7 research outputs found
Atmospheric variability and the Atlantic multidecadal oscillation: mathematical analysis of low-order models
Get PDFObservations of the surface temperature of the North Atlantic Ocean indicate the presence of variability with a time scale of several decades. This variability is referred to as the Atlantic Multidecadal Oscillation (AMO). Models for the large scale ocean circulation suggest that the pattern and time scale of the AMO are explained by variations in the thermohaline circulation. However, the amplitude of the AMO is presumably determined by the atmosphere above the North Atlantic Ocean.
In this thesis we investigate (1) the dynamics of low-frequency variability of the atmosphere at midlatitudes and (2) its effect on the AMO. To that end, we study so-called low-order models, which are derived by projecting the (unknown) solution of a system of partial differential equations onto a suitably chosen finite-dimensional function space. A systematic investigation of attractors and their bifurcations gives a coherent view of the model's dynamics. Of particular importance are the transitions from orderly to more complex, or even chaotic, dynamics.
The three main results of this thesis are (1) a new dynamical scenario for atmospheric low-frequency variability in which strange attractors represent irregular planetary waves, (2) a strongly simplified model that captures the qualitative aspects of the AMO, and (3) a deterministic mechanism in which the AMO is excited by a chaotic atmosphere.
Atmospheric variability and the Atlantic multidecadal oscillation:mathematical analysis of low-order models
Get PDFAtmospheric variability and the Atlantic multidecadal oscillation:mathematical analysis of low-order models
Get PDFAtmospheric variability and the Atlantic multidecadal oscillation:mathematical analysis of low-order models
Get PDFReaction–diffusion transport into core-shell geometry:Well-posedness and stability of stationary solutions
Get PDFWe formulate and investigate a nonlinear parabolic reaction–diffusion equation describing the oxygen concentration in encapsulated pancreatic cells with a general core-shell geometry. This geometry introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. We apply monotone operator theory to show the well-posedness of the problem in the strong form. Furthermore, the stationary solutions are unique and asymptotically stable. These results rely on the gradient structure of the underlying PDE. Our results provide necessary theoretical steps for validation of the model.</p
WELL-POSEDNESS RESULTS for GENERAL REACTION-DIFFUSION TRANSPORT of OXYGEN in ENCAPSULATED CELLS
Get PDFWe provide well-posedness results for nonlinear parabolic partial differential equations (PDEs) given by reaction-diffusion equations describing the concentration of oxygen in encapsulated cells. The cells are described in terms of a core and a shell, which introduces a discontinuous diffusion coefficient as the material properties of the core and shell differ. In addition, the cells are subject to general nonlinear consumption of oxygen. As no monotonicity condition is imposed on the consumption, monotone operator theory cannot be used. Moreover, the discontinuity in the diffusion coefficient bars us from applying classical results on strong solutions. However, by directly applying a Galerkin method, we obtain uniqueness and existence of the strong form solution. These results provide the basis to study the dynamics of cells in critical states.</p
Well-posedness results for general reaction-diffusion transport of oxygen in encapsulated cells
No full texthttp://dx.doi.org/10.1017/S000497271200033
