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Victor Rodriguez-Mendez

Publications and source records attributed to Victor Rodriguez-Mendez.

4 recordsLinked to original sources

A Comparative Analysis of Clustering Algorithms for Characterizing Surface Ocean Variability in the Western Mediterranean

Understanding regional dynamical structures in the sea is fundamental to characterize energy transfer and transport properties, with implications in physical and biogeochemical modeling and characterization. In this work, we study the potential of clustering techniques to identify regional patterns, persistent or recurrent configurations, out of daily snapshots of sea surface temperature and kinetic energy in a region of the western Mediterranean Sea. From the methodological perspective, we use different clustering techniques: K-means, Self-Organizing Maps and InfoMap to verify if the patterns found are coherent across methods. Our results show that K-means and Self-Organizing Maps consistently delineate four distinct clusters of sea surface temperature configurations, aligned with the seasons even after removing the annual cycle, which indicates the persistence of seasonal structures beyond a mean effect in the temperature field. The study of surface kinetic energy, characterized by higher spatial and temporal variability, reveals more complex circulation regimes. While K-means and Self-Organizing Maps provide a robust and convergent classification of the dominant large-scale energy patterns, InfoMap uncovers finer-scale features such as localized jets and eddies. InfoMap, in particular, provides a complementary perspective to the partition-based methods, validating subtle yet significant hydrodynamic structures and acting as an anomaly detector for extreme events.

physics.ao-ph

Lagrangian Flow Network approach to an open flow model

Concepts and tools from network theory, the so-called Lagrangian Flow Network framework, have been successfully used to obtain a coarse-grained description of transport by closed fluid flows. Here we explore the application of this methodology to open chaotic flows, and check it with numerical results for a model open flow, namely a jet with a localized wave perturbation. We find that network nodes with high values of out-degree and of finite-time entropy in the forward-in-time direction identify the location of the chaotic saddle and its stable manifold, whereas nodes with high in-degree and backwards finite-time entropy highlight the location of the saddle and its unstable manifold. The cyclic clustering coefficient, associated to the presence of periodic orbits, takes non-vanishing values at the location of the saddle itself.

physics.flu-dyn

Clustering coefficient and periodic orbits in flow networks

We show that the clustering coefficient, a standard measure in network theory, when applied to flow networks, i.e. graph representations of fluid flows in which links between nodes represent fluid transport between spatial regions, identifies approximate locations of periodic trajectories in the flow system. This is true for steady flows and for periodic ones in which the time interval $τ$ used to construct the network is the period of the flow or a multiple of it. In other situations the clustering coefficient still identifies cyclic motion between regions of the fluid. Besides the fluid context, these ideas apply equally well to general dynamical systems. By varying the value of $τ$ used to construct the network, a kind of spectroscopy can be performed so that the observation of high values of mean clustering at a value of $τ$ reveals the presence of periodic orbits of period $3τ$ which impact phase space significantly. These results are illustrated with examples of increasing complexity, namely a steady and a periodically perturbed model two-dimensional fluid flow, the three-dimensional Lorenz system, and the turbulent surface flow obtained from a numerical model of circulation in the Mediterranean sea.

nlin.CD

Percolation-based precursors of transitions in extended systems

Abrupt transitions are ubiquitous in the dynamics of complex systems. Finding precursors, i.e. early indicators of their arrival, is fundamental in many areas of science ranging from electrical engineering to climate. However, obtaining warnings of an approaching transition well in advance remains an elusive task. Here we show that a functional network, constructed from spatial correlations of the system's time series, experiences a percolation transition way before the actual system reaches a bifurcation point due to the collective phenomena leading to the global change. Concepts from percolation theory are then used to introduce early warning precursors that anticipate the system's tipping point. We illustrate the generality and versatility of our percolation-based framework with model systems experiencing different types of bifurcations and with Sea Surface Temperature time series associated to El Nino phenomenon.

cond-mat.stat-mech