Convergence in C([0,T];L2(Ω))C(\lbrack0,T\rbrack;L^2(\Omega)) of weak solutions to perturbed doubly degenerate parabolic equations

We study the behaviour of solutions to a class of nonlinear degenerate parabolic problems when the data are perturbed. The class includes the Richards equation, Stefan problem and the parabolic $p$-Laplace equation. We show that, up to a subsequence, weak solutions of the perturbed problem converge uniformly-in-time to weak solutions of the original problem as the perturbed data approach the original data. We do not assume uniqueness or additional regularity of the solution. However, when uniqueness is known, our result demonstrates that the weak solution is uniformly temporally stable to perturbations of the data. Beginning with a proof of temporally-uniform, spatially-weak convergence, we strengthen the latter by relating the unknown to an underlying convex structure that emerges naturally from energy estimates on the solution. The double degeneracy --- shown to be equivalent to a maximal monotone operator framework --- is handled with techniques inspired by a classical monotonicity argument and a simple variant of the compensated compactness phenomenon.Comment: J. Differential Equations, 201

Mercury deposition in southern New Hampshire, 2006–2009

The atmospheric deposition of mercury (Hg) occurs via several mechanisms including wet, dry, and occult processes. In an effort to understand the atmospheric cycling and seasonal depositional characteristics of Hg, event-based wet deposition samples and reactive gaseous Hg (RGM) measurements were collected for approximately 3 years at Thompson Farm (TF), a near-coastal rural site in Durham, NH, part of the University of New Hampshire AIRMAP Observing Network. Total aqueous mercury exhibited seasonal patterns in Hg wet deposition at TF. The lowest Hg wet deposition was measured in the winter with an average total seasonal deposition of 1.56 μg m−2compared to the summer average of 4.71 μg m−2. Inter-annual differences in total wet deposition are generally linked with precipitation volume, with the greatest deposition occurring in the wettest year. Relationships between surface level RGM and Hg wet deposition were also investigated based on continuous RGM measurements at TF from November 2006 to September 2009. No correlations were observed between RGM mixing ratios and Hg wet deposition, however the ineffective scavenging of RGM during winter precipitation events was evidenced by the less frequent depletion of RGM below the detection level. Seasonal dry deposition of reactive gaseous Hg (RGM) was estimated using an order-of-magnitude approach. RGM mixing ratios and dry deposition estimates were greatest during the winter and spring. The seasonal ratios of Hg wet deposition to RGM dry deposition vary by up to a factor of 80

Evolution of the Pulp.

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A causal look into the quantum Talbot effect

A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.Comment: 12 pages, 6 figure

Large-scale distributions of tropospheric nitric, formic, and acetic acids over the western Pacific basin during wintertime

We report here measurements of the acidic gases nitric (HNO3), formic (HCOOH), and acetic (CH3COOH) over the western Pacific basin during the February-March 1994 Pacific Exploratory Mission-West (PEM-West B). These data were obtained aboard the NASA DC-8 research aircraft as it flew missions in the altitude range of 0.3–12.5 km over equatorial regions near Guam and then further westward encompassing the entire Pacific Rim arc. Aged marine air over the equatorial Pacific generally exhibited mixing ratios of acidic gases \u3c100 parts per trillion by volume (pptv). Near the Asian continent, discrete plumes encountered below 6 km altitude contained up to 8 parts per billion by volume (ppbv) HNO3 and 10 ppbv HCOOH and CH3COOH. Overall there was a general correlation between mixing ratios of acidic gases with those of CO, C2H2, and C2Cl4, indicative of emissions from combustion and industrial sources. The latitudinal distributions of HNO3 and CO showed that the largest mixing ratios were centered around 15°N, while HCOOH, CH3COOH, and C2Cl4 peaked at 25°N. The mixing ratios of HCOOH and CH3COOH were highly correlated (r2 = 0.87) below 6 km altitude, with a slope (0.89) characteristic of the nongrowing season at midlatitudes in the northern hemisphere. Above 6 km altitude, HCOOH and CH3COOH were marginally correlated (r2 = 0.50), and plumes well defined by CO, C2H2, and C2Cl4 were depleted in acidic gases, most likely due to scavenging during vertical transport of air masses through convective cloud systems over the Asian continent. In stratospheric air masses, HNO3 mixing ratios were several parts per billion by volume (ppbv), yielding relationships with O3 and N2O consistent with those previously reported for NOy