952 research outputs found
Skill assessment of multiple hypoxia models in Chesapeake Bay and implications for management decisions
The Chesapeake Bay Program (CBP) has used their coupled watershed-water quality modeling system to develop a set of Total Maximum Daily Loads (TMDLs) for nutrients and sediment in an effort to reduce eutrophication impacts which include decreasing the seasonal occurrence of hypoxia within the Bay. The CBP is now considering the use of a multiple model approach to enhance the confidence in their model projections and to better define uncertainty. This study statistically compares the CBP regulatory model with multiple implementations of the Regional Ocean Modeling System (ROMS) in terms of skill in reproducing monthly profiles of hydrodynamics, nutrients, chlorophyll and dissolved oxygen at ~30 stations throughout the Bay. Preliminary results show that although all the models substantially underestimate stratification throughout the Bay, they all have significant skill in reproducing the mean and seasonal variability of bottom dissolved oxygen. This study demonstrates that multiple community models can be used together to provide independent confidence bounds for management decisions based on CBP model results
Well-posedness of boundary layer equations for time-dependent flow of non-Newtonian fluids
We consider the flow of an upper convected Maxwell fluid in the limit of high
Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be
imposed on the solutions. We derive equations for the resulting boundary layer
and prove the well-posedness of these equations. A transformation to Lagrangian
coordinates is crucial in the argument
One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities
A one-dimensional discrete Stark Hamiltonian with a continuous electric field
is constructed by extension theory methods. In absence of the impurities the
model is proved to be exactly solvable, the spectrum is shown to be simple,
continuous, filling the real axis; the eigenfunctions, the resolvent and the
spectral measure are constructed explicitly. For this (unperturbed) system the
resonance spectrum is shown to be empty. The model considering impurity in a
single node is also constructed using the operator extension theory methods.
The spectral analysis is performed and the dispersion equation for the
resolvent singularities is obtained. The resonance spectrum is shown to contain
infinite discrete set of resonances. One-to-one correspondence of the
constructed Hamiltonian to some Lee-Friedrichs model is established.Comment: 20 pages, Latex, no figure
Star-unitary transformations. From dynamics to irreversibility and stochastic behavior
We consider a simple model of a classical harmonic oscillator coupled to a
field. In standard approaches Langevin-type equations for {\it bare} particles
are derived from Hamiltonian dynamics. These equations contain memory terms and
are time-reversal invariant. In contrast the phenomenological Langevin
equations have no memory terms (they are Markovian equations) and give a time
evolution split in two branches (semigroups), each of which breaks time
symmetry. A standard approach to bridge dynamics with phenomenology is to
consider the Markovian approximation of the former. In this paper we present a
formulation in terms of {\it dressed} particles, which gives exact Markovian
equations. We formulate dressed particles for Poincar\'e nonintegrable systems,
through an invertible transformation operator \Lam introduced by Prigogine
and collaborators. \Lam is obtained by an extension of the canonical
(unitary) transformation operator that eliminates interactions for
integrable systems. Our extension is based on the removal of divergences due to
Poincar\'e resonances, which breaks time-symmetry. The unitarity of is
extended to ``star-unitarity'' for \Lam. We show that \Lam-transformed
variables have the same time evolution as stochastic variables obeying Langevin
equations, and that \Lam-transformed distribution functions satisfy exact
Fokker-Planck equations. The effects of Gaussian white noise are obtained by
the non-distributive property of \Lam with respect to products of dynamical
variables. Therefore our method leads to a direct link between dynamics of
Poincar\'e nonintegrable systems, probability and stochasticity.Comment: 24 pages, no figures. Made more connections with other work.
Clarified ideas on irreversibilit
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