Lie algebroid structures on a class of affine bundles

We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the theory of Lagrangian systems on Lie algebroids. An extensive discussion is given of a way one can think of forms acting on sections of the affine bundle. It is further shown that the affine Lie algebroid structure gives rise to a coboundary operator on such forms. The concept of admissible curves and dynamical systems whose integral curves are admissible, brings an associated affine bundle into the picture, on which one can define in a natural way a prolongation of the original affine Lie algebroid structure.Comment: 28 page

Driven cofactor systems and Hamilton-Jacobi separability

This is a continuation of the work initiated in a previous paper on so-called driven cofactor systems, which are partially decoupling second-order differential equations of a special kind. The main purpose in that paper was to obtain an intrinsic, geometrical characterization of such systems, and to explain the basic underlying concepts in a brief note. In the present paper we address the more intricate part of the theory. It involves in the first place understanding all details of an algorithmic construction of quadratic integrals and their involutivity. It secondly requires explaining the subtle way in which suitably constructed canonical transformations reduce the Hamilton-Jacobi problem of the (a priori time-dependent) driven part of the system into that of an equivalent autonomous system of St\"ackel type

Algebraic theories of brackets and related (co)homologies

A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.Comment: 14 pages; v2: minor correction

Tetrad gravity, electroweak geometry and conformal symmetry

A partly original description of gauge fields and electroweak geometry is proposed. A discussion of the breaking of conformal symmetry and the nature of the dilaton in the proposed setting indicates that such questions cannot be definitely answered in the context of electroweak geometry.Comment: 21 pages - accepted by International Journal of Geometric Methods in Modern Physics - v2: some minor changes, mostly corrections of misprint

Many parameter Hoelder perturbation of unbounded operators

If $u\mapsto A(u)$ is a $C^{0,\alpha}$-mapping, for $0< \alpha \le 1$, having as values unbounded self-adjoint operators with compact resolvents and common domain of definition, parametrized by $u$ in an (even infinite dimensional) space, then any continuous (in $u$) arrangement of the eigenvalues of $A(u)$ is indeed $C^{0,\alpha}$ in $u$.Comment: LaTeX, 4 pages; The result is generalized from Lipschitz to Hoelder. Title change

Local Drivers of Marine Heatwaves: A Global Analysis With an Earth System Model

Marine heatwaves (MHWs) are periods of extreme warm ocean temperatures that can have devastating impacts on marine organisms and socio-economic systems. Despite recent advances in understanding the underlying processes of individual events, a global view of the local oceanic and atmospheric drivers of MHWs is currently missing. Here, we use daily-mean output of temperature tendency terms from a comprehensive fully coupled coarse-resolution Earth system model to quantify the main local processes leading to the onset and decline of surface MHWs in different seasons. The onset of MHWs in the subtropics and mid-to-high latitudes is primarily driven by net ocean heat uptake associated with a reduction of latent heat loss in all seasons, increased shortwave heat absorption in summer and reduced sensible heat loss in winter, dampened by reduced vertical mixing from the non-local portion of the K-Profile Parameterization boundary layer scheme (KPP) especially in summer. In the tropics, ocean heat uptake is reduced and lowered vertical local mixing and diffusion cause the warming. In the subsequent decline phase, increased ocean heat loss to the atmosphere due to enhanced latent heat loss in all seasons together with enhanced vertical local mixing and diffusion in the high latitudes during summer dominate the temperature decrease globally. The processes leading to the onset and decline of MHWs are similar for short and long MHWs, but there are differences in the drivers between summer and winter. Different types of MHWs with distinct driver combinations are identified within the large variability among events. Our analysis contributes to a better understanding of MHW drivers and processes and may therefore help to improve the prediction of high-impact marine heatwaves

The Stratified Structure of Spaces of Smooth Orbifold Mappings

We consider four notions of maps between smooth C^r orbifolds O, P with O compact (without boundary). We show that one of these notions is natural and necessary in order to uniquely define the notion of orbibundle pullback. For the notion of complete orbifold map, we show that the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) manifold. For the notion of complete reduced orbifold map, the corresponding set of C^r maps between O and P with the C^r topology carries the structure of a smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifold. The remaining two notions carry a stratified structure: The C^r orbifold maps between O and P is locally a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) manifolds while the set of C^r reduced orbifold maps between O and P locally has the structure of a stratified space with strata modeled on smooth C^\infty Banach (r finite)/Frechet (r=infty) orbifolds. Furthermore, we give the explicit relationship between these notions of orbifold map. Applying our results to the special case of orbifold diffeomorphism groups, we show they inherit the structure of C^\infty Banach (r finite)/Frechet (r=infty) manifolds. In fact, for r finite they are topological groups, and for r=infty they are convenient Frechet Lie groups.Comment: 31 pages, 2 figures; corrected and expande

Impact of deoxygenation and warming on global marine species in the 21st century

Ocean temperature and dissolved oxygen shape marine habitats in an interplay with species' physiological characteristics. Therefore, the observed and projected warming and deoxygenation of the world's oceans in the 21st century may strongly affect species' habitats. Here, we implement an extended version of the Aerobic Growth Index (AGI), which quantifies whether a viable population of a species can be sustained in a particular location. We assess the impact of projected deoxygenation and warming on the contemporary habitat of 47 representative marine species covering the epipelagic, mesopelagic, and demersal realms. AGI is calculated for these species for the historical period and into the 21st century using bias-corrected environmental data from six comprehensive Earth system models. While habitat viability decreases nearly everywhere with global warming, the impact of this decrease is strongly species dependent. Most species lose less than 5 % of their contemporary habitat volume at 2 ∘C of global warming relative to preindustrial levels, although some individual species are projected to incur losses 2–3 times greater than that. We find that the in-habitat spatiotemporal variability of O2 and temperature (and hence AGI) provides a quantifiable measure of a species' vulnerability to change. In the event of potential large habitat losses (over 5 %), species vulnerability is the most important indicator. Vulnerability is more critical than changes in habitat viability, temperature, or pO2 levels. Loss of contemporary habitat is for most epipelagic species driven by the warming of ocean water and is therefore elevated with increased levels of global warming. In the mesopelagic and demersal realms, habitat loss is also affected by pO2 decrease for some species. Our analysis is constrained by the uncertainties involved in species-specific critical thresholds, which we quantify; by data limitations on 3D species distributions; and by high uncertainty in model O2 projections in equatorial regions. A focus on these topics in future research will strengthen our confidence in assessing climate-change-driven losses of contemporary habitats across the global oceans.</p

Concurrent π\pi-vector fields and energy beta-change

The present paper deals with an \emph{intrinsic} investigation of the notion of a concurrent $\pi$-vector field on the pullback bundle of a Finsler manifold $(M,L)$. The effect of the existence of a concurrent $\pi$-vector field on some important special Finsler spaces is studied. An intrinsic investigation of a particular $\beta$-change, namely the energy $\beta$-change ($\widetilde{L}^{2}(x,y)=L^{2}(x,y)+ B^{2}(x,y) with \ B:=g(\bar{\zeta},\bar{\eta})$;$\bar{\zeta} $being a concurrent$\pi$-vector field), is established. The relation between the two Barthel connections$\Gamma$and$\widetilde{\Gamma}$, corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy$\beta$-change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is concluded. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.Comment: 27 pages, LaTex file, Some typographical errors corrected, Some formulas simpifie