30 research outputs found
Analysis of tidal flows through the Strait of Gibraltar using Dynamic Mode Decomposition
The Strait of Gibraltar is a region characterized by intricate oceanic
sub-mesoscale features, influenced by topography, tidal forces, instabilities,
and nonlinear hydraulic processes, all governed by the nonlinear equations of
fluid motion. In this study, we aim to uncover the underlying physics of these
phenomena within 3D MIT general circulation model simulations, including waves,
eddies, and gyres. To achieve this, we employ Dynamic Mode Decomposition (DMD)
to break down simulation snapshots into Koopman modes, with distinct
exponential growth/decay rates and oscillation frequencies. Our objectives
encompass evaluating DMD's efficacy in capturing known features, unveiling new
elements, ranking modes, and exploring order reduction. We also introduce
modifications to enhance DMD's robustness, numerical accuracy, and robustness
of eigenvalues. DMD analysis yields a comprehensive understanding of flow
patterns, internal wave formation, and the dynamics of the Strait of Gibraltar,
its meandering behaviors, and the formation of a secondary gyre, notably the
Western Alboran Gyre, as well as the propagation of Kelvin and coastal-trapped
waves along the African coast. In doing so, it significantly advances our
comprehension of intricate oceanographic phenomena and underscores the immense
utility of DMD as an analytical tool for such complex datasets, suggesting that
DMD could serve as a valuable addition to the toolkit of oceanographers
Universal neural field computation
Turing machines and G\"odel numbers are important pillars of the theory of
computation. Thus, any computational architecture needs to show how it could
relate to Turing machines and how stable implementations of Turing computation
are possible. In this chapter, we implement universal Turing computation in a
neural field environment. To this end, we employ the canonical symbologram
representation of a Turing machine obtained from a G\"odel encoding of its
symbolic repertoire and generalized shifts. The resulting nonlinear dynamical
automaton (NDA) is a piecewise affine-linear map acting on the unit square that
is partitioned into rectangular domains. Instead of looking at point dynamics
in phase space, we then consider functional dynamics of probability
distributions functions (p.d.f.s) over phase space. This is generally described
by a Frobenius-Perron integral transformation that can be regarded as a neural
field equation over the unit square as feature space of a dynamic field theory
(DFT). Solving the Frobenius-Perron equation yields that uniform p.d.f.s with
rectangular support are mapped onto uniform p.d.f.s with rectangular support,
again. We call the resulting representation \emph{dynamic field automaton}.Comment: 21 pages; 6 figures. arXiv admin note: text overlap with
arXiv:1204.546