Splitting Polytopes

A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to the splits of $P$ (with a split prime remainder). This generalizes a result of Bandelt and Dress [Adv. Math. 92 (1992)] on the decomposition of finite metric spaces. Introducing the concept of compatibility of splits gives rise to a finite simplicial complex associated with any polytope $P$, the split complex of $P$. Complete descriptions of the split complexes of all hypersimplices are obtained. Moreover, it is shown that these complexes arise as subcomplexes of the tropical (pre-)Grassmannians of Speyer and Sturmfels [Adv. Geom. 4 (2004)].Comment: 25 pages, 7 figures; minor corrections and change

Correlation of circular differential optical absorption with geometric chirality in plasmonic meta-atoms

We report a strong correlation between the calculated broadband circular differential optical absorption (CDOA) and the geometric chirality of plasmonic meta-atoms with two-dimensional chirality. We investigate this correlation using three common gold meta-atom geometries: L-shapes, triangles, and nanorod dimers, over a broad range of geometric parameters. We show that this correlation holds for both contiguous plasmonic meta-atoms and non-contiguous structures which support plasmonic coupling effects. A potential application for this correlation is the rapid optimization of plasmonic nanostructure for maximum broadband CDOA

The Regional Incidence of European Agricultural Policy: Measurement Concept and Empirical Evidence

Agricultural and Food Policy,

Markets Segmented by Regional - Origin Labeling with Quality Control

It is the objective of this paper to provide a methodological framework for the analysis of regional marketing programs which include regional-origin labeling as well as quality assurance and control. Such programs are increasingly introduced in Europe and other parts of the world as a means against quality uncertainty in globalized markets. An equilibrium - displacement model is developed for a segmented market with differential qualities that can be utilized for a broad variety of marketing programs. It is applied to one selected European case, i.e. "Gepruefte Qualitaet - Bayern". It is shown that the price impacts on high-quality and low-quality segments depend crucially on substitutive relationships between the markets and the advertising elasticities. Welfare implications for producers in a program depend strongly on advertising elasticities, too, but also on the costs of participation including quality control and on the co-financing mechanism between government and producers.regional-origin labeling, segmented markets, generic promotion, Gepruefte Qualitaet - Bayern, economic welfare, Marketing,

Regional-Origin Labeling with Quality Control: An Economic Analysis

Marketing,

Natural conditions in agriculture and the regional distribution of EU producer support

The redistributive implications of the Common Agricultural Policy (CAP) of the European Union (EU) have regained a strong interest in recent years since economic and social cohe-sion has become a major goal of European policy. The empirical evidence is surprisingly di-verse and ranges from a clearly positive to a clearly negative regional redistributive impact of the CAP. Therefore, the objectives of this paper are threefold. First, the interregional alloca-tion of EU producer support under the CAP is measured at the NUTS III-level in the period 1986-2002 for 26 regions of the German Bundesland Hesse. Second, the role of the measure-ment concept for the magnitude and distribution of the regional transfers is elaborated. Third, the interregional allocation of EU producer support is explained by natural conditions and farm structure variables within a quantitative analysis. A major result is that the interregional allocation of producer support is unequal, depends on the measure of protection used and is affected by a number of variables characterizing farm structure and natural conditions

Atom Interferometry with up to 24-Photon-Momentum-Transfer Beam Splitters

We present up to 24-photon Bragg diffraction as a beam splitter in light-pulse atom interferometers to achieve the largest splitting in momentum space so far. Relative to the 2-photon processes used in the most sensitive present interferometers, these large momentum transfer beam splitters increase the phase shift 12-fold for Mach-Zehnder (MZ-) and 144-fold for Ramsey-Borde (RB-) geometries. We achieve a high visibility of the interference fringes (up to 52% for MZ or 36% for RB) and long pulse separation times that are possible only in atomic fountain setups. As the atom's internal state is not changed, important systematic effects can cancel.Comment: New introduction. 4 pages, 4 figure

Trees, Tight-Spans and Point Configuration

Tight-spans of metrics were first introduced by Isbell in 1964 and rediscovered and studied by others, most notably by Dress, who gave them this name. Subsequently, it was found that tight-spans could be defined for more general maps, such as directed metrics and distances, and more recently for diversities. In this paper, we show that all of these tight-spans as well as some related constructions can be defined in terms of point configurations. This provides a useful way in which to study these objects in a unified and systematic way. We also show that by using point configurations we can recover results concerning one-dimensional tight-spans for all of the maps we consider, as well as extend these and other results to more general maps such as symmetric and unsymmetric maps.Comment: 21 pages, 2 figure

On the mechanisms of ionic conductivity in BaLiF3: A molecular dynamics study

The mechanisms of ionic conductivity in BaLiF3 are investigated using molecular simulations. Direct molecular dynamics simulations of (quasi) single crystalline super cell models hint at the preferred mobility mechanism which is based on fluoride interstitial (and to a smaller extent F- vacancy) migration. Analogous to previous modeling studies, the energy related to Frenkel defect formation in the ideal BaLiF3 crystal was found as 4-5 eV which is in serious controversy to the experimentally observed activation barrier to ionic conductivity of only 1 eV. However, this controversy could be resolved by incorporating Ba2+ ↔ Li+ exchange defects into the elsewise single crystalline model systems. Indeed, in the neighborhood of such cation exchange defects the F- Frenkel defect formation energy was identified to reduce to 1.3 eV whilst the cation exchange defect itself is related to a formation energy of 1.0 eV. Thus, our simulations hint at the importance of multiple defect scenarios for the ionic conductivity in BaLiF3. © 2011 the Owner Societies