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Structure of the medium formed in heavy ion collisions
(MDPI, 2023-06-01) Alvarado García, Jesús Ricardo; Rosales Herrera, Diana; Fernández Téllez, Arturo; Díaz Jiménez, Bogar; Ramírez Cancino, Jhony Eredy; European Commission; Universidad Carlos III de Madrid; Agencia Estatal de Investigación (España)
We investigate the structure of the medium formed in heavy ion collisions using three different models: the Color String Percolation Model (CSPM), the Core–Shell-Color String Percolation Model (CSCSPM), and the Color Glass Condensate (CGC) framework. We analyze the radial distribution function of the transverse representation of color flux tubes in each model to determine the medium’s structure. Our results indicate that the CSPM behaves as an ideal gas, while the CSCSPM exhibits a structural phase transition from a gas-like to a liquid-like structure. Additionally, our analysis of the CGC framework suggests that it produces systems that behave like non-ideal gases for AuAu central collisions at RHIC energies and liquid-like structures for PbPb central collisions at LHC energies.
Classical analogs of generalized purities, entropies, and logarithmic negativity
(American Physical Society, 2023-07-01) Díaz Jiménez, Bogar; González, Diego; Hernández, Marcos J.; Vergara, J. David; European Commission; Universidad Carlos III de Madrid; Agencia Estatal de Investigación (España)
It has recently been proposed classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the corresponding quantum system is in a Gaussian state. We generalized these results by providing classical analogs of the generalized purities, Bastiaans-Tsallis entropies, Rényi entropies, and logarithmic negativity for classical integrable systems. These classical analogs are entirely characterized by the classical covariance matrix. We compute these classical analogs exactly in the cases of linearly coupled harmonic oscillators, a generalized harmonic oscillator chain, and a one-dimensional circular lattice of oscillators. In all of these systems, the classical analogs reproduce the results of their quantum counterparts whenever the system is in a Gaussian state. In this context, our results show that quantum information of Gaussian states can be reproduced by classical information.
Freestanding graphene heat engine analyzed using stochastic thermodynamics
(AIP Advances, 2023-07-13) Durbin, J.; Mangum, J. M.; Gikunda, M. N.; Harerimana, F.; Amin, T.; Kumar, P.; López Bonilla, Luis Francisco; Thibado, P. M.
We present an Ito-Langevin model for freestanding graphene connected to an electrical circuit. The graphene is treated as a Brownian particle in a double-well potential and is adjacent to a fixed electrode to form a variable capacitor. The capacitor is connected in series with a battery and a load resistor. The capacitor and resistor are given separate thermal reservoirs. We have solved the coupled Ito-Langevin equations for a broad range of temperature differences between the two reservoirs. Using ensemble averages, we report the rate of change in energy, heat, and work using stochastic thermodynamics. When the resistor is held at higher temperatures, the efficiency of the heat engine rises linearly with temperature. However, when the graphene is held at higher temperatures, the efficiency instantly rises and then plateaus. Also, twice as much entropy is produced when the resistor is hotter compared to when the graphene is hotter. Unexpectedly, the temperature of the capacitor is found to alter the dissipated power of the resistor.
Scale-free chaos in the confined Vicsek flocking model
(American Physical Society, 2023-01-17) González Albaladejo, Rafael; Carpio Rodríguez, Ana María; López Bonilla, Luis Francisco; Comunidad de Madrid; Ministerio de Economía y Competitividad (España); Ministerio de Ciencia, Innovación y Universidades (España); Agencia Estatal de Investigación (España)
The Vicsek model encompasses the paradigm of active dry matter. Motivated by collective behavior of insects in swarms, we have studied finite-size effects and criticality in the three-dimensional, harmonically confined Vicsek model. We have discovered a phase transition that exists for appropriate noise and small confinement strength. On the critical line of confinement versus noise, swarms are in a state of scale-free chaos characterized by minimal correlation time, correlation length proportional to swarm size and topological data analysis. The critical line separates dispersed single clusters from confined multicluster swarms. Scale-free chaotic swarms occupy a compact region of space and comprise a recognizable 'condensed'nucleus and particles leaving and entering it. Susceptibility, correlation length, dynamic correlation function, and largest Lyapunov exponent obey power laws. The critical line and a narrow criticality region close to it move simultaneously to zero confinement strength for infinitely many particles. At the end of the first chaotic window of confinement, there is another phase transition to infinitely dense clusters of finite size that may be termed flocking black holes.
