On classification of discrete, scalar-valued Poisson Brackets

We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on target space of dimension 1. It is proved that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be reduced to cubic PB of standard Volterra lattice by discrete Miura-type transformations. Finally, improving a consolidation lattice procedure, we obtain new families of non-degenerate, vector-valued and first order dDGPBs, which can be considered in the framework of admissible Lie-Poisson group theory.Comment: 24 page

Submesoscale physicochemical dynamics directly shape bacterioplankton community structure in space and time

Submesoscale eddies and fronts are important components of oceanic mixing and energy fluxes. These phenomena occur in the surface ocean for a period of several days, on scales between a few hundred meters and few tens of kilometers. Remote sensing and modeling suggest that eddies and fronts may influence marine ecosystem dynamics, but their limited temporal and spatial scales make them challenging for observation and in situ sampling. Here, the study of a submesoscale filament in summerly Arctic waters (depth 0–400 m) revealed enhanced mixing of Polar and Atlantic water masses, resulting in a ca. 4 km wide and ca. 50 km long filament with distinct physical and biogeochemical characteristics. Compared to the surrounding waters, the filament was characterized by a distinct phytoplankton bloom, associated with depleted inorganic nutrients, elevated chlorophyll a concentrations, as well as twofold higher phyto- and bacterioplankton cell abundances. High-throughput 16S rRNA gene sequencing of bacterioplankton communities revealed enrichment of typical phytoplankton bloom-associated taxonomic groups (e.g., Flavobacteriales) inside the filament. Furthermore, linked to the strong water subduction, the vertical export of organic matter to 400 m depth inside the filament was twofold higher compared to the surrounding waters. Altogether, our results show that physical submesoscale mixing can shape distinct biogeochemical conditions and microbial communities within a few kilometers of the ocean. Hence, the role of submesoscale features in polar waters for surface ocean biodiversity and biogeochemical processes need further investigation, especially with regard to the fate of sea ice in the warming Arctic Ocean

Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries

The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwiners associated with the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$ a three parameter family of auxiliary matrices is constructed. The elements of this family satisfy a functional relation with the transfer matrix allowing one to solve the eigenvalue problem of the model and to derive the Bethe ansatz equations. This functional relation is obtained from the decomposition of a tensor product of evaluation representations and involves auxiliary matrices with different parameters. Because of this dependence on additional parameters the auxiliary matrices break in general the finite symmetries of the six-vertex model, such as spin-reversal or spin conservation. More importantly, they also lift the extra degeneracies of the transfer matrix due to the loop symmetry present at rational coupling values. The extra parameters in the auxiliary matrices are shown to be directly related to the elements in the enlarged center of the quantum loop algebra $U_q(\tilde{sl}_2)$ at $q^N=1$. This connection provides a geometric interpretation of the enhanced symmetry of the six-vertex model at rational coupling. The parameters labelling the auxiliary matrices can be interpreted as coordinates on a three-dimensional complex hypersurface which remains invariant under the action of an infinite-dimensional group of analytic transformations, called the quantum coadjoint action.Comment: 52 pages, TCI LaTex, v2: equation (167) corrected, two references adde

Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion

It is well known that the long-range nature of the Coulomb interaction makes the definition of asymptotic ``in'' and ``out'' states of charged particles problematic in quantum field theory. In particular, the notion of a simple particle pole in the vacuum charged particle propagator is untenable and should be replaced by a more complicated branch cut structure describing an electron interacting with a possibly infinite number of soft photons. Previous work suggests a Dirac propagator raised to a fractional power dependent upon the fine structure constant, however the exponent has not been calculated in a unique gauge invariant manner. It has even been suggested that the fractal ``anomalous dimension'' can be removed by a gauge transformation. Here, a gauge invariant non-perturbative calculation will be discussed yielding an unambiguous fractional exponent. The closely analogous case of soft graviton exponents is also briefly explored.Comment: Updated with a corrected sign error, longer discussion of fractal dimension, and more reference

COMPETITIVE METHODS FOR CHALLENGE BETWEEN SHIPPING LINES IN CASE OF BUILDING AND PRFORMING SEA SHIPPING CONTAINER LINES

There was competition between world alliances for many years. In this work we found historical economic aspects of competition of international container shipping lines and possibilities to enter the world container market for new entities

COMPETITIVE METHODS FOR CHALLENGE BETWEEN SHIPPING LINES IN CASE OF BUILDING AND PRFORMING SEA SHIPPING CONTAINER LINES

There was competition between world alliances for many years. In this work we found historical economic aspects of competition of international container shipping lines and possibilities to enter the world container market for new entities

Deformed dimensional regularization for odd (and even) dimensional theories

I formulate a deformation of the dimensional-regularization technique that is useful for theories where the common dimensional regularization does not apply. The Dirac algebra is not dimensionally continued, to avoid inconsistencies with the trace of an odd product of gamma matrices in odd dimensions. The regularization is completed with an evanescent higher-derivative deformation, which proves to be efficient in practical computations. This technique is particularly convenient in three dimensions for Chern-Simons gauge fields, two-component fermions and four-fermion models in the large N limit, eventually coupled with quantum gravity. Differently from even dimensions, in odd dimensions it is not always possible to have propagators with fully Lorentz invariant denominators. The main features of the deformed technique are illustrated in a set of sample calculations. The regularization is universal, local, manifestly gauge-invariant and Lorentz invariant in the physical sector of spacetime. In flat space power-like divergences are set to zero by default. Infinitely many evanescent operators are automatically dropped.Comment: 27 pages, 3 figures; v2: expanded presentation of some arguments, IJMP