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Arán-Tapia I, Soto-Varela A, Pérez-Muñuzuri V, Santos-Pérez S, Arán I, Muñuzuri AP. Numerical Simulations of the Epley Maneuver With Clinical Implications. Ear Hear 2024:00003446-990000000-00261. [PMID: 38439150 DOI: 10.1097/aud.0000000000001493] [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] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2024]
Abstract
OBJECTIVES Canalith repositioning procedures to treat benign paroxysmal positional vertigo are often applied following standardized criteria, without considering the possible anatomical singularities of the membranous labyrinth for each individual. As a result, certain patients may become refractory to the treatment due to significant deviations from the ideal membranous labyrinth, that was considered when the maneuvers were designed. This study aims to understand the dynamics of the endolymphatic fluid and otoconia, within the membranous labyrinth geometry, which may contribute to the ineffectiveness of the Epley maneuver. Simultaneously, the study seeks to explore methods to avoid or reduce treatment failure. DESIGN We conducted a study on the Epley maneuver using numerical simulations based on a three-dimensional medical image reconstruction of the human left membranous labyrinth. A high-quality micro-computed tomography of a human temporal bone specimen was utilized for the image reconstruction, and a mathematical model for the endolymphatic fluid was developed and coupled with a spherical particle model representing otoconia inside the fluid. This allowed us to measure the position and time of each particle throughout all the steps of the maneuver, using equations that describe the physics behind benign paroxysmal positional vertigo. RESULTS Numerical simulations of the standard Epley maneuver applied to this membranous labyrinth model yielded unsatisfactory results, as otoconia do not reach the frontside of the utricle, which in this study is used as the measure of success. The resting times between subsequent steps indicated that longer intervals are required for smaller otoconia. Using different angles of rotation can prevent otoconia from entering the superior semicircular canal or the posterior ampulla. Steps 3, 4, and 5 exhibited a heightened susceptibility to failure, as otoconia could be accidentally displaced into these regions. CONCLUSIONS We demonstrate that modifying the Epley maneuver based on the numerical results obtained in the membranous labyrinth of the human specimen under study can have a significant effect on the success or failure of the treatment. The use of numerical simulations appears to be a useful tool for future canalith repositioning procedures that aim to personalize the treatment by modifying the rotation planes currently defined as the standard criteria.
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Affiliation(s)
- Ismael Arán-Tapia
- Group of Non-Linear Physics, Department of Physics, Campus Sur, University of Santiago de Compostela, Santiago de Compostela, Spain
- Galician Center for Mathematical Research and Technology, Santiago de Compostela, Spain
- Cross-disciplinary Research Center in Environmental Technologies (CRETUS), University of Santiago de Compostela, Santiago de Compostela, Spain
| | - Andrés Soto-Varela
- Division of Neurotology, Department of Otorhinolaryngology, Complexo Hospitalario Universitario, Santiago de Compostela, Spain
- Department of Surgery and Medical-Surgical Specialities, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
- Health Research Institute of Santiago, Santiago de Compostela, Spain; and
| | - Vicente Pérez-Muñuzuri
- Group of Non-Linear Physics, Department of Physics, Campus Sur, University of Santiago de Compostela, Santiago de Compostela, Spain
- Cross-disciplinary Research Center in Environmental Technologies (CRETUS), University of Santiago de Compostela, Santiago de Compostela, Spain
| | - Sofía Santos-Pérez
- Division of Neurotology, Department of Otorhinolaryngology, Complexo Hospitalario Universitario, Santiago de Compostela, Spain
- Department of Surgery and Medical-Surgical Specialities, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
- Health Research Institute of Santiago, Santiago de Compostela, Spain; and
| | - Ismael Arán
- Department of Otorhinolaryngology, Complexo Hospitalario Universitario de Pontevedra, Pontevedra, Spain
| | - Alberto P Muñuzuri
- Group of Non-Linear Physics, Department of Physics, Campus Sur, University of Santiago de Compostela, Santiago de Compostela, Spain
- Galician Center for Mathematical Research and Technology, Santiago de Compostela, Spain
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2
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Arán-Tapia I, Soto-Varela A, Pérez-Muñuzuri V, Santos-Pérez S, Arán I, Muñuzuri AP. Numerical simulations to determine the stimulation of the crista ampullaris during the Head Impulse Test. Comput Biol Med 2023; 163:107225. [PMID: 37437361 DOI: 10.1016/j.compbiomed.2023.107225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2023] [Revised: 06/13/2023] [Accepted: 06/30/2023] [Indexed: 07/14/2023]
Abstract
The Head Impulse Test, the most widely accept test to assess the vestibular function, comprises rotations of the head based on idealized orientations of the semicircular canals, instead of their individual arrangement specific for each patient. In this study, we show how computational modelling can help personalize the diagnosis of vestibular diseases. Based on a micro-computed tomography reconstruction of the human membranous labyrinth and their simulation using Computational Fluid Dynamics and Fluid-Solid Interaction techniques, we evaluated the stimulus experienced by the six cristae ampullaris under different rotational conditions mimicking the Head Impulse Test. The results show that the maximum stimulation of the crista ampullaris occurs for directions of rotation that are more aligned with the orientation of the cupulae (average deviation from alignment of 4.7°, 9.8°, and 19.4° for the horizontal, posterior, and superior maxima, respectively) than with the planes of the semicircular canals (average deviation from alignment of 32.4°, 70.5°, and 67.8° for the horizontal, posterior, and superior maxima, respectively). A plausible explanation is that when rotations are applied with respect to the center of the head, the inertial forces acting directly over the cupula become dominant over the endolymphatic fluid forces generated in the semicircular canals. Our results indicate that it is necessary to consider cupulae orientation to ensure optimal conditions for testing the vestibular function.
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Affiliation(s)
- Ismael Arán-Tapia
- Group of Non-Linear Physics, Campus Sur, University of Santiago de Compostela, Spain; Galician Center for Mathematical Research and Technology (CITMAga), Santiago de Compostela, Spain; CRETUS Institute, Santiago de Compostela, Spain.
| | - Andrés Soto-Varela
- Division of Neurotology, Department of Otorhinolaryngology, Complexo Hospitalario Universitario, Santiago de Compostela, Spain; Department of Surgery and Medical-Surgical Specialities, Universidade de Santiago de Compostela, Santiago de Compostela, Spain; Health Research Institute of Santiago (IDIS), Santiago de Compostela, Spain
| | - Vicente Pérez-Muñuzuri
- Group of Non-Linear Physics, Campus Sur, University of Santiago de Compostela, Spain; CRETUS Institute, Santiago de Compostela, Spain
| | - Sofía Santos-Pérez
- Division of Neurotology, Department of Otorhinolaryngology, Complexo Hospitalario Universitario, Santiago de Compostela, Spain; Department of Surgery and Medical-Surgical Specialities, Universidade de Santiago de Compostela, Santiago de Compostela, Spain
| | - Ismael Arán
- Otoneurology Unit of the Complexo Hospitalario Universitario de Pontevedra, Spain
| | - Alberto P Muñuzuri
- Group of Non-Linear Physics, Campus Sur, University of Santiago de Compostela, Spain; Galician Center for Mathematical Research and Technology (CITMAga), Santiago de Compostela, Spain.
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3
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Rodríguez FY, Muñuzuri AP. A Goodwin Model Modification and Its Interactions in Complex Networks. Entropy (Basel) 2023; 25:894. [PMID: 37372238 DOI: 10.3390/e25060894] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/26/2023] [Revised: 05/17/2023] [Accepted: 05/30/2023] [Indexed: 06/29/2023]
Abstract
The global economy cannot be understood without the interaction of smaller-scale economies. We addressed this issue by considering a simplified economic model that still preserves the basic features, and analyzed the interaction of a set of such economies and the collective emerging dynamic. The topological structure of the economies' network appears to correlate with the collective properties observed. In particular, the strength of the coupling between the different networks as well as the specific connectivity of each node happen to play a crucial role in the determination of the final state.