Mean field theory of chaotic insect swarms
(APS, 2023-06) González Albaladejo, Rafael; López Bonilla, Luis Francisco; Comunidad de Madrid; Ministerio de Economía y Competitividad (España); Ministerio de Ciencia e Innovación (España)
The harmonically confined Vicsek model displays qualitative and quantitative features observed in natural insect swarms. It exhibits a scale-free transition between single and multicluster chaotic phases. Finite-size scaling indicates that this unusual phase transition occurs at zero confinement [Phys. Rev. E 107, 014209 (2023)]. While the evidence of the scale-free-chaos phase transition comes from numerical simulations, here we present its mean-field theory. Analytically determined critical exponents are those of the Landau theory of equilibrium phase transitions plus dynamical critical exponent z = 1 and a new critical exponent φ = 0.5 for the largest Lyapunov exponent. The phase transition occurs at zero confinement and noise in the mean-field theory. The noise line of zero largest Lyapunov exponents informs observed behavior: (i) the qualitative shape of the swarm (on average, the center of mass rotates slowly at the rate marked by the winding number and its trajectory fills compactly the space, similarly to the observed condensed nucleus surrounded by vapor) and (ii) the critical exponents resemble those observed in natural swarms. Our predictions include power laws for the frequency of the maximal spectral amplitude and the winding number.
Tracking collective cell motion by topological data analysis
(PLOS, 2020-12-23) López Bonilla, Luis Francisco; Carpio, Ana; Trenado, Carolina; Agencia Estatal de Investigación (España); Ministerio de Ciencia, Innovación y Universidades (España)
By modifying and calibrating an active vertex model to experiments, we have simulated numerically a confluent cellular monolayer spreading on an empty space and the collision of two monolayers of different cells in an antagonistic migration assay. Cells are subject to inertial forces and to active forces that try to align their velocities with those of neighboring ones. In agreement with experiments in the literature, the spreading test exhibits formation of fingers in the moving interfaces, there appear swirls in the velocity field, and the polar order parameter and the correlation and swirl lengths increase with time. Numerical simulations show that cells inside the tissue have smaller area than those at the interface, which has been observed in recent experiments. In the antagonistic migration assay, a population of fluidlike Ras cells invades a population of wild type solidlike cells having shape parameters above and below the geometric critical value, respectively. Cell mixing or segregation depends on the junction tensions between different cells. We reproduce the experimentally observed antagonistic migration assays by assuming that a fraction of cells favor mixing, the others segregation, and that these cells are randomly distributed in space. To characterize and compare the structure of interfaces between cell types or of interfaces of spreading cellular monolayers in an automatic manner, we apply topological data analysis to experimental data and to results of our numerical simulations. We use time series of data generated by numerical simulations to automatically group, track and classify the advancing interfaces of cellular aggregates by means of bottleneck or Wasserstein distances of persistent homologies. These techniques of topological data analysis are scalable and could be used in studies involving large amounts of data. Besides applications to wound healing and metastatic cancer, these studies are relevant for tissue engineering, biological effects of materials, tissue and organ regeneration.
Anomalous angiogenesis in retina
(MDPI, 2021-02) Vega Martínez, Rocío; Carretero Cerrajero, Manuel; López Bonilla, Luis Francisco; Agencia Estatal de Investigación (España)
Age-related macular degeneration (AMD) may cause severe loss of vision or blindness, particularly in elderly people. Exudative AMD is characterized by the angiogenesis of blood vessels growing from underneath the macula, crossing the blood-retina barrier (which comprises Bruch's membrane (BM) and the retinal pigmentation epithelium (RPE)), leaking blood and fluid into the retina and knocking off photoreceptors. Here, we simulate a computational model of angiogenesis from the choroid blood vessels via a cellular Potts model, as well as BM, RPE cells, drusen deposits and photoreceptors. Our results indicate that improving AMD may require fixing the impaired lateral adhesion between RPE cells and with BM, as well as diminishing Vessel Endothelial Growth Factor (VEGF) and Jagged proteins that affect the Notch signaling pathway. Our numerical simulations suggest that anti-VEGF and anti-Jagged therapies could temporarily halt exudative AMD while addressing impaired cellular adhesion, which could be more effective over a longer time-span.
