An economic model of pollution prevention

Pollution prevention is modelled with an approach that combines the substitutability of inputs in the twice-differentiable neoclassical production function and the discreteness of linear activity analysis. The polluting firm's emissions, which result from its use of a toxic input, can be reduced by substituting other inputs for the toxic input and&2.urule;or by switching to a nonpolluting process. The strengths of the model are that zero emissions are achievable at a finite marginal cost, the nonconvexity that may occur in conventional activity analysis does not occur in this model, and there is a range of output levels at which polluting and nonpolluting firms in the same industry realistically coexist.     

Direct measurement of transverse coherence length of hard X rays from interference fringes

We propose a simple interferometric technique for hard x-ray spatial coherence characterization, recording a Fresnel interference pattern produced by a round fiber or a slit. We have derived analytical formulas that give a direct relation between a visibility of interference fringes and either the source size or the transverse coherence length. The technique is well suited to third-generation synchrotron radiation sources and was experimentally applied to determine the spatial coherence length and the source size at the European Synchrotron Radiation Facility.     

X-ray standing wave analysis of the effect of isotopic composition on the lattice constants of Si and Ge

The x-ray standing wave (XSW) technique is used to measure the isotopic mass dependence of the lattice constants of Si and Ge. Backreflection allows substrates of moderate crystallinity to be used while high order reflection yields high accuracy. The XSW, generated by the substrate, serves as a reference for the lattice planes of an epilayer of different isotopic composition. Employing XSW and photoemission, the position of the surface planes is determined from which the lattice constant difference Deltaa is calculated. Scaled to DeltaM = 1 amu we find (Deltaa/a) of -0.36x10(-5) and -0.88x10(-5) for Ge and -1.8x10(-5) and -3.0x10(-5) for Si at 300 and 30 K, respectively.     

Wrinkles as the Result of Compressive Stresses in an Annular Thin Film

It is well‐known that an elastic sheet loaded in tension will wrinkle and that the length scale of the wrinkles tends to 0 with vanishing thickness of the sheet [Cerda and Mahadevan, Phys. Rev. Lett. 90, 074302 (2003)]. We give the first mathematically rigorous analysis of such a problem. Since our methods require an explicit understanding of the underlying (convex) relaxed problem, we focus on the wrinkling of an annular sheet loaded in the radial direction [Davidovitch et al., Proc. Natl. Acad. Sci. 108 (2011), 18227]. Our main achievement is identification of the scaling law of the minimum energy as the thickness of the sheet tends to 0. This requires proving an upper bound and a lower bound that scale the same way. We prove both bounds first in a simplified Kirchhoff‐Love setting and then in the nonlinear three‐dimensional setting. To obtain the optimal upper bound, we need to adjust a naive construction (one family of wrinkles superimposed on a planar deformation) by introducing a cascade of wrinkles. The lower bound is more subtle, since it must be ansatz‐free. © 2014 Wiley Periodicals, Inc.     

Transmission of an X‐ray beam through a two‐dimensional photonic crystal and the Talbot effect

Results of computer simulations of the transmission of an X‐ray beam through a two‐dimensional photonic crystal as well as the propagation of an X‐ray beam in free space behind the photonic crystal are reported. The photonic crystal consists of a square lattice of silicon cylinders of diameter 0.5 µm. The amount of matter in the path of the X‐ray beam rapidly decreases at the sides of the cylinder projections. Therefore the transmission is localized near the boundaries, and appears like a channeling effect. The iterative method of computer simulations is applied. This method is similar to the multi‐slice method that is widely used in electron microscopy. It allows a solution to be obtained with acceptable accuracy. A peculiarity in the intensity distribution inside the Talbot period z_T in free space was found when the intensity is approximately equal to the initial value at a distance 0.46z_T, and it is shifted by half a period at distance 0.5z_T. The reason for this effect is the existence of a periodic phase of the wavefunction of radiation inside the intensity peaks. Simulations with zero phase do not show this effect. Symmetry rules for the Talbot effect are discussed.     

Computational study of ground-state properties of μ2-bridged group 14 porphyrinic sandwich complexes

The structural properties of μ₂-bridged porphyrinic double-decker complexes are investigated and the influence of various ligands, metals, substituents, and bridging atoms on the dominant structural motif is elucidated. A variety of quantum chemical methods including semiempirical (SQM) methods and density functional theory (DFT) is assessed for the calculation of ecliptic and staggered conformational energies. Local coupled cluster (DLPNO-CCSD(T1)) data are generated for reference. The r²SCAN-3c composite scheme as well as the B2PLYP-D4/def2-QZVPP approach are identified as reliable methods. Energy decomposition analyses (EDA) and localized molecular orbital analyses (LMO) are used to investigate the bonding situation and the nature of the inter-ligand interaction energy underlining the crucial role of attractive London dispersion interactions. Targeted modification of the bridging atom, e.g., by replacing O²⁻ by S²⁻ is shown to drastically change the major structural features of the investigated complexes. Further, the influence of different substituents of varying size at the phthalocyanine ligand regarding the dominant conformation is described.