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Affiliation(s)
- Francisco Yáñez Rodríguez
- Group of NonLinear Physics, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Group of NonLinear Physics, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
- Galician Center for Mathematical Research and Technology (CITMAga), 15782 Santiago de Compostela, Spain
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4
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Muñuzuri AP, Gagnon JS, Pérez-Mercader J. Numerical and renormalization group analysis of the phase diagram of a stochastic cubic autocatalytic reaction-diffusion system. Phys Rev E 2023; 107:034213. [PMID: 37073065 DOI: 10.1103/physreve.107.034213] [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] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 03/14/2023] [Indexed: 04/20/2023]
Abstract
The renormalization group is a set of tools that can be used to incorporate the effect of fluctuations in a dynamical system as a rescaling of the system's parameters. Here, we apply the renormalization group to a pattern-forming stochastic cubic autocatalytic reaction-diffusion model and compare its predictions with numerical simulations. Our results demonstrate a good agreement within the range of validity of the theory and show that external noise can be used as a control parameter in such systems.
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Affiliation(s)
- Alberto P Muñuzuri
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138-1204, USA
- Group of Nonlinear Physics, University of Santiago de Compostela, 15706 Santiago de Compostela, Spain
- Galician Center for Mathematical Research and Technology (CITMAga), 15782 Santiago de Compostela, Spain
| | - Jean-Sébastien Gagnon
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138-1204, USA
- Department of Physics, Norwich University, Northfield, Vermont 05663, USA
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138-1204, USA
- Santa Fe Institute, Santa Fe, New Mexico 87501, USA
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5
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Saavedra M, Pérez-Mercader J, Muñuzuri AP. Intermittent regimes as a synchronization phenomenon in two sets of nonlinear chemical oscillators. Chaos 2022; 32:113125. [PMID: 36456329 DOI: 10.1063/5.0104610] [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: 06/20/2022] [Accepted: 10/10/2022] [Indexed: 06/17/2023]
Abstract
Systems of nonlinear chemical oscillators can exhibit a large diversity of non-trivial states depending on the parameters that characterize them. Among these, a synchronization phenomenon is of special interest due to its direct link with chemical and biological processes in nature. We carry out numerical experiments for two different sets of chemical oscillators with different properties and immersed in a Belousov-Zhabotinsky solution. We document the emergence of different states of synchronization that depend on the parameters characterizing the solution. We also show that, in the interface regions, this system generates a stable dynamics of intermittency between the different synchronization states where interesting phenomena, such as the "devil's staircase," emerge. In general, the added complexity introduced with the additional set of oscillators results in more complex non-trivial synchronization states.
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Affiliation(s)
- Martín Saavedra
- Group of NonLinear Physics, Faculty of Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts 02138-1204, USA
| | - Alberto P Muñuzuri
- Group of NonLinear Physics, Faculty of Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
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6
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Carballosa A, Balsa-Barreiro J, Boullosa P, Garea A, Mira J, Miramontes Á, Muñuzuri AP. Assessing the risk of pandemic outbreaks across municipalities with mathematical descriptors based on age and mobility restrictions. Chaos Solitons Fractals 2022; 160:112156. [PMID: 35637663 PMCID: PMC9132613 DOI: 10.1016/j.chaos.2022.112156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/31/2022] [Accepted: 04/24/2022] [Indexed: 06/15/2023]
Abstract
By March 14th 2022, Spain is suffering the sixth wave of the COVID-19 pandemic. All the previous waves have been intimately related to the degree of imposed mobility restrictions and its consequent release. Certain factors explain the incidence of the virus across regions revealing the weak locations that probably require some medical reinforcements. The most relevant ones relate with mobility restrictions by age and administrative competence, i.e., spatial constrains. In this work, we aim to find a mathematical descriptor that could identify the critical communities that are more likely to suffer pandemic outbreaks and, at the same time, to estimate the impact of different mobility restrictions. We analyze the incidence of the virus in combination with mobility flows during the so-called second wave (roughly from August 1st to November 30th, 2020) using a SEIR compartmental model. After that, we derive a mathematical descriptor based on linear stability theory that quantifies the potential impact of becoming a hotspot. Once the model is validated, we consider different confinement scenarios and containment protocols aimed to control the virus spreading. The main findings from our simulations suggest that the confinement of the economically non-active individuals may result in a significant reduction of risk, whose effects are equivalent to the confinement of the total population. This study is conducted across the totality of municipalities in Spain.
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Affiliation(s)
- Alejandro Carballosa
- Group of Nonlinear Physics, Fac. Physics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
- Galician Center for Mathematical Research and Technology (CITMAga), 15782 Santiago de Compostela, Spain
| | - José Balsa-Barreiro
- Institute IDEGA, Department of Geography, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
- MIT Media Lab, Massachusetts Institute of Technology, 75 Amherst St, Cambridge, MA 02139, USA
| | - Pablo Boullosa
- Group of Nonlinear Physics, Fac. Physics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Adrián Garea
- Group of Nonlinear Physics, Fac. Physics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Jorge Mira
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
- Instituto de Materiais (iMATUS), Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Ángel Miramontes
- Institute IDEGA, Department of Geography, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, Fac. Physics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
- Galician Center for Mathematical Research and Technology (CITMAga), 15782 Santiago de Compostela, Spain
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7
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Carballosa A, Balsa-Barreiro J, Garea A, García-Selfa D, Miramontes Á, Muñuzuri AP. Risk evaluation at municipality level of a COVID-19 outbreak incorporating relevant geographic data: the study case of Galicia. Sci Rep 2021; 11:21248. [PMID: 34711874 PMCID: PMC8553869 DOI: 10.1038/s41598-021-00342-2] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/09/2021] [Accepted: 10/11/2021] [Indexed: 11/22/2022] Open
Abstract
The COVID-19 pandemic was an inevitable outcome of a globalized world in which a highly infective disease is able to reach every country in a matter of weeks. While lockdowns and strong mobility restrictions have proven to be efficient to contain the exponential transmission of the virus, its pervasiveness has made it impossible for economies to maintain this kind of measures in time. Understanding precisely how the spread of the virus occurs from a territorial perspective is crucial not only to prevent further infections but also to help with policy design regarding human mobility. From the large spatial differences in the behavior of the virus spread we can unveil which areas have been more vulnerable to it and why, and with this information try to assess the risk that each community has to suffer a future outbreak of infection. In this work we have analyzed the geographical distribution of the cumulative incidence during the first wave of the pandemic in the region of Galicia (north western part of Spain), and developed a mathematical approach that assigns a risk factor for each of the different municipalities that compose the region. This risk factor is independent of the actual evolution of the pandemic and incorporates geographic and demographic information. The comparison with empirical information from the first pandemic wave demonstrates the validity of the method. Our results can potentially be used to design appropriate preventive policies that help to contain the virus.
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Affiliation(s)
- Alejandro Carballosa
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - José Balsa-Barreiro
- Group of Territorial Analysis, Institute IDEGA, University of Santiago de Compostela, Santiago de Compostela, Spain.,MIT Media Lab, Massachusetts Institute of Technology, 75 Amherst St, Cambridge, MA, 02139, USA
| | - Adrián Garea
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - David García-Selfa
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain.,CESGA (Supercomputing Center of Galicia), Avda. de Vigo s/n, Campus Sur, 15705, Santiago de Compostela, Spain
| | - Ángel Miramontes
- Group of Territorial Analysis, Institute IDEGA, University of Santiago de Compostela, Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain.
