Study of a family of higher order nonlocal degenerate parabolic equations: from the porous medium equation to the thin film equation

In this paper, we study a nonlocal degenerate parabolic equation of order {\alpha} + 2 for 0<{\alpha}<2. The equation is a generalization of the one arising in the modeling of hydraulic fractures studied by Imbert and Mellet in 2011. Using the same approach, we prove the existence of solutions for this equation for 0<{\alpha}<2 and for nonnegative initial data satisfying appropriate assumptions. The main difference is the compactness results due to different Sobolev embeddings. Furthermore, for {\alpha} > 1, we construct a nonnegative solution for nonnegative initial data under weaker assumptions.Comment: arXiv admin note: text overlap with arXiv:1001.5105 by other author

Graphene Terahertz Plasmon Oscillators

In this paper we propose and discuss coherent terahertz sources based on charge density wave (plasmon) amplification in two dimensional graphene. The coupling of the plasmons to interband electron-hole transitions in population inverted graphene layers can lead to plasmon amplification through stimulated emission. Plasmon gain values in graphene can be very large due to the small group velocity of the plasmons and the strong confinement of the plasmon field in the vicinity of the graphene layer. We present a transmission line model for plasmon propagation in graphene that includes plasmon dissipation and plasmon interband gain due to stimulated emission. Using this model, we discuss design for terahertz plasmon oscillators and derive the threshold condition for oscillation taking into account internal losses and also losses due to external coupling. The large gain values available at terahertz frequencies in graphene can lead to integrated oscillators that have dimensions in the 1-10 micron range.Comment: To appear in IEEE Transactions on Nanotechnology (TNANO

Delivering light-weight online geographic information analysis using ArcIMS

As of July 9, 2002, more than 300 websites, which provide automated mapping and facilities management over the internet, are registered in the ESRI Internet Map Server (IMS) user registry [1]. But it won’t be an exaggeration to assume that this is only a tiny fraction of the actual number of IMS sold and used over the world. In fact, realising the potential scope and issues of this new form of geographic information delivery, the International Cartographic Association has formed a Commission dedicated to Maps and the Internet [2]. The IMS software has also kept pace with the growing demand and progress in technology. IMS has evolved from the simple HTML image maps to sophisticated servelet-driven mapping services. During this period, a very significant event happened with the arrival of ArcIMS. With the ArcIMS the use of IMS changed from merely an interactive visualisation and query of the spatial databases to a platform for sharing remote spatial databases. In other words, the ArcIMS made the scale of operation of IMS global. While the accessibility and usability of the IMS have certainly increased in the past 5- 6 years, the functionalities provided by IMS however remained fairly static. A widely felt but unreported criticism of IMS has been that the lack of a broader range of spatial analysis functions (except the usual buffering) in the off-the-shelf IMS installation. Therefore a couple of eyebrows always tend to rise if the word “Internet GIS” is used for IMS. Oddly enough, the ArcIMS 3.x and the older versions carry this limitation as well. Essentially, IMS suffer from the limitation for not being able to allow simultaneous update and dynamic manipulation of the thematic content of the online maps. For example, in the case of ArcIMS while there are provisions for complex scale-dependent rendering, it is not easily possible to manipulate (for example add layers or delete layers) the crucial axl file of a mapping service on the fly. The recent launch of ArcIMS 4 promises to bridge this gap by allowing an enhanced integration with the ArcGIS. The aim of this article is to propose a generic framework, which makes the link between an IMS and a standard GIS, to provide geographic analysis in online maps. We will take the example of such a framework developed for ArcIMS

Isovist Analyst - An Arcview extension for planning visual surveillance

7-11 August, 2006, San Diego, CA, USA. Visual Surveillance e.g. CCTV, is now an essential part of the urban infrastructure in modern cities. One of the primary aims in visual surveillance is to ensure a maximum visual coverage of an area with the least number of visual surveillance installations, which is a NP-Hard maximal coverage problem. The planning of visual surveillance is a highly sensitive and costly task that has traditionally been done with a gut-feel process of establishing sight lines in CAD software. This paper demonstrates the ArcView extension Isovist Analyst, which automatically identifies a minimal number of potential visual surveillance sites that ensure complete visual coverage of an area. The paper proposes a Stochastical Rank and Overlap Elimination (S-ROPE) method, which iteratively identifies the optimal visual surveillance sites. S-ROPE method is essentially based on a greedy search technique, which has been improved by a combination of selective sampling strategy and random initialisation

\u3ci\u3eChevron\u3c/i\u3e Without the Courts? The Supreme Court\u27s Recent \u3cem\u3eChevron\u3c/em\u3e Jurisprudence Through an Immigration Lens

The limits of administrative law are undergoing a seismic shift in the immigration arena. Chevron divides interpretive and decision-making authority between the federal courts and agencies in each of two steps. The Supreme Court may now be transforming this division in largely unrecognized ways. These shifts, currently playing out in the immigration context, may threaten to reshape deference jurisprudence by handing more power to the immigration agency just when the agency may be least able to handle that power effectively. An unprecedented surge in immigration cases—now approximately 90% of the federal administrative docket—has arrived just as the Court is whittling away the judicial role while expanding agency authority, significantly transforming traditional deference doctrine. In its immigration docket, the Court is shifting the judicial role away from questions of statutory interpretation and towards a mere evaluation of when the agency’s interpretation should be granted deference. Assessment of the “reasonableness” of the agency’s action has given way to marking the outer boundaries of agency action, merging the court’s traditional oversight analysis into a form of “arbitrary and capriciousness” review. The costs of the Court’s reformulation of Chevron are particularly visible in immigration law because recent legislation and structural changes at the immigration agency have already constrained judicial review. However, the reformulation of Chevron occurring in immigration law may threaten to remake administrative law generally. Unfortunately, these developments have received little scholarly attention. Understanding this transformation is imperative as ultimately we may be heading towards “Chevron without the Courts”—wherein the judicial interpretive role is being constrained in the very instances where agencies are least able to function effectively

Use of plan curvature variations for the identification of ridges and channels on DEM

This paper proposes novel improvements in the traditional algorithms for the identification of ridge and channel (also called ravines) topographic features on raster digital elevation models (DEMs). The overall methodology consists of two main steps: (1) smoothing the DEM by applying a mean filter, and (2) detection of ridge and channel features as cells with positive and negative plan curvature respectively, along with a decline and incline in plan curvature away from the cell in direction orthogonal to the feature axis respectively. The paper demonstrates a simple approach to visualize the multi-scale structure of terrains and utilize it for semi-automated topographic feature identification. Despite its simplicity, the revised algorithm produced markedly superior outputs than a comparatively sophisticated feature extraction algorithm based on conic-section analysis of terrain

Fast approximation of visibility dominance using topographic features as targets and the associated uncertainty

An approach to reduce visibility index computation time andmeasure the associated uncertainty in terrain visibility analysesis presented. It is demonstrated that the visibility indexcomputation time in mountainous terrain can be reduced substantially,without any significant information loss, if the lineof sight from each observer on the terrain is drawn only to thefundamental topographic features, i.e., peaks, pits, passes,ridges, and channels. However, the selected sampling of targetsresults in an underestimation of the visibility index ofeach observer. Two simple methods based on iterative comparisonsbetween the real visibility indices and the estimatedvisibility indices have been proposed for a preliminary assessmentof this uncertainty. The method has been demonstratedfor gridded digital elevation models