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Ferri I, Gaya-Àvila A, Díaz-Guilera A. Three-state opinion model with mobile agents. Chaos 2023; 33:093121. [PMID: 37712914 DOI: 10.1063/5.0152674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2023] [Accepted: 08/21/2023] [Indexed: 09/16/2023]
Abstract
We study an agent-based opinion model with two extreme (opposite) opinion states and a neutral intermediate one. We adjust the relative degree of conviction between extremists and neutrals through a dimensionless parameter called the "neutrality parameter" to investigate its impact on the outcome of the system. In our model, agents move randomly on a plane with periodic boundary conditions and interact with each other only when they are within a fixed distance threshold. We examine different movement mechanisms and their interplay with the neutrality parameter. Our results show that in general, mobility promotes the global consensus, especially for extreme opinions. However, it takes significantly less time to reach a consensus on the neutral opinion.
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Affiliation(s)
- I Ferri
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - A Gaya-Àvila
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - A Díaz-Guilera
- Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
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2
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Beardo A, Prignano L, Sagarra O, Díaz-Guilera A. Influence of topology in the mobility enhancement of pulse-coupled oscillator synchronization. Phys Rev E 2017; 96:062306. [PMID: 29347286 DOI: 10.1103/physreve.96.062306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2017] [Indexed: 06/07/2023]
Abstract
In this work we revisit the nonmonotonic behavior (NMB) of synchronization time with velocity reported for systems of mobile pulse-coupled oscillators (PCOs). We devise a control parameter that allows us to predict in which range of velocities NMB may occur, also uncovering the conditions allowing us to establish the emergence of NMB based on specific features of the connectivity rule. Specifically, our results show that if the connectivity rule is such that the interaction patterns are sparse and, more importantly, include a large fraction of nonreciprocal interactions, then the system will display NMB. We furthermore provide a microscopic explanation relating the presence of such features of the connectivity patterns to the existence of local clusters unable to synchronize, termed frustrated clusters, for which we also give a precise definition in terms of simple graph concepts. We conclude that, if the probability of finding a frustrated cluster in a system of moving PCOs is high enough, NMB occurs in a predictable range of velocities.
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Affiliation(s)
- A Beardo
- Complexity Lab Barcelona, Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - L Prignano
- Complexity Lab Barcelona, Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
| | - O Sagarra
- Complexity Lab Barcelona, Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- DRIBIA Data Research, Carrer de Roc Boronat 117, 08018 Barcelona, Spain
| | - A Díaz-Guilera
- Complexity Lab Barcelona, Departament de Física de la Matèria Condensada, Universitat de Barcelona, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems (UBICS), Universitat de Barcelona, 08028 Barcelona, Spain
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3
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Abstract
In this study we present an extension of the dynamics of diffusion in multiplex graphs, which makes the equations compatible with the replicator equation with mutations. We derive an exact formula for the diffusion term, which shows that, while diffusion is linear for numbers of agents, it is necessary to account for nonlinear terms when working with fractions of individuals. We also derive the transition probabilities that give rise to such macroscopic behavior, completing the bottom-up description. Finally, it is shown that the usual assumption of constant population sizes induces a hidden selective pressure due to the diffusive dynamics, which favors the increase of fast diffusing strategies.
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Affiliation(s)
- R J Requejo
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franques 1, 08028 Barcelona, Spain
| | - A Díaz-Guilera
- Departament de Física Fonamental, Universitat de Barcelona, Martí i Franques 1, 08028 Barcelona, Spain
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4
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Gutiérrez-Roig M, Sagarra O, Oltra A, Palmer JRB, Bartumeus F, Díaz-Guilera A, Perelló J. Active and reactive behaviour in human mobility: the influence of attraction points on pedestrians. R Soc Open Sci 2016; 3:160177. [PMID: 27493774 PMCID: PMC4968466 DOI: 10.1098/rsos.160177] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/10/2016] [Accepted: 06/16/2016] [Indexed: 06/06/2023]
Abstract
Human mobility is becoming an accessible field of study, thanks to the progress and availability of tracking technologies as a common feature of smart phones. We describe an example of a scalable experiment exploiting these circumstances at a public, outdoor fair in Barcelona (Spain). Participants were tracked while wandering through an open space with activity stands attracting their attention. We develop a general modelling framework based on Langevin dynamics, which allows us to test the influence of two distinct types of ingredients on mobility: reactive or context-dependent factors, modelled by means of a force field generated by attraction points in a given spatial configuration and active or inherent factors, modelled from intrinsic movement patterns of the subjects. The additive and constructive framework model accounts for some observed features. Starting with the simplest model (purely random walkers) as a reference, we progressively introduce different ingredients such as persistence, memory and perceptual landscape, aiming to untangle active and reactive contributions and quantify their respective relevance. The proposed approach may help in anticipating the spatial distribution of citizens in alternative scenarios and in improving the design of public events based on a facts-based approach.
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Affiliation(s)
- M. Gutiérrez-Roig
- Departament de Física Fonamental, Universitat de Barcelona. Martí i Franqués 1, 08028 Barcelona, Spain
| | - O. Sagarra
- Departament de Física Fonamental, Universitat de Barcelona. Martí i Franqués 1, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems UBICS, 08028 Barcelona, Spain
| | - A. Oltra
- Centre d’Estudis Avançats de Blanes (CEAB-CSIC), Accés a la Cala Sant Francesc, 17300 Blanes, Spain
- Centre de Recerca Ecològica i Aplicacions Forestals (CREAF), Campus de Bellaterra (UAB) Edifici C, 08193 Cerdanyola del Vallès, Spain
| | - J. R. B. Palmer
- Centre de Recerca Ecològica i Aplicacions Forestals (CREAF), Campus de Bellaterra (UAB) Edifici C, 08193 Cerdanyola del Vallès, Spain
| | - F. Bartumeus
- Centre d’Estudis Avançats de Blanes (CEAB-CSIC), Accés a la Cala Sant Francesc, 17300 Blanes, Spain
- Centre de Recerca Ecològica i Aplicacions Forestals (CREAF), Campus de Bellaterra (UAB) Edifici C, 08193 Cerdanyola del Vallès, Spain
- ICREA, Passeig Lluis Companys 23, 08010 Barcelona, Spain
| | - A. Díaz-Guilera
- Departament de Física Fonamental, Universitat de Barcelona. Martí i Franqués 1, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems UBICS, 08028 Barcelona, Spain
| | - J. Perelló
- Departament de Física Fonamental, Universitat de Barcelona. Martí i Franqués 1, 08028 Barcelona, Spain
- Universitat de Barcelona Institute of Complex Systems UBICS, 08028 Barcelona, Spain
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5
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Sagarra O, Pérez Vicente CJ, Díaz-Guilera A. Role of adjacency-matrix degeneracy in maximum-entropy-weighted network models. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 92:052816. [PMID: 26651753 DOI: 10.1103/physreve.92.052816] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/03/2015] [Indexed: 06/05/2023]
Abstract
Complex network null models based on entropy maximization are becoming a powerful tool to characterize and analyze data from real systems. However, it is not easy to extract good and unbiased information from these models: A proper understanding of the nature of the underlying events represented in them is crucial. In this paper we emphasize this fact stressing how an accurate counting of configurations compatible with given constraints is fundamental to build good null models for the case of networks with integer-valued adjacency matrices constructed from an aggregation of one or multiple layers. We show how different assumptions about the elements from which the networks are built give rise to distinctively different statistics, even when considering the same observables to match those of real data. We illustrate our findings by applying the formalism to three data sets using an open-source software package accompanying the present work and demonstrate how such differences are clearly seen when measuring network observables.
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Affiliation(s)
- O Sagarra
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain
| | - C J Pérez Vicente
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain
| | - A Díaz-Guilera
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain
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6
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Sagarra O, Pérez Vicente CJ, Díaz-Guilera A. Statistical mechanics of multiedge networks. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 88:062806. [PMID: 24483510 DOI: 10.1103/physreve.88.062806] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/14/2013] [Indexed: 06/03/2023]
Abstract
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.
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Affiliation(s)
- O Sagarra
- Departament de Física Fonamental, Universitat de Barcelona, E-08028 Barcelona, Spain
| | - C J Pérez Vicente
- Departament de Física Fonamental, Universitat de Barcelona, E-08028 Barcelona, Spain
| | - A Díaz-Guilera
- Departament de Física Fonamental, Universitat de Barcelona, E-08028 Barcelona, Spain
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7
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Solé-Ribalta A, De Domenico M, Kouvaris NE, Díaz-Guilera A, Gómez S, Arenas A. Spectral properties of the Laplacian of multiplex networks. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 88:032807. [PMID: 24125312 DOI: 10.1103/physreve.88.032807] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2013] [Indexed: 06/02/2023]
Abstract
One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gómez et al. [Phys. Rev. Lett. 110, 028701 (2013)], some of the authors proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability.