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8
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Silva CJ, Cruz C, Torres DFM, Muñuzuri AP, Carballosa A, Area I, Nieto JJ, Fonseca-Pinto R, Passadouro R, Santos ESD, Abreu W, Mira J. Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal. Sci Rep 2021; 11:3451. [PMID: 33568716 PMCID: PMC7876047 DOI: 10.1038/s41598-021-83075-6] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 01/27/2021] [Indexed: 02/08/2023] Open
Abstract
The COVID-19 pandemic has forced policy makers to decree urgent confinements to stop a rapid and massive contagion. However, after that stage, societies are being forced to find an equilibrium between the need to reduce contagion rates and the need to reopen their economies. The experience hitherto lived has provided data on the evolution of the pandemic, in particular the population dynamics as a result of the public health measures enacted. This allows the formulation of forecasting mathematical models to anticipate the consequences of political decisions. Here we propose a model to do so and apply it to the case of Portugal. With a mathematical deterministic model, described by a system of ordinary differential equations, we fit the real evolution of COVID-19 in this country. After identification of the population readiness to follow social restrictions, by analyzing the social media, we incorporate this effect in a version of the model that allow us to check different scenarios. This is realized by considering a Monte Carlo discrete version of the previous model coupled via a complex network. Then, we apply optimal control theory to maximize the number of people returning to "normal life" and minimizing the number of active infected individuals with minimal economical costs while warranting a low level of hospitalizations. This work allows testing various scenarios of pandemic management (closure of sectors of the economy, partial/total compliance with protection measures by citizens, number of beds in intensive care units, etc.), ensuring the responsiveness of the health system, thus being a public health decision support tool.
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Affiliation(s)
- Cristiana J Silva
- Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal.
| | - Carla Cruz
- Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal
| | - Delfim F M Torres
- Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA), University of Aveiro, 3810-193, Aveiro, Portugal
| | - Alberto P Muñuzuri
- Department of Physics, Institute CRETUS, Group of Nonlinear Physics, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Alejandro Carballosa
- Department of Physics, Institute CRETUS, Group of Nonlinear Physics, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Iván Area
- Departamento de Matemática Aplicada II, E. E. Aeronáutica e do Espazo, Campus de Ourense, Universidade de Vigo, 32004, Ourense, Spain
| | - Juan J Nieto
- Instituto de Matemáticas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Rui Fonseca-Pinto
- Center for Innovative Care and Health Technology (ciTechCare), Polytechnic of Leiria, Leiria, Portugal
| | - Rui Passadouro
- Center for Innovative Care and Health Technology (ciTechCare), Polytechnic of Leiria, Leiria, Portugal
- ACES Pinhal Litoral-ARS Centro, Leiria, Portugal
| | | | - Wilson Abreu
- School of Nursing and Research Centre "Centre for Health Technology and Services Research/ESEP-CINTESIS", Porto, Portugal
| | - Jorge Mira
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain.
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9
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Tafur N, Escala DM, Soto A, Muñuzuri AP. Highly viscous fluid displaced by a chemically controlled reactive interface. Chaos 2021; 31:023135. [PMID: 33653047 DOI: 10.1063/5.0031058] [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: 09/27/2020] [Accepted: 02/01/2021] [Indexed: 06/12/2023]
Abstract
Displacement of a viscous fluid by a less viscous one is a challenging problem that usually involves the formation of interfacial digitations propagating into each one of the fluids, mixing them and preventing their normal displacement. We propose in this manuscript a protocol that is implemented via numerical simulation of the corresponding equations to improve the efficiency of the displacement. We consider a chemically active interface between the two chemically active fluids that produce a large viscosity interface that facilitates the process. All the relevant parameters of the mechanism are numerically analyzed aiming to optimize the efficiency of the method.
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Affiliation(s)
- Néstor Tafur
- Institute CRETUS, Group of Nonlinear Physics, Department of Physics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Darío M Escala
- Institute CRETUS, Group of Nonlinear Physics, Department of Physics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Ana Soto
- Institute CRETUS, Group EQUIFASE, Department of Chemical Engineering, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Institute CRETUS, Group of Nonlinear Physics, Department of Physics, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
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10
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Carballosa A, Mussa-Juane M, Muñuzuri AP. Incorporating social opinion in the evolution of an epidemic spread. Sci Rep 2021; 11:1772. [PMID: 33469092 PMCID: PMC7815732 DOI: 10.1038/s41598-021-81149-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 12/24/2020] [Indexed: 01/20/2023] Open
Abstract
The evolution of the COVID19 pandemic worldwide has shown that the most common and effective strategy to control it used worldwide involve imposing mobility constrains to the population. A determinant factor in the success of such policies is the cooperation of the population involved but this is something, at least, difficult to measure. In this manuscript, we propose a method to incorporate in epidemic models empirical data accounting for the society predisposition to cooperate with the mobility restriction policies.
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Affiliation(s)
- Alejandro Carballosa
- Group of Nonlinear Physics, Institute CRETUS, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Mariamo Mussa-Juane
- Group of Nonlinear Physics, Institute CRETUS, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, Institute CRETUS, Faculty of Physics, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain.
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11
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Escala DM, Muñuzuri AP. Interface Fingering Instability Triggered by a Density-Coupled Oscillatory Chemical Reaction via Precipitation. Langmuir 2019; 35:13769-13781. [PMID: 31560207 DOI: 10.1021/acs.langmuir.9b02092] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
A density fingering hydrodynamic instability is triggered by a chemical reaction at the interface between two fluids. The density instability is controlled by the density gradient between both solutions, while the excitability of the bubble-free Belousov-Zhabotinsky-1,4-cyclohexanedione (BZ-CHD) oscillatory chemical reaction controls the importance of the chemistry in the system. Both parameters are thoroughly analyzed, and the mechanism underlying the instability is unveiled. The experimental observations lead us to modify the existing and accepted models for the BZ-CHD reaction within this context. The important role played by precipitation is considered in this context and included into the model. The modified kinetic model once coupled with fluid dynamics along with the precipitation mechanism was able to reproduce the experimental observations.
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Affiliation(s)
- Dario M Escala
- Group of Nonlinear Physics, Facultad de Físicas , Universidade de Santiago de Compostela , Campus Sur , 15782 Santiago de Compostela , Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, Facultad de Físicas , Universidade de Santiago de Compostela , Campus Sur , 15782 Santiago de Compostela , Spain
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12
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García-Selfa D, Muñuzuri AP, Pérez-Mercader J, Simakov DSA. Resonant Behavior in a Periodically Forced Nonisothermal Oregonator. J Phys Chem A 2019; 123:8083-8088. [PMID: 31441660 DOI: 10.1021/acs.jpca.9b05238] [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] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Nonisothermal chemical oscillators are poorly studied systems because chemical oscillations are conventionally studied under isothermal conditions. Coupling chemical reactions with heat generation and removal in a nonisothermal oscillatory system can lead to a highly nontrivial nonlinear dynamic behavior. For the current study, we considered the three-variable Oregonator model with the temperature incorporated as a variable (not a parameter), thus adding an energy balance to the set of equations. The effect of temperature on reaction rates is included through the temperature-dependent reaction rate coefficients (Arrhenius law). To model a continuous operation in a laboratory environment, the system was subjected to external forcing through the coolant temperature and infrared irradiation. By conducting numerical simulations and parametric studies, we found that the system is capable of a resonant behavior exhibiting induced oscillations. Our findings indicate that an external source of heat (e.g., via an infrared light emitting diode) can be used to induce a Hopf bifurcation under resonant conditions in an experimental Belousov-Zhabotinsky reactor.
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Affiliation(s)
- David García-Selfa
- Group of Nonlinear Physics , Universidad de Santiago de Compostela , Campus Sur , 15782 Santiago de Compostela , Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics , Universidad de Santiago de Compostela , Campus Sur , 15782 Santiago de Compostela , Spain.,Department of Earth and Planetary Sciences, Origins of Life Initiative , Harvard University , Cambridge , Massachusetts 02138 , United States
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences, Origins of Life Initiative , Harvard University , Cambridge , Massachusetts 02138 , United States.,Santa Fe Institute , Santa Fe , New Mexico 87501 , United States
| | - David S A Simakov
- Department of Chemical Engineering , University of Waterloo , Waterloo , Ontario N2L 3G1 , Canada
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13
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Mimar S, Juane MM, Park J, Muñuzuri AP, Ghoshal G. Turing patterns mediated by network topology in homogeneous active systems. Phys Rev E 2019; 99:062303. [PMID: 31330727 DOI: 10.1103/physreve.99.062303] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Indexed: 06/10/2023]
Abstract
Mechanisms of pattern formation-of which the Turing instability is an archetype-constitute an important class of dynamical processes occurring in biological, ecological, and chemical systems. Recently, it has been shown that the Turing instability can induce pattern formation in discrete media such as complex networks, opening up the intriguing possibility of exploring it as a generative mechanism in a plethora of socioeconomic contexts. Yet much remains to be understood in terms of the precise connection between network topology and its role in inducing the patterns. Here we present a general mathematical description of a two-species reaction-diffusion process occurring on different flavors of network topology. The dynamical equations are of the predator-prey class that, while traditionally used to model species population, has also been used to model competition between antagonistic features in social contexts. We demonstrate that the Turing instability can be induced in any network topology by tuning the diffusion of the competing species or by altering network connectivity. The extent to which the emergent patterns reflect topological properties is determined by a complex interplay between the diffusion coefficients and the localization properties of the eigenvectors of the graph Laplacian. We find that networks with large degree fluctuations tend to have stable patterns over the space of initial perturbations, whereas patterns in more homogenous networks are purely stochastic.
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Affiliation(s)
- Sayat Mimar
- Department of Physics & Astronomy, University of Rochester, Rochester, New York 14607, USA
| | - Mariamo Mussa Juane
- Group of Nonlinear Physics, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
| | - Juyong Park
- Graduate School of Culture Technology, Korea Advanced Institute of Science and Technology, Daejon 305-701, Korea
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, University of Santiago de Compostela, Santiago de Compostela 15782, Spain
| | - Gourab Ghoshal
- Department of Physics & Astronomy, University of Rochester, Rochester, New York 14607, USA
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14
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Abstract
Sociolinguistic phenomena often involve interactions across different scales and result in social and linguistic changes that can be tracked over time. Here, we focus on the dynamics of language shift in Galicia, a bilingual community in northwest Spain. Using historical data on Galician and Spanish speakers, we show that the rate at which shift dynamics unfold correlates inversely with the internal complexity of a region (approximated by the proportion of urban area). Less complex areas converge faster to steady states, while more complex ones sustain transitory dynamics longer. We further explore the contextual relevance of each region within the network of regions that constitute Galicia. The network is observed to sustain or reverse the dynamic rates. This model can introduce a competition between the internal complexity of a region and its contextual relevance in the network. Harnessing these sociodynamic features may prove useful in policy making to limit conflicts. In areas with two or more spoken languages, linguistic shift may occur as speakers of one language switch to the other. Here, the authors show that linguistic shift is faster in rural compared to urban regions of Galicia, a bilingual community in Spain, due to the competition of internal complexity and network relevance.
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Affiliation(s)
- Mariamo Mussa Juane
- Group of Nonlinear Physics. Departamento de Física de Partículas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
| | - Luis F Seoane
- ICREA-Complex Systems Lab, UPF-PRBB. Dr Aiguader 88, 08003, Barcelona, Spain.,Institute Evolutionary Biology, UPF-CSIC, Pg Maritim Barceloneta 37, 08003, Barcelona, Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics. Departamento de Física de Partículas, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain.
| | - Jorge Mira
- Departamento de Física Aplicada, Universidade de Santiago de Compostela, 15782, Santiago de Compostela, Spain
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15
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Abstract
A pH-changing clock chemical system, also known to induce changes in viscosity, is shown experimentally to induce a viscous fingering instability during the displacement of reactive solutions in a Hele-Shaw cell. Specifically, a low-viscosity solution of formaldehyde is displaced by a more viscous solution of sulfite and of a pH-sensitive poly(acrylic acid) polymer. The pH change triggered by the formaldehyde-sulfite clock reaction in the reactive contact zone between the two solutions affects the polymer and induces a local increase of the viscosity that destabilizes the displacement via a viscous fingering instability. The influence of changes in the chemical parameters on this fingering instability is analyzed using different techniques and the results are compared with numerical simulations.
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Affiliation(s)
- D M Escala
- Group of Nonlinear Physics , Universidade de Santiago de Compostela , E-15782 Santiago de Compostela , Spain
| | - A De Wit
- Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique , Université libre de Bruxelles (ULB) , CP231, Campus Plaine , 1050 Brussels , Belgium
| | - J Carballido-Landeira
- Facultad de Ciencias, Departamento de Física , Universidad de Oviedo, Campus de Llamaquique , C/Calvo Sotelo, s/n , 33007 Oviedo , Spain
| | - A P Muñuzuri
- Group of Nonlinear Physics , Universidade de Santiago de Compostela , E-15782 Santiago de Compostela , Spain
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16
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Muñuzuri AP, Busupalli B, Pérez-Mercader J. Osmotically Induced Membrane Fission in Giant Polymer Vesicles: Multilamellarity and Effect of the Amphiphilic Block Lengths. Langmuir 2018; 34:10984-10992. [PMID: 30157654 DOI: 10.1021/acs.langmuir.8b01590] [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] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Amphiphilic block co-polymers are used to form large spherical vesicles. A sudden change in the osmotic pressure across the polymer membrane is used to induce the fission of the polymer vesicle. The membrane area to volume ratio, as expected, is observed to be a parameter suitable to describe the process and even mark the critical points along this transition. The effect of the length of the hydrophobic and hydrophilic chains on the fission process is analyzed. The effects of membrane lamellarity and initial polydispersity are thoroughly analyzed from the experimental data following mathematical models, and the phenomenon of fission in these polymer vesicles is understood via measurements characterizing the membrane, i.e., area stretch modulus.
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Affiliation(s)
- Alberto P Muñuzuri
- Department of Earth and Planetary Sciences , Harvard University , Cambridge , Massachusetts 02138-1204 , United States
- University of Santiago de Compostela , Santiago de Compostela 15706 , Spain
| | - Balanagulu Busupalli
- Department of Earth and Planetary Sciences , Harvard University , Cambridge , Massachusetts 02138-1204 , United States
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences , Harvard University , Cambridge , Massachusetts 02138-1204 , United States
- The Santa Fe Institute , Santa Fe , New Mexico 87501 , United States
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17
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Serna H, Muñuzuri AP, Barragán D. Thermodynamic and morphological characterization of Turing patterns in non-isothermal reaction-diffusion systems. Phys Chem Chem Phys 2018; 19:14401-14411. [PMID: 28435963 DOI: 10.1039/c7cp00543a] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
The effect of temperature on the bifurcation diagram and Turing instability domain under non isothermal conditions is studied in the reversible Gray-Scott model. After adding the energy balance to the cubic autocatalytic model, the thermostat temperature and heat transfer coefficient are used as control parameters in the Turing pattern formation. The patterns obtained in the domain of the thermal parameter are characterized by quantifying the overall entropy generation rate and two topological indices; Shannon entropy and Minkowski functionals. The results show that it is possible to induce transitions between Turing patterns of different morphologies by regulating the temperature, and that these transitions take place at a lower entropy generation value compared to other parameters, such as kinetic constants and reactant fluxes. Finally, a correlation between entropy generation and topological indices shows that a difference between direct and inverse patterns is mainly morphological and not energetic.
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Affiliation(s)
- Horacio Serna
- Group of Calorimetry and Irreversible Processes Thermodynamics, Department of Chemistry, Faculty of Sciences, Universidad Nacional de Colombia, Campus El Volador, Bloque 16. Calle 59A 63-20, Medellín, Colombia.
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18
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Vidal-Franco I, Guiu-Souto J, Muñuzuri AP. Social media enhances languages differentiation: a mathematical description. R Soc Open Sci 2017; 4:170094. [PMID: 28573016 PMCID: PMC5451817 DOI: 10.1098/rsos.170094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/12/2017] [Accepted: 04/13/2017] [Indexed: 06/07/2023]
Abstract
Understanding and predicting the evolution of competing languages is a topic of high interest in a world with more than 6000 languages competing in a highly connected environment. We consider a reasonable mathematical model describing a situation of competition between two languages and analyse the effect of the speakers' connectivity (i.e. social networks). Surprisingly, instead of homogenizing the system, a high degree of connectivity helps to introduce differentiation for the appropriate parameters.
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Affiliation(s)
- Ignacio Vidal-Franco
- Group of NonLinear Physics, Universidade Santiago de Compostela, 15706 Santiago de Compostela, Spain
| | - Jacobo Guiu-Souto
- Group of NonLinear Physics, Universidade Santiago de Compostela, 15706 Santiago de Compostela, Spain
- Department of Medical Physics, Universitary Hospital of Santiago de Compostela, 15706 Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Group of NonLinear Physics, Universidade Santiago de Compostela, 15706 Santiago de Compostela, Spain
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19
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Abstract
Synchronization of intercommunicating individual oscillators is an important form of collective behavior used in nature as a mechanism to face dangers, act collectively, and communicate. The involvement of the medium where oscillators exist is an important ingredient. Because of their nature and their multiple different components, the medium and the environment are often perceived as stochastic relative to the deterministic nature of the individuals on some scale. This injects energy/matter into the system in ways that can enhance or de-enhance communication in a stochastic manner. Here we experimentally consider a large number of coupled nonlinear-chemical oscillators under the effect of a controlled normally distributed noise. Experiments show that the collective behavior of the oscillator is triggered by this stochastic perturbation, and we observe the dependence on the noise parameters. Our results point to the potential use of environmental fluctuations in determining the emergence and properties of collective behaviors in complex systems.
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Affiliation(s)
- Alberto P Muñuzuri
- Department of Earth and Planetary Sciences, Harvard University . Cambridge, Massachusetts 02138-1204, United States.,University of Santiago de Compostela , 15706 Santiago de Compostela, Spain
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences, Harvard University . Cambridge, Massachusetts 02138-1204, United States.,Santa Fe Institute , Santa Fe, New Mexico 87501, United States
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20
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Pérez-Muñuzuri V, Garaboa-Paz D, Muñuzuri AP. Nonperfect mixing affects synchronization on a large number of chemical oscillators immersed in a chemically active time-dependent chaotic flow. Phys Rev E 2016; 94:013103. [PMID: 27575213 DOI: 10.1103/physreve.94.013103] [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] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2016] [Indexed: 06/06/2023]
Abstract
The problem of synchronization of finite-size chemical oscillators described by active inertial particles is addressed for situations in which they are immersed in a reacting nonstationary chaotic flow. Active substances in the fluid will be modeled by Lagrangian particles closely following the fluid streamlines. Their interaction with the active inertial particles as well as the properties of the fluid dynamics will result in modifying the synchronization state of the chemical oscillators. This behavior is studied in terms of the exchange rate between the Lagrangian and inertial particles, and the finite-time Lyapunov exponents characterizing the flow. The coherence of the population of oscillators is determined by means of the order parameter introduced by Kuramoto. The different dynamics observed for the inertial particles (chemical oscillators) and Lagrangian particles (describing chemicals in the flow) lead to nonlinear interactions and patches of synchronized regions within the domain.
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Affiliation(s)
- V Pérez-Muñuzuri
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
| | - D Garaboa-Paz
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
| | - A P Muñuzuri
- Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
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21
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Ghoshal G, Muñuzuri AP, Pérez-Mercader J. Emergence of a super-synchronized mobbing state in a large population of coupled chemical oscillators. Sci Rep 2016; 6:19186. [PMID: 26753772 PMCID: PMC4709686 DOI: 10.1038/srep19186] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2015] [Accepted: 12/07/2015] [Indexed: 11/09/2022] Open
Abstract
Oscillatory phenomena are ubiquitous in Nature. The ability of a large population of coupled oscillators to synchronize constitutes an important mechanism to express information and establish communication among members. To understand such phenomena, models and experimental realizations of globally coupled oscillators have proven to be invaluable in settings as varied as chemical, biological and physical systems. A variety of rich dynamical behavior has been uncovered, although usually in the context of a single state of synchronization or lack thereof. Through the experimental and numerical study of a large population of discrete chemical oscillators, here we report on the unexpected discovery of a new phenomenon revealing the existence of dynamically distinct synchronized states reflecting different degrees of communication. Specifically, we discover a novel large-amplitude super-synchronized state separated from the conventionally reported synchronized and quiescent states through an unusual sharp jump transition when sampling the strong coupling limit. Our results assume significance for further elucidating globally coherent phenomena, such as in neuropathologies, bacterial cell colonies, social systems and semiconductor lasers.
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Affiliation(s)
- Gourab Ghoshal
- Department of Earth and Planetary Sciences. Harvard University, Cambridge, MA 02138, USA
| | - Alberto P. Muñuzuri
- Department of Earth and Planetary Sciences. Harvard University, Cambridge, MA 02138, USA
| | - Juan Pérez-Mercader
- Department of Earth and Planetary Sciences. Harvard University, Cambridge, MA 02138, USA
- The Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
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22
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Abstract
The effect of centrifugal forces is analyzed in a pattern-forming reaction-diffusion system. Numerical simulations conducted on the appropriate extension of the Oregonator model for the Belousov-Zhabotinsky reaction show a great variety of dynamical behaviors in such a system. In general, the system exhibits an anisotropy that results in new types of patterns or in a global displacement of the previous one. We consider the effect of both constant and periodically modulated centrifugal forces on the different types of patterns that the system may exhibit. A detailed analysis of the patterns and behaviors observed for the different parameter values considered is presented here.
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Affiliation(s)
- Dario M Escala
- Group of Nonlinear Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Jacobo Guiu-Souto
- Group of Nonlinear Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
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23
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Abstract
We report the destabilization of stationary Turing patterns and the subsequent emergence of fast spatiotemporal dynamics due to reactant consumption. The localized hexagonal Turing spots switch from a stationary regime to a dynamics state by exhibiting spatial oscillations with two characteristic wavelengths and one representative temporal period. These oscillatory Turing spots are not temporally stable and evolve into traveling spiral tips that, in addition to the unexpected birth of spots, rapidly transform into target patterns and originate multiple collisions and wave breakups due to their proximity, degenerating into a chaotic scenario.
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Affiliation(s)
- Jorge Carballido-Landeira
- Group of Nonlinear Physics, Universidade de Santiago de Compostela, Santiago de Compostela E-15782, Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, Universidade de Santiago de Compostela, Santiago de Compostela E-15782, Spain
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24
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Guiu-Souto J, Muñuzuri AP. Influence of oscillatory centrifugal forces on the mechanism of Turing pattern formation. Phys Rev E Stat Nonlin Soft Matter Phys 2015; 91:012917. [PMID: 25679692 DOI: 10.1103/physreve.91.012917] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/29/2014] [Indexed: 06/04/2023]
Abstract
Constantly acting centrifugal forces on Turing pattern forming systems have been observed to induce orientation and wavelength changes on Turing structures. Here, we will consider a periodic modulation of such centrifugal forces and their effects on pattern formation. Depending on the oscillation period the system exhibits a wide variety of stationary (stripes, H(0), etc.) or nonstationary patterns (black eyes, etc.), as well as transitions and instabilities such as Eckhaus, zigzag, etc. In this paper, a detailed description of the different patterns and patterning mechanisms will be described and understood within the previous context. The system considered is the Belousov-Zhabotinsky reaction encapsulated in AOT micelles modeled by the adapted version of the Oregonator model.
