Critical Parameter Values and Reconstruction Properties of Discrete Tomography: Application to Experimental Fluid Dynamics

We analyze representative ill-posed scenarios of tomographic PIV with a focus on conditions for unique volume reconstruction. Based on sparse random seedings of a region of interest with small particles, the corresponding systems of linear projection equations are probabilistically analyzed in order to determine (i) the ability of unique reconstruction in terms of the imaging geometry and the critical sparsity parameter, and (ii) sharpness of the transition to non-unique reconstruction with ghost particles when choosing the sparsity parameter improperly. The sparsity parameter directly relates to the seeding density used for PIV in experimental fluids dynamics that is chosen empirically to date. Our results provide a basic mathematical characterization of the PIV volume reconstruction problem that is an essential prerequisite for any algorithm used to actually compute the reconstruction. Moreover, we connect the sparse volume function reconstruction problem from few tomographic projections to major developments in compressed sensing.Comment: 22 pages, submitted to Fundamenta Informaticae. arXiv admin note: text overlap with arXiv:1208.589

Modeling Storage and Demand Management in Electricity Distribution Grids

Storage devices and demand control may constitute beneficial tools to optimize electricity generation with a large share of intermittent resources through inter-temporal substitution of load. We quantify the related cost reductions in a simulation model of a simplified stylized medium-voltage grid (10kV) under uncertain demand and wind output. Benders Decomposition Method is applied to create a two-stage stochastic program. The model informs an optimal investment sizing decision as regards specific 'smart grid' applications such as storage facilities and meters enabling load control. Model results indicate that central storage facilities are a more promising option for generation cost reductions as compared to demand management. Grid extensions are not appropriate in any of our scenarios. A sensitivity analysis is applied with respect to the market penetration of uncoordinated Plug-In Electric Vehicles which are found to strongly encourage investment into load control equipment for `smart` charging and slightly improve the case for central storage devices.Storage, demand management, stochastic optimization, Benders Decomposition

Enhancing the cosmic-ray mass sensitivity of air-shower arrays by combining radio and muon detectors

The muonic and electromagnetic components of air showers are sensitive to the mass of the primary cosmic particle. The sizes of the components can be measured with particle detectors on ground, and the electromagnetic component in addition indirectly via its radio emission in the atmosphere. The electromagnetic particles do not reach the ground for very inclined showers. On the contrary, the atmosphere is transparent for the radio emission and its footprint on ground increases with the zenith angle. Therefore, the radio technique offers a reliable detection over the full range of zenith angles, and in particular for inclined showers. In this work, the mass sensitivity of a combination of the radio emission with the muons is investigated in a case study for the site of the Pierre Auger Observatory using CORSIKA Monte Carlo simulations of showers in the EeV energy range. It is shown, that the radio-muon combination features superior mass separation power in particular for inclined showers, when compared to established mass observables such as a combination of muons and electrons or the shower maximum Xmax. Accurate measurements of the energy-dependent mass composition of ultra-high energy cosmic rays are essential to understand their still unknown origin. Thus, the combination of muon and radio detectors can enhance the scientific performance of future air-shower arrays and offers a promising upgrade option for existing arrays

What Determines the Inclusion in a Sustainability Stock Index? A Panel Data Analysis for European Companies

This paper examines the determinants of the inclusion of European companies in the Dow Jones Sustainability World Index and the Dow Jones STOXX Sustainability Index. In doing so, the paper contributes to the micro-econometric literature analyzing the determinants and economic effects of sustainability performance in three respects: First, it examines a broad measure of corporate sustainability behavior and thus does not only apply narrow measures of environmental performance such as toxic releases which is common in other studies. Second, the paper examines the effect of internal assessment processes regarding corporate sustainability performance by an independent financial service institution. Finally, it analyzes the influence of unobserved heterogeneity in the framework of panel data models. The analysis shows that the probability for an inclusion in the sustainability indexes strongly decreases if a company does not respond to the written survey of the assessing institution. Furthermore, time invariant random effects and an autoregressive structure in the stochastic components are important factors. In contrast, a significant influence of past economic performance cannot be confirmed robustly

Global spatial regularity for elasticity models with cracks, contact and other nonsmooth constraints

A global higher differentiability result in Besov spaces is proved for the displacement fields of linear elastic models with self contact. Domains with cracks are studied, where nonpenetration conditions/Signorini conditions are imposed on the crack faces. It is shown that in a neighborhood of crack tips (in 2D) or crack fronts (3D) the displacement fields are B 3/2 2,∞ regular. The proof relies on a difference quotient argument for the directions tangential to the crack. In order to obtain the regularity estimates also in the normal direction, an argument due to Ebmeyer/Frehse/Kassmann is modified. The methods are then applied to further examples like contact problems with nonsmooth rigid foundations, to a model with Tresca friction and to minimization problems with nonsmooth energies and constraints as they occur for instance in the modeling of shape memory alloys. Based on Falk's approximation Theorem for variational inequalities, convergence rates for FE-discretizations of contact problems are derived relying on the proven regularity properties. Several numerical examples illustrate the theoretical results