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Автор: Grafiati
Опубліковано: 6 вересня 2023

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Статті в журналах з теми "Reaction-Diffusion Network Model"

1

Wang, Ling, and Hongyong Zhao. "Synchronized stability in a reaction–diffusion neural network model." Physics Letters A 378, no. 48 (November 2014): 3586–99. http://dx.doi.org/10.1016/j.physleta.2014.10.019.

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2

Ji, Yansu, and Jianwei Shen. "Turing Instability of Brusselator in the Reaction-Diffusion Network." Complexity 2020 (October 5, 2020): 1–12. http://dx.doi.org/10.1155/2020/1572743.

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Анотація:
Turing instability constitutes a universal paradigm for the spontaneous generation of spatially organized patterns, especially in a chemical reaction. In this paper, we investigated the pattern dynamics of Brusselator from the view of complex networks and considered the interaction between diffusion and reaction in the random network. After a detailed theoretical analysis, we obtained the approximate instability region about the diffusion coefficient and the connection probability of the random network. In the meantime, we also obtained the critical condition of Turing instability in the network-organized system and found that how the network connection probability and diffusion coefficient affect the reaction-diffusion system of the Brusselator model. In the end, the reason for arising of Turing instability in the Brusselator with the random network was explained. Numerical simulation verified the theoretical results.
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3

Zhao, Hongyong, and Linhe Zhu. "Dynamic Analysis of a Reaction–Diffusion Rumor Propagation Model." International Journal of Bifurcation and Chaos 26, no. 06 (June 15, 2016): 1650101. http://dx.doi.org/10.1142/s0218127416501017.

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The rapid development of the Internet, especially the emergence of the social networks, leads rumor propagation into a new media era. Rumor propagation in social networks has brought new challenges to network security and social stability. This paper, based on partial differential equations (PDEs), proposes a new SIS rumor propagation model by considering the effect of the communication between the different rumor infected users on rumor propagation. The stabilities of a nonrumor equilibrium point and a rumor-spreading equilibrium point are discussed by linearization technique and the upper and lower solutions method, and the existence of a traveling wave solution is established by the cross-iteration scheme accompanied by the technique of upper and lower solutions and Schauder’s fixed point theorem. Furthermore, we add the time delay to rumor propagation and deduce the conditions of Hopf bifurcation and stability switches for the rumor-spreading equilibrium point by taking the time delay as the bifurcation parameter. Finally, numerical simulations are performed to illustrate the theoretical results.
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4

Kumar, Dinesh, Jatin Gupta, and Soumyendu Raha. "Partitioning a reaction–diffusion ecological network for dynamic stability." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2223 (March 2019): 20180524. http://dx.doi.org/10.1098/rspa.2018.0524.

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The loss of dispersal connections between habitat patches may destabilize populations in a patched ecological network. This work studies the stability of populations when one or more communication links is removed. An example is finding the alignment of a highway through a patched forest containing a network of metapopulations in the patches. This problem is modelled as that of finding a stable cut of the graph induced by the metapopulations network, where nodes represent the habitat patches and the weighted edges model the dispersal between habitat patches. A reaction–diffusion system on the graph models the dynamics of the predator–prey system over the patched ecological network. The graph Laplacian's Fiedler value, which indicates the well-connectedness of the graph, is shown to affect the stability of the metapopulations. We show that, when the Fiedler value is sufficiently large, the removal of edges without destabilizing the dynamics of the network is possible. We give an exhaustive graph partitioning procedure, which is suitable for smaller networks and uses the criterion for both the local and global stability of populations in partitioned networks. A heuristic graph bisection algorithm that preserves the preassigned lower bound for the Fiedler value is proposed for larger networks and is illustrated with examples.
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5

Doremus, R. H. "Diffusion of water in crystalline and glassy oxides: Diffusion–reaction model." Journal of Materials Research 14, no. 9 (September 1999): 3754–58. http://dx.doi.org/10.1557/jmr.1999.0508.

