Chapter 3 Translation invariance in data envelopment analysis: A generalization

In this paper, we undertake a revision and a generalization of the results contained in the only paper so far published on the matter of translation invariance by allowing inputs and outputs to take not only zero but negative values. This broadens the field of application of the DEA methodology.     

Equivalent dose distribution analysis of Holocene eolian and fluvial quartz sands from Central Oklahoma

Holocene quartz sands were collected from fluvial terrace deposits and eolian dune deposits adjacent to the North Canadian and Cimarron Rivers and their tributaries in Central Oklahoma. Single aliquot regenerative dose optically stimulated luminescence techniques were employed to generate equivalent dose (ED) distribution histograms for each sample. We hypothesize that the ED distributions are convolutions of the distribution arising from natural sedimentary processes, influenced primarily by the degree of solar resetting experienced by individual grains, and a distribution due to experimental error. An estimation of the experimental error distribution for each sample was made and this was then deconvolved from the experimentally measured ED distribution to reveal the ‘sedimentary process’ ED distribution. Objective methods for determining EDs, uncertainties, and confidence parameters from the deconvolved distributions are presented.     

Radiation efficiency of a guitar top plate linked with edge or corner modes and intercell cancellation

This paper was based on a theoretical framework to determine strong and weak radiation by a guitar top plate, vibrating through deflections hard to analyze: multipolar mode shapes. The air-structure interaction was examined in terms of edge modes or corner modes, and considering even or odd number modes. A numerical model was implemented and experimentally calibrated, exhibiting several advantages exploring the coupling between vibratory and acoustic waves in a top plate. Two analyses were applied detecting high or low radiation efficiency for the structure. First, the addition of volume velocity for odd numbers of poles and cancellation for even numbers were examined. In fact, both behaviors can happen at the same time, as it was shown for a corner radiator case used as an example. Second, the ratio between bending and acoustic wavenumbers was explored. To illustrate the importance of this ratio, some theoretical features of a more efficient radiator than the corner mode were exposed in an edge mode example. Labeling multipolar mode shapes as efficient or inefficient radiators showed to be a useful alternative analyzing the top plate behavior. It can be applied knowing the nodal lines of the vibration pattern and estimating the bending and acoustic wavelengths.     

Large circular dichroism and optical rotation in titanium doped chiral silver nanorods

The circular dichroism of titanium‐doped silver chiral nanorod arrays grown using the glancing angle deposition (GLAD) method is investigated in the visible and near infrared ranges using transmission ellipsometry and spectroscopy. These films are found to have significant circular polarization effects across broad ranges of the visible to NIR spectrum, including large values for optical rotation. The characteristics of these circular polarization effects are strongly influenced by the morphology of the deposited arrays. Thus, the morphological control of the optical activity in these nanostructures demonstrates significant optimization capability of the GLAD technique for fabricating chiral plasmonic materials.

     

Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

We prove that theq-state Potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) wheneverq>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay forq7), triangular lattice (q11), hexagonal lattice (q4), and Kagomé lattice (q6). The proofs are based on the Dobrushin uniqueness theorem.     

Dissipative-Hamiltonian decomposition of smooth vector fields based on symmetries

We propose a method to decompose a smooth vector field into conservative and dissipative components. The procedure is based on the identification of the kernel of a linear operator associated with a given Hamiltonian combined with the use of Lie transformations for vector fields. Moreover, under certain conditions the nonconservative part of the splitting can be dropped at a given order of the transformation, obtaining after truncation, a Hamilton vector field. The technique is illustrated through the application to the motion of a particle subject to the potential of a champagne bottle plus a small friction.