428 research outputs found
Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport
We formulate a model for the mass exchange between oil at and below the sea
surface. This is a particularly important aspect of modeling oil spills.
Surface and subsurface oil have different chemical and transport
characteristics and lumping them together would compromise the accuracy of the
resulting model. Without observational or computational constraints, it is thus
not possible to quantitatively predict oil spills based upon partial field
observations of surface and/or sub-surface oil. The primary challenge in
capturing the mass exchange is that the principal mechanisms are on the
microscale. This is a serious barrier to developing practical models for oil
spills that are capable of addressing questions regarding the fate of oil at
the large spatio-temporal scales, as demanded by environmental questions. We
use upscaling to propose an environmental-scale model which incorporates the
mass exchange between surface and subsurface oil due to oil droplet dynamics,
buoyancy effects, and sea surface and subsurface mechanics. While the mass
exchange mechanism detailed here is generally applicable to oil transport
models, it addresses the modeling needs of a particular to an oil spill model
[1]. This transport model is designed to capture oil spills at very large
spatio-temporal scales. It accomplishes this goal by specializing to
shallow-water environments, in which depth averaging is a perfectly good
approximation for the flow, while at the same time retaining mass conservation
of oil over the whole oceanic domain.Comment: 18 pages, 6 figure
Approximating the largest eigenvalue of network adjacency matrices
The largest eigenvalue of the adjacency matrix of a network plays an
important role in several network processes (e.g., synchronization of
oscillators, percolation on directed networks, linear stability of equilibria
of network coupled systems, etc.). In this paper we develop approximations to
the largest eigenvalue of adjacency matrices and discuss the relationships
between these approximations. Numerical experiments on simulated networks are
used to test our results.Comment: 7 pages, 4 figure
Predicting criticality and dynamic range in complex networks: effects of topology
The collective dynamics of a network of coupled excitable systems in response
to an external stimulus depends on the topology of the connections in the
network. Here we develop a general theoretical approach to study the effects of
network topology on dynamic range, which quantifies the range of stimulus
intensities resulting in distinguishable network responses. We find that the
largest eigenvalue of the weighted network adjacency matrix governs the network
dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a
critical regime with maximum dynamic range. We gain deeper insight on the
effects of network topology using a nonlinear analysis in terms of additional
spectral properties of the adjacency matrix. We find that homogeneous networks
can reach a higher dynamic range than those with heterogeneous topology. Our
analysis, confirmed by numerical simulations, generalizes previous studies in
terms of the largest eigenvalue of the adjacency matrix.Comment: 4 pages, 3 figure
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