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Анотація:
Diffusion of water in oxides is modeled as resulting from the solution and diffusion of molecular water in the oxide. This dissolved water can react and exchange with the oxide network to form immobile OH groups and different hydrogen and oxygen isotopes in the oxide. The model agrees with many experiments on water diffusion in oxides. The activation energy for diffusion of water in oxides correlates with the structural openness of the oxide, suggesting that molecular water is the diffusing species.
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6

BANERJEE, SUBHASIS, SHRESTHA BASU MALLICK, and INDRANI BOSE. "REACTION–DIFFUSION PROCESSES ON RANDOM AND SCALE-FREE NETWORKS." International Journal of Modern Physics C 15, no. 08 (October 2004): 1075–86. http://dx.doi.org/10.1142/s0129183104006534.

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Анотація:
We study the discrete Gierer–Meinhardt model of reaction–diffusion on three different types of networks: regular, random and scale-free. The model dynamics lead to the formation of stationary Turing patterns in the steady state in certain parameter regions. Some general features of the patterns are studied through numerical simulation. The results for the random and scale-free networks show a marked difference from those in the case of the regular network. The difference may be ascribed to the small world character of the first two types of networks.
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7

Smith, Stephen, and Neil Dalchau. "Model reduction enables Turing instability analysis of large reaction–diffusion models." Journal of The Royal Society Interface 15, no. 140 (March 2018): 20170805. http://dx.doi.org/10.1098/rsif.2017.0805.

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Анотація:
Synthesizing a genetic network which generates stable Turing patterns is one of the great challenges of synthetic biology, but a significant obstacle is the disconnect between the mathematical theory and the biological reality. Current mathematical understanding of patterning is typically restricted to systems of two or three chemical species, for which equations are tractable. However, when models seek to combine descriptions of intercellular signal diffusion and intracellular biochemistry, plausible genetic networks can consist of dozens of interacting species. In this paper, we suggest a method for reducing large biochemical systems that relies on removing the non-diffusible species, leaving only the diffusibles in the model. Such model reduction enables analysis to be conducted on a smaller number of differential equations. We provide conditions to guarantee that the full system forms patterns if the reduced system does, and vice versa. We confirm our technique with three examples: the Brusselator, an example proposed by Turing, and a biochemically plausible patterning system consisting of 17 species. These examples show that our method significantly simplifies the study of pattern formation in large systems where several species can be considered immobile.
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8

Slavova, Angela, and Ronald Tetzlaff. "Edge of chaos in reaction diffusion CNN model." Open Mathematics 15, no. 1 (February 2, 2017): 21–29. http://dx.doi.org/10.1515/math-2017-0002.

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Анотація:
Abstract In this paper, we study the dynamics of a reaction-diffusion Cellular Nonlinear Network (RD-CNN) nodel in which the reaction term is represented by Brusselator cell. We investigate the RD-CNN dynamics by means of describing function method. Comparison with classical results for Brusselator equation is provided. Then we introduce a new RD-CNN model with memristor coupling, for which the edge of chaos regime in the parameter space is determined. Numerical simulations are presented for obtaining dynamic patterns in the RD-CNN model with memristor coupling.
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9

Liu, Chen, Shupeng Gao, Mingrui Song, Yue Bai, Lili Chang, and Zhen Wang. "Optimal control of the reaction–diffusion process on directed networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063115. http://dx.doi.org/10.1063/5.0087855.

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Анотація:
Reaction–diffusion processes organized in networks have attracted much interest in recent years due to their applications across a wide range of disciplines. As one type of most studied solutions of reaction–diffusion systems, patterns broadly exist and are observed from nature to human society. So far, the theory of pattern formation has made significant advances, among which a novel class of instability, presented as wave patterns, has been found in directed networks. Such wave patterns have been proved fruitful but significantly affected by the underlying network topology, and even small topological perturbations can destroy the patterns. Therefore, methods that can eliminate the influence of network topology changes on wave patterns are needed but remain uncharted. Here, we propose an optimal control framework to steer the system generating target wave patterns regardless of the topological disturbances. Taking the Brusselator model, a widely investigated reaction–diffusion model, as an example, numerical experiments demonstrate our framework’s effectiveness and robustness. Moreover, our framework is generally applicable, with minor adjustments, to other systems that differential equations can depict.
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10

Liu, Chen, Shupeng Gao, Mingrui Song, Yue Bai, Lili Chang, and Zhen Wang. "Optimal control of the reaction–diffusion process on directed networks." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 6 (June 2022): 063115. http://dx.doi.org/10.1063/5.0087855.

