4,099 research outputs found
Climate dynamics and fluid mechanics: Natural variability and related uncertainties
The purpose of this review-and-research paper is twofold: (i) to review the
role played in climate dynamics by fluid-dynamical models; and (ii) to
contribute to the understanding and reduction of the uncertainties in future
climate-change projections. To illustrate the first point, we focus on the
large-scale, wind-driven flow of the mid-latitude oceans which contribute in a
crucial way to Earth's climate, and to changes therein. We study the
low-frequency variability (LFV) of the wind-driven, double-gyre circulation in
mid-latitude ocean basins, via the bifurcation sequence that leads from steady
states through periodic solutions and on to the chaotic, irregular flows
documented in the observations. This sequence involves local, pitchfork and
Hopf bifurcations, as well as global, homoclinic ones. The natural climate
variability induced by the LFV of the ocean circulation is but one of the
causes of uncertainties in climate projections. Another major cause of such
uncertainties could reside in the structural instability in the topological
sense, of the equations governing climate dynamics, including but not
restricted to those of atmospheric and ocean dynamics. We propose a novel
approach to understand, and possibly reduce, these uncertainties, based on the
concepts and methods of random dynamical systems theory. As a very first step,
we study the effect of noise on the topological classes of the Arnol'd family
of circle maps, a paradigmatic model of frequency locking as occurring in the
nonlinear interactions between the El Nino-Southern Oscillations (ENSO) and the
seasonal cycle. It is shown that the maps' fine-grained resonant landscape is
smoothed by the noise, thus permitting their coarse-grained classification.
This result is consistent with stabilizing effects of stochastic
parametrization obtained in modeling of ENSO phenomenon via some general
circulation models.Comment: Invited survey paper for Special Issue on The Euler Equations: 250
Years On, in Physica D: Nonlinear phenomen
Robust Stability Assessment in the Presence of Load Dynamics Uncertainty
Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially difficult and may compromise the security of the system. We propose a novel mathematical “robust stability” criterion for the assessment of small-signal stability of operating points. Whenever the criterion is satisfied for a given operating point, it provides mathematical guarantees that the operating point will be stable with respect to small disturbances for any dynamic response of the loads. The criterion can be naturally used for identification of operating regions secure from the occurrence of Hopf bifurcation. Several possible applications of the criterion are discussed, most importantly the concept of robust stability assessment (RSA), that could be integrated in dynamic security assessment packages and used in contingency screening and other planning and operational studies
Nonequilibrium scaling explorations on a 2D Z(5)-symmetric model
We have investigated the dynamic critical behavior of the two-dimensional
Z(5)-symmetric spin model by using short-time Monte Carlo (MC) simulations. We
have obtained estimates of some critical points in its rich phase diagram and
included, among the usual critical lines the study of first-order (weak)
transition by looking into the order-disorder phase transition. Besides, we
also investigated the soft-disorder phase transition by considering empiric
methods. A study of the behavior of along the self-dual critical
line has been performed and special attention has been devoted to the critical
bifurcation point, or FZ (Fateev-Zamolodchikov) point. Firstly, by using a
refinement method and taking into account simulations out-of-equilibrium, we
were able to localize parameters of this point. In a second part of our study,
we turned our attention to the behavior of the model at the early stage of its
time evolution in order to find the dynamic critical exponent z as well as the
static critical exponents and of the FZ-point on square
lattices. The values of the static critical exponents and parameters are in
good agreement with the exact results, and the dynamic critical exponent
very close of the 4-state Potts model ().Comment: 11 pages, 7 figure
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