Products of multisymplectic manifolds and homotopy moment maps

Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an L-infinity-embedding of the L-infinity-algebra of observables of the individual factors into the observables of the product, and that homotopy moment maps for the individual factors induce a homotopy moment map for the product. As a by-product, we associate to every multisymplectic form a curved L-infinity-algebra, whose curvature is the multisymplectic form itself.Comment: 27 pages. Version to be published in Journal of Lie Theor

Spin(7)-manifolds in compactifications to four dimensions

We describe off-shell $\mathcal{N}=1$ M-theory compactifications down to four dimensions in terms of eight-dimensional manifolds equipped with a topological $Spin(7)$-structure. Motivated by the exceptionally generalized geometry formulation of M-theory compactifications, we consider an eight-dimensional manifold $\mathcal{M}_{8}$ equipped with a particular set of tensors $\mathfrak{S}$ that allow to naturally embed in $\mathcal{M}_{8}$ a family of $G_{2}$-structure seven-dimensional manifolds as the leaves of a codimension-one foliation. Under a different set of assumptions, $\mathfrak{S}$ allows to make $\mathcal{M}_{8}$ into a principal $S^{1}$ bundle, which is equipped with a topological $Spin(7)$-structure if the base is equipped with a topological $G_{2}$-structure. We also show that $\mathfrak{S}$ can be naturally used to describe regular as well as a singular elliptic fibrations on $\mathcal{M}_{8}$, which may be relevant for F-theory applications, and prove several mathematical results concerning the relation between topological $G_{2}$-structures in seven dimensions and topological $Spin(7)$-structures in eight dimensions.Comment: 50 pages. We have included Proposition 6.4 about elliptic fibrations in relation to a pair of vector fields. We have also included Remark 5.13, thanks to an internal communication by Dominic Joyce. Discussion about the relation of singular foliations and D7-branes include

Adding integrable defects to the Boussinesq equation

The purpose of this paper is to extend the store of models able to support integrable defects by investigating the two-dimensional Boussinesq nonlinear wave equation. As has been previously noted in many examples, insisting that a defect contributes to energy and momentum to ensure their conservation, despite the presence of discontinuities and the explicit breaking of translation invariance, leads to sewing conditions relating the two fields and their derivatives on either side of the defect. The manner in which several types of soliton solutions to the Boussinesq equation are affected by the defect is explored and reveals new effects that have not been observed in other integrable systems, such as the possibility of a soliton reflecting from a defect or of a defect decaying into one or two solitons.Comment: 28 pages, 9 figure

Type II defects revisited

Energy and momentum conservation in the context of a type II, purely transmitting, defect, within a single scalar relativistic two-dimensional field theory, places a severe constraint not only on the nature of the defect but also on the potentials for the scalar fields to either side of it. The constraint is of an unfamiliar type since it requires the Poisson Bracket of the defect contributions to energy and momentum with respect to the defect discontinuity and its conjugate to be balanced by the potential difference across the defect. It is shown that the only solutions to the constraint correspond to the known integrable field theories

Integrable defects at junctions within a network

The purpose of this article is to explore the properties of integrable, purely transmitting, defects placed at the junctions of several one-dimensional domains within a network. The defect sewing conditions turn out to be quite restrictive—for example, requiring the number of domains meeting at a junction to be even—and there is a clear distinction between the behaviour of conformal and massive integrable models. The ideas are mainly developed within classical field theory and illustrated using a variety of field theory models defined on the branches of the network, including both linear and nonlinear examples

A novel protocol for the one-pot borylation/Suzuki reaction provides easy access to hinge-binding groups for kinase inhibitors

The one-pot borylation/Suzuki reaction is a very efficient means of accessing cross-coupling products of two aryl-halide partners that generally requires the use of specific catalysts or ligands and/or relatively long reaction times. This new microwave-assisted method provides a quick one-pot borylation/Suzuki reaction protocol that we applied to the synthesis of various bi- or poly-aryl scaffolds, including a variety of aryl and heteroaryl ring systems and the core frameworks of kinase inhibitors vemurafenib and GDC-0879

Tropical to extratropical : marine environmental changes associated with Superstorm Sandy prior to its landfall

