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

Electric fishing survey of the gravel addition sites on the River Wyre, Grizedale Beck and Joshua's Beck.

Although geographically the River Wyre lies between two rivers containing major migrations of adult salmon and sea trout, its rod & line fisheries have for a number of years produced exceptionally low catches. In order to determine the causes of this the Wyre Salmon and Sea trout Restoration Group (WSSRG) was conceived in 1994 as a partnership between the then National Rivers Authority (now Environment Agency), local landowners, angling clubs and interested parties. Two studies of 1994 and 1995 stated that there is a shortage of useable spawning gravels on the river. This is compounded by Abbeystead Reservoir acting as a gravel trap, the siltation of gravels on several side becks and problems with access to available gravels by returning adults. There was also perceived to be a need for accurate fishery data from the river encompassing redd counts, catch data and surveys of fry populations. The 1995 report suggested a number of management proposals which might be adopted in order to improve and create available spawning habitat for migratory salmonids. Funding was made available to create three spawning gravels on each of two side becks (Grizedale Beck and Joshua's Beck) and the addition of gravels to a site oh the main river below Abbeystead Reservoir. Modifications were also made to the fish pass at Abbeystead to allow easier passage of fish. These improvements were made in the autumn of 1995. Salmonid spawning redd counting was undertaken on the whole Wyre catchment in 1995/1996 and specific surveys by electric fishing on the gravel enhancement sites in the summer of 1996. This report details the current state of the improvement works that were undertaken and presents the results of electric fishing surveys in September 1996. A number of lessons have been learnt which will be of great benefit to the Fisheries Function in other parts of the Wyre catchment and the Central Area in general

Unified convergence analysis of numerical schemes for a miscible displacement problem

This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the framework of the gradient discretisation method for diffusion operators on generic grids. We use it to establish a novel convergence result in $L^\infty(0,T; L^2(\Omega))$ of the approximate concentration using minimal regularity assumptions on the solution to the continuous problem. The convection term in the concentration equation is discretised using a centred scheme. We present a variety of numerical tests from the literature, as well as a novel analytical test case. The performance of two schemes are compared on these tests; both are poor in the case of variable viscosity, small diffusion and medium to small time steps. We show that upstreaming is not a good option to recover stable and accurate solutions, and we propose a correction to recover stable and accurate schemes for all time steps and all ranges of diffusion

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 Catholic Response to Global Climate Change Migration

This Article examines Catholic Social Teaching’s approach to the challenges of human migration and environmental refugees. By juxtaposing the inadequacies of current international frameworks for protecting environmental migrants with previous sources of Catholic Social Teaching, this Article speculates on the possible moral argument to be made by the Church in support of efforts to fill a gap in the international legal framework around climate change induced migration. Ultimately, the Paper speculates that such an argument would include three components: (1) a broadening of the definition of refugee, (2) a recognition of our interconnected and interdependent lives, and (3) the expectation that those responsible for climate change have a special obligation to care for those most vulnerable to it

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