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Affiliation(s)
- A Solé-Ribalta
- Departament d'Enginyeria Informática i Matemátiques, Universitat Rovira i Virgili, Tarragona, Spain
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8
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Prignano L, Sagarra O, Díaz-Guilera A. Tuning synchronization of integrate-and-fire oscillators through mobility. Phys Rev Lett 2013; 110:114101. [PMID: 25166539 DOI: 10.1103/physrevlett.110.114101] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/22/2012] [Indexed: 06/03/2023]
Abstract
We analyze the emergence of synchronization in a population of moving integrate-and-fire oscillators. Oscillators, while moving on a plane, interact with their nearest neighbor upon firing time. We discover a nonmonotonic dependence of the synchronization time on the velocity of the agents. Moreover, we find that mechanisms that drive synchronization are different for different dynamical regimes. We report the extreme situation where an interplay between the time scales involved in the dynamical processes completely inhibits the achievement of a coherent state. We also provide estimators for the transitions between the different regimes.
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Affiliation(s)
- L Prignano
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain
| | - O Sagarra
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain
| | - A Díaz-Guilera
- Departament de Física Fonamental, Universitat de Barcelona, 08028 Barcelona, Spain
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9
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Gómez S, Díaz-Guilera A, Gómez-Gardeñes J, Pérez-Vicente CJ, Moreno Y, Arenas A. Diffusion dynamics on multiplex networks. Phys Rev Lett 2013; 110:028701. [PMID: 23383947 DOI: 10.1103/physrevlett.110.028701] [Citation(s) in RCA: 292] [Impact Index Per Article: 26.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2012] [Indexed: 05/05/2023]
Abstract
We study the time scales associated with diffusion processes that take place on multiplex networks, i.e., on a set of networks linked through interconnected layers. To this end, we propose the construction of a supra-laplacian matrix, which consists of a dimensional lifting of the laplacian matrix of each layer of the multiplex network. We use perturbative analysis to reveal analytically the structure of eigenvectors and eigenvalues of the complete network in terms of the spectral properties of the individual layers. The spectrum of the supra-laplacian allows us to understand the physics of diffusionlike processes on top of multiplex networks.
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Affiliation(s)
- S Gómez
- Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, 43007 Tarragona, Spain
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10
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Vragović I, Louis E, Díaz-Guilera A. Efficiency of informational transfer in regular and complex networks. Phys Rev E Stat Nonlin Soft Matter Phys 2005; 71:036122. [PMID: 15903508 DOI: 10.1103/physreve.71.036122] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2004] [Indexed: 05/02/2023]
Abstract
We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study nonclustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.
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Affiliation(s)
- I Vragović
- Departamento de Física Aplicada, Instituto Universitario de Materiales and Unidad Asociada CSIC-UA, Universidad de Alicante, E-03080 Alicante, Spain
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11
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Guimerà R, Danon L, Díaz-Guilera A, Giralt F, Arenas A. Self-similar community structure in a network of human interactions. Phys Rev E Stat Nonlin Soft Matter Phys 2003; 68:065103. [PMID: 14754250 DOI: 10.1103/physreve.68.065103] [Citation(s) in RCA: 339] [Impact Index Per Article: 16.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2003] [Revised: 05/09/2003] [Indexed: 05/24/2023]
Abstract
We propose a procedure for analyzing and characterizing complex networks. We apply this to the social network as constructed from email communications within a medium sized university with about 1700 employees. Email networks provide an accurate and nonintrusive description of the flow of information within human organizations. Our results reveal the self-organization of the network into a state where the distribution of community sizes is self-similar. This suggests that a universal mechanism, responsible for emergence of scaling in other self-organized complex systems, as, for instance, river networks, could also be the underlying driving force in the formation and evolution of social networks.
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Affiliation(s)
- R Guimerà
- Departament d'Enginyeria Química, Universitat Rovira i Virgili, 43007 Tarragona, Catalunya, Spain
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12
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Guimerà R, Díaz-Guilera A, Vega-Redondo F, Cabrales A, Arenas A. Optimal network topologies for local search with congestion. Phys Rev Lett 2002; 89:248701. [PMID: 12484988 DOI: 10.1103/physrevlett.89.248701] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2002] [Indexed: 05/24/2023]
Abstract
The problem of searchability in decentralized complex networks is of great importance in computer science, economy, and sociology. We present a formalism that is able to cope simultaneously with the problem of search and the congestion effects that arise when parallel searches are performed, and we obtain expressions for the average search cost both in the presence and the absence of congestion. This formalism is used to obtain optimal network structures for a system using a local search algorithm. It is found that only two classes of networks can be optimal: starlike configurations, when the number of parallel searches is small, and homogeneous-isotropic configurations, when it is large.
