanism is then required to transport the energy flux away from the Sun into interplanetary space. He pointed out that this additional mechanism is advection: i.e. the stationary hydrodynamic expansion of the corona. In other words the corona is unable to stay in hydrostatic equilibrium. The hydrodynamic solar wind expansion is thus a physical consequence of the too steep (superadiabatic) temperature gradient beyond the peak of coronal temperature that can be determined from white light brightness distributions observed during solar eclipses. The thermodynamic argument for the existence of a continuous solar wind expansion which is presented here, complements Parker's classical argument based on boundary conditions imposed to the solutions of the hydrodynamic equations for the coronal expansion: i.e. the inability of the mechanical forces to hold the corona in hydrostatic equilibrium. The thermodynamic argument presented here is based on the energy transport equation. It relies on the temperature distribution which becomes super-adiabatic above a certain altitude in the inner corona.Comment: 4 pages, 3 figures, presented at SW12 conference (2009); Copyright 2010 American Institute of Physics 978-0-7354-0759-6/10. This article may be downloaded for personal use only. The following article appeared in CP1216 and may be found at http://proceedings.aip.or

Half a Century of Kinetic Solar Wind Models

I outline the development of four generations of kinetic models, starting with Chamberlain's solar breeze exospheric model. It is shown why this first kinetic model did not give apposite supersonic evaporation velocities, like early hydrodynamic models of the solar wind. When a self-consistent polarization electric potential distribution is used in the coronal plasma, instead of the Pannekoek-Rosseland's one, supersonic bulk velocities are readily obtained in the second generation of kinetic models. It is outlined how the third and fourth generations of these models have improved the agreement with observations of slow and fast speed solar wind streams.Comment: 10 pages, 3 figures, presented at SW12 conf. ; Copyright (2010 AIP 978-0-7354-0759-6/10) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics The following article appeared in (CP1216) and may be found at (http://proceedings.aip.org

A note on the moving hyperplane method

We give more precision on the regularity of the domain that is needed to have the monotonicity and symmetry results recently proved by Damascelli and Pacella, result concerning p-Laplace equations. For this purpose, we study the continuity and semicontinuity of some parameters linked with the moving hyperplane method.Comment: 4 pages, 2 figure

Multilevel Richardson-Romberg extrapolation

We propose and analyze a Multilevel Richardson-Romberg (MLRR) estimator which combines the higher order bias cancellation of the Multistep Richardson-Romberg method introduced in [Pa07] and the variance control resulting from the stratification introduced in the Multilevel Monte Carlo (MLMC) method (see [Hei01, Gi08]). Thus, in standard frameworks like discretization schemes of diffusion processes, the root mean squared error (RMSE) $\varepsilon > 0$ can be achieved with our MLRR estimator with a global complexity of $\varepsilon^{-2} \log(1/\varepsilon)$ instead of $\varepsilon^{-2} (\log(1/\varepsilon))^2$ with the standard MLMC method, at least when the weak error $\mathbf{E}[Y_h]-\mathbf{E}[Y_0]$ of the biased implemented estimator $Y_h$ can be expanded at any order in $h$ and $\|Y_h - Y_0\|_2 = O(h^{\frac{1}{2}})$. The MLRR estimator is then halfway between a regular MLMC and a virtual unbiased Monte Carlo. When the strong error $\|Y_h - Y_0\|_2 = O(h^{\frac{\beta}{2}})$, $\beta < 1$, the gain of MLRR over MLMC becomes even more striking. We carry out numerical simulations to compare these estimators in two settings: vanilla and path-dependent option pricing by Monte Carlo simulation and the less classical Nested Monte Carlo simulation.Comment: 38 page

Incremental Construction of an Associative Network from a Corpus

This paper presents a computational model of the incremental construction of an associative network from a corpus. It is aimed at modeling the development of the human semantic memory. It is not based on a vector representation, which does not well reproduce the asymmetrical property of word similarity, but rather on a network representation. Compared to Latent Semantic Analysis, it is incremental which is cognitively more plausible. It is also an attempt to take into account higher-order co-occurrences in the construction of word similarities. This model was compared to children association norms. A good correlation as well as a similar gradient of similarity were found

Coalescence 2.0: a multiple branching of recent theoretical developments and their applications

Population genetics theory has laid the foundations for genomics analyses including the recent burst in genome scans for selection and statistical inference of past demographic events in many prokaryote, animal and plant species. Identifying SNPs under natural selection and underpinning species adaptation relies on disentangling the respective contribution of random processes (mutation, drift, migration) from that of selection on nucleotide variability. Most theory and statistical tests have been developed using the Kingman coalescent theory based on the Wright-Fisher population model. However, these theoretical models rely on biological and life-history assumptions which may be violated in many prokaryote, fungal, animal or plant species. Recent theoretical developments of the so called multiple merger coalescent models are reviewed here ({\Lambda}-coalescent, beta-coalescent, Bolthausen-Snitzman, {\Xi}-coalescent). We explicit how these new models take into account various pervasive ecological and biological characteristics, life history traits or life cycles which were not accounted in previous theories such as 1) the skew in offspring production typical of marine species, 2) fast adapting microparasites (virus, bacteria and fungi) exhibiting large variation in population sizes during epidemics, 3) the peculiar life cycles of fungi and bacteria alternating sexual and asexual cycles, and 4) the high rates of extinction-recolonization in spatially structured populations. We finally discuss the relevance of multiple merger models for the detection of SNPs under selection in these species, for population genomics of very large sample size and advocate to potentially examine the conclusion of previous population genetics studies.Comment: 3 Figure

Joint Modelling of Gas and Electricity spot prices

The recent liberalization of the electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this paper, we modelize jointly gas and electricity spot prices using a mean-reverting model which fits the correlations structures for the two commodities. The dynamics are based on Ornstein processes with parameterized diffusion coefficients. Moreover, using the empirical distributions of the spot prices, we derive a class of such parameterized diffusions which captures the most salient statistical properties: stationarity, spikes and heavy-tailed distributions. The associated calibration procedure is based on standard and efficient statistical tools. We calibrate the model on French market for electricity and on UK market for gas, and then simulate some trajectories which reproduce well the observed prices behavior. Finally, we illustrate the importance of the correlation structure and of the presence of spikes by measuring the risk on a power plant portfolio

On some Non Asymptotic Bounds for the Euler Scheme

We obtain non asymptotic bounds for the Monte Carlo algorithm associated to the Euler discretization of some diffusion processes. The key tool is the Gaussian concentration satisfied by the density of the discretization scheme. This Gaussian concentration is derived from a Gaussian upper bound of the density of the scheme and a modification of the so-called "Herbst argument" used to prove Logarithmic Sobolev inequalities. We eventually establish a Gaussian lower bound for the density of the scheme that emphasizes the concentration is sharp.Comment: 26 page