arXiv subjects

Emilio Hernandez-Garcia

Publications and source records attributed to Emilio Hernandez-Garcia.

At least 19 recordsLinked to original sources

arXiv2026

Hydrodynamic description of proliferating active matter

We develop a continuum theory for proliferating active matter starting from a microscopic stochastic model of self-propelled particles undergoing birth, death, and nonlocal competition. Beginning from the master equation, we derive mean-field evolution equations for the particle density and polarization fields and close the resulting hierarchy through a von Mises ansatz, providing a coupled hydrodynamic description applicable to a broad class of proliferating active systems. As an application, we study the recently introduced Active Brownian Bug model, in which the form of flocking emerges despite the absence of explicit alignment interactions. Linear stability analysis predicts both Turing and Hopf instabilities, whose analytical thresholds agree with numerical simulations. The continuum model reproduces the principal dynamical regimes of the underlying particle system, including homogeneous states, stationary periodic clusters, and coherently propagating flocking states. These results establish a general continuum framework for proliferating active matter and provide a physical interpretation of collective motion driven by the interplay between activity and population dynamics.

cond-mat.soft↗

arXiv2026

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↗

arXiv2020

Patterns, localized structures and fronts in a reduced model of clonal plant growth

A simplified model of clonal plant growth is formulated, motivated by observations of spatial structures in Posidonia oceanica meadows in the Mediterranean Sea. Two levels of approximation are considered for the scale-dependent feedback terms. Both take into account mortality and clonal, or vegetative, growth as well as competition and facilitation, but the first version is nonlocal in space while the second is local. Study of the two versions of the model in the one-dimensional case reveals that both cases exhibit qualitatively similar behavior (but quantitative differences) and describe the competition between three spatially extended states, the bare soil state, the populated state, and a pattern state, and the associated spatially localized structures. The latter are of two types, holes in the populated state and vegetation patches on bare ground, and are organized within distinct snaking bifurcation diagrams. Fronts between the three extended states are studied and a transition between pushed and pulled fronts identified. Numerical simulations in one spatial dimension are used to determine front speeds and confront the predictions from the marginal stability condition for pulled fronts.

nlin.PS↗

arXiv2019

Spatial inhomogeneities in the sedimentation of biogenic particles in ocean flows: analysis in the Benguela region

Sedimentation of particles in the ocean leads to inhomogeneous horizontal distributions at depth, even if the release process is homogeneous. We study this phenomenon considering a horizontal sheet of sinking particles immersed in an oceanic flow, and determine how the particles are distributed when they sediment on the seabed (or are collected at a given depth). The study is performed from a Lagrangian viewpoint attending to the properties of the oceanic flow and the physical characteristics (size and density) of typical biogenic sinking particles. Two main processes determine the distribution, the stretching of the sheet caused by the flow and its projection on the surface where particles accumulate. These mechanisms are checked, besides an analysis of their relative importance to produce inhomogeneities, with numerical experiments in the Benguela region. Faster (heavier or larger) sinking particles distribute more homogeneously than slower ones.

physics.ao-ph↗

arXiv2018

Crossroads of the mesoscale circulation

Quantifying the mechanisms of tracer dispersion in the ocean remains a central question in oceanography, for problems ranging from nutrient delivery to phytoplankton, to the early detection of contaminants. Most analyses have been based on Lagrangian concepts of transport, focusing on the identification of features minimizing fluid exchange among regions, or more recently on network tools which focus on connectivity and transport pathways. Neither of these approaches allows ranking the geographical sites of major water passage and selecting them so that they monitor waters coming from separate parts of the ocean. These are instead key criteria when deploying an observing network. Here we address this issue by estimating at any point the extent of the ocean surface which transits through it in a given time window. With such information we are able to rank the sites with major fluxes that intercept waters originating from different regions. We show that this allows us to optimize an observing network, where a set of sampling sites can be chosen for monitoring the largest flux of water dispersing out of a given region. When the analysis is performed backward in time, this method allows us to identify the major sources which feed a target region. The method is first applied to a minimalistic model of a mesoscale eddy field, and then to realistic satellite-derived ocean currents in the Kerguelen area. In this region we identify the optimal location of fixed stations capable of intercepting the trajectories of 43 surface drifters, along with statistics on the temporal persistence of the stations determined in this way. We then identify possible hotspots of micro-nutrient enrichment for the recurrent spring phytoplanktonic bloom occuring here. Promising applications to other fields, such as larval connectivity, marine spatial planning or contaminant detection, are then discussed.

physics.ao-ph↗

arXiv2018

Cluster crystals for Brownian particles with combined soft and hard-core repulsive interactions

Particle systems interacting with a soft repulsion, at thermal equilibrium and under some circumstances, are known to form cluster crystals, i.e. periodic arrangements of particle aggregates. We study here how these states are modified by the presence of an additional hard-core repulsion, accounting for particle size. To this end we consider a two-dimensional system of Brownian particles interacting through a potential which includes a hard-core and a soft-core (of the GEM-α type) repulsive terms. The system shows different phases, and we focus in the regime where cluster crystals form. We consider two situations: the low-temperature one in which particles inside the clusters also show an ordered structure (crystal cluster-crystal phase), and the one occurring at higher temperature in which particles within the clusters are spatially disordered (fluid cluster crystal). An explicit expression for the energy in terms of the typical distance among clusters and the typical distance of the particles within the clusters is obtained for vanishing temperature, which helps to understand the balance between the different forces involved. Finite-temperature corrections are also discussed.

cond-mat.stat-mech↗

arXiv2017

Characterization of the structure and cross-shore transport properties of a coastal upwelling filament using three-dimensional finite-size Lyapunov exponents

The three dimensional structure, dynamics and dispersion characteristics of a simulated upwelling filament in the Iberian upwelling system are analyzed using Lagrangian tools. We used a realistic regional simulation of the western Iberian shelf which is concomitant with an in-situ oceanographic campaign that surveyed the area. We compute 3d fields of finite--size Lyapunov exponents (FSLE) from 3d velocity fields and extract the field's ridges to study the spatial distribution and temporal evolution of the Lagrangian Coherent Structures (LCSs) evolving around the filament. We find that the most intense curtain-like LCSs delimit the boundaries of the whole filamentary structure whose general properties match well the observations. The filament interior is characterized by small dispersion of fluid elements. Furthermore, we identify a weak LCS separating the filament into a warmer vein and a colder filament associated with the interaction of a mesoscale eddy with the upwelling front. The cold upwelled water parcels move along the filament conserving their density. The filament itself is characterized by small dispersion of fluid elements in its interior. The comparison of LCSs with potential temperature and salinity gradient fields shows that the outer limits of the filament coincide with regions of large hydrographic gradients, similar to those observed, explaining the isolation of the interior of the filament with the surrounding waters. We conclude that the Lagrangian analysis used in this work is useful in explaining the dynamics of cross-shore exchanges of materials between coastal regions and the open ocean due to mesoscale processes.

physics.ao-ph↗

arXiv2017

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↗

arXiv2016

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↗

arXiv2016

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↗

arXiv2015

Most probable paths in temporal weighted networks: An application to ocean transport

We consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of paths, and to a subset of highly probable paths which incorporate most of the connection probability. These concepts are used to provide alternative definitions of betweenness centrality. We apply our formalism to a transport network describing surface flow in the Mediterranean sea. Despite the full transport dynamics is described by a very large number of paths we find that, for realistic time scales, only a very small subset of high probability paths (or even a single most probable one) is enough to characterize global connectivity properties of the network.

physics.soc-ph↗

arXiv2015

Flow networks: A characterization of geophysical fluid transport

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is useful to analyze fluid dynamics in geophysical contexts, as illustrated by the construction of a flow network associated to the surface circulation in the Mediterranean sea. We use network-theory tools to analyze the flow network and gain insights into transport processes. In particular we quantitatively relate dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes. A family of network entropies is defined from the network adjacency matrix, and related to the statistics of stretching in the fluid, in particular to the Lyapunov exponent field. Finally we use a network community detection algorithm, Infomap, to partition the Mediterranean network into coherent regions, i.e. areas internally well mixed, but with little fluid interchange between them.

physics.ao-ph↗

arXiv2015

Anomalous scaling in an age-dependent branching model

We introduce a one-parametric family of tree growth models, in which branching probabilities decrease with branch age $τ$ as $τ^{-α}$. Depending on the exponent $α$, the scaling of tree depth with tree size $n$ displays a transition between the logarithmic scaling of random trees and an algebraic growth. At the transition ($α=1$) tree depth grows as $(\log n)^2$. This anomalous scaling is in good agreement with the trend observed in evolution of biological species, thus providing a theoretical support for age-dependent speciation and associating it to the occurrence of a critical point.

q-bio.PE↗

arXiv2014

Vegetation pattern formation in semiarid systems without facilitative mechanisms

Regular vegetation patterns in semiarid ecosystems are believed to arise from the interplay between long-range competition and facilitation processes acting at smaller distances. We show that, under rather general conditions, long-range competition alone may be enough to shape these patterns. To this end we propose a simple, general model for the dynamics of vegetation, which includes only long-range competition between plants. Competition is introduced through a nonlocal term, where the kernel function quantifies the intensity of the interaction. We recover the full spectrum of spatial structures typical of vegetation models that also account for facilitation in addition to competition.

q-bio.PE↗

arXiv2014

Spatial patterns of competing random walkers

We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals perform random walks of different types (Gaussian diffusion and Lévy flights). We focus on how competition and random motions affect each other, from which spatial instabilities and extinctions arise. Under suitable conditions, competitive interactions lead to clustering of individuals and periodic pattern formation. Random motion has a homogenizing effect and then delays this clustering instability. When individuals from species differing in their random walk characteristics are allowed to compete together, the ones with a tendency to form narrower clusters get a competitive advantage over the others. Mean-field deterministic equations are analyzed and compared with the outcome of the individual-based simulations.

q-bio.PE↗

arXiv2014

Self-localized states in species competition

We study the conditions under which species interaction, as described by continuous versions of the competitive Lotka-Volterra model (namely the nonlocal Kolmogorov-Fisher model, and its differential approximation), can support the existence of localized states, i.e. patches of species with enhanced population surrounded in niche space by species at smaller densities. These states would arise from species interaction, and not by any preferred niche location or better fitness. In contrast to previous works we include only quadratic nonlinearities, so that the localized patches appear on a background of homogeneously distributed species coexistence, instead than on top of the no-species empty state. For the differential model we find and describe in detail the stable localized states. For the full nonlocal model, however competitive interactions alone do not allow the conditions for the observation of self-localized states, and we show how the inclusion of additional facilitative interactions lead to the appearance of them.

nlin.PS↗

arXiv2013

The noisy Hegselmann-Krause model for opinion dynamics

In the model for continuous opinion dynamics introduced by Hegselmann and Krause, each individual moves to the average opinion of all individuals within an area of confidence. In this work we study the effects of noise in this system. With certain probability, individuals are given the opportunity to change spontaneously their opinion to another one selected randomly inside the opinion space with different rules. If the random jump does not occur, individuals interact through the Hegselmann-Krause's rule. We analyze two cases, one where individuals can carry out opinion random jumps inside the whole opinion space, and other where they are allowed to perform jumps just inside a small interval centered around the current opinion. We found that these opinion random jumps change the model behavior inducing interesting phenomena. Using pattern formation techniques, we obtain approximate analytical results for critical conditions of opinion cluster formation. Finally, we compare the results of this work with the noisy version of the Deffuant et al. model for continuous-opinion dynamics.

physics.soc-ph↗

arXiv2010

Synchronization and entrainment of coupled circadian oscillators

Circadian rhythms in mammals are controlled by the neurons located in the suprachiasmatic nucleus of the hypothalamus. In physiological conditions, the system of neurons is very efficiently entrained by the 24-hour light-dark cycle. Most of the studies carried out so far emphasize the crucial role of the periodicity imposed by the light dark cycle in neuronal synchronization. Nevertheless, heterogeneity as a natural and permanent ingredient of these cellular interactions is seemingly to play a major role in these biochemical processes. In this paper we use a model that considers the neurons of the suprachiasmatic nucleus as chemically-coupled modified Goodwin oscillators, and introduce non-negligible heterogeneity in the periods of all neurons in the form of quenched noise. The system response to the light-dark cycle periodicity is studied as a function of the interneuronal coupling strength, external forcing amplitude and neuronal heterogeneity. Our results indicate that the right amount of heterogeneity helps the extended system to respond globally in a more coherent way to the external forcing. Our proposed mechanism for neuronal synchronization under external periodic forcing is based on heterogeneity-induced oscillators death, damped oscillators being more entrainable by the external forcing than the self-oscillating neurons with different periods.

physics.bio-ph↗