Radial basis function interpolation in the limit of increasingly flat basis functions
(Elsevier, 2016-02-15) Kindelan Segura, Manuel; Moscoso, Miguel; González Rodríguez, Pedro; Ministerio de Ciencia e Innovación (España)
We propose a new approach to study Radial Basis Function (RBF) interpolation in the limit of increasingly flat functions. The new approach is based on the semi-analytical computation of the Laurent series of the inverse of the RBF interpolation matrix described in a previous paper [3]. Once the Laurent series is obtained, it can be used to compute the limiting polynomial interpolant, the optimal shape parameter of the RBFs used for interpolation, and the weights of RBF finite difference formulas, among other things.
Band depth based initialization of K-means for functional data clustering
(Springer, 2023-06) Albert Smet, Javier; Torrente Orihuela, Ester Aurora; Romo, Juan; Ministerio de Ciencia, Innovación y Universidades (España)
The k-Means algorithm is one of the most popular choices for clustering data but is well-known to be sensitive to the initialization process. There is a substantial number of methods that aim at finding optimal initial seeds for k-Means, though none of them is universally valid. This paper presents an extension to longitudinal data of one of such methods, the BRIk algorithm, that relies on clustering a set of centroids derived from bootstrap replicates of the data and on the use of the versatile Modified Band Depth. In our approach we improve the BRIk method by adding a step where we fit appropriate B-splines to our observations and a resampling process that allows computational feasibility and handling issues such as noise or missing data. We have derived two techniques for providing suitable initial seeds, each of them stressing respectively the multivariate or the functional nature of the data. Our results with simulated and real data sets indicate that our Functional Data Approach to the BRIK method (FABRIk) and our Functional Data Extension of the BRIK method (FDEBRIk) are more effective than previous proposals at providing seeds to initialize k-Means in terms of clustering recovery.
Model architecture can transform catastrophic forgetting into positive transfer
(Nature Research, 2022-06-24) Ruiz García, Miguel; European Commission
The work of McCloskey and Cohen popularized the concept of catastrophic interference. They used a neural network that tried to learn addition using two groups of examples as two different tasks. In their case, learning the second task rapidly deteriorated the acquired knowledge about the previous one. We hypothesize that this could be a symptom of a fundamental problem: addition is an algorithmic task that should not be learned through pattern recognition. Therefore, other model architectures better suited for this task would avoid catastrophic forgetting. We use a neural network with a different architecture that can be trained to recover the correct algorithm for the addition of binary numbers. This neural network includes conditional clauses that are naturally treated within the back-propagation algorithm. We test it in the setting proposed by McCloskey and Cohen and training on random additions one by one. The neural network not only does not suffer from catastrophic forgetting but it improves its predictive power on unseen pairs of numbers as training progresses. We also show that this is a robust effect, also present when averaging many simulations. This work emphasizes the importance that neural network architecture has for the emergence of catastrophic forgetting and introduces a neural network that is able to learn an algorithm.
Edge observables of the Maxwell-Chern-Simons theory
(American Physical Society (APS), 2022-07-15) Barbero G., J. Fernando; Díaz Jiménez, Bogar; Margalef Bentabol, Juan; Sánchez Villaseñor, Eduardo Jesús; Comunidad de Madrid; European Commission; Ministerio de Ciencia, Innovación y Universidades (España); Universidad Carlos III de Madrid
We analyze the Lagrangian and Hamiltonian formulations of the Maxwell-Chern-Simons theory defined on a manifold with boundary for two different sets of boundary equations derived from a variational principle. We pay special attention to the identification of the infinite chains of boundary constraints and their resolution. We identify edge observables and their algebra [which corresponds to the well-known U (1) Kac-Moody algebra]. Without performing any gauge fixing, and using the Hodge-Morrey theorem, we solve the Hamilton equations whenever possible. In order to give explicit solutions, we consider the particular case in which the fields are defined on a 2-disk. Finally, we study the Fock quantization of the system and discuss the quantum edge observables and states.
