Equilibrium and eigenfunctions estimates in the semi-classical regime

We establish eigenfunctions estimates, in the semi-classical regime, for critical energy levels associated to an isolated singularity. For Schr\"odinger operators, the asymptotic repartition of eigenvectors is the same as in the regular case, excepted in dimension 1 where a concentration at the critical point occurs. This principle extends to pseudo-differential operators and the limit measure is the Liouville measure as long as the singularity remains integrable.Comment: 13 pages, 1 figure, perhaps to be revise

Implications of spatial distributions of snow mass and melt rate for snow-cover depletion: observations in a subarctic mountain catchment

Spatial statistics of snow water equivalent (SWE) and melt rate were measured using spatially distributed, sequential ground surveys of depth and density in forested, shrub and alpine tundra environments over several seasons within a 185 km(2) mountain catchment in Yukon Territory, Canada. When stratified by slope/aspect sub-units within landscape classes, SWE frequency distributions matched the log-normal, but multiclass surveys showed a more bimodal distribution. Within-class variability of winter SWE could be grouped into (i) windswept tundra and (ii) sheltered tundra/forest regimes. During melt, there was little association between the standard deviation and mean of SWE. At small scales, a negative correlation developed between spatial distributions of pre-melt SWE and melt rate where shrubs were exposed above the snow. This was not evident in dense-forest, alpine-tundra or deep-snowdrift landscape classes. At medium scales, adja-negative SWE and melt-rate correlations were also found between mean values from adjacent slope sub-units of the tundra landscape class. The medium-scale correlation was likely due to slope effects on insolation and blowing-snow redistribution. At the catchment scale, the correlation between mean SWE and melt rate from various landscape classes reversed to a positive one, likely influenced by intercepted and blowing regimes, shrub exposure during melt and adiabatic cooling with elevation rise. Covariance at the catchment scale resulted in a 40% acceleration of snow depletion. These results suggest that the spatial variability and covariability of both SWE and melt rate are scale- and landscape-class-specific and need to be considered in a landscape-stratified manner at the appropriate scale when snow depletion is described and the snowmelt duration predicted.</p

Observationally Verifiable Predictions of Modified Gravity

MOG is a fully relativistic modified theory of gravity based on an action principle. The MOG field equations are exactly solvable numerically in two important cases. In the spherically symmetric, static case of a gravitating mass, the equations also admit an approximate solution that closely resembles the Reissner-Nordstrom metric. Furthermore, for weak gravitational fields, a Yukawa-type modification to the Newtonian acceleration law can be obtained, which can be used to model a range of astronomical observations. Without nonbaryonic dark matter, MOG provides good agreement with the data for galaxy rotation curves, galaxy cluster masses, and gravitational lensing, while predicting no appreciable deviation from Einstein's predictions on the scale of the solar system. Another solution of the field equations is obtained for the case of a a spatially homogeneous, isotropic cosmology. MOG predicts an accelerating universe without introducing Einstein's cosmological constant; it also predicts a CMB acoustic power spectrum and a mass power spectrum that are consistent with observations without relying on non-baryonic dark matter. Increased sensitivity in future observations or space-based experiments may be sufficient to distinguish MOG from other theories, notably the LCDM "standard model" of cosmology.Comment: 8 pages, 9 figures. Talk given by JWM at the "The Invisible Universe" conference, Paris, France, June 29-July 3, 200

Can Modified Gravity (MOG) explain the speeding Bullet (Cluster)?

We apply our scalar-tensor-vector (STVG) modified gravity theory (MOG) to calculate the infall velocities of the two clusters constituting the Bullet Cluster 1E0657-06. In the absence of an applicable two-body solution to the MOG field equations, we adopt an approximate acceleration formula based on the spherically symmetric, static, vacuum solution of the theory in the presence of a point source. We find that this formula predicts an infall velocity of the two clusters that is consistent with estimates based on hydrodynamic simulations.Comment: 4 page