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The Newtonian regime of a recent nonlocal extension of general relativity is investigated. Nonlocality is introduced via a scalar “constitutive” kernel in a special case of the translational gauge theory of gravitation, namely, the teleparallel equivalent of general relativity. In this theory, the nonlocal aspect of gravity simulates dark matter. A nonlocal and nonlinear generalization of Poisson’s equation of Newtonian gravitation is presented. The implications of nonlocality for the gravitational physics in the solar system are briefly studied.
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(2010)
Chemical imaging systems allow the visualisation of the distribution of chemical species on the sensor surface. This work represents a new flexible approach of read out in a light-addressable potentiometric sensor (LAPS) with the help of a digital light processing (DLP) set-up. The DLP, known well for video projectors, consists of a mirror-array MEMS device which allows fast and flexible generation of light patterns. With the help of these light patterns the sensor surface of the LAPS device can be read out sequentially in a raster like scheme (scanning LAPS). The DLP approach has several advantages compared to conventional scanning LAPS set-ups, e.g., the spot size, the shape and the intensity of the light pointer can be changed easily and no mechanical movement is necessary, which reduces the size of the set-up and increases the stability and speed of measurement.
Recently, we introduced and mathematically analysed a new method for grid deformation (Grajewski et al., 2009) [15] we call basic deformation method (BDM) here. It generalises the method proposed by Liao et al. (Bochev et al., 1996; Cai et al., 2004; Liao and Anderson, 1992) [4], [6], [20]. In this article, we employ the BDM as core of a new multilevel deformation method (MDM) which leads to vast improvements regarding robustness, accuracy and speed. We achieve this by splitting up the deformation process in a sequence of easier subproblems and by exploiting grid hierarchy. Being of optimal asymptotic complexity, we experience speed-ups up to a factor of 15 in our test cases compared to the BDM. This gives our MDM the potential for tackling large grids and time-dependent problems, where possibly the grid must be dynamically deformed once per time step according to the user's needs. Moreover, we elaborate on implementational aspects, in particular efficient grid searching, which is a key ingredient of the BDM.