Adiabatic lapse rate of real gases
(American Physical Society (APS), 2022-07) Díaz Jiménez, Bogar; García Ariza, Miguel Ángel; Ramírez, J. E.; European Commission; Ministerio de Ciencia, Innovación y Universidades (España)
We derive a formula for the dry adiabatic lapse rate of atmospheres composed of real gases. We restrict our study to those described by a family of two-parameter cubic equations of state and the recent Guevara-Rodríguez noncubic equation. Since our formula depends on the adiabatic curves, we compute them all at once, considering molecules that can move, rotate, and vibrate, for any equation of state. To illustrate our results, we estimate the lapse rate of the troposphere of Titan, obtaining a better approximation to the observed data in some instances, when compared to the estimation provided by the virial expansion up to the third order.
Classical analogs of the covariance matrix, purity, linear entropy, and von Neumann entropy
(American Physical Society, 2022-06) Díaz Jiménez, Bogar; García González, Diego; Gutiérrez-Ruiz, Daniel; Vergara, J. David; European Commission; Universidad Carlos III de Madrid
We obtain a classical analog of the quantum covariance matrix by performing its classical approximation for any continuous quantum state, and we illustrate this approach with the anharmonic oscillator. Using this classical covariance matrix, we propose classical analogs of the purity, linear quantum entropy, and von Neumann entropy for classical integrable systems, when the quantum counterpart of the system under consideration is in a Gaussian state. As is well known, this matrix completely characterizes the purity, linear quantum entropy, and von Neumann entropy for Gaussian states. These classical analogs can be interpreted as quantities that reveal how much information from the complete system remains in the considered subsystem. To illustrate our approach, we calculate these classical analogs for three coupled harmonic oscillators and two linearly coupled oscillators. We find that they exactly reproduce the results of their quantum counterparts. In this sense, it is remarkable that we can calculate these quantities from the classical viewpoint.
Consistent and non-consistent deformations of gravitational theories
(Springer, 2022-05) Barbero G., J. Fernando; Basquens, Marc; Díaz Jiménez, Bogar; Sánchez Villaseñor, Eduardo Jesús; Agencia Estatal de Investigación (España); Universidad Carlos III de Madrid; European Commission
We study the internally abelianized version of a range of gravitational theories, written in connection tetrad form, and study the possible interaction terms that can be added to them in a consistent way. We do this for 2+1 and 3+1 dimensional models. In the latter case we show that the Cartan-Palatini and Holst actions are not consistent deformations of their abelianized versions. We also show that the Husain-Kuchař and Euclidean self-dual actions are consistent deformations of their abelianized counterparts. This suggests that if the latter can be quantized, it could be possible to devise a perturbative scheme leading to the quantization of Euclidean general relativity along the lines put forward by Smolin in the early nineties.
Proof of the equivalence of the symplectic forms derived from the canonical and the covariant phase space formalisms
(American Physical Society, 2022-05-15) Margalef Bentabol, Juan; Sánchez Villaseñor, Eduardo Jesús; Comunidad de Madrid; Ministerio de Ciencia e Innovación (España); Universidad Carlos III de Madrid
We prove that, for any theory defined over a space-time with boundary, the symplectic form derived in the covariant phase space is equivalent to the one derived from the canonical formalism.
