A Direct Multigrid Poisson Solver for Oct-Tree Adaptive Meshes

We describe a finite-volume method for solving the Poisson equation on oct-tree adaptive meshes using direct solvers for individual mesh blocks. The method is a modified version of the method presented by Huang and Greengard (2000), which works with finite-difference meshes and does not allow for shared boundaries between refined patches. Our algorithm is implemented within the FLASH code framework and makes use of the PARAMESH library, permitting efficient use of parallel computers. We describe the algorithm and present test results that demonstrate its accuracy.Comment: 10 pages, 6 figures, accepted by the Astrophysical Journal; minor revisions in response to referee's comments; added char

Analytic evaluation of the dipole Hessian matrix in coupled-cluster theory

The general theory required for the calculation of analytic third energy derivatives at the coupled-cluster level of theory is presented and connected to preceding special formulations for hyperpolarizabilities and polarizability gradients. Based on our theory, we have implemented a scheme for calculating the dipole Hessian matrix in a fully analytical manner within the coupled-cluster singles and doubles approximation. The dipole Hessian matrix is the second geometrical derivative of the dipole moment and thus a third derivative of the energy. It plays a crucial role in IR spectroscopy when taking into account anharmonic effects and is also essential for computing vibrational corrections to dipole moments. The superior accuracy of the analytic evaluation of third energy derivatives as compared to numerical differentiation schemes is demonstrated in some pilot calculations

The Beta Generalized Exponential Distribution

We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the moment generating function and the $r$th moment thus generalizing some results in the literature. Expressions for the density, moment generating function and $r$th moment of the order statistics also are obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix. We observe in one application to real data set that this model is quite flexible and can be used quite effectively in analyzing positive data in place of the beta exponential and generalized exponential distributions

Thermodynamic curvature measures interactions

Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most statistical mechanics texts. I review work showing how to go beyond the Gaussian approximation by adding covariance, conservation, and consistency. This generalization leads to a fundamentally new object: the thermodynamic Riemannian curvature scalar $R$, a thermodynamic invariant. I argue that $|R|$ is related to the correlation length and suggest that the sign of $R$ corresponds to whether the interparticle interactions are effectively attractive or repulsive.Comment: 29 pages, 7 figures (added reference 27

Aircraft pollution: a futuristic view

International audienceImpacts of NOx, H2O and aerosol emissions from a projected 2050 aircraft fleet, provided in the EU project SCENIC, are investigated using the Oslo CTM2, a 3-D chemical transport model including comprehensive chemistry for the stratosphere and the troposphere. The aircraft emission scenarios comprise emissions from subsonic and supersonic aircraft. The increases in NOy due to emissions from the mixed fleet are comparable for subsonic (at 11–12 km) and supersonic (at 18–20 km) aircraft, with annual zonal means of 1.35 ppbv and 0.83 ppbv, respectively. H2O increases are also comparable at these altitudes: 630 and 599 ppbv, respectively. The aircraft emissions increase tropospheric ozone by about 10 ppbv in the Northern Hemisphere due to increased ozone production, mainly because of subsonic aircraft. Supersonic aircraft contribute to a reduction of stratospheric ozone due to increased ozone loss at higher altitudes. In the Northern Hemisphere the reduction is about 39 ppbv, but also in the Southern Hemisphere a 22 ppbv stratospheric decrease is modeled due to transport of supersonic aircraft emissions and ozone depleted air. The total ozone column is increased in lower and Northern mid-latitudes, otherwise the increase of ozone loss contributes to a decrease of the total ozone column. Two exceptions are the Northern Hemispheric spring, where the ozone loss increase is small due to transport processes, and tropical latitudes during summer where the effect of subsonic aircraft is low due to a high tropopause. Aerosol particles emitted by aircraft reduce both aircraft and background NOx, more than counterweighting the effect of NOx and H2O aircraft emissions in the stratosphere. Above about 20 km altitude, the NOx (and thus ozone loss) reduction is large enough to give an increase in ozone due to aircraft emissions. This effect is comparable in the Northern and Southern Hemisphere. At 11–20 km altitude, however, ozone production is reduced due to less NOx. Also ClONO2 is increased at this altitude due to enhanced heterogeneous reactions (lowered HCl), and ClO is increased due to less NOx, further enhancing ozone loss in this region. This results in a 14 ppbv further reduction of ozone. Mainly, this results in an increase of the total ozone column due to a decrease in ozone loss caused by the NOx cycle (at the highest altitudes). At the lowermost latitudes, the reduced loss due to the NOx cycle is small. However, ozone production at lower altitudes is reduced and the loss due to ClO is increased, giving a decrease in the total ozone column. Also, at high latitudes during spring the heterogeneous chemistry is more efficient on PSCs, increasing the ozone loss

Photon inner product and the Gauss linking number

It is shown that there is an interesting interplay between self-duality, loop representation and knots invariants in the quantum theory of Maxwell fields in Minkowski space-time. Specifically, in the loop representation based on self-dual connections, the measure that dictates the inner product can be expressed as the Gauss linking number of thickened loops.Comment: 18 pages, Revtex. No figures. To appear in Class. Quantum Gra

Gauss Linking Number and Electro-magnetic Uncertainty Principle

It is shown that there is a precise sense in which the Heisenberg uncertainty between fluxes of electric and magnetic fields through finite surfaces is given by (one-half $\hbar$ times) the Gauss linking number of the loops that bound these surfaces. To regularize the relevant operators, one is naturally led to assign a framing to each loop. The uncertainty between the fluxes of electric and magnetic fields through a single surface is then given by the self-linking number of the framed loop which bounds the surface.Comment: 13 pages, Revtex file, 3 eps figure

Ehrenrettung

n/