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Анотація:
Reaction–diffusion processes organized in networks have attracted much interest in recent years due to their applications across a wide range of disciplines. As one type of most studied solutions of reaction–diffusion systems, patterns broadly exist and are observed from nature to human society. So far, the theory of pattern formation has made significant advances, among which a novel class of instability, presented as wave patterns, has been found in directed networks. Such wave patterns have been proved fruitful but significantly affected by the underlying network topology, and even small topological perturbations can destroy the patterns. Therefore, methods that can eliminate the influence of network topology changes on wave patterns are needed but remain uncharted. Here, we propose an optimal control framework to steer the system generating target wave patterns regardless of the topological disturbances. Taking the Brusselator model, a widely investigated reaction–diffusion model, as an example, numerical experiments demonstrate our framework’s effectiveness and robustness. Moreover, our framework is generally applicable, with minor adjustments, to other systems that differential equations can depict.
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Більше джерел

Дисертації з теми "Reaction-Diffusion Network Model"

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CATTANI, ANNA. ""Multispecies" models to describe large neuronal networks." Doctoral thesis, Politecnico di Torino, 2014. http://hdl.handle.net/11583/2535730.

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Анотація:
Today modeling large neural network is a topic more relevant than ever. In particular, the set up of computer simulations describing complex networks with a huge number of nodes is a formidable challenge. The intrinsic difficulties concerning the prohibitive computational costs may be handled to some extent by exploiting what we call ``multispecies'' models. From a mathematical perspective this issue consists in formalizing the PDE-based continuum models which describe the high-density populations inside the network and studying interactions between them and the ODE-based discrete models for each neuron belonging to the low-density populations. In particular, we exploit such an approach to describe the Golgi-Granular cell loop network in the Cerebellum. Each single cell is described by means of the FitzHugh-Nagumo model and both electrical and chemical (excitatory and inhibitory) synapses are taken into account. Several simulations describing interesting phenomena as synchronization and travelling waves have been done. Biological aspects have also been examined in order to provide our work with scientific completeness.
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2

Subramanian, Kartik. "Spatiotemporal Model of the Asymmetric Division Cycle of Caulobacter crescentus." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/65156.

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Анотація:
The life cycle of Caulobacter crescentus is of interest because of the asymmetric nature of cell division that gives rise to progeny that have distinct morphology and function. One daughter called the stalked cell is sessile and capable of DNA replication, while the second daughter called the swarmer cell is motile but quiescent. Advances in microscopy combined with molecular biology techniques have revealed that macromolecules are localized in a non-homogeneous fashion in the cell cytoplasm, and that dynamic localization of proteins is critical for cell cycle progression and asymmetry. However, the molecular-level mechanisms that govern protein localization, and enable the cell to exploit subcellular localization towards orchestrating an asymmetric life cycle remain obscure. There are also instances of researchers using intuitive reasoning to develop very different verbal explanations of the same biological process. To provide a complementary view of the molecular mechanism controlling the asymmetric division cycle of Caulobacter, we have developed a mathematical model of the cell cycle regulatory network. Our reaction-diffusion models provide additional insight into specific mechanism regulating different aspects of the cell cycle. We describe a molecular mechanism by which the bifunctional histidine kinase PleC exhibits bistable transitions between phosphatase and kinase forms. We demonstrate that the kinase form of PleC is crucial for both swarmer-to-stalked cell morphogenesis, and for replicative asymmetry in the predivisional cell. We propose that localization of the scaffolding protein PopZ can be explained by a Turing-type mechanism. Finally, we discuss a preliminary model of ParA- dependent chromosome segregation. Our model simulations are in agreement with experimentally observed protein distributions in wild-type and mutant cells. In addition to predicting novel mutants that can be tested in the laboratory, we use our models to reconcile competing hypotheses and provide a unified view of the regulatory mechanisms that direct the Caulobacter cell cycle.
Ph. D.
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3

Adam, Ihusan. "Structure and collective behaviour: a focus on the inverse problem." Doctoral thesis, 2021. http://hdl.handle.net/2158/1230776.

