Quantitative isoperimetric inequalities for log-convex probability measures on the line

The purpose of this paper is to analyze the isoperimetric inequality for symmetric log-convex probability measures on the line. Using geometric arguments we first re-prove that extremal sets in the isoperimetric inequality are intervals or complement of intervals (a result due to Bobkov and Houdr\'e). Then we give a quantitative form of the isoperimetric inequality, leading to a somehow anomalous behavior. Indeed, it could be that a set is very close to be optimal, in the sense that the isoperimetric inequality is almost an equality, but at the same time is very far (in the sense of the symmetric difference between sets) to any extremal sets! From the results on sets we derive quantitative functional inequalities of weak Cheeger type

Critical exponents for the long-range Ising chain using a transfer matrix approach

The critical behavior of the Ising chain with long-range ferromagnetic interactions decaying with distance $r^\alpha$, $1<\alpha<2$, is investigated using a numerically efficient transfer matrix (TM) method. Finite size approximations to the infinite chain are considered, in which both the number of spins and the number of interaction constants can be independently increased. Systems with interactions between spins up to 18 sites apart and up to 2500 spins in the chain are considered. We obtain data for the critical exponents $\nu$ associated with the correlation length based on the Finite Range Scaling (FRS) hypothesis. FRS expressions require the evaluation of derivatives of the thermodynamical properties, which are obtained with the help of analytical recurrence expressions obtained within the TM framework. The Van den Broeck extrapolation procedure is applied in order to estimate the convergence of the exponents. The TM procedure reduces the dimension of the matrices and circumvents several numerical matrix operations.Comment: 10 pages, 2 figures, Conference NEXT Sigma Ph

The Homflypt polynomial and the oriented Thompson group

We show how to construct unitary representations of the oriented Thompson group $\vec{F}$ from oriented link invariants. In particular we show that the suitably normalised HOMFLYPT polynomial defines a positive definite function of $\vec{F}$.Comment: To appear in Quantum Topolog

Magnetic reversals in a simple model of MHD

We study a simple magnetohydrodynamical approach in which hydrodynamics and MHD turbulence are coupled in a shell model, with given dynamo constrains in the large scales. We consider the case of a low Prandtl number fluid for which the inertial range of the velocity field is much wider than that of the magnetic field. Random reversals of the magnetic field are observed and it shown that the magnetic field has a non trivial evolution linked to the nature of the hydrodynamics turbulence.Comment: 4 pages, submitted to PR

Equation of Motion for the Solvent Polarization Apparent Charges in the Polarizable Continuum Model: Application to Time-Dependent CI

The dynamics of the electrons for a molecule in solution is coupled to the dynamics of its polarizable environment, i.e., the solvent. To theoretically investigate such electronic dynamics, we have recently developed equations of motion (EOM) for the apparent solvent polarization charges that generate the reaction field in the Polarizable Continuum Model (PCM) for solvation and we have coupled them to a real-time time-dependent density functional theory (RT TDDFT) description of the solute [Corni et al. J. Phys. Chem. A 119, 5405 (2014)]. Here we present an extension of the EOM-PCM approach to a Time-Dependent Configuration Interaction (TD CI) description of the solute dynamics, which is free from the qualitative artifacts of RT TDDFT in the adiabatic approximation. As tests of the developed approach, we investigate the solvent Debye relaxation after an electronic excitation of the solute obtained either by a $\pi$ pulse of light or by assuming the idealized sudden promotion to the excited state. Moreover, we present EOM for the Onsager solvation model and we compare the results with PCM. The developed approach provides qualitatively correct real-time evolutions and is promising as a general tool to investigate the electron dynamics elicited by external electromagnetic fields for molecules in solution.Comment: This is the final peer-reviewed manuscript accepted for publication in The Journal of Chemical Physics. Copyright by AIP, the final published version can be found at http://scitation.aip.org/content/aip/journal/jcp/146/6/10.1063/1.497562

World natural gas endowment as a bridge towards zero carbon emissions

We use global energy market (GEM) model to show that natural gas has the potential to help stabilize global carbon emissions in a span of about 50-100 years and pave the way towards low and zero carbon energy. The GEM provides a close fit of the global energy mix between 1850 and 2005. It also matches historical carbon and CO2 emissions generated by the combination of fossil fuels. The model is used them to forecast the future energy mix, as well as the carbon and CO2 emissions, up to the year 2150. Historical data show relative decarbonization and an increase in the amount of hydrogen burned as a percent of fossil fuel use between 1850 and 1970. The GEM indicates that with a larger contribution of natural gas to the future energy market, the burned hydrogen percentage will increase. This decarbonization will help to advance economic and environmental sustainability

