Global Classical Solutions of the Boltzmann Equation with Long-Range Interactions and Soft Potentials

In this work we prove global stability for the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse power intermolecular potentials, $r^{-(p-1)}$ with $p>2$. This completes the work which we began in (arXiv:0912.0888v1). We more generally cover collision kernels with parameters $s\in (0,1)$ and $\gamma$ satisfying $\gamma > -(n-2)-2s$ in arbitrary dimensions $\mathbb{T}^n \times \mathbb{R}^n$ with $n\ge 2$. Moreover, we prove rapid convergence as predicted by the Boltzmann H-Theorem. When $\gamma + 2s \ge 0$, we have exponential time decay to the Maxwellian equilibrium states. When $\gamma + 2s < 0$, our solutions decay polynomially fast in time with any rate. These results are constructive. Additionally, we prove sharp constructive upper and lower bounds for the linearized collision operator in terms of a geometric fractional Sobolev norm; we thus observe that a spectral gap exists only when $\gamma + 2s \ge 0$, as conjectured in Mouhot-Strain (2007).Comment: This file has not changed, but this work has been combined with (arXiv:0912.0888v1), simplified and extended into a new preprint, please see the updated version: arXiv:1011.5441v

Integrating effects of species composition and soil properties to predict shifts in montane forest carbon-water relations.

This study was designed to address a major source of uncertainty pertaining to coupled carbon-water cycles in montane forest ecosystems. The Sierra Nevada of California was used as a model system to investigate connections between the physiological performance of trees and landscape patterns of forest carbon and water use. The intrinsic water-use efficiency (iWUE)-an index of CO2 fixed per unit of potential water lost via transpiration-of nine dominant species was determined in replicated transects along an ∼1,500-m elevation gradient, spanning a broad range of climatic conditions and soils derived from three different parent materials. Stable isotope ratios of carbon and oxygen measured at the leaf level were combined with field-based and remotely sensed metrics of stand productivity, revealing that variation in iWUE depends primarily on leaf traits (∼24% of the variability), followed by stand productivity (∼16% of the variability), climatic regime (∼13% of the variability), and soil development (∼12% of the variability). Significant interactions between species composition and soil properties proved useful to predict changes in forest carbon-water relations. On the basis of observed shifts in tree species composition, ongoing since the 1950s and intensified in recent years, an increase in water loss through transpiration (ranging from 10 to 60% depending on parent material) is now expected in mixed conifer forests throughout the region

Programmable telemetry system Patent

Time division multiplexed telemetry transmitting system controlled by programmed memor

Studying Migrant Assimilation Through Facebook Interests

Migrants' assimilation is a major challenge for European societies, in part because of the sudden surge of refugees in recent years and in part because of long-term demographic trends. In this paper, we use Facebook's data for advertisers to study the levels of assimilation of Arabic-speaking migrants in Germany, as seen through the interests they express online. Our results indicate a gradient of assimilation along demographic lines, language spoken and country of origin. Given the difficulty to collect timely migration data, in particular for traits related to cultural assimilation, the methods that we develop and the results that we provide open new lines of research that computational social scientists are well-positioned to address.Comment: Accepted as a short paper at Social Informatics 2018 (https://socinfo2018.hse.ru/). Please cite the SocInfo versio

Numerical Bifurcation Analysis of Conformal Formulations of the Einstein Constraints

The Einstein constraint equations have been the subject of study for more than fifty years. The introduction of the conformal method in the 1970's as a parameterization of initial data for the Einstein equations led to increased interest in the development of a complete solution theory for the constraints, with the theory for constant mean curvature (CMC) spatial slices and closed manifolds completely developed by 1995. The first general non-CMC existence result was establish by Holst et al. in 2008, with extensions to rough data by Holst et al. in 2009, and to vacuum spacetimes by Maxwell in 2009. The non-CMC theory remains mostly open; moreover, recent work of Maxwell on specific symmetry models sheds light on fundamental non-uniqueness problems with the conformal method as a parameterization in non-CMC settings. In parallel with these mathematical developments, computational physicists have uncovered surprising behavior in numerical solutions to the extended conformal thin sandwich formulation of the Einstein constraints. In particular, numerical evidence suggests the existence of multiple solutions with a quadratic fold, and a recent analysis of a simplified model supports this conclusion. In this article, we examine this apparent bifurcation phenomena in a methodical way, using modern techniques in bifurcation theory and in numerical homotopy methods. We first review the evidence for the presence of bifurcation in the Hamiltonian constraint in the time-symmetric case. We give a brief introduction to the mathematical framework for analyzing bifurcation phenomena, and then develop the main ideas behind the construction of numerical homotopy, or path-following, methods in the analysis of bifurcation phenomena. We then apply the continuation software package AUTO to this problem, and verify the presence of the fold with homotopy-based numerical methods.Comment: 13 pages, 4 figures. Final revision for publication, added material on physical implication

