Relevant bibliographies by topics / Équations de Poisson-Nernst Planck

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Équations de Poisson-Nernst Planck'

Author: Grafiati
Published: 28 September 2024
Last updated: 31 July 2025

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Journal articles on the topic "Équations de Poisson-Nernst Planck"

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Zheng, Qiong, and Guo-Wei Wei. "Poisson–Boltzmann–Nernst–Planck model." Journal of Chemical Physics 134, no. 19 (2011): 194101. http://dx.doi.org/10.1063/1.3581031.

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Xie, Yan, Jie Cheng, Benzhuo Lu, and Linbo Zhang. "Parallel Adaptive Finite Element Algorithms for Solving the Coupled Electro-diffusion Equations." Computational and Mathematical Biophysics 1 (April 24, 2013): 90–108. http://dx.doi.org/10.2478/mlbmb-2013-0005.

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Abstractrithms for solving the 3D electro-diffusion equations such as the Poisson-Nernst-Planck equations and the size-modified Poisson-Nernst-Planck equations in simulations of biomolecular systems in ionic liquid. A set of transformation methods based on the generalized Slotboom variables is used to solve the coupled equations. Calculations of the diffusion-reaction rate coefficients, electrostatic potential and ion concentrations for various systems verify the method’s validity and stability. The iterations between the Poisson equation and the Nernst- Planck equations in the primitive metho
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Yang, Ying, and Benzhuo Lu. "An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations." Advances in Applied Mathematics and Mechanics 5, no. 1 (2013): 113–30. http://dx.doi.org/10.4208/aamm.11-m11184.

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AbstractPoisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources, which describe the electrodiffusion of ions in a solvated biomolecular system. In this paper, some error bounds for a piecewise finite element approximation to this problem are derived. Several numerical examples including biomolecular problems are shown to support our analysis.
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Meng, Da, Bin Zheng, Guang Lin, and Maria L. Sushko. "Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment." Communications in Computational Physics 16, no. 5 (2014): 1298–322. http://dx.doi.org/10.4208/cicp.040913.120514a.

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AbstractWe have developed efficient numerical algorithms for solving 3D steady-state Poisson-Nernst-Planck (PNP) equations with excess chemical potentials described by the classical density functional theory (cDFT). The coupled PNP equations are discretized by a finite difference scheme and solved iteratively using the Gummel method with relaxation. The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation. Then, the algebraic multigrid method is applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations. A novel s
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Chaudhry, Jehanzeb Hameed, Jeffrey Comer, Aleksei Aksimentiev, and Luke N. Olson. "A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore." Communications in Computational Physics 15, no. 1 (2014): 93–125. http://dx.doi.org/10.4208/cicp.101112.100413a.

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AbstractThe conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a n
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Hashemi Amrei, S. M. H., Gregory H. Miller, Kyle J. M. Bishop, and William D. Ristenpart. "A perturbation solution to the full Poisson–Nernst–Planck equations yields an asymmetric rectified electric field." Soft Matter 16, no. 30 (2020): 7052–62. http://dx.doi.org/10.1039/d0sm00417k.

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Hineman, Jay L., and Rolf J. Ryham. "Very weak solutions for Poisson–Nernst–Planck system." Nonlinear Analysis: Theory, Methods & Applications 115 (March 2015): 12–24. http://dx.doi.org/10.1016/j.na.2014.11.018.

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Eisenberg, Bob, Tzyy-Leng Horng, Tai-Chia Lin, and Chun Liu. "Steric PNP (Poisson-Nernst-Planck): Ions in Channels." Biophysical Journal 104, no. 2 (2013): 509a. http://dx.doi.org/10.1016/j.bpj.2012.11.2809.

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González Granada, José Rodrigo, and Victor A. Kovtunenko. "Entropy method for generalized Poisson–Nernst–Planck equations." Analysis and Mathematical Physics 8, no. 4 (2018): 603–19. http://dx.doi.org/10.1007/s13324-018-0257-1.

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Prohl, Andreas, and Markus Schmuck. "Convergent discretizations for the Nernst–Planck–Poisson system." Numerische Mathematik 111, no. 4 (2008): 591–630. http://dx.doi.org/10.1007/s00211-008-0194-2.

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Dissertations / Theses on the topic "Équations de Poisson-Nernst Planck"

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Paragot, Paul. "Analyse numérique du système d'équations Poisson-Nernst Planck pour étudier la propagation d'un signal transitoire dans les neurones." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ5020.

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Les questions neuroscientifiques concernant les dendrites incluent la compréhension de leur plasticité structurale en réponse à l'apprentissage et la manière dont elles intègrent les signaux. Les chercheurs visent à élucider ces aspects pour améliorer notre compréhension de la fonction neuronale et de ses complexités. Cette thèse vise à offrir des perspectