arXiv subjects

Damià Gomila

Publications and source records attributed to Damià Gomila.

14 recordsLinked to original sources

arXiv2025

Solitons, chaos, and quantum phenomena: a deterministic approach to the Schrödinger equation

We show that the Schrödinger equation describes the ensemble mean dynamics of solitons in a Galilean invariant field theory where we interpret solitons as particles. On a zero background, solitons move classically, following Newton`s second law, however, on a non-zero amplitude chaotic background, their momentum and position fluctuate fulfilling an exact uncertainty relation, which give rise to the emergence of quantum phenomena. The Schrodinger equation for the ensemble of solitons is obtained from this exact uncertainty relation, and the amplitude of the background fluctuations is what corresponds to the value of $\hbar$. We confirm our analytical results running simulations of solitons moving against a potential barrier and comparing the ensemble probabilities with the predictions of the time dependent Schrödinger equation, providing a deterministic version of the quantum tunneling effect. We conclude with a discussion of how our theory does not present statistical independence between measurement and experiment outcome.

quant-ph↗

arXiv2025

Excitable dynamics and coral reef formation: A simple model of macro-scale structure development

In this work, we demonstrate that key aspects of the dynamical behavior of coral reefs at the macro scale, which evolve over time scales of centuries, can be accurately described using a model that integrates a few fundamental ecological and physical mechanisms. The model displays excitable behavior generating, among other dynamical regimes, traveling pulses and waves, which result in the formation of spatial structures resembling those observed in real reefs, without involving a classical pattern formation mechanism, like the Turing scenario. We conduct an in-depth exploration of the bifurcations exhibited by the model as a function of the two most ecologically significant parameters. This establishes the groundwork for using the presented model as a tool to explain coral reef formation.

q-bio.PE↗

arXiv2024

Transmission grid stability with large interregional power flows

We propose a general methodology for identifying critical lines in the long-distance transmission of power across large electric grids. When the system is pushed to its operational limit, for instance by large power imbalances such as those generated by high penetration of variable renewable energy sources, the network gets destabilized and loses synchrony. We investigate a model of the synchronous AC grid of continental Europe under tunable large interregional power flows. When those flows exceed some critical value, we find that instabilities emerge due to topological constraints. We identify two different scenarios triggering these instabilities. In the first one, specific sets of lines reach their maximal load simultaneously, causing the grid to split into two desynchronized zones. In the second one, one or few lines become overloaded, which eventually renders one Lyapunov exponent positive. The first scenario is obviously less generic and we develop a numerical approach to force the splitting of the AC grid into disconnected areas. Remarkably, the critical lines identified in this way match those that triggered the separation of the synchronous grid of continental Europe in two instances in 2021. We further discuss how the modes of the system provide information on which areas are more susceptible to lose synchrony with each other.

physics.soc-ph↗

arXiv2023

A model for seagrass species competition: dynamics of the symmetric case

We propose a general population dynamics model for two seagrass species growing and interacting in two spatial dimensions. The model includes spatial terms accounting for the clonal growth characteristics of seagrasses, and coupling between species through the net mortality rate. We consider both intraspecies and interspecies facilitative and competitive interactions, allowing density-dependent interaction mechanisms. Here we study the case of very similar species with reciprocal interactions, which allows reducing the number of the model parameters to just four, and whose bifurcation structure can be considered the backbone of the complete system. We find that the parameter space can be divided into ten regions with qualitatively different bifurcation diagrams. These regimes can be further grouped into just five regimes with different ecological interpretations. Our analysis allows the classifying of all possible density distributions and dynamical behaviors of meadows with two coexisting species.

q-bio.PE↗

arXiv2023

Predicting the power grid frequency of European islands

Modelling, forecasting and overall understanding of the dynamics of the power grid and its frequency are essential for the safe operation of existing and future power grids. Much previous research was focused on large continental areas, while small systems, such as islands are less well-studied. These natural island systems are ideal testing environments for microgrid proposals and artificially islanded grid operation. In the present paper, we utilize measurements of the power grid frequency obtained in European islands: the Faroe Islands, Ireland, the Balearic Islands and Iceland and investigate how their frequency can be predicted, compared to the Nordic power system, acting as a reference. The Balearic islands are found to be particularly deterministic and easy to predict in contrast to hard-to-predict Iceland. Furthermore, we show that typically 2-4 weeks of data are needed to improve prediction performance beyond simple benchmarks.

stat.AP↗

arXiv2022

Bifurcation structure of traveling pulses in Type-I excitable media

We have studied the existence of traveling pulses in a general Type-I excitable 1-dimensional medium. We have obtained the stability region and characterized the different bifurcations behind either the destruction or loss of stability of the pulses. In particular, some of the bifurcations delimiting the stability region have been connected, using singular limits, with the two different scenarios that mediated the Type-I local excitability, i.e. homoclinic (saddle-loop) and Saddle-Node on the Invariant Circle bifurcations. The existence of the traveling pulses has been linked, outside the stability region, to a drift pitchfork instability of localized steady structures.

nlin.PS↗

arXiv2021

Traveling pulses in Class-I excitable media

We study Class-I excitable $1$-dimensional media showing the appearance of propagating traveling pulses. We consider a general model exhibiting Class-I excitability mediated by two different scenarios: a homoclinic (saddle-loop) and a SNIC (Saddle-Node on the Invariant Circle) bifurcations. The distinct properties of Class-I with respect to Class-II excitability infer unique properties to traveling pulses in Class-I excitable media. We show how the pulse shape inherit the infinite period of the homoclinic and SNIC bifurcations at threshold, exhibiting scaling behaviors in the spatial thickness of the pulses that are equivalent to the scaling behaviors of characteristic times in the temporal case.

nlin.PS↗

arXiv2020

Resilience and performance of the power grid with high penetration of renewable energy sources: the Balearic Islands as a case study

We analyze the dynamics of the power grid with a high penetration of renewable energy sources using the ORNL-PSERC-Alaska (OPA) model. In particular we consider the power grid of the Balearic Islands with a high share of solar photovoltaic power as a case study. Day-to-day fluctuations of the solar generation and the use of storage are included in the model. Resilience is analyzed through the blackout distribution and performance is measured as the average fraction of the demand covered by solar power generation. We find that with the present consumption patterns and moderate storage, solar generation can replace conventional power plants without compromising reliability up to $30\%$ of the total installed capacity. We also find that using source redundancy it is possible to cover up to $80\%$ or more of the demand with solar plants, while keeping the risk similar to that with full conventional generation. However this requires oversizing the installed solar power to be at least $2.5$ larger than the average demand. The potential of wind energy is also briefly discussed

eess.SY↗

arXiv2020

A general model for vegetation patterns including rhizome growth

Vegetation patterns, a natural phenomenon observed worldwide, are typically driven by spatially distributed feedback. However, the spatial colonization mechanisms of clonal plants, driven by the growth of a rhizome, are usually not considered in prototypical models. Here we propose a general equation for the vegetation density that includes all main clonal-growth features as well as the essential ingredients leading to spatial self-organization. This generic model reproduces the phase diagram of a fully detailed model of clonal growth. The relation of each term of the model with the mechanisms of clonal growth is discussed.

q-bio.PE↗

arXiv2020

Effects of demand control on the complex dynamics of electric power system blackouts

The propagation of failures and blackouts in electric networks is a complex problem. Typical models, such as the ORNL-PSerc-Alaska (OPA), are based on a combination of fast and a slow dynamics. The first describes the cascading failures while the second the grid evolution though line and generation upgrades as well as demand growth, all taking place in time scales from days to years. The growing integration of renewable energy sources, whose power fluctuates in time scales from seconds to hours, together with the increase in demand, which also present fast fluctuations, require the incorporation of distributed methods of control in the demand side to avoid the high cost of ordinary control in conventional power plants. In this work, we extend the OPA model to include fluctuations in the demand at time scales of the order of minutes, intraday demand variations and the effect of demand control. We find that demand control effectively reduces the number of blackouts without increasing the probability of large-scale events.

eess.SY↗

arXiv2020

Observation of the Eckhaus Instability in Whispering-Gallery Mode Resonators

The Eckhaus instability is a secondary instability of nonlinear spatiotemporal patterns in which high-wavenumber periodic solutions become unstable against small-wavenumber perturbations. We show in this letter that this instability can take place in Kerr combs generated with ultra-high $Q$ whispering-gallery mode resonators. In our experiment, sub-critical Turing patterns (rolls) undergo Eckhaus instabilities upon changes in the laser detuning leading to cracking patterns with long-lived transients. In the spectral domain, this results in a metastable Kerr comb dynamics with a timescale that can be larger than one minute. This ultra-slow timescale is at least seven orders of magnitude larger than the intracavity photon lifetime, and is in sharp contrast with all the transient behaviors reported so far in cavity nonlinear optics, that are typically only few photon lifetimes long (i.e., in the ps range). We show that this phenomenology is well explained by the Lugiato-Lefever model, as the result of an Eckhaus instability. Our theoretical analysis is found to be in excellent agreement with the experimental measurements.

nlin.PS↗

arXiv2018

Reduction of power grid fluctuations by communication between smart devices

The increase of electric demand and the progressive integration of renewable sources threatens the stability of the power grid. To solve this issue, several methods have been proposed to control the demand side instead of increasing the spinning reserve on the supply side. Here we focus on dynamic demand control (DDC), a method in which appliances can delay its scheduled operation if the electric frequency is outside a suitable range. We have recently shown that DDC effectively reduces small and medium-size frequency fluctuations but, due to the need of recovering pending tasks, the probability of large demand peaks, and hence large frequency fluctuations, may actually increase. Although these events are very rare they can potentially trigger a failure of the system and therefore strategies to avoid them have to be addressed. In this work, we introduce a new method including communication among DDC devices belonging to a given group, such that they can coordinate opposite actions to keep the group demand more stable. We show that for this method the amount of pending tasks decreases by a factor 10 while large frequency fluctuations are significantly reduced or even completely avoided.

eess.SY↗

arXiv2018

Curing Braess' Paradox by Secondary Control in Power Grids

Robust operation of power transmission grids is essential for most of today's technical infrastructure and our daily life. Adding renewable generation to power grids requires grid extensions and sophisticated control actions on different time scales to cope with short-term fluctuations and long-term power imbalance. Braess' paradox constitutes a counterintuitive collective phenomenon that occurs if adding new transmission line capacity to a network increases loads on other lines, effectively reducing the system's performance and potentially even entirely removing its operating state. Combining simple analytical considerations with numerical investigations on a small sample network, we here study dynamical consequences of secondary control in AC power grid models. We demonstrate that sufficiently strong control not only implies dynamical stability of the system but may also cure Braess' paradox. Our results highlight the importance of demand control in conjunction with grid topology for stable operation and reveal a new functional benefit of secondary control.

nlin.AO↗

arXiv2017

Fairy circle landscapes under the sea

Short-scale interactions yield large-scale vegetation patterns that, in turn, shape ecosystem function across landscapes. Fairy circles, which are circular patches bare of vegetation within otherwise continuous landscapes, are characteristic features of semiarid grasslands. We report the occurrence of submarine fairy circle seascapes in seagrass meadows and propose a simple model that reproduces the diversity of seascapes observed in these ecosystems as emerging from plant interactions within the meadow. These seascapes include two extreme cases, a continuous meadow and a bare landscape, along with intermediate states that range from the occurrence of persistent but isolated fairy circles, or solitons, to seascapes with multiple fairy circles, banded vegetation, and "leopard skin" patterns consisting of bare seascapes patterns consisting of bare seascapes dotted with plant patches. The model predicts that these intermediate seascapes extending across kilometers emerge as a consequence of local demographic imbalances along with facilitative and competitive interactions among the plants with a characteristic spatial scale of 20 to 30 m, consistent with known drivers of seagrass performance. The model, which can be extended to clonal growth plants in other landscapes showing fairy rings, reveals that the different seascapes observed hold diagnostic power as to the proximity of seagrass meadows to extinction points that can be used to identify ecosystems at risks.

q-bio.PE↗