Stochastic Resonance in a simple model of magnetic reversals

We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria.Comment: 6 page

Link Between Endowments, Economics and Environment in Conventinal and unconventional Gas Reservoirs

This paper presents a methodology for connecting endowments, economics and the environment in conventional, tight, shale and Coalbed Methane (CBM) reservoirs. The volumetric estimates are generated by a Variable Shape Distribution model (VSD). The VSD has been shown in the past to be useful for the evaluation of conventional and tight gas reservoirs. However, this is the first paper in which the method is used to also include shale gas and CBM formations. Results indicate a total gas endowment of 70,000 tcf, split between 15,000 tcf in conventional reservoirs, 15,000 tcf in tight gas, 30,000 tcf in shale gas and 10,000 tcf in CBM reservoirs. Thus, natural gas formations have potential to provide a significant contribution to global energy demand estimated at approximately 790 quads by 2035. A common thread between unconventional formations is that nearly all of them must be hydraulically fractured to attain commercial production. A significant volume of data indicates that the probabilities of hydraulic fracturing (fracking) fluids and/or methane contaminating ground water through the hydraulically-created fractures are very low. Since fracking has also raised questions about the economic viability of producing unconventional gas in some parts of the world, supply curves are estimated in this paper for the global gas portfolio. The curves show that, in some cases, the costs of producing gas from unconventional reservoirs are comparable to those of conventional gas. The conclusion is that there is enough natural gas to supply the energy market for nearly 400 years at current rates of consumption and 110 years with a growth rate in production of 2% per year. With appropriate regulation, this may be done safely, commercially, and in a manner that is more benign to the environment as compared with other fossil fuels

Micro-RNA-1 is decreased by hypoxia and contributes to the development of pulmonary vascular remodeling via regulation of sphingosine kinase 1

Sphingosine kinase 1 (SphK1) upregulation is associated with pathologic pulmonary vascular remodeling in pulmonary arterial hypertension (PAH), but the mechanisms controlling its expression are undefined. In this study, we sought to characterize the regulation of SphK1 expression by micro-RNAs (miRs). In silico analysis of the SphK1 3'-untranslated region identified several putative miR binding sites, with miR-1-3p (miR-1) being the most highly predicted target. Therefore we further investigated the role of miR-1 in modulating SphK1 expression and characterized its effects on the phenotype of pulmonary artery smooth muscle cells (PASMCs) and the development of experimental pulmonary hypertension in vivo. Our results demonstrate that miR-1 is downregulated by hypoxia in PASMCs and can directly inhibit SphK1 expression. Overexpression of miR-1 in human PASMCs inhibits basal and hypoxia-induced proliferation and migration. Human PASMCs isolated from PAH patients exhibit reduced miR-1 expression. We also demonstrate that miR-1 is downregulated in mouse lung tissues during experimental hypoxia-mediated pulmonary hypertension (HPH), consistent with upregulation of SphK1. Furthermore, administration of miR-1 mimics in vivo prevented the development of HPH in mice and attenuated induction of SphK1 in PASMCs. These data reveal the importance of miR-1 in regulating SphK1 expression during hypoxia in PASMCs. A pivotal role is played by miR-1 in pulmonary vascular remodeling, including PASMC proliferation and migration, and its overexpression protects from the development of HPH in vivo. These studies improve our understanding of the molecular mechanisms underlying the pathogenesis of pulmonary hypertension

Relaxation times of kinetically constrained spin models with glassy dynamics

We analyze the density and size dependence of the relaxation time $\tau$ for kinetically constrained spin systems. These have been proposed as models for strong or fragile glasses and for systems undergoing jamming transitions. For the one (FA1f) or two (FA2f) spin facilitated Fredrickson-Andersen model at any density $\rho<1$ and for the Knight model below the critical density at which the glass transition occurs, we show that the persistence and the spin-spin time auto-correlation functions decay exponentially. This excludes the stretched exponential relaxation which was derived by numerical simulations. For FA2f in $d\geq 2$, we also prove a super-Arrhenius scaling of the form $\exp(1/(1-\rho))\leq \tau\leq\exp(1/(1-\rho)^2)$. For FA1f in $d$=$1,2$ we rigorously prove the power law scalings recently derived in \cite{JMS} while in $d\geq 3$ we obtain upper and lower bounds consistent with findings therein. Our results are based on a novel multi-scale approach which allows to analyze $\tau$ in presence of kinetic constraints and to connect time-scales and dynamical heterogeneities. The techniques are flexible enough to allow a variety of constraints and can also be applied to conservative stochastic lattice gases in presence of kinetic constraints.Comment: 4 page