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Affiliation(s)
- Jacobo Guiu-Souto
- Group of Nonlinear Physics, Department of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
| | - Alberto P Muñuzuri
- Group of Nonlinear Physics, Department of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
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25
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Makki R, Muñuzuri AP, Perez-Mercader J. Periodic Perturbation of Chemical Oscillators: Entrainment and Induced Synchronization. Chemistry 2014; 20:14213-7. [PMID: 25214439 DOI: 10.1002/chem.201403647] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 01/01/2023]
Affiliation(s)
- Rabih Makki
- Department of Earth and Planetary Sciences, Harvard University, Cambridge, MA 02138-1204 (USA) http://www.fas.harvard.edu/∼topdownsynthbio/index.cgi
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26
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Escala DM, Budroni MA, Carballido-Landeira J, De Wit A, Muñuzuri AP. Self-Organized Traveling Chemo-Hydrodynamic Fingers Triggered by a Chemical Oscillator. J Phys Chem Lett 2014; 5:413-8. [PMID: 26276584 DOI: 10.1021/jz402625z] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Pulsatile chemo-hydrodynamic patterns due to a coupling between an oscillating chemical reaction and buoyancy-driven hydrodynamic flows can develop when two solutions of separate reactants of the Belousov-Zhabotinsky reaction are put in contact in the gravity field and conditions for chemical oscillations are met in the contact zone. In regular oscillatory conditions, localized periodic changes in the concentration of intermediate species induce pulsatile density gradients, which, in turn, generate traveling convective fingers breaking the transverse symmetry. These patterns are the self-organized result of a genuine coupling between chemical and hydrodynamic modes.
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Affiliation(s)
- D M Escala
- †Nonlinear Physics Group, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - M A Budroni
- ‡Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
| | - J Carballido-Landeira
- †Nonlinear Physics Group, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - A De Wit
- ‡Nonlinear Physical Chemistry Unit, Service de Chimie Physique et Biologie Théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium
| | - A P Muñuzuri
- †Nonlinear Physics Group, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
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27
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von Kameke A, Huhn F, Muñuzuri AP, Pérez-Muñuzuri V. Measurement of large spiral and target waves in chemical reaction-diffusion-advection systems: turbulent diffusion enhances pattern formation. Phys Rev Lett 2013; 110:088302. [PMID: 23473206 DOI: 10.1103/physrevlett.110.088302] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2012] [Indexed: 06/01/2023]
Abstract
In the absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present that can be parametrized in terms of effective or turbulent diffusion D(*), these patterns should be attainable on a much greater, boosted length scale. However, so far, experimental evidence of these boosted patterns in a turbulent flow was lacking. Here, we report the first experimental observation of boosted target and spiral patterns in an excitable chemical reaction in a quasi-two-dimensional turbulent flow. The wave patterns observed are ~50 times larger than in the case of molecular diffusion only. We vary the turbulent diffusion coefficient D(*) of the flow and find that the fundamental Fisher-Kolmogorov-Petrovsky-Piskunov equation, v(f) proportional sqrt[D(*)], for the asymptotic speed of a reactive wave remains valid. However, not all measures of the boosted wave scale with D(*) as expected from molecular diffusion, since the wave fronts turn out to be highly filamentous.
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Affiliation(s)
- A von Kameke
- Group of Nonlinear Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain.
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28
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Guiu-Souto J, Carballido-Landeira J, Muñuzuri AP. Characterizing topological transitions in a Turing-pattern-forming reaction-diffusion system. Phys Rev E Stat Nonlin Soft Matter Phys 2012; 85:056205. [PMID: 23004841 DOI: 10.1103/physreve.85.056205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2011] [Revised: 02/03/2012] [Indexed: 06/01/2023]
Abstract
Turing structures appear naturally and they are demonstrated under different spatial configurations such as stripes and spots as well as mixed states. The traditional tool to characterize these patterns is the Fourier transformation, which accounts for the spatial wavelength, but it fails to discriminate among different spatial configurations or mixed states. In this paper, we propose a parameter that clearly differentiates the different spatial configurations. As an application, we considered the transitions induced by an external forcing in a reaction-diffusion system although the results are straightforwardly extended to different problems with similar topologies. The method was also successfully tested on a temporally evolving pattern.
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Affiliation(s)
- Jacobo Guiu-Souto
- Group of Nonlinear Physics, Department of Physics, University of Santiago de Compostela, Spain.
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29
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Carballido-Landeira J, Goy-López S, Muñuzuri AP, Taboada P, Mosquera V. In situ formation of one-dimensional assemblies of gold nanoparticles in confined media. Chemphyschem 2012; 13:1347-53. [PMID: 22287253 DOI: 10.1002/cphc.201100796] [Citation(s) in RCA: 3] [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: 10/10/2011] [Revised: 12/12/2011] [Indexed: 11/10/2022]
Abstract
The spontaneous in situ formation of one-dimensional (1D) assemblies of gold nanoparticles (NP) in oleylamine/bis(2-ethylhexyl) sulfosuccinate sodium salt/water/octane (OAm/AOT/w/o) microemulsions by exploiting both the aurophilic bonding between OAm and gold salt, and the interactions between OAm and AOT surfactant is presented. Control on the structure of the resulting assemblies is achieved by changing in the solvent quality, the [Au]/[AOT] molar ratio and the presence of different cosolutes. A possible mechanism of the formation of the 1D parallel Au NP arrays is proposed.
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Affiliation(s)
- Jorge Carballido-Landeira
- Grupo de Física No Lineal y Departamento de Física de la Materia Condensada, Facultad de Física, Universidad de Santiago de Compostela, Campus Sur, 15782 Santiago de Compostela, Spain.
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30
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Abstract
We investigate the interaction between reaction-diffusion systems coupled by diffusion. The photosensitive CDIMA (chorine dioxide-iodine-malonic acid) reaction allows us to study experimentally the mutual influence of two layers of Turing patterns coupled via a diffusive interaction. By illuminating each of the layers with different intensities of homogeneous external light, the chemical conditions in each layer can be shifted, allowing us to study the result of diffusive interaction between Turing patterns with different spatial configurations. Our experiments suggest a complex scenario for the interaction between different patterns, strongly dependent on the spatial characteristics of the interacting patterns. Numerical simulations are also reported in full agreement with experimental observations.
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Affiliation(s)
- David G Míguez
- Department of Physics of Condensed Matter, Facultad de Ciencias, Universidad Autónoma de Madrid, Madrid 28049, Spain.
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31
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von Kameke A, Huhn F, Fernández-García G, Muñuzuri AP, Pérez-Muñuzuri V. Double cascade turbulence and Richardson dispersion in a horizontal fluid flow induced by Faraday waves. Phys Rev Lett 2011; 107:074502. [PMID: 21902399 DOI: 10.1103/physrevlett.107.074502] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2011] [Indexed: 05/31/2023]
Abstract
We report the experimental observation of Richardson dispersion and a double cascade in a thin horizontal fluid flow induced by Faraday waves. The energy spectra and the mean spectral energy flux obtained from particle image velocimetry data suggest an inverse energy cascade with Kolmogorov type scaling E(k) ∝ k(γ), γ ≈ -5/3 and an E(k) ∝ k(γ), γ ≈ -3 enstrophy cascade. Particle transport is studied analyzing absolute and relative dispersion as well as the finite size Lyapunov exponent (FSLE) via the direct tracking of real particles and numerical advection of virtual particles. Richardson dispersion with <ΔR(2)(t)> ∝ t(3) is observed and is also reflected in the slopes of the FSLE (Λ ∝ ΔR(-2/3)) for virtual and real particles.