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Affiliation(s)
- R Guimerà
- Departament d'Enginyeria Química, Universitat Rovira i Virgili, 43007 Tarragona, Spain
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13
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Guardiola X, Díaz-Guilera A, Pérez CJ, Arenas A, Llas M. Modeling diffusion of innovations in a social network. ACTA ACUST UNITED AC 2002; 66:026121. [PMID: 12241251 DOI: 10.1103/physreve.66.026121] [Citation(s) in RCA: 59] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2002] [Indexed: 11/07/2022]
Abstract
A simple model of diffusion of innovations in a social network with upgrading costs is introduced. Agents are characterized by a single real variable, their technological level. According to local information, agents decide whether to upgrade their level or not, balancing their possible benefit with the upgrading cost. A critical point where technological avalanches display a power-law behavior is also found. This critical point is characterized by a macroscopic observable that turns out to optimize technological growth in the stationary state. Analytical results supporting our findings are found for the globally coupled case.
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Affiliation(s)
- X Guardiola
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
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14
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Abstract
We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous phase transition between a sparse and a congested regime is observed and accurately described by an order parameter and the power spectra. At the critical point the behavior of the model is totally independent of the number of hierarchical levels. Also scaling properties are observed when the size of the system varies. The presence of noise in the communication is shown to break the transition. The analytical results are a useful guide to forecasting the main features of real networks.
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Affiliation(s)
- A Arenas
- Departament d'Enginyeria Informáticat, Universitat Rovira i Virgili, Tarragona, Spain
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15
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Arenas A, Díaz-Guilera A, Pérez CJ, Vega-Redondo F. Self-organized evolution in a socioeconomic environment. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 61:3466-3469. [PMID: 11088123 DOI: 10.1103/physreve.61.3466] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/1999] [Indexed: 05/23/2023]
Abstract
We propose a general scenario to analyze technological changes in socio-economic environments. We illustrate the ideas with a model that incorporating the main trends is simple enough to extract analytical results and, at the same time, sufficiently complex to display a rich dynamic behavior. Our study shows that there exists a macroscopic observable that is maximized in a regime where the system is critical, in the sense that the distribution of events follow power laws. Computer simulations show that, in addition, the system always self-organizes to achieve the optimal performance in the stationary state.
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Affiliation(s)
- A Arenas
- Departament d'Enginyeria Informàtica, Universitat Rovira i Virgili, Carretera Salou s/n, E-43006 Tarragona, Spain
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16
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Guardiola X, Díaz-Guilera A. Pattern selection in a lattice of pulse-coupled oscillators. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 60:3626-32. [PMID: 11970196 DOI: 10.1103/physreve.60.3626] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/1999] [Revised: 05/14/1999] [Indexed: 04/18/2023]
Abstract
We study spatio-temporal pattern formation in a ring of N oscillators with inhibitory unidirectional pulselike interactions. The attractors of the dynamics are limit cycles where each oscillator fires once and only once. Since some of these limit cycles lead to the same pattern, we introduce the concept of pattern degeneracy to take it into account. Moreover, we give a qualitative estimation of the volume of the basin of attraction of each pattern by means of some probabilistic arguments and pattern degeneracy, and show how they are modified as we change the value of the coupling strength. In the limit of small coupling, our estimative formula gives a perfect agreement with numerical simulations.
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Affiliation(s)
- X Guardiola
- Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain.
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17
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Corral Á, Pérez CJ, Díaz-Guilera A, Arenas A. Synchronization in a lattice model of pulse-coupled oscillators. Phys Rev Lett 1995; 75:3697-3700. [PMID: 10059704 DOI: 10.1103/physrevlett.75.3697] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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18
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Corral Á, Pérez CJ, Díaz-Guilera A, Arenas A. Self-organized criticality and synchronization in a lattice model of integrate-and-fire oscillators. Phys Rev Lett 1995; 74:118-121. [PMID: 10057713 DOI: 10.1103/physrevlett.74.118] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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20
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Díaz-Guilera A, Rodríguez MA, Rubí JM. Heat transfer in the coolant channel of a heat-exchanger system based on fluctuation theories. Phys Rev A Gen Phys 1988; 38:4822-4831. [PMID: 9900950 DOI: 10.1103/physreva.38.4822] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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21
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Díaz-Guilera A, Rubí JM. Internal and external fluctuations around nonequilibrium steady states in one-dimensional heat-conduction problems. Phys Rev A Gen Phys 1986; 34:462-467. [PMID: 9897271 DOI: 10.1103/physreva.34.462] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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22
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Rodríguez M, Díaz-Guilera A, Sancho J. Asymptotic analysis of a stochastic non-linear nuclear reactor model. ANN NUCL ENERGY 1986. [DOI: 10.1016/0306-4549(86)90116-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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