Dissertations / Theses on the topic 'Excitable media'
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Theisen, Bjørn Bjørge. "Waves in Excitable Media." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for matematiske fag, 2012. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-19373.
Full textSailer, Franz-Xaver. "Controlling excitable media with noise." Doctoral thesis, [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=980114284.
Full textArmstrong, Gavin Robert. "Chemical waves in excitable media." Thesis, University of Leeds, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427767.
Full textCourtemanche, Marc. "Reentrant waves in excitable media." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186311.
Full textWeimar, Jörg Richard. "Cellular automata models for excitable media /." This resource online, 1991. http://scholar.lib.vt.edu/theses/available/etd-03032009-040651/.
Full textWeimar, Jörg Richard. "Cellular automata models for excitable media." Thesis, Virginia Tech, 1991. http://hdl.handle.net/10919/41365.
Full textA cellular automaton is developed for simulating excitable media. First, general "masks" as discrete approximations to the diffusion equation are examined, showing how to calculate the diffusion coefficient from the elements of the mask. The mask is then combined with a thresholding operation to simulate the propagation of waves (shock fronts) in excitable media, showing that (for well-chosen masks) the waves obey a linear "speedcurvature" relation with slope given by the predicted diffusion coefficient. The utility of different masks in terms of computational efficiency and adherence to a linear speed-curvature relation is assessed. Then, a cellular automaton model for wave propagation in reaction diffusion systems is constructed based on these "masks" for the diffusion component and on singular perturbation analysis for the reaction component. The cellular automaton is used to model spiral waves in the Belousov-Zhabotinskii reaction. The behavior of the spiral waves and the movement of the spiral tip are analyzed. By comparing these results to solutions of the Oregonator PDE model, the automaton is shown to be a useful and efficient replacement for the standard numerical solution of the PDE's.
Master of Science
Beato, Valentina. "Noise-induced pattern formation in excitable media." [S.l.] : [s.n.], 2006. http://opus.kobv.de/tuberlin/volltexte/2007/1419.
Full textXu, Jinshan. "Dynamics and synchronization in biological excitable media." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00776373.
Full textBorek, Bartlomiej. "Dynamics of heterogeneous excitable media with pacemakers." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=107795.
Full textLe coeur est un tissu hétérogène excitable qui contient des générateurs de rythme. Pour comprendre les règles fondamentales qui dirigent son comportement, il est utile d'étudier l'interaction entre la structure et la dynamique des modèles expérimentaux et mathématiques simplifiés. Dans cette thèse, j'utilise des modèles d'équations de FitzHugh-Nagumo. Ces modèles sont motivés par l'expérimentation avec des tissus cardiaques modifiés pour étudier comment les propriétés des conceptions influencent la dynamique d'ondes. Tout d'abord, une relation fonctionelle entre la densité des hétérogénéités distribuées au hasard et la vitesse de conduction est proposée dans un modèle numérique de deux dimensions de média hétérogènes excitables. Les transitions à l'onde rupturée sont différentes pour deux types de substrats hétérogènes. Les effets des régions automatiques sont alors considérés avec une étude théorique des transitions dans les ondes unidimensionelles des générateurs de rythme réinitialisés par une seule impulsion d'une distance. Des solutions d'ondes réfléchies se trouvent près de la discontinuité apparente de la courbe de transition de phase du système et deviennent des trajectoires plus complexes pour une discrétisation spatiale plus grossière du modèle. Enfin, les modèles d'ondes résultant de l'interaction de deux générateurs de rythme dans des médias hétérogènes excitables sont étudiés. Une nouvelle culture de tissu cardiaque de poussin est développée pour présenter la dynamique dominante déterminée par un générateur de rythme. Ce rythme stable subit des transitions à des modèles d'ondes réentrants plus complexes suivant l'induction de nouveaux générateurs de rythme, par l'application du bloqueur des canaux potassiques, E-4031. La dynamique est reproduite par le modèle FitzHugh-Nagumo, prévoyant l'effet de la taille du générateur de rythme et la densité de l'hétérogèneité sur la transition de l'onde rupturée et à la réentrée. Ces résultants contribuent à notre compréhension des mécanismes de média hétérogènes excitables avec des générateurs de rythme, dont les coeurs sains et malades.
Henze, Christopher Ernest. "Vortex filaments in three dimensional excitable media." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186300.
Full textChirila, Florin. "Feedback control of wave propagation patterns in excitable media." Morgantown, W. Va. : [West Virginia University Libraries], 2003. http://etd.wvu.edu/templates/showETD.cfm?recnum=2820.
Full textTitle from document title page. Document formatted into pages; contains xii, 156 p. : ill. (some col.) + MPEG video files. Includes MPEG video files. Includes abstract. Includes bibliographical references.
Guo, Hongjun. "Transition fronts and propagation speeds in diffusive excitable media." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0216.
