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Journal articles on the topic 'Reaction-diffusion processes'

Author: Grafiati

Published: 28 June 2021

Last updated: 1 February 2022

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1

Chen, Mufa. "Reaction-diffusion processes." Chinese Science Bulletin 43, no. 17 (September 1998): 1409–20. http://dx.doi.org/10.1007/bf02884118.

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2

Mufa, Chen. "Infinite dimensional reaction-diffusion processes." Acta Mathematica Sinica 1, no. 3 (September 1985): 261–73. http://dx.doi.org/10.1007/bf02564823.

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3

Hu, Jifeng, Hye-Won Kang, and Hans G. Othmer. "Stochastic Analysis of Reaction–Diffusion Processes." Bulletin of Mathematical Biology 76, no. 4 (May 30, 2013): 854–94. http://dx.doi.org/10.1007/s11538-013-9849-y.

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4

Gorecki, J., K. Gizynski, J. Guzowski, J. N. Gorecka, P. Garstecki, G. Gruenert, and P. Dittrich. "Chemical computing with reaction–diffusion processes." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2046 (July 28, 2015): 20140219. http://dx.doi.org/10.1098/rsta.2014.0219.

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Chemical reactions are responsible for information processing in living organisms. It is believed that the basic features of biological computing activity are reflected by a reaction–diffusion medium. We illustrate the ideas of chemical information processing considering the Belousov–Zhabotinsky (BZ) reaction and its photosensitive variant. The computational universality of information processing is demonstrated. For different methods of information coding constructions of the simplest signal processing devices are described. The function performed by a particular device is determined by the geometrical structure of oscillatory (or of excitable) and non-excitable regions of the medium. In a living organism, the brain is created as a self-grown structure of interacting nonlinear elements and reaches its functionality as the result of learning. We discuss whether such a strategy can be adopted for generation of chemical information processing devices. Recent studies have shown that lipid-covered droplets containing solution of reagents of BZ reaction can be transported by a flowing oil. Therefore, structures of droplets can be spontaneously formed at specific non-equilibrium conditions, for example forced by flows in a microfluidic reactor. We describe how to introduce information to a droplet structure, track the information flow inside it and optimize medium evolution to achieve the maximum reliability. Applications of droplet structures for classification tasks are discussed.

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5

Richardson, M. J. E., and Y. Kafri. "Boundary effects in reaction-diffusion processes." Physical Review E 59, no. 5 (May 1, 1999): R4725—R4728. http://dx.doi.org/10.1103/physreve.59.r4725.

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6

Alimohammadi, M., and N. Ahmadi. "Class of integrable diffusion-reaction processes." Physical Review E 62, no. 2 (August 1, 2000): 1674–82. http://dx.doi.org/10.1103/physreve.62.1674.

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7

Kurganov, Alexander, and Philip Rosenau. "On reaction processes with saturating diffusion." Nonlinearity 19, no. 1 (November 8, 2005): 171–93. http://dx.doi.org/10.1088/0951-7715/19/1/009.

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8

Alimohammadi, Masoud. "Solvable reaction-diffusion processes without exclusion." Journal of Mathematical Physics 47, no. 2 (February 2006): 023304. http://dx.doi.org/10.1063/1.2168398.

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9

Alimohammadi, M., and N. Ahmadi. "p-species integrable reaction–diffusion processes." Journal of Physics A: Mathematical and General 35, no. 6 (February 4, 2002): 1325–37. http://dx.doi.org/10.1088/0305-4470/35/6/301.

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10

Chen, Mu Fa. "Ergodic theorems for reaction-diffusion processes." Journal of Statistical Physics 58, no. 5-6 (March 1990): 939–66. http://dx.doi.org/10.1007/bf01026558.

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11

Ding, Wan-Ding, Richard Durrett, and Thomas M. Liggett. "Ergodicity of reversible reaction diffusion processes." Probability Theory and Related Fields 85, no. 1 (March 1990): 13–26. http://dx.doi.org/10.1007/bf01377624.

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12

Ru-Sheng, Li. "Local Equilibrium Assumption and Reaction-diffusion Processes." Acta Physico-Chimica Sinica 10, no. 01 (1994): 38–43. http://dx.doi.org/10.3866/pku.whxb19940110.

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13

Rosenau, Philip. "On reaction processes with a logarithmic-diffusion." Physics Letters A 381, no. 2 (January 2017): 94–101. http://dx.doi.org/10.1016/j.physleta.2016.10.056.

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14

H. Chang, K., K. G. Park, K. D. Ahan, Soo Yong Kim, Deock-Ho Ha, and Kyungsik Kim. "Reaction-Diffusion Processes on Scale-Free Networks." Journal of the Physical Society of Japan 76, no. 3 (March 15, 2007): 035001. http://dx.doi.org/10.1143/jpsj.76.035001.

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15

Zanette, Damián H. "Multistate cellular automaton for reaction-diffusion processes." Physical Review A 46, no. 12 (December 1, 1992): 7573–77. http://dx.doi.org/10.1103/physreva.46.7573.

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16

Gajewski, H., and K. Gröger. "Reaction—Diffusion Processes of Electrically Charged Species." Mathematische Nachrichten 177, no. 1 (1996): 109–30. http://dx.doi.org/10.1002/mana.19961770108.

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17

Stundzia, Audrius B., and Charles J. Lumsden. "Stochastic Simulation of Coupled Reaction–Diffusion Processes." Journal of Computational Physics 127, no. 1 (August 1996): 196–207. http://dx.doi.org/10.1006/jcph.1996.0168.

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18

Dubljevic, Stevan, Panagiotis D. Christofides, and Ioannis G. Kevrekidis. "Distributed nonlinear control of diffusion–reaction processes." International Journal of Robust and Nonlinear Control 14, no. 2 (December 12, 2003): 133–56. http://dx.doi.org/10.1002/rnc.867.

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19

Dubljevic, Stevan. "Model predictive control of diffusion-reaction processes." Chemical Industry and Chemical Engineering Quarterly 11, no. 1 (2005): 10–18. http://dx.doi.org/10.2298/ciceq0501010d.

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Parabolic partial differential equations naturally arise as an adequate representation of a large class of spatially distributed systems, such as diffusion-reaction processes, where the interplay between diffusive and reaction forces introduces complexity in the characterization of the system, for the purpose of process parameter identification and subsequent control. In this work we introduce a model predictive control (MPC) framework for the control of input and state constrained parabolic partial differential equation (PDEs) systems. Model predictive control (MPC) is one of the most popular control formulations among chemical engineers, manly due to its ability to account for the actuator (input) constraints that inevitably exist due to finite actuator power and its ability to handle state constraints within an optimal control setting. In controller synthesis, the initially parabolic partial differential equation of the diffusion reaction type is transformed by the Galerkin method into a system of ordinary differential equations (ODEs) that capture the dominant dynamics of the PDE system. Systems obtained in such a way (ODEs) are used as the basis for the synthesis of the MPC controller that explicitly accounts for the input and state constraints. Namely, the modified MPC formulation includes a penalty term that is directly added to the objective function and through the appropriate structure of the controller state constraints accounts for the infinite dimensional nature of the state of the PDE system. The MPC controller design method is successively applied to control of the diffusion-reaction process described by linear parabolic PDE, by demonstrating stabilization of the non-dimensional temperature profile around a spatially uniform unstable steady-state under satisfaction of the input (actuator) constraints and allowable non-dimensional temperature (state) constraints.

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20

Le Roux, Marie-Noëlle. "Numerical Solution of Nonlinear Reaction Diffusion Processes." SIAM Journal on Numerical Analysis 37, no. 5 (January 2000): 1644–56. http://dx.doi.org/10.1137/s0036142998335996.

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21

Bayati, Basil, Philippe Chatelain, and Petros Koumoutsakos. "Multiresolution stochastic simulations of reaction–diffusion processes." Physical Chemistry Chemical Physics 10, no. 39 (2008): 5963. http://dx.doi.org/10.1039/b810795e.

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22

Grynberg, Marcelo D., and Robin B. Stinchcombe. "Autocorrelation Functions of Driven Reaction-Diffusion Processes." Physical Review Letters 76, no. 5 (January 29, 1996): 851–54. http://dx.doi.org/10.1103/physrevlett.76.851.

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23

H. Chang, K., Kyungsik Kim, M. K. Yum, J. S. Choi, and T. Odagaki. "Reaction–Diffusion Processes on Small-World Networks." Journal of the Physical Society of Japan 74, no. 10 (October 2005): 2860–61. http://dx.doi.org/10.1143/jpsj.74.2860.

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24

Canet, L., and H. J. Hilhorst. "Single-Site Approximation for Reaction-Diffusion Processes." Journal of Statistical Physics 125, no. 3 (October 5, 2006): 517–31. http://dx.doi.org/10.1007/s10955-006-9206-8.