Rigidity transitions and constraint counting in amorphous networks: beyond the mean-field approach

Subj-class: Disordered Systems and Neural NetworksComment: 12 pages, revtex, 3 figure

Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics

In this article we develop some new existence results for the Einstein constraint equations using the Lichnerowicz-York conformal rescaling method. The mean extrinsic curvature is taken to be an arbitrary smooth function without restrictions on the size of its spatial derivatives, so that it can be arbitrarily far from constant. The rescaled background metric belongs to the positive Yamabe class, and the freely specifiable part of the data given by the traceless-transverse part of the rescaled extrinsic curvature and the matter fields are taken to be sufficiently small, with the matter energy density not identically zero. Using topological fixed-point arguments and global barrier constructions, we then establish existence of solutions to the constraints. Two recent advances in the analysis of the Einstein constraint equations make this result possible: A new type of topological fixed-point argument without smallness conditions on spatial derivatives of the mean extrinsic curvature, and a new construction of global super-solutions for the Hamiltonian constraint that is similarly free of such conditions on the mean extrinsic curvature. For clarity, we present our results only for strong solutions on closed manifolds. However, our results also hold for weak solutions and for other cases such as compact manifolds with boundary; these generalizations will appear elsewhere. The existence results presented here for the Einstein constraints are apparently the first such results that do not require smallness conditions on spatial derivatives of the mean extrinsic curvature.Comment: 4 pages, no figures, accepted for publication in Physical Review Letters. (Abstract shortenned and other minor changes reflecting v4 version of arXiv:0712.0798

Is the quantum world composed of propensitons?

In this paper I outline my propensiton version of quantum theory (PQT). PQT is a fully micro-realistic version of quantum theory that provides us with a very natural possible solution to the fundamental wave/particle problem, and is free of the severe defects of orthodox quantum theory (OQT) as a result. PQT makes sense of the quantum world. PQT recovers all the empirical success of OQT and is, furthermore, empirically testable (although not as yet tested). I argue that Einstein almost put forward this version of quantum theory in 1916/17 in his papers on spontaneous and induced radiative transitions, but retreated from doing so because he disliked the probabilistic character of the idea. Subsequently, the idea was overlooked because debates about quantum theory polarised into the Bohr/Heisenberg camp, which argued for the abandonment of realism and determinism, and the Einstein/Schrödinger camp, which argued for the retention of realism and determinism, no one, as a result, pursuing the most obvious option of retaining realism but abandoning determinism. It is this third, overlooked option that leads to PQT. PQT has implications for quantum field theory, the standard model, string theory, and cosmology. The really important point, however, is that it is experimentally testable. I indicate two experiments in principle capable of deciding between PQT and OQT

New postnatal urinary incontinence: obstetric and other risk factors in primparae.

Objective To identify obstetric and other risk factors for urinary incontinence which occurs during pregnancy or after childbirth. Design Questionnaire survey of women. Setting Maternity units in Aberdeen (Scotland), Birmingham (England) and Dunedin (New Zealand). Population 3405 primiparous women with singleton births delivered during one year. Methods Questionnaire responses and obstetric casenote data were analysed using multivariate analysis to identify associations with urinary incontinence. Main outcome measures Urinary incontinence at three months after delivery first starting in pregnancy or after birth. Results The prevalence of urinary incontinence was 29%. New incontinence first beginning after delivery was associated with higher maternal age (oldest versus youngest group, odds ratio, OR 2.02, 95% CI 1.35 to 3.02); and method of delivery (caesarean section versus spontaneous vaginal delivery, OR 0.28, 95% CI 0.19 to 0.41). There were no significant associations with forceps delivery (OR 1.18, 95% CI 0.92 to 1.51) or vacuum delivery (OR 1.16, 95% CI 0.83 to 1.63). Incontinence first occurring during pregnancy and still present at three months was associated with higher maternal body mass index (BMI > 25, OR 1.68, 95% CI 1.16 to 2.43), and heavier babies (birthweight in top quartile, OR 1.56, 95% CI 1.12 to 2.19). In these women, caesarean section was associated with less incontinence (OR 0.39, 95% CI 0.27 to 0.58) but incontinence was not associated with age. Conclusions Women have less urinary incontinence after a first delivery by caesarean section whether or not that first starts during pregnancy. Older maternal age was associated with new postnatal incontinence, and higher body mass index and heavier babies with incontinence first starting during pregnancy. The effect of further deliveries may modify these findings