Full textThis dissertation is concerned with transition fronts in various media, which generalize the standard notions of traveling fronts. The main results are as following. For bistable reaction, we prove the time monotonicity of all transition fronts with non-zero global mean speed, whatever shape their level sets may have. For time-periodic bistable reaction and combustion-type reaction, we prove the existence and the uniqueness of the global mean speed. Meantime, we show that almost-planar fronts are actually planar and we show the existence of non-standard transitions fronts in $\mathbb{R}^N$. For spatially periodic bistable reaction, we show some continuity and differentiability properties of the front speeds and profiles with respect to the direction $e$ by providing the existence of pulsating fronts with nonzero speed in all directions $e$. Then, we prove that the propagating speed of any transition front is bounded by the minimal speed and the maximal speed of pulsating fronts. Finally, we study the mean speed of bistable transition fronts in unbounded domains: exterior domains and domains with multiple cylindrical branches. In both domains, we prove the existence and uniqueness of the global mean speed of any transition front under some assumptions
Zhao, Yifan. "System Identification for Cellular Automata with Applications to Excitable Media." Thesis, University of Sheffield, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485082.
Full textMantel, Rolf-Martin. "Periodic forcing and symmetry breaking of waves in excitable media." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.263610.
Full textBordyugov, Grigory. "Dynamics and stability of pulses and pulse trains in excitable media." [S.l.] : [s.n.], 2006. http://deposit.ddb.de/cgi-bin/dokserv?idn=981984177.
Full textMcGowan, Robert. "Eikonal analysis of excitable reaction-diffusion equations in anisotropic and inhomogeneous media." Thesis, Glasgow Caledonian University, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309345.
Full textSchmid, Gerhard. "Channel noise in excitable membranes /." Aachen : Shaker, 2005. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=013064715&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
Full textLiceaga, Daniel Olmos. "Pseudospectral solutions of reaction-diffusion equations that model excitable media : convergence of solutions and applications." Thesis, University of British Columbia, 2007. http://hdl.handle.net/2429/31453.
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Mathematics, Department of
Graduate
Stevens, Roger P., and n/a. "A Computer Model of the Cellular Slime Mould Dictyostelium Discoideum." Griffith University. School of Computing and Information Technology, 2002. http://www4.gu.edu.au:8080/adt-root/public/adt-QGU20050906.112225.
Full textStevens, Roger P. "A Computer Model of the Cellular Slime Mould Dictyostelium Discoideum." Thesis, Griffith University, 2002. http://hdl.handle.net/10072/365409.
Full textThesis (Masters)
Master of Philosophy (MPhil)
School of Computing and Information Technology
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Goodfellow, Marc. "Spatio-temporal modelling and analysis of epileptiform EEG." Thesis, University of Manchester, 2011. https://www.research.manchester.ac.uk/portal/en/theses/spatiotemporal-modelling-and-analysis-of-epileptiform-eeg(0f76259a-1a58-44a9-b08b-1402c9b49896).html.
Full textYu, Han Baek. "Combinatorial and probabilistic aspects of coupled oscillators." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1524195989591036.
Full textMenon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." Thesis, The University of Sydney, 2008. http://hdl.handle.net/2123/3685.
Full textMenon, Shakti Narayana. "Bifurcation problems in chaotically stirred reaction-diffusion systems." University of Sydney, 2008. http://hdl.handle.net/2123/3685.
Full textA detailed theoretical and numerical investigation of the behaviour of reactive systems under the influence of chaotic stirring is presented. These systems exhibit stationary solutions arising from the balance between chaotic advection and diffusion. Excessive stirring of such systems results in the termination of the reaction via a saddle-node bifurcation. The solution behaviour of these systems is analytically described using a recently developed nonperturbative, non-asymptotic variational method. This method involves fitting appropriate parameterised test functions to the solution, and also allows us to describe the bifurcations of these systems. This method is tested against numerical results obtained using a reduced one-dimensional reaction-advection-diffusion model. Four one- and two-component reactive systems with multiple homogeneous steady-states are analysed, namely autocatalytic, bistable, excitable and combustion systems. In addition to the generic stirring-induced saddle-node bifurcation, a rich and complex bifurcation scenario is observed in the excitable system. This includes a previously unreported region of bistability characterised by a hysteresis loop, a supercritical Hopf bifurcation and a saddle-node bifurcation arising from propagation failure. Results obtained with the nonperturbative method provide a good description of the bifurcations and solution behaviour in the various regimes of these chaotically stirred reaction-diffusion systems.
Lenk, Claudia [Verfasser], Michael [Akademischer Betreuer] Köhler, Philipp [Gutachter] Maaß, and Oliver [Gutachter] Steinbock. "Role of coupling conditions for pattern formation in excitable media : study of atrial fibrillation mechanisms and oscillator arrays in the Belousov-Zhabotinsky reaction / Claudia Lenk ; Gutachter: Philipp Maaß, Oliver Steinbock ; Betreuer: J. Michael Köhler." Ilmenau : TU Ilmenau, 2017. http://d-nb.info/1178142566/34.
Full textSilva, Pedro André Arroyo. "Modelo matemático com parâmetros que dependem da discretização: aplicação ao estudo de fenômenos de propagação discreta em meios excitáveis." Universidade Federal de Juiz de Fora (UFJF), 2018. https://repositorio.ufjf.br/jspui/handle/ufjf/7194.
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A formação de padrões espaço-temporais são observados em processos químicos e bio-lógicos. Apesar dos sistemas bioquímicos serem altamente heterogêneos, aproximações homogenizadas contínuas formadas por equações diferenciais parciais são utilizadas fre-quentemente. Estas aproximações são usualmente justificadas pela diferença de escalas entre as heterogeneidades e o tamanho da característica espacial dos padrões. Em certas condições do meio, por exemplo, quando há um acoplamento fraco entre as células car-díacas, os modelos homogenizados discretos são mais adequados. Entretanto, os modelos discretos são menos manejáveis, por exemplo, na geração de malha para 2D e 3D, se comparado com os modelos contínuos. Aqui estudamos um modelo matemático homoge-nizado contínuo que se aproxima do modelo homogenizado. Este modelo é dado a partir de equações diferencias parciais com um parâmetro que depende da discretização da ma-lha. Dessa maneira nos referimos a este por um modelo matemático com parâmetros que dependem da discretização. Validamos nossa aproximação em um meio excitável genérico que simula três fenômenos em 1D: a propagação do potencial de ação transmembrânico no tecido cardíaco, a propagação do potencial de ação em filamentos de axônios cobertos por bainhas de mielina e a propagação do ativador e inibidor em microemulsões químicas. Para o caso 2D desenvolvemos uma versão da nossa aproximação que reproduz ondas espirais em um meio com acoplamento fraco.
The spatio-temporal patterns formations are observed in chemical and biological pro-cesses. Although biochemical systems are highly heterogeneous, homogenized continuum approaches formed by partial differential equations have been employed frequently. These approaches are usually justified by the difference scales between the characteristic spatial size of the patterns. Under some conditions of the medium, for instance, under weak coupling between cardiac cells, discrete models are more adequate. On the other hand discrete models may be less manageable, for instance, in terms of mesh generation, com-pared to the continuum models. Here we study a mathematical model to approach the discreteness which permits the computer implementation on non-uniform meshes. The model is cast as a partial differential equation but with a parameter that depends on the discretization mesh. Therefore we refer to it as a mathematical model with parameters dependent of discretization. We validate the approach in a generic excitable media that simulates three different phenomena in 1D: the propagation of action potential in car-diac tissue, the propation of the action potentialin filaments of axons wrapped by myelin sheaths, and the propagation of the activator/inhibitor in chemical microemulsions. For the 2D case we develop a version to this approach in microemulsions where it was possible to reproduce spiral waves with weak coupling of the medium.
Yermakov, Leonid M. "Type 2 Diabetes Leads to Impairment of Cognitive Flexibility and Disruption of Excitable Axonal Domains in the Brain." Wright State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=wright1559401756413422.
Full textGravner, Janko. "Mathematical aspects of excitable media." 1991. http://catalog.hathitrust.org/api/volumes/oclc/24563504.html.
Full textTypescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 120-123).
Sailer, Franz-Xaver [Verfasser]. "Controlling excitable media with noise / von Franz-Xaver Sailer." 2006. http://d-nb.info/980114284/34.
Full textBeato, Valentina [Verfasser]. "Noise-induced pattern formation in excitable media / vorgelegt von Valentina Beato." 2006. http://d-nb.info/983001995/34.
Full textUang, Ting Fang, and 汪庭芳. "The emergency of transition layer and the front propagation equations in excitable media." Thesis, 1993. http://ndltd.ncl.edu.tw/handle/56116389105588795388.
Full textBordyugov, Grigory [Verfasser]. "Dynamics and stability of pulses and pulse trains in excitable media / vorgelegt von Grigory Bordyugov." 2006. http://d-nb.info/981984177/34.
Full textWang, Guanqun. "Investigation and Construction of Self-oscillating Systems." Thesis, 2010. http://hdl.handle.net/1969.1/ETD-TAMU-2010-05-7997.
Full text(8039297), Xiaoling Zhai. "SIGNAL PROPAGATION WITHIN A HETEROGENEOUS BACTERIAL COMMUNITY." Thesis, 2019.
Find full textChristoph, Jan. "Intramural Visualization of Scroll Waves in the Heart." Doctoral thesis, 2014. http://hdl.handle.net/11858/00-1735-0000-0023-9642-D.
Full textBerg, Sebastian Stephan. "Characterization and Control of Wave Propagation in the Heart." Doctoral thesis, 2018. http://hdl.handle.net/11858/00-1735-0000-002E-E607-5.
Full textBittihn, Philip. "Complex Structure and Dynamics of the Heart." Doctoral thesis, 2013. http://hdl.handle.net/11858/00-1735-0000-0001-BBB6-B.
Full textLilienkamp, Thomas. "A State Space Odyssey — The Multiplex Dynamics of Cardiac Arrhythmias." Doctoral thesis, 2018. http://hdl.handle.net/11858/00-1735-0000-002E-E4D8-0.
Full textDormann, Sabine. "Pattern Formation in Cellular Automaton Models - Characterisation, Examples and Analysis." Doctoral thesis, 2000. https://repositorium.ub.uni-osnabrueck.de/handle/urn:nbn:de:gbv:700-2000102612.
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