A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Zooplankton and chlorophyll in upper water layers within research polygons in the Atlantic Ocean, June-September 2001

During Cruise 46 of R/V Akademik Mstislav Keldysh (from June to September 2001), vertical distributions of Radiolaria (Acantharia - Bac and Euradiolaria - Beur), mesozooplankton (from 0.2 to 3.0 mm size, Bm), and chlorophyll a (Cchl) in the epipelagic zone of the North Atlantic were studied. To examine the above-listed characteristics, samples were taken by Niskin 30 l bottles from 12-16 depth levels within the upper 100 to 200 m layer in the subarctic (48°11'N, 16°06'W) and subtropical (27°31'N, 75°51'W) waters, as well as in the transitional zone (41°44'N, 49°57'W). The latter proved to be characterized by the highest values of all averaged parameters examined by us within the upper 100 m layer (Bm - 365mg/m**3, Bac - 140 mg/m**3, Beur - 0.37 mg/m**3, and Cchl - 0.32 mg/m**3). For subarctic and subtropical waters corresponding characteristics were as follows: Bm - 123 and 53 mg/m**3, Bac - 0 and 0.06 mg/m**3, Beur - 0.17 and 0.19 mg/m**3, and Cchl - 0.27 and 0.05 mg/m**3, respectively. Percentage of Acantharia in total biomass of Radiolaria and zooplankton ranged from 0 to 39%, whereas that of Euradiolaria varied from 0.01 to 0.36%. Depth levels with maximum abundance of Acantharia were located above maxima of zooplankton and chlorophyll a or coincided with them. As for Euradiolaria, vertical profiles of their biomass were more diverse as compared with Acantharia. The latter group preferred more illuminated depth levels for its maximum development (10-100% of surface irradiance, E0) with respect to Euradiolaria (1-60% of E0). Possible reasons for this difference are discussed.

Heavy metal contents in Fe-Mn nodules and crusts from R/V Vityaz polygons and stations in the East Indian Ocean

Regional variations in abundance, morphology, and chemical composition of Fe-Mn nodules have a zonal character. Due to circumcontinental zonality of terrigenous sedimentation the main mass of the nodules occurs in the pelagic part of the ocean, in areas of minimal sedimentation rates. In spatial variations in morphology and chemical composition of the nodules the latitudinal zonality is very clear and associated with latitudinal changes in facial conditions of sedimentation. Elevated contents of Mn, Ni, and Cu and of Mn/Fe ratio occur in nodules from the radiolarian belt. Changes of chemical composition of the nodules with depth (vertical zonality of mineralization) are confirmed. Local variations in abundance, morphology and chemical composition of the nodules are caused by ruggedness of relief and depth variations, variations in sedimentation rate, age of ore formation, intensity of diagenetic redistribution of metals.

An efficient algorithm for partitioning parameterized polygons into rectangles

In this paper, we propose an algorithm for partitioning parameterized orthogonal polygons into rectangles. The algorithm is based on the plane-sweep technique and can be used for partitioning polygons which contain holes. The input to the algorithm consists of the contour of a parameterized polygon to be partitioned and the constraints for those parameters which reside in the contour. The algorithm uses horizontal cuts only and generates a minimum number of rectangles whose union is the original orthogonal polygon. The proposed algorithm can be used as the basis to build corner stitching data structure for parameterized VLSI layouts and has been implemented in Java programming language. Copyright © 2010 ACM, Inc.