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Affiliation(s)
- A von Kameke
- Group of Nonlinear Physics, University of Santiago de Compostela, Spain.
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32
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Villar Álvarez E, Carballido-Landeira J, Guiu-Souto J, Taboada P, Muñuzuri AP. Modulation of volume fraction results in different kinetic effects in Belousov–Zhabotinsky reaction confined in AOT-reverse microemulsion. J Chem Phys 2011; 134:094512. [DOI: 10.1063/1.3561684] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Roncaglia DI, Carballido-Landeira J, Muñuzuri AP. Pattern formation in the Belousov–Zhabotinsky-PAMAM dendrimer system. Phys Chem Chem Phys 2011; 13:7426-32. [DOI: 10.1039/c0cp02656e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Carballido-Landeira J, Taboada P, Muñuzuri AP. Nanoscale changes induce microscale effects in Turing patterns. Phys Chem Chem Phys 2011; 13:4596-9. [DOI: 10.1039/c0cp02362k] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Guiu-Souto J, Carballido-Landeira J, Pérez-Villar V, Muñuzuri AP. Manipulation of diffusion coefficients via periodic vertical forcing controls the mechanism of Turing pattern formation. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 82:066209. [PMID: 21230725 DOI: 10.1103/physreve.82.066209] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2010] [Indexed: 05/30/2023]
Abstract
We study, theoretically and experimentally, the dynamical response of macroscopic Turing patterns to a mechanical periodic forcing which implies a sinusoidal modulation of gravity. Theoretical predictions indicate that the extra energy, due to the forcing, modifies the diffusion coefficient at a microscopic level, producing changes in the Turing domain and in the pattern characteristics, in particular its wavelength. To check the theoretical analysis, we perform numerical simulations with standard models. Experiments were also performed in the closed Belousov-Zhabotinsky reaction confined in AOT microemulsion (BZ-AOT system). Experiments as well as numerical and theoretical results show good agreement.
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Affiliation(s)
- Jacobo Guiu-Souto
- Department of Physics, University of Santiago de Compostela, Santiago de Compostela, Spain.
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von Kameke A, Huhn F, Fernández-García G, Muñuzuri AP, Pérez-Muñuzuri V. Propagation of a chemical wave front in a quasi-two-dimensional superdiffusive flow. Phys Rev E Stat Nonlin Soft Matter Phys 2010; 81:066211. [PMID: 20866505 DOI: 10.1103/physreve.81.066211] [Citation(s) in RCA: 5] [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: 04/06/2010] [Indexed: 05/29/2023]
Abstract
Pattern formation in reaction-diffusion systems is an important self-organizing mechanism in nature. Dynamics of systems with normal diffusion do not always reflect the processes that take place in real systems when diffusion is enhanced by a fluid flow. In such reaction-diffusion-advection systems diffusion might be anomalous for certain time and length scales. We experimentally study the propagation of a chemical wave occurring in a Belousov-Zhabotinsky reaction subjected to a quasi-two-dimensional chaotic flow created by the Faraday experiment. We present a novel analysis technique for the local expansion of the active wave front and find evidence of its superdiffusivity. In agreement with these findings the variance σ(2)(t)∝t(γ) of the reactive wave grows supralinear in time with an exponent γ>2. We study the characteristics of the underlying flow with microparticles. By statistical analysis of particle trajectories we derive flight time and jump length distributions and find evidence that tracer-particles undergo complex trajectories related to Lévy statistics. The propagation of active and passive media in the flow is compared.
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Affiliation(s)
- A von Kameke
- Group of Nonlinear Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain.
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McGraw PN, Menzinger M, Muñuzuri AP. Harmonic resonant excitation of flow-distributed oscillation waves and Turing patterns driven at a growing boundary. Phys Rev E 2009; 80:026209. [PMID: 19792233 DOI: 10.1103/physreve.80.026209] [Citation(s) in RCA: 4] [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: 11/12/2008] [Indexed: 11/07/2022]
Abstract
We perform numerical studies of a reaction-diffusion system that is both Turing and Hopf unstable, and that grows by addition at a moving boundary (which is equivalent by a Galilean transformation to a reaction-diffusion-advection system with a fixed boundary and a uniform flow). We model the conditions of a recent set of experiments which used a temporally varying illumination in the boundary region to control the formation of patterns in the bulk of the photosensitive medium. The frequency of the illumination variations can select patterns from among the competing instabilities of the medium. In the usual case, the waves that are excited have frequencies (as measured at a constant distance from the upstream boundary) matching the driving frequency. In contrast to the usual case, we find that both Turing patterns and flow-distributed oscillation waves can be excited by forcing at subharmonic multiples of the wave frequencies. The final waves (with frequencies at integer multiples of the driving frequency) are formed by a process in which transient wave fronts break up and reconnect. We find ratios of response to driving frequency as high as 10.
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Affiliation(s)
- Patrick N McGraw
- Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 3H6
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Míguez DG, McGraw P, Muñuzuri AP, Menzinger M. Selection of flow-distributed oscillation and Turing patterns by boundary forcing in a linearly growing, oscillating medium. Phys Rev E Stat Nonlin Soft Matter Phys 2009; 80:026208. [PMID: 19792232 DOI: 10.1103/physreve.80.026208] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2008] [Indexed: 05/28/2023]
Abstract
We studied the response of a linearly growing domain of the oscillatory chemical chlorine dioxide-iodide-malonic acid (CDIMA) medium to periodic forcing at its growth boundary. The medium is Hopf-, as well as Turing-unstable and the system is convectively unstable. The results confirm numerical predictions that two distinct modes of pattern can be excited by controlling the driving frequency at the boundary, a flow-distributed-oscillation (FDO) mode of traveling waves at low values of the forcing frequency f , and a mode of stationary Turing patterns at high values of f . The wavelengths and phase velocities of the experimental patterns were compared quantitatively with results from dynamical simulations and with predictions from linear dispersion relations. The results for the FDO waves agreed well with these predictions, and obeyed the kinematic relations expected for phase waves with frequencies selected by the boundary driving frequency. Turing patterns were also generated within the predicted range of forcing frequencies, but these developed into two-dimensional structures which are not fully accounted for by the one-dimensional numerical and analytical models. The Turing patterns excited by boundary forcing persist when the forcing is removed, demonstrating the bistability of the unforced, constant size medium. Dynamical simulations at perturbation frequencies other than those of the experiments showed that in certain ranges of forcing frequency, FDO waves become unstable, breaking up into harmonic waves of different frequency and wavelength and phase velocity.
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Affiliation(s)
- David G Míguez
- Department of Chemistry and Center for Complex Systems, MS015, Brandeis University, Waltham, Massachusetts 02454-9110, USA
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Berenstein I, Muñuzuri AP, Yang L, Dolnik M, Zhabotinsky AM, Epstein IR. Breathing spiral waves in the chlorine dioxide-iodine-malonic acid reaction-diffusion system. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 78:025101. [PMID: 18850879 DOI: 10.1103/physreve.78.025101] [Citation(s) in RCA: 6] [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: 08/31/2007] [Revised: 02/23/2008] [Indexed: 05/26/2023]
Abstract
Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reactor is increased. The breathing period is determined by the period of bulk oscillations in the feeding chamber. Similar behavior is obtained in the Lengyel-Epstein model of this system, where small amplitude parametric forcing of spiral waves near the spiral wave frequency leads to the formation of breathing spiral waves in which the period of breathing is equal to the period of forcing.