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25

Schütz, Gunter M. "Reaction-diffusion processes of hard-core particles." Journal of Statistical Physics 79, no. 1-2 (April 1995): 243–64. http://dx.doi.org/10.1007/bf02179389.

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26

Christofides, Panagiotis D., and Prodromos Daoutidis. "Nonlinear control of diffusion-convection-reaction processes." Computers & Chemical Engineering 20 (January 1996): S1071—S1076. http://dx.doi.org/10.1016/0098-1354(96)00186-x.

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27

Marin, D., L. M. S. Guilherme, M. K. Lenzi, L. R. da Silva, E. K. Lenzi, and T. Sandev. "Diffusion—Reaction processes on a backbone structure." Communications in Nonlinear Science and Numerical Simulation 85 (June 2020): 105218. http://dx.doi.org/10.1016/j.cnsns.2020.105218.

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28

Wilhelmsson, H., and B. Etlicher. "Effects of stimulated diffusion for simultaneous reaction and diffusion processes." Physica Scripta 39, no. 5 (May 1, 1989): 610–12. http://dx.doi.org/10.1088/0031-8949/39/5/012.

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29

Safaryan, R. G. "BRANCHING DIFFUSION PROCESSES AND SYSTEMS OF REACTION-DIFFUSION DIFFERENTIAL EQUATIONS." Mathematics of the USSR-Sbornik 62, no. 2 (February 28, 1989): 525–39. http://dx.doi.org/10.1070/sm1989v062n02abeh003252.

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30

DEMONGEOT, JACQUES, JEAN GAUDART, ATHANASIOS LONTOS, JULIE MINTSA, EMMANUEL PROMAYON, and MUSTAPHA RACHDI. "ZERO-DIFFUSION DOMAINS IN REACTION–DIFFUSION MORPHOGENETIC AND EPIDEMIOLOGIC PROCESSES." International Journal of Bifurcation and Chaos 22, no. 02 (February 2012): 1250028. http://dx.doi.org/10.1142/s0218127412500289.

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Classical models of morphogenesis by Murray and Meinhardt and of epidemics by Ross and McKendrick can be revisited in order to consider the colocalizations favoring interaction between morphogens and cells or between pathogens and hosts. The classical epidemic models suppose, for example, that the populations in interaction have a constant size and are spatially fixed during the epidemic waves, but the presently observed pandemics show that the long duration of their spread during months or years imposes to take into account the pathogens, hosts and vectors migration in epidemics, as well as the morphogens and cells diffusion in morphogenesis. That leads naturally to study the occurrence of complex spatio-temporal behaviors in dynamics of population sizes and also to consider preferential zones of interaction, i.e. the zero-diffusion sets, for respectively building anatomic frontiers and confining contagion domains. Three examples of application will be presented, the first proposing a model of Black Death spread in Europe (1348–1350), and the last ones related to two morphogenetic processes, feather morphogenesis in chicken and gastrulation in Drosophila.

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31

Sinder, M., V. Sokolovsky, and J. Pelleg. "Reaction rate in reversible A↔B reaction-diffusion processes." Applied Physics Letters 96, no. 7 (February 15, 2010): 071905. http://dx.doi.org/10.1063/1.3319840.

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32

Mufa, Chen, Ding Wanding, and Zhu Dongjin. "Ergodicity of reversible reaction diffusion processes with general reaction rates." Acta Mathematica Sinica 10, no. 1 (March 1994): 99–112. http://dx.doi.org/10.1007/bf02561553.

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33

Pojman, John A., Alejandro L. Garcia, Dilip K. Kondepudi, and Christian Van den Broeck. "Nonequilibrium processes in polymers undergoing interchange reactions. 2. Reaction-diffusion processes." Journal of Physical Chemistry 95, no. 14 (July 1991): 5655–60. http://dx.doi.org/10.1021/j100167a051.

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34

O' Riordan, Eugene, Maria L. Pickett, and Georgii I. Shishkin. "Singularly Perturbed Problems Modeling Reaction-convection-diffusion Processes." Computational Methods in Applied Mathematics 3, no. 3 (2003): 424–42. http://dx.doi.org/10.2478/cmam-2003-0028.

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AbstractIn this paper, parameter - uniform numerical methods for singularly perturbed ordinary differential equations containing two small parameters are studied.Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. A numerical algorithm based on an upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are given to illustrate the parameter-uniform convergence of numerical approximations.