Estrategias de movilidad basadas en la teoría de percolación para evitar la diseminación de enfermedades: COVID-19
(Sociedad Mexicana de Física, A.C., 2022-01) Ramirez, Jhony E.; Rosales Herrera, Diana; Velázquez Castro, Jorge; Díaz Jiménez, Bogar; Martínez, Mario Iván; Vázquez Juárez, Patricia; Fernández Téllez, Arturo; European Commission
La movilidad de las personas es uno de los principales factores que propician la propagación espacial de epidemias. Las medidas de control epidemiológico basadas en la restricción de movilidad son generalmente poco populares y las consecuencias económicas pueden llegar aser muy grandes. Debido a los altos costos de estas medidas, es de gran relevancia tener estrategias globales que optimicen las medidas minimizando los costos. En este trabajo, se calcula el umbral de percolación de la propagación de enfermedades en redes. De manera particular, se encuentra el número de caminos a restringir y localidades que tienen que ser aisladas para limitar la propagación global de COVID-19 en el Estado de Puebla, México. Simulaciones computacionales donde se implementan las medidas de restricción de movilidadentre los diferentes municipios, junto con las medidas de confinamiento, muestran que es posible reducir un 94 % de la población afectada comparado con el caso en el que no se implementa ninguna medida. Esta metodología puede ser aplicada a distintas zonas para ayudar a las autoridades de salud en la toma de decisiones. Human mobility is an important factor in the spatial propagation of infectious diseases. On the other hand, the control strategies based on mobility restrictions are generally unpopular and costly. These high social and economic costs make it very important to design global protocols where the cost is minimized and effects maximized. In this work, we calculate the percolation threshold of the spread in a network of a disease. In particular, we found the number of roads to close and regions to isolate in the Puebla State, Mexico, to avoid the global spread of COVID-19. Computational simulations taking into account the proposed strategy show a potential reduction of 94 % of infections. This methodology can be used in broader and different areas to help in the design of health policies
Propagation of premixed laminar flames in 3D narrow open ducts using RBF-generated finite differences
(Taylor & Francis Group, 2013-10-01) Bayona Revilla, Víctor; Kindelan Segura, Manuel; Ministerio de Ciencia e Innovación (España)
Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts.
Optimal constant shape parameter for multiquadric based RBF-FD method
(Elsevier, 2011-08-10) Bayona Revilla, Víctor; Moscoso, Miguel; Kindelan Segura, Manuel; Comunidad de Madrid; Ministerio de Ciencia e Innovación (España)
Radial basis functions (RBFs) have become a popular method for interpolation and solution of partial differential equations (PDEs). Many types of RBFs used in these problems contain a shape parameter, and there is much experimental evidence showing that accuracy strongly depends on the value of this shape parameter. In this paper, we focus on PDE problems solved with a multiquadric based RBF finite difference (RBF-FD) method. We propose an efficient algorithm to compute the optimal value of the shape parameter that minimizes the approximation error. The algorithm is based on analytical approximations to the local RBF-FD error derived in [1]. We show through several examples in 1D and 2D, both with structured and unstructured nodes, that very accurate solutions (compared to finite differences) can be achieved using the optimal value of the constant shape parameter.
Optimal variable shape parameter for multiquadric based RBF-FD method
(Elsevier, 2012-03-20) Bayona Revilla, Víctor; Moscoso, Miguel; Kindelan Segura, Manuel; Comunidad de Madrid; Ministerio de Ciencia e Innovación (España)
In this follow up paper to our previous study in Bayona et al. (2011) [2], we present a new technique to compute the solution of PDEs with the multiquadric based RBF finite difference method (RBF-FD) using an optimal node dependent variable value of the shape parameter. This optimal value is chosen so that, to leading order, the local approximation error of the RBF-FD formulas is zero. In our previous paper (Bayona et al., 2011) [2] we considered the case of an optimal (constant) value of the shape parameter for all the nodes. Our new results show that, if one allows the shape parameter to be different at each grid point of the domain, one may obtain very significant accuracy improvements with a simple and inexpensive numerical technique. We analyze the same examples studied in Bayona et al. (2011) [2], both with structured and unstructured grids, and compare our new results with those obtained previously. We also find that, if there are a significant number of nodes for which no optimal value of the shape parameter exists, then the improvement in accuracy deteriorates significantly. In those cases, we use generalized multiquadrics as RBFs and choose the exponent of the multiquadric at each node to assure the existence of an optimal variable shape parameter.
RBF-FD Formulas and Convergence Properties
(Elsevier, 2010-11-01) Bayona Revilla, Víctor; Moscoso, Miguel; Carretero Cerrajero, Manuel; Kindelan Segura, Manuel; Comunidad de Madrid; Ministerio de Educación, Cultura y Deporte (España)
The local RBF is becoming increasingly popular as an alternative to the global version that suffers from ill-conditioning. In this paper, we study analytically the convergence behavior of the local RBF method as a function of the number of nodes employed in the scheme, the nodal distance, and the shape parameter. We derive exact formulas for the first and second derivatives in one dimension, and for the Laplacian in two dimensions. Using these formulas we compute Taylor expansions for the error. From this analysis, we find that there is an optimal value of the shape parameter for which the error is minimum. This optimal parameter is independent of the nodal distance. Our theoretical results are corroborated by numerical experiments.

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