Aubry-Mather measures in the non convex setting

The adjoint method, introduced in [L. C. Evans, Arch. Ration. Mech. Anal., 197 (2010), pp. 1053–1088] and [H. V. Tran, Calc. Var. Partial Differential Equations, 41 (2011), pp. 301–319], is used to construct analogues to the Aubry–Mather measures for nonconvex Hamiltonians. More precisely, a general construction of probability measures, which in the convex setting agree with Mather measures, is provided. These measures may fail to be invariant under the Hamiltonian flow and a dissipation arises, which is described by a positive semidefinite matrix of Borel measures. However, in the case of uniformly quasiconvex Hamiltonians the dissipation vanishes, and as a consequence the invariance is guaranteed. Copyright © 2011 Society for Industrial and Applied Mathematic

The rate of convergence of new Lax-Oleinik type operators for time-periodic positive definite Lagrangian systems

Assume that the Aubry set of the time-periodic positive definite Lagrangian $L$ consists of one hyperbolic 1-periodic orbit. We provide an upper bound estimate of the rate of convergence of the family of new Lax-Oleinik type operators associated with $L$ introduced by the authors in \cite{W-Y}. In addition, we construct an example where the Aubry set of a time-independent positive definite Lagrangian system consists of one hyperbolic periodic orbit and the rate of convergence of the Lax-Oleinik semigroup cannot be better than $O(\frac{1}{t})$

Meridional variations of the springtime phytoplankton community in the Sargasso Sea

Meridional distributions of particle, pigment, optical, chemical and physical in situ oceanographic properties, as well as satellite-sensed sea-surface temperature and color imagery, are used to investigate phytoplankton community distributions and their relation to the near-surface water masses of the S bnargasso Sea. 0-H3059 Measurements were made during April of 1985 along a 1200 km transect on 70W (from 24N to 35N). The seasonal evolution of subtropical Mode water (18° water) is shown to be the primary factor controlling the spatial distribution and evolution of the phytoplankton community in the northern Sargasso Sea (31 to 35N). The springtime near-surface restratification of recently ventilated 18° water initiated a diatom-dominated phytoplankton bloom. As the bloom declined, the phytoplankton community evolved into a diverse assemblage. The consequences of these phytoplankton successions were observed both temporally and as spatial variations along the meridional section. South of the region of 18° water wintertime ventilation (south of 31N), phytoplankton concentrations were considerably less and appeared to be regulated by different processes than the northern region. In particular, influences of subtropical convergence fronts were observed. For the northern Sargasso Sea, the wintertime ventilation of 18° water is shown to be the primary new nutrient flux into the euphotic zone, comprising most of the expected annual new production for this region

A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems

In this paper we introduce a new kind of Lax-Oleinik type operator with parameters associated with positive definite Lagrangian systems for both the time-periodic case and the time-independent case. On one hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution in the time-periodic case, while it was shown by Fathi and Mather that there is no such convergence of the Lax-Oleinik semigroup. On the other hand, the new family of Lax-Oleinik type operators with an arbitrary $u\in C(M,\mathbb{R}^1)$ as initial condition converges to a backward weak KAM solution faster than the Lax-Oleinik semigroup in the time-independent case.Comment: We give a new definition of Lax-Oleinik type operator; add some reference

Geodesics and the competition interface for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Stationary cocycles and Busemann functions for the corner growth model

We study the directed last-passage percolation model on the planar square lattice with nearest-neighbor steps and general i.i.d. weights on the vertices, out- side of the class of exactly solvable models. Stationary cocycles are constructed for this percolation model from queueing fixed points. These cocycles serve as bound- ary conditions for stationary last-passage percolation, solve variational formulas that characterize limit shapes, and yield existence of Busemann functions in directions where the shape has some regularity. In a sequel to this paper the cocycles are used to prove results about semi-infinite geodesics and the competition interface

Ammonium regeneration: Its contribution to phytoplankton nitrogen requirements in a eutrophic environment

Ammonium regeneration, nutrient uptake, bacterial activity and primary production were measured from March to August 1980 in Bedford Basin, Nova Scotia, Canada, a eutrophic environment. Rates of regeneration and nutrient uptake were determined using 15N isotope dilution and tracer methodology. Although primary production, nutrient uptake and ammonium regeneration were significantly intercorrelated, no relationship was detected between these parameters and heterotrophic activity. The average contribution of ammonium to total nitrogen (ammonium+nitrate) uptake was similar in the spring and in the summer (approximately 60%). On a seasonal average basis, 36% of the phytoplankton ammonium uptake could be supplied by rapid remineralization processes. In spite of the high average contribution of NH4 regeneration to phytoplankton ammonia uptake, there is indirect evidence suggesting that other NH4 sources may occasionally be important