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35

K. Maini, Philip, Luisa Malaguti, Cristina Marcelli, and Serena Matucci. "Diffusion-aggregation processes with mono-stable reaction terms." Discrete & Continuous Dynamical Systems - B 6, no. 5 (2006): 1175–89. http://dx.doi.org/10.3934/dcdsb.2006.6.1175.

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36

Wilhelmsson, Hans. "Simultaneous diffusion and reaction processes in plasma dynamics." Physical Review A 38, no. 3 (August 1, 1988): 1482–89. http://dx.doi.org/10.1103/physreva.38.1482.

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37

Ignatyuk, V. V. "Reaction-diffusion processes in the “adsorbate-substrate” system." European Physical Journal Special Topics 216, no. 1 (January 2013): 153–63. http://dx.doi.org/10.1140/epjst/e2013-01738-x.

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38

Zhang, Wen-Biao, and Ming Yi. "Reaction-anomalous diffusion processes for A+B⇌C." Physica A: Statistical Mechanics and its Applications 527 (August 2019): 121347. http://dx.doi.org/10.1016/j.physa.2019.121347.

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39

Taitelbaum, Haim, and Zbigniew Koza. "Reaction–diffusion processes: exotic phenomena in simple systems." Physica A: Statistical Mechanics and its Applications 285, no. 1-2 (September 2000): 166–75. http://dx.doi.org/10.1016/s0378-4371(00)00299-5.

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40

Bachmann, P., and D. Sünder. "Multi-Fluid Plasma Description of Reaction-Diffusion Processes." Contributions to Plasma Physics 38, no. 1-2 (1998): 290–95. http://dx.doi.org/10.1002/ctpp.2150380144.

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41

Fujii, Yasuhiro, and Miki Wadati. "Reaction-Diffusion Processes with Multi-Species of Particles." Journal of the Physical Society of Japan 66, no. 12 (December 15, 1997): 3770–77. http://dx.doi.org/10.1143/jpsj.66.3770.

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42

Epstein, Irving R., and Bing Xu. "Reaction–diffusion processes at the nano- and microscales." Nature Nanotechnology 11, no. 4 (April 2016): 312–19. http://dx.doi.org/10.1038/nnano.2016.41.

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43

Canet, Léonie. "Reaction–diffusion processes and non-perturbative renormalization group." Journal of Physics A: Mathematical and General 39, no. 25 (June 7, 2006): 7901–12. http://dx.doi.org/10.1088/0305-4470/39/25/s07.

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44

Rubinstein, Jacob, Peter Sternberg, and Joseph B. Keller. "Reaction-Diffusion Processes and Evolution to Harmonic Maps." SIAM Journal on Applied Mathematics 49, no. 6 (December 1989): 1722–33. http://dx.doi.org/10.1137/0149104.

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45

Hou, Ru, and Weihua Deng. "Feynman–Kac equations for reaction and diffusion processes." Journal of Physics A: Mathematical and Theoretical 51, no. 15 (March 15, 2018): 155001. http://dx.doi.org/10.1088/1751-8121/aab1af.

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46

Li, Mingheng, and Panagiotis D. Christofides. "OPTIMAL TRANSITION CONTROL OF DIFFUSION-CONVECTION-REACTION PROCESSES." IFAC Proceedings Volumes 40, no. 5 (2007): 135–40. http://dx.doi.org/10.3182/20070606-3-mx-2915.00021.

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47

Bayati, Basil, Philippe Chatelain, and Petros Koumoutsakos. "Adaptive mesh refinement for stochastic reaction–diffusion processes." Journal of Computational Physics 230, no. 1 (January 2011): 13–26. http://dx.doi.org/10.1016/j.jcp.2010.08.035.

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48

Hellander, Stefan, and Per Lötstedt. "Flexible single molecule simulation of reaction–diffusion processes." Journal of Computational Physics 230, no. 10 (May 2011): 3948–65. http://dx.doi.org/10.1016/j.jcp.2011.02.020.

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49

Schütz, G. M. "Dynamic matrix ansatz for integrable reaction-diffusion processes." European Physical Journal B 5, no. 3 (October 1998): 589–97. http://dx.doi.org/10.1007/s100510050483.

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50

Carlon, E., M. Henkel, and U. Schollwöck. "Density matrix renormalization group and reaction-diffusion processes." European Physical Journal B 12, no. 1 (October 1999): 99–114. http://dx.doi.org/10.1007/s100510050983.

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