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The aim of this thesis is to inform our understanding of the exquisite relationship between function and structure of complex systems with a particular focus on the inverse problem of inferring structure from collective expression. There exists a rich body of work explaining complex collective behaviour through its interdependence on structure and this forms the core subject matter of the field complex networks. However, in many cases of interest, the underlying structure of the observed system is often unknown and can only be studied through limited measurements. The first chapters of this thesis develop and refine a method of inferring the structure of a priori unknown networks by leveraging the celebrated Heterogeneous mean-field approximations. The inverse protocol is first formulated for and rigorously challenged against synthetic simulations of reactive-random-walkers to successfully recover the degree distributions from partial observations of the system. The reconstruction framework developed is powerful enough to be applicable to many real-world systems of great interest. This is demonstrated by the extension of the method to a nonlinear Leaky-Integrate and Fire (LIF) excitatory neuronal model evolving on a directed network support to recover both the in-degree distribution and the distribution of associated current in Chapter 5. In this chapter, this method is also applied to wide-field calcium imaging data from the brains of mice undergoing stroke and rehabilitation, which is presented as a spatiotemporal analysis in Chapter 4. The findings of Chapters 4 and 5 complement each other to showcase two potential non-invasive ways of tracking the post-stroke recovery of these animals. One analysis focuses on the subtle changes in propagation patterns quantified through three novel biomarkers, while the other shifts the attention to the changes in structure and inherent dynamics as seen through the inverse protocol. This reconstruction recipe has also been extended to a more general two species LIF model accounting for both inhibitory and excitatory neurons. in Chapter 6. This was applied to two-photon light-sheet microscopy data from zebrafish brains upon successful validation in silico. Lastly, Chapter 7 studies a particular phenomenon of interest where structure and inherent dynamics affect the function in a different but popular class of networks. A zero-mean noise-like prestrain is used to induce contractions in 1D Elastic Network Models. The analysis shows that the exact solution is difficult to probe analytically, while the mean behaviours of the networks are predictable and controllable by tuning the magnitude of the applied prestrain.
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Книги з теми "Reaction-Diffusion Network Model"

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Adam, M. Shiham. Use of neural networks with advection-diffusion-reaction models to estimate large-scale movements of Skipjack tuna from tagging data. Honolulu, Hawaii: Pelagic Fisheries Research Program, University of Hawaii at Manoa, 2004.

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2

Prescott, Tony J., and Leah Krubitzer. Evo-devo. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199674923.003.0008.

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Анотація:
This chapter explores how principles underlying natural evo-devo (evolution and development) continue to inspire the design of artificial systems from models of cell growth through to simulated three-dimensional evolved creatures. Research on biological evolvability shows that phenotypic outcomes depend on multiple interactions across different organizational levels—the adult organism is the outcome of a series of genetic cascades modulated in time and space by the wider embryological, bodily, and environmental context. This chapter reviews evo-devo principles discovered in biology and explores their potential for improving the evolvability of artificial systems. Biological topics covered include adaptive, selective, and generative mechanisms, and the role of epigenetic processes in creating phenotypic diversity. Modeling approaches include L-systems, Boolean networks, reaction-diffusion processes, genetic algorithms, and artificial embryogeny. A particular focus is on the evolution and development of the mammalian brain and the possibility of designing, using synthetic evo-devo approaches, brain-like control architectures for biomimetic robots.
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Частини книг з теми "Reaction-Diffusion Network Model"

1

Dan, Tingting, Hongmin Cai, Zhuobin Huang, Paul Laurienti, Won Hwa Kim, and Guorong Wu. "Neuro-RDM: An Explainable Neural Network Landscape of Reaction-Diffusion Model for Cognitive Task Recognition." In Lecture Notes in Computer Science, 365–74. Cham: Springer Nature Switzerland, 2022. http://dx.doi.org/10.1007/978-3-031-16452-1_35.