Author Posting. © American Geophysical Union, 2014. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geophysical Research Letters 41 (2014): 8935–8943, doi:10.1002/2014GL061357.Superstorm Sandy was a massive storm that impacted the U.S. East Coast on 22–31 October 2012, generating large waves, record storm surges, and major damage. The Coupled Ocean-Atmosphere-Wave-Sediment Transport modeling system was applied to hindcast this storm. Sensitivity experiments with increasing complexity of air-sea-wave coupling were used to depict characteristics of this immense storm as it underwent tropical to extratropical transition. Regardless of coupling complexity, model-simulated tracks were all similar to the observations, suggesting the storm track was largely determined by large-scale synoptic atmospheric circulation, rather than by local processes resolved through model coupling. Analyses of the sea surface temperature, ocean heat content, and upper atmospheric shear parameters showed that as a result of the extratropical transition and despite the storm encountering much cooler shelf water, its intensity and strength were not significantly impacted. Ocean coupling was not as important as originally thought for Sandy.Research support provided by USGS Coastal Process Project, NOAA grant NA11NOS0120033, and NASA grant NNX13AD80G is much appreciated.2015-06-1

Nonadiabatic effects in the dynamics of atoms confined in a cylindric time-orbiting-potential magnetic trap

In a time-orbiting-potential magnetic trap the neutral atoms are confined by means of an inhomogeneous magnetic field superimposed to an uniform rotating one. We perform an analytic study of the atomic motion by taking into account the nonadiabatic effects arising from the spin dynamics about the local magnetic field. Geometric-like magnetic-fields determined by the Berry's phase appear within the quantum description. The application of a variational procedure on the original quantum equation leads to a set of dynamical evolution equations for the quantum average value of the position operator and of the spin variables. Within this approximation we derive the quantum-mechanical ground state configuration matching the classical adiabatic solution and perform some numerical simulations.Comment: 12 pages, 4 figure

Anwendung des Penetrationsmodells von Chlorid bei der Beurteilung des Zustands beim Brückenmanagement

Although there is a large number of established Bridge Management Systems worldwide, there seems to be a lack of those that utilise the knowledge on material properties and environmental loading. Hence, as a supplement to current practice, the paper examines the use of the chloride ingress model, supported by the International Federation for Structural Concrete, for preliminary assessment in bridge management. The focus is set on analysing application of the model in realistic situations on existing concrete bridges for which the information on material and environmental properties is lacking.Iako se danas diljem svijeta primjenjuju brojni sustavi za gospodarenje mostovima, čini se da ipak nema dovoljno sustava u kojima bi se koristilo znanje o svojstvima materijala i opterećenju iz okoliša. U ovom se radu, kao doprinos sadašnjoj praksi, analizira primjena modela prodora klorida, što podržava Međunarodni savez za betonske konstrukcije, a koristi se za preliminarno ocjenjivanje u okviru gospodarenja mostovima. Prije svega, analizira se primjena modela u realnim situacijama za ocjenu postojećih betonskih mostova za koje ne postoje podaci o materijalima i svojstvima okoliša.Obwohl heute weltweit zahlreiche Brückenmanagementsysteme angewendet werden, scheint es jedoch nicht ausreichend Systeme zu geben, in denen die Kenntnisse über die Materialeigenschaften und die Umweltbelastung angewendet werden. In dieser Abhandlung wird als Beitrag zur aktuellen Praxis die Anwendung des Penetrationsmodells von Chlorid analysiert, was vom Internationalen Verband für Betonkonstruktionen unterstützt wird, und wird als vorläufige Beurteilung im Rahmen des Brückenmanagements angewendet. Zunächst wird die Anwendung des Modells unter realen Bedingungen für die Beurteilung der bestehenden Betonbrücken analysiert, zu denen Daten über die Materialien und die Umwelteigenschaften vorliegen.The authors would like to show their gratitude for the support received during the project “Life – Cycle Assessment for Railway Structures”, funded by the ÖBB-Infrastruktur Bau AG, Vienna. For the support in the analysis of existing standards, authors would like to express special appreciation to Smart Minerals GmbH