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Scattering of spin-0 and spin- 1 2 particles is formulated in momentum space based on basis states being not expanded in partial waves. No sequential calculations with increasing angular momentum are performed to reach physical convergence, which depends on the scattering energy and the interaction range. Both nonrelativistic and relativistic cases are described. We put forward for consideration the utilization of this approach. By taking some simple interaction models we show some advantages in calculations representing those of high energy scattering as well as those of scattering governed by long range interactions. [ABSTRACT FROM AUTHOR]

Angularity and surface texture of aggregate particles are important morphological characteristics and have great influences on the performance of asphalt mix. Several approaches have been developed to characterize the angularity and surface texture of aggregate particles in the past decade. Most existing techniques are limited to the two-dimensional (2D) scheme. In this study, a three-dimensional (3D) approach is proposed to determine the angularity index (AI) and surface texture index (STI) of aggregates, namely the 3D Sobel-Feldman operation, which has not been well used in civil engineering. First, aggregate particles are subjected to X-ray scanning to obtain cross-sectional images, which are then processed and stacked to construct the 3D voxel-based images. Then the gradient vector of each voxel on the surfaces is calculated based on the 3D Sobel-Feldman operation, which was derived and verified in this study based on the 2D Sobel-Feldman operation. The results showed that the 3D Sobel-Feldman operation derived in this study is correct and feasible to be used to determine the 3D AI of aggregates. The AI is determined by the accumulative change of gradient vectors of some selected surface voxels. A pretreatment (dilation followed by erosion) is used to reduce the effect of surface texture on the AI calculation. The surface texture index is determined by the relative loss of voxels after a morphological opening (erosion followed by dilation) operation on the 3D image. User-written coding was used to deal with the massive calculation. A total of 15 aggregate particles were used as case study to investigate the feasibility of the proposed approach to measure the 3D AI and STI. Some factors that affect the AI and STI values were also discussed to find the optimum approach. The 3D STI results were also compared to the 2D results to justify the benefits of the 3D approach. [ABSTRACT FROM AUTHOR]

The aim of the authors was to compare values of 2D and 3D landscape metrics in high mountains. The first part of the work takes into consideration the spatial structure of vegetation (the rank of landscape facias/ecotopes) of Kocioł Goryczkowy Świński, which was investigated in 1999 by Anna Kozłowska and Anna Jakomulska. The calculation of landscape metrics is resumed using the true surface geometries and compared with the result of traditional measurements on a reference plane. In the second part of the paper, a set of commonly used landscape metrics is calculated for the geocomplexes (rank of uroczysko unit) in the Morskie Oko catchment using both true surface and plain geometries. Finally average surface roughness is computed for the both study areas and some remarks for landscape metrics computed for geometric fields are given. The comparison shows that appropriate 2D and 3D metrics may differ significantly. Moreover, there is a strong correlation between the size of the discrepancy and the surface slope. For that reason, it is very important to distinguish between 2D and 3D metrics and to use them consciously, according to the particular problem. [ABSTRACT FROM AUTHOR]

This paper analyzes the political economy of the creeping militarization of U.S. foreign policy. The core argument is that in integrating the “3D” approach—defense, development, and diplomacy—policymakers have assigned responsibilities to military personnel which go beyond their comparative advantage, requiring them to become social engineers tasked with constructing entire societies. Evidence from The U.S. Army Stability Operations Field Manual is presented to illustrate the wide scope of responsibilities assigned to the U.S. military. The tools of political economy are used to analyze some of the implications. [ABSTRACT FROM AUTHOR]