Modular classes of skew algebroid relations

Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous nowhere-vanishing 1-density on E* which is invariant with respect to all Hamiltonian vector fields if and only if E is modular, i.e. mod(E)=0. Further, relative modular class of a subalgebroid is introduced and studied together with its application to holonomy, as well as modular class of a skew algebroid relation. These notions provide, in particular, a unified approach to the concepts of a modular class of a Lie algebroid morphism and that of a Poisson map.Comment: 20 page

Double Field Theory Formulation of Heterotic Strings

We extend the recently constructed double field theory formulation of the low-energy theory of the closed bosonic string to the heterotic string. The action can be written in terms of a generalized metric that is a covariant tensor under O(D,D+n), where n denotes the number of gauge vectors, and n additional coordinates are introduced together with a covariant constraint that locally removes these new coordinates. For the abelian subsector, the action takes the same structural form as for the bosonic string, but based on the enlarged generalized metric, thereby featuring a global O(D,D+n) symmetry. After turning on non-abelian gauge couplings, this global symmetry is broken, but the action can still be written in a fully O(D,D+n) covariant fashion, in analogy to similar constructions in gauged supergravities.Comment: 28 pages, v2: minor changes, version published in JHE

D-branes in Generalized Geometry and Dirac-Born-Infeld Action

The purpose of this paper is to formulate the Dirac-Born-Infeld (DBI) action in a framework of generalized geometry and clarify its symmetry. A D-brane is defined as a Dirac structure where scalar fields and gauge field are treated on an equal footing in a static gauge. We derive generalized Lie derivatives corresponding to the diffeomorphism and B-field gauge transformations and show that the DBI action is invariant under non-linearly realized symmetries for all types of diffeomorphisms and B-field gauge transformations. Consequently, we can interpret not only the scalar field but also the gauge field on the D-brane as the generalized Nambu-Goldstone boson.Comment: 32 pages, 4 figures, ver2:typos corrected, references adde

A Partitioned Finite Element Method for the Structure-Preserving Discretization of Damped Infinite-Dimensional Port-Hamiltonian Systems with Boundary Control

Many boundary controlled and observed Partial Differential Equations can be represented as port-Hamiltonian systems with dissipation, involving a Stokes-Dirac geometrical structure together with constitutive relations. The Partitioned Finite Element Method, introduced in Cardoso-Ribeiro et al. (2018), is a structure preserving numerical method which defines an underlying Dirac structure, and constitutive relations in weak form, leading to finite-dimensional port-Hamiltonian Differential Algebraic systems (pHDAE). Different types of dissipation are examined: internal damping, boundary damping and also diffusion models

Increasing the Depth of Current Understanding: Sensitivity Testing of Deep-Sea Larval Dispersal Models for Ecologists

Larval dispersal is an important ecological process of great interest to conservation and the establishment of marine protected areas. Increasing numbers of studies are turning to biophysical models to simulate dispersal patterns, including in the deep-sea, but for many ecologists unassisted by a physical oceanographer, a model can present as a black box. Sensitivity testing offers a means to test the models' abilities and limitations and is a starting point for all modelling efforts. The aim of this study is to illustrate a sensitivity testing process for the unassisted ecologist, through a deep-sea case study example, and demonstrate how sensitivity testing can be used to determine optimal model settings, assess model adequacy, and inform ecological interpretation of model outputs. Five input parameters are tested (timestep of particle simulator (TS), horizontal (HS) and vertical separation (VS) of release points, release frequency (RF), and temporal range (TR) of simulations) using a commonly employed pairing of models. The procedures used are relevant to all marine larval dispersal models. It is shown how the results of these tests can inform the future set up and interpretation of ecological studies in this area. For example, an optimal arrangement of release locations spanning a release area could be deduced; the increased depth range spanned in deep-sea studies may necessitate the stratification of dispersal simulations with different numbers of release locations at different depths; no fewer than 52 releases per year should be used unless biologically informed; three years of simulations chosen based on climatic extremes may provide results with 90% similarity to five years of simulation; and this model setup is not appropriate for simulating rare dispersal events. A step-by-step process, summarising advice on the sensitivity testing procedure, is provided to inform all future unassisted ecologists looking to run a larval dispersal simulation

Conservation Laws and Lumped System Dynamics

Physical systems modeling, aimed at network modeling of complex multi-physics systems, has especially flourished in the fifties and sixties of the 20-th century, see e.g. [11, 12] and references provided therein. With the reinforcement of the ’systems’ legacy in Systems & Control, the growing recognition that ’control’ is not confined to developing algorithms for processing the measurements of the system into control signals (but instead is concerned with the design of the total controlled system), and facing the complexity of modern technological and natural systems, systematic methods for physical systems modeling of large-scale lumpedand distributed-parameter systems capturing their basic physical characteristics are needed more than ever