The Stability of Orthotropic Elliptic Cylinders in Pure Bending

The theoretical critical bending stress of elliptic cylindrical shells is determined on the assumption of infinite shell length and absence of local instability phenomena. The results of the tests on isotropic elliptic cylindrical shells stressed in bending are compared with the theoretical results. The practical applicability of the theory is discussed

Methods and formulas for calculating the strength of plate and shell constructions as used in airplane design

This report is a compilation of previously published articles on formulas and methods of calculation for the determination of the strength and stability of plate and shell construction as employed in airplane design. In particular, it treats the problem of isotropic, orthotopic, and stiffened rectangular plates, thin curved panels, and circular cylinders under various loading conditions. The purpose of appending the pertinent literature references following the subjects discussed was to facilitate a comprehensive study of the treated problems

Vacuum stability and the Cholesky decomposition

We discuss how the Cholesky decomposition may be used to ascertain whether a critical point of the field theory scalar potential provides a stable vacuum configuration. We then use this method to derive the stability conditions in a specific example.Comment: 7 page

How do nutrient conditions and species identity influence the impact of mesograzers in eelgrass-epiphyte systems?

Coastal eutrophication is thought to cause excessive growth of epiphytes in eelgrass beds, threatening the health and survival of these ecologically and economically valuable ecosystems worldwide. Mesograzers, small crustacean and gastropod grazers, have the potential to prevent seagrass loss by grazing preferentially and efficiently on epiphytes. We tested the impact of three mesograzers on epiphyte biomass and eelgrass productivity under threefold enriched nutrient concentrations in experimental indoor mesocosm systems under summer conditions. We compared the results with earlier identical experiments that were performed under ambient nutrient supply. The isopod Idotea baltica, the periwinkle Littorina littorea, and the small gastropod Rissoa membranacea significantly reduced epiphyte load under high nutrient supply with Rissoa being the most efficient grazer, but only high densities of Littorina and Rissoa had a significant positive effect on eelgrass productivity. Although all mesograzers increased epiphyte ingestion with higher nutrient load, most likely as a functional response to the quantitatively and qualitatively better food supply, the promotion of eelgrass growth by Idotea and Rissoa was diminished compared to the study performed under ambient nutrient supply. Littorina maintained the level of its positive impact on eelgrass productivity regardless of nutrient concentrations

Explorations of the Extended ncKP Hierarchy

A recently obtained extension (xncKP) of the Moyal-deformed KP hierarchy (ncKP hierarchy) by a set of evolution equations in the Moyal-deformation parameters is further explored. Formulae are derived to compute these equations efficiently. Reductions of the xncKP hierarchy are treated, in particular to the extended ncKdV and ncBoussinesq hierarchies. Furthermore, a good part of the Sato formalism for the KP hierarchy is carried over to the generalized framework. In particular, the well-known bilinear identity theorem for the KP hierarchy, expressed in terms of the (formal) Baker-Akhiezer function, extends to the xncKP hierarchy. Moreover, it is demonstrated that N-soliton solutions of the ncKP equation are also solutions of the first few deformation equations. This is shown to be related to the existence of certain families of algebraic identities.Comment: 34 pages, correction of typos in (7.2) and (7.5

Evolution of the cosmic ray anisotropy above 10^{14} eV

The amplitude and phase of the cosmic ray anisotropy are well established experimentally between 10^{11} eV and 10^{14} eV. The study of their evolution into the energy region 10^{14}-10^{16} eV can provide a significant tool for the understanding of the steepening ("knee") of the primary spectrum. In this letter we extend the EAS-TOP measurement performed at E_0 around 10^{14} eV, to higher energies by using the full data set (8 years of data taking). Results derived at about 10^{14} and 4x10^{14} eV are compared and discussed. Hints of increasing amplitude and change of phase above 10^{14} eV are reported. The significance of the observation for the understanding of cosmic ray propagation is discussed.Comment: 4 pages, 3 figures, accepted for publication on ApJ Letter

A new approach to deformation equations of noncommutative KP hierarchies

Partly inspired by Sato's theory of the Kadomtsev-Petviashvili (KP) hierarchy, we start with a quite general hierarchy of linear ordinary differential equations in a space of matrices and derive from it a matrix Riccati hierarchy. The latter is then shown to exhibit an underlying 'weakly nonassociative' (WNA) algebra structure, from which we can conclude, refering to previous work, that any solution of the Riccati system also solves the potential KP hierarchy (in the corresponding matrix algebra). We then turn to the case where the components of the matrices are multiplied using a (generalized) star product. Associated with the deformation parameters, there are additional symmetries (flow equations) which enlarge the respective KP hierarchy. They have a compact formulation in terms of the WNA structure. We also present a formulation of the KP hierarchy equations themselves as deformation flow equations.Comment: 25 page