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2

von Below, Joachim, and José A. Lubary. "Stability Matters for Reaction–Diffusion–Equations on Metric Graphs Under the Anti-Kirchhoff Vertex Condition." In Discrete and Continuous Models in the Theory of Networks, 1–28. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-44097-8_1.

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3

Gomez, Karina Mabell, Daniele Miorandi, and David Lowe. "Data Highways." In Biologically Inspired Networking and Sensing, 223–41. IGI Global, 2012. http://dx.doi.org/10.4018/978-1-61350-092-7.ch012.

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Анотація:
The design of efficient routing algorithms is an important issue in dense ad hoc wireless networks. Previous theoretical work has shown that benefits can be achieved through the creation of a set of data “highways” that carry packets across the network, from source(s) to sink(s). Current approaches to the design of these highways however require a–priori knowledge of the global network topology, with consequent communications burden and scalability issues, particularly with regard to reconfiguration after node failures. In this chapter, we describe a bio–inspired approach to generating these data highways through a distributed reaction–diffusion model that uses localized convolution with activation–inhibition filters. The result is the distributed emergence of data highways that can be tuned to provide appropriate highway separation and connection to data sinks. In this chapter, we present the underlying models, algorithms, and protocols for generating data highways in a dense wireless sensor network. The proposed methods are validated through extensive simulations performed using OMNeT++.
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4

Samil Demirkol, Ahmet, Alon Ascoli, Ioannis Messaris, and Ronald Tetzlaff. "Pattern Formation in a RD-MCNN with Locally Active Memristors." In Memristor - An Emerging Device for Post-Moore’s Computing and Applications. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.100463.

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This chapter presents the mathematical investigation of the emergence of static patterns in a Reaction–Diffusion Memristor Cellular Nonlinear Network (RD-MCNN) structure via the application of the theory of local activity. The proposed RD-MCNN has a planar grid structure, which consists of identical memristive cells, and the couplings are established in a purely resistive fashion. The single cell has a compact design being composed of a locally active memristor in parallel with a capacitor, besides the bias circuitry, namely a DC voltage source and its series resistor. We first introduce the mathematical model of the locally active memristor and then study the main characteristics of its AC equivalent circuit. Later on, we perform a stability analysis to obtain the stability criteria for the single cell. Consequently, we apply the theory of local activity to extract the parameter space associated with locally active, edge-of-chaos, and sharp-edge-of-chaos domains, performing all the necessary calculations parametrically. The corresponding parameter space domains are represented in terms of intrinsic cell characteristics such as the DC operating point, the capacitance, and the coupling resistance. Finally, we simulate the proposed RD-MCNN structure where we demonstrate the emergence of pattern formation for various values of the design parameters.
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Тези доповідей конференцій з теми "Reaction-Diffusion Network Model"

1

Cao, Yuexin, Yibei Li, Lirong Zheng, and Xiaoming Hu. "Network Controllability of Turing Reaction and Diffusion Model." In 2022 41st Chinese Control Conference (CCC). IEEE, 2022. http://dx.doi.org/10.23919/ccc55666.2022.9902569.

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2

Long, Pham Hong, and Pham Thuong Cat. "Real-time Image Processing by Cellular Neural Network Using Reaction-Diffusion Model." In 2009 International Conference on Knowledge and Systems Engineering (KSE). IEEE, 2009. http://dx.doi.org/10.1109/kse.2009.35.

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3

Zhang, Jingwen, Defu Yang, Wei He, Guorong Wu, and Minghan Chen. "A Network-Guided Reaction-Diffusion Model of AT[N] Biomarkers in Alzheimer’s Disease." In 2020 IEEE 20th International Conference on Bioinformatics and Bioengineering (BIBE). IEEE, 2020. http://dx.doi.org/10.1109/bibe50027.2020.00044.