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Affiliation(s)
- Igal Berenstein
- Group of Complex Systems, Universidade de Santiago de Compostela, E-15782, Santiago de Compostela, Spain
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Cuiñas D, Berenstein I, Carballido-Landeira J, Muñuzuri AP. Transition from traveling to standing waves as a function of frequency in a reaction-diffusion system. J Chem Phys 2008; 128:244907. [DOI: 10.1063/1.2946697] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Fernández-García G, Roncaglia DI, Pérez-Villar V, Muñuzuri AP, Pérez-Muñuzuri V. Chemical-wave dynamics in a vertically oscillating fluid layer. Phys Rev E Stat Nonlin Soft Matter Phys 2008; 77:026204. [PMID: 18352100 DOI: 10.1103/physreve.77.026204] [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: 05/07/2007] [Revised: 10/09/2007] [Indexed: 05/26/2023]
Abstract
Classical Faraday experiments were conducted on the oscillatory chemical Belousov-Zhabotinsky (BZ) reaction. The vertical periodic modulation of the acceleration induces flows in the system that change the BZ dynamics, and thus the patterns exhibited. The resulting reaction-diffusion-advection system exhibits four different types of pattern for increasing stirring amplitude: deformed targets and spiral waves, filamentary patterns arranged in large-scale vortices, advection phase waves, and finally front annihilation where the medium becomes homogeneous. A wave period analysis of the forced system has been carried out. Contrary to what is expected, i.e., a continuous increase of the wave period with increasing forcing, the period changes dramatically at the boundaries between pattern domains.
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Affiliation(s)
- G Fernández-García
- Group of Nonlinear Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
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Carballido-Landeira J, Berenstein I, Taboada P, Mosquera V, Vanag VK, Epstein IR, Pérez-Villar V, Muñuzuri AP. Long-lasting dashed waves in a reactive microemulsion. Phys Chem Chem Phys 2008; 10:1094-6. [DOI: 10.1039/b714705h] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Abstract
This paper is focused on the study of the stripes orientation in the fish skin patterns. Based on microscopic observations of the pigment cells behavior at the embryonic stage, the key aspects of the pigmentation process are implemented in an experimental reaction-diffusion system. The experiment consists of a photosensitive Turing pattern of stripes growing directionally in one direction with controlled velocity. Different growth velocities of the system rearrange the stripes in the same three possible orientations observed in the skin of the colored fishes: parallel, oblique, and perpendicular. Our results suggest that the spreading velocity of the pigment cells in the fish dermis selects the orientation in the patterning processes.
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Affiliation(s)
- David G Míguez
- Chemistry Department and Center for Complex Systems, Brandeis University, 415 South St. Chemistry Office MS 015 University, Waltham, MA 02454-9110, USA.
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Míguez DG, Alonso S, Muñuzuri AP, Sagués F. Experimental evidence of localized oscillations in the photosensitive chlorine dioxide-iodine-malonic acid reaction. Phys Rev Lett 2006; 97:178301. [PMID: 17155511 DOI: 10.1103/physrevlett.97.178301] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2006] [Indexed: 05/12/2023]
Abstract
The interaction between Hopf and Turing modes has been the subject of active research in recent years. We present here experimental evidence of the existence of mixed Turing-Hopf modes in a two-dimensional system. Using the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) and external constant background illumination as a control parameter, standing spots oscillating in amplitude and with hexagonal ordering were observed. Numerical simulations in the Lengyel-Epstein model for the CDIMA reaction confirmed the results.
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Affiliation(s)
- David G Míguez
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts 02115, USA
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Pérez-Villar V, Porteiro JLF, Muñuzuri AP. Active media under rotational forcing. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 74:046203. [PMID: 17155149 DOI: 10.1103/physreve.74.046203] [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: 03/24/2006] [Indexed: 05/12/2023]
Abstract
The bubble-free Belousov-Zhabotinsky reaction has been used to study the effects of centrifugal forces on autowave propagation. The reaction parameters were chosen such that the system oscillates naturally creating target waves. In the present study, the system was forced to rotate with a constant velocity around a central axis. In studying the effects of such a forcing on the system, we focused on target dynamics. The system reacts to this forcing in different ways, the most spectacular being a dramatic increase in the period of the target, the effect growing stronger as we move away from the center of rotation. A numerical study was carried out using the two-variable Oregonator model, modified to include convective effects through the diffusion coefficient. The numerical results showed a good qualitative agreement with those of the experiments.
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Affiliation(s)
- Vicente Pérez-Villar
- Group of Complex Systems, Faculty of Physics, University of Santiago de Compostela, E-15782 Santiago de Compostela, Spain
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Berenstein I, Muñuzuri AP. Waving patterns: a general transition from stationary to moving forced Turing structures. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 74:036202. [PMID: 17025724 DOI: 10.1103/physreve.74.036202] [Citation(s) in RCA: 1] [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: 04/18/2006] [Indexed: 05/12/2023]
Abstract
We perform experiments on the chlorine dioxide-iodine-malonic acid (CDIMA) reaction forced with light with a pattern of moving stripes in which the spatiotemporal behavior is the oscillating movement of stripes (waving). This behavior is seen for different relative wavelengths between stationary and moving patterns. Different velocities of forcing may produce different modes of relaxation of the pattern in order to get to the natural Turing wavelength. Zigzag or Eckhaus instabilities may affect the symmetry of the pattern but do not influence the waving movement of stripes.
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Affiliation(s)
- Igal Berenstein
- Group of Complex Systems, Universidade de Santiago de Compostela, E-15782, Santiago de Compostela, Spain
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Abstract
We have performed one-dimensional and two-dimensional experiments and simulations to study the formation of patterns in a system that grows continuously in one direction. Depending on the growth velocity, three basic spatial configurations can be obtained: stripes that are parallel, oblique, or perpendicular to the growth direction. The dependence of the wavelength on the growth velocity has also been observed. Our results illustrate the importance of these growth mechanisms in determining the final configuration of chemical and biological pattern-forming processes.
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Affiliation(s)
- David G Míguez
- Department of Chemistry and Center for Complex Systems, MS015, Brandeis University, Waltham, Massachusetts 02454-9110, USA.
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Míguez DG, Satnoianu RA, Muñuzuri AP. Experimental steady pattern formation in reaction-diffusion-advection systems. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:025201. [PMID: 16605385 DOI: 10.1103/physreve.73.025201] [Citation(s) in RCA: 7] [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: 09/26/2005] [Indexed: 05/08/2023]
Abstract
We present here experimental evidence of a mechanism of a steady-chemical pattern formation called "flow-and-diffusion structures" (FDS). Experiments were performed using the photosensitive chlorine dioxide-iodine-malonic acid reaction, where the differential diffusion can be chemically controlled. Using the analogy between an advection boundary and a moving boundary, we obtain the formation of spatially periodic steady patterns, which matches all the previously theoretical predictions for FDS patterns. Numerical simulations are also reported in agreement with the experimental results.
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Affiliation(s)
- David G Míguez
- Chemistry Department, Brandeis University, Waltham, Massachusetts 02454, USA.
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Míguez DG, Izús GG, Muñuzuri AP. Robustness and stability of flow-and-diffusion structures. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:016207. [PMID: 16486258 DOI: 10.1103/physreve.73.016207] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2005] [Indexed: 05/06/2023]
Abstract
Reaction-diffusion-advection systems have revealed an interesting variety of pattern formation mechanism during the last years. Inside this field, flow-and-diffusion structures (FDSs) appear as a generalization of the mechanism of spatial symmetry breaking for different diffusion coefficients and flow rates of activator and inhibitor. The recent experimental validation of FDSs situates these structures in the focus of the actual research. We will report here an experimental and numerical analysis of the theoretically predicted robustness of these flow-and-diffusion structures by using different boundary profiles of illumination used to obtain FDSs. The results here shown reveal important characteristics related with the coexistence and interaction between these structures.
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Affiliation(s)
- David G Míguez
- Chemistry Department, Brandeis University, Waltham, Massachusetts 02454, USA.
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