On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation

Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare nuclear masses. This maintains an adiabatic-like point of view: the nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy

Major Surge Activity of Super-Active Region NOAA 10484

We observed two surges in H-alpha from the super-active region NOAA 10484. The first surge was associated with an SF/C4.3 class flare. The second one was a major surge associated with a SF/C3.9 flare. This surge was also observed with SOHO/EIT in 195 angstrom and NoRh in 17 GHz, and showed similar evolution in these wavelengths. The major surge had an ejective funnel-shaped spray structure with fast expansion in linear (about 1.2 x 10^5 km) and angular (about 65 deg) size during its maximum phase. The mass motion of the surge was along open magnetic field lines, with average velocity about 100 km/s. The de-twisting motion of the surge reveals relaxation of sheared and twisted magnetic flux. The SOHO/MDI magnetograms reveal that the surges occurred at the site of companion sunspots where positive flux emerged, converged, and canceled against surrounding field of opposite polarity. Our observations support magnetic reconnection models for the surges and jets.Comment: 4 pages, 3 figures; To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Series, Springer-Verlag, Heidelberg, Berlin, 200

Meter-scale spark X-ray spectrumstatistics

X-ray emission by sparks implies bremsstrahlung from a population of energetic electrons, but the details of this process remain a mystery. We present detailed statistical analysis of X-ray spectra detected by multiple detectors during sparks produced by 1 MV negative high-voltage pulses with 1 $\mu$s risetime. With over 900 shots, we statistically analyze the signals, assuming that the distribution of spark X-ray fluence behaves as a power law and that the energy spectrum of X-rays detectable after traversing $\sim$2 m of air and a thin aluminum shield is exponential. We then determine the parameters of those distributions by fitting cumulative distribution functions to the observations. The fit results match the observations very well if the mean of the exponential X-ray energy distribution is 86 $\pm$ 7 keV and the spark X-ray fluence power law distribution has index -1.29 $\pm$ 0.04 and spans at least 3 orders of magnitude in fluence

Comprehensive maximum likelihood estimation of diffusion compartment models towards reliable mapping of brain microstructure

open4siDiffusion MRI is a key in-vivo non invasive imaging capability that can probe the microstructure of the brain. However,its limited resolution requires complex voxelwise generative models of the diffusion. Diffusion Compartment (DC) models divide the voxel into smaller compartments in which diffusion is homogeneous. We present a comprehensive framework for maximum likelihood estimation (MLE) of such models that jointly features ML estimators of (i) the baseline MR signal,(ii) the noise variance,(iii) compartment proportions,and (iv) diffusion-related parameters. ML estimators are key to providing reliable mapping of brain microstructure as they are asymptotically unbiased and of minimal variance. We compare our algorithm (which efficiently exploits analytical properties of MLE) to alternative implementations and a state-of-theart strategy. Simulation results show that our approach offers the best reduction in computational burden while guaranteeing convergence of numerical estimators to the MLE. In-vivo results also reveal remarkably reliable microstructure mapping in areas as complex as the centrum semiovale. Our ML framework accommodates any DC model and is available freely for multi-tensor models as part of the ANIMA software (https://github.com/Inria-Visages/Anima-Public/wiki).Stamm, Aymeric; Commowick, Olivier; Warfield, Simon K.; Vantini, SimoneStamm, Aymeric; Commowick, Olivier; Warfield, Simon K.; Vantini, Simon

A physical mechanism for the prediction of the sunspot number during solar cycle 21

On physical grounds it is suggested that the sun's polar field strength near a solar minimum is closely related to the following cycle's solar activity. Four methods of estimating the sun's polar magnetic field strength near solar minimum are employed to provide an estimate of cycle 21's yearly mean sunspot number at solar maximum of 140 plus or minus 20. This estimate is considered to be a first order attempt to predict the cycle's activity using one parameter of physical importance

How to evaluate community predictions without thresholding?

Stacked species distribution models (S-SDM) provide a tool to make spatial predictions about communities by first modelling individual species and then stacking the modelled predictions to form assemblages. The evaluation of the predictive performance is usually based on a comparison of the observed and predicted community properties (e.g. species richness, composition). However, the most available and widely used evaluation metrics require the thresholding of single species' predicted probabilities of occurrence to obtain binary outcomes (i.e. presence/absence). This binarization can introduce unnecessary bias and error. Herein, we present and demonstrate the use of several groups of new or rarely used evaluation approaches and metrics for both species richness and community composition that do not require thresholding but instead directly compare the predicted probabilities of occurrences of species to the presence/absence observations in the assemblages. Community AUC, which is based on traditional AUC, measures the ability of a model to differentiate between species presences or absences at a given site according to their predicted probabilities of occurrence. Summing the probabilities gives the expected species richness and allows the estimation of the probability that the observed species richness is not different from the expected species richness based on the species' probabilities of occurrence. The traditional Sorensen and Jaccard similarity indices (which are based on presences/absences) were adapted to maxSorensen and maxJaccard and to probSorensen and probJaccard (which use probabilities directly). A further approach (improvement over null models) compares the predictions based on S-SDMs with the expectations from the null models to estimate the improvement in both species richness and composition predictions. Additionally, all metrics can be described against the environmental conditions of sites (e.g. elevation) to highlight the abilities of models to detect the variation in the strength of the community assembly processes in different environments. These metrics offer an unbiased view of the performance of community predictions compared to metrics that requiring thresholding. As such, they allow more straightforward comparisons of model performance among studies (i.e. they are not influenced by any subjective thresholding decisions).Peer reviewe