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4

Katsuya Hyodo, Naoki Wakamiya, and Masayuki Murata. "Reaction-diffusion based autonomous control of camera sensor networks." In 2007 2nd Bio-Inspired Models of Network, Information and Computing Systems (BIONETICS). IEEE, 2007. http://dx.doi.org/10.1109/bimnics.2007.4610091.

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5

Nelson, George J., Comas Haynes, and William Wepfer. "A Fractal Approach for Modeling SOFC Electrode Mass Transport." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-12870.

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Fractal modeling approaches are common in the study of porous media and may be applied to describe pore surface morphology and network topology within a porous medium. Fractal structures can serve as templates for the pore structure and allow for the more detailed examination of diffusion phenomena within pore structures. In the present work a fractal pore morphology model is applied toward modeling diffusion within the electrochemically active region of an SOFC electrode. The porous electrode is separated into bulk and electrochemically active regions. Within the bulk electrode a one-dimensional model is applied based on the dusty-gas formalism assuming volume average microstructural parameters. The electrochemically active region is modeled using a two-dimensional finite element model based on a Koch pore cross-section as a fractal template. This fractal model is compared to a one-dimensional transport model applying the common assumption of a planar reaction zone. Performance variations that may exist for electrodes with the same average bulk properties are investigated in initial studies. These studies allow for exploration of the merits of fractal approaches in modeling diffusive transport within porous SOFC electrodes.
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6

Hyodo, Katsuya, Naoki Wakamiya, and Masayuki Murata. "Reaction-Diffusion based Autonomous Control of Camera Sensor Networks." In 2nd International ICST Conference on Bio-Inspired Models of Network, Information, and Computing Systems. IEEE, 2007. http://dx.doi.org/10.4108/icst.bionetics2007.2436.

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7

Suthar, Kamlesh J., Muralidhar K. Ghantasala, and Derrick C. Mancini. "Simulation of Hydrogel Responsiveness to Blood Glucose." In ASME 2013 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/smasis2013-3167.

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This paper presents the results of our fully coupled, two-dimensional (2D) simulation of the swelling behavior of glucose-sensitive hydrogels at a constant glucose level with change in the surrounding pH. The model consists of a system of glucose-sensitive hydrogel and ionic fluid as a solvent. The hydrogel consists of two enzymes: glucose-oxidase and catalase, which are immobilized on the polymeric network. The surrounding solvent has certain level of glucose. The diffusion of glucose from a solvent and its reaction within the hydrogel are simulated using the Nernst-Planck equation. The local electrical charge is calculated by the Poisson’s equation, and deformation of the hydrogel is determined by the mechanical field equation. These equations are fully coupled and simulations are performed for varying pH and glucose concentrations. The glucose concentration was taken at 7.7mM (140mg/mL) and the pH is varied from 6.8 to 7.4. As glucose reacts with oxygen, gluconic acid is produced in the presence of glucose-oxidase. The formation of gluconic acid within the gel results in protonation and thereby causes the hydrogel expansion. The glucose level in the surrounding solution limits diffusion in the hydrogel. As the surrounding solution pH increases the available fixed charged for ionization increases, which results in an increase in maximum equilibrium swelling and gluconic acid as a product of the reaction. The gluconic acid production was found to be proportional to the change in pH. The gluconic acid decreases the internal pH of the hydrogel, which ultimately reduced the deformation of the gel.
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8

Bhaumik, B., and C. M. Markan. "Orientation map: a reaction-diffusion based model." In Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium. IEEE, 2000. http://dx.doi.org/10.1109/ijcnn.2000.857841.

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9

Szatmari, Istvan. "Pattern formation in oscillatory media: Beyond reaction-diffusion model." In 2010 12th International Workshop on Cellular Nanoscale Networks and their Applications (CNNA 2010). IEEE, 2010. http://dx.doi.org/10.1109/cnna.2010.5430312.

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10

Ishizaki, Takayuki, Kenji Kashima, Jun-ichi Imura, and Kazuyuki Aihara. "Model order reduction for MIMO linear dynamical networks via Reaction-Diffusion transformation." In 2011 American Control Conference. IEEE, 2011. http://dx.doi.org/10.1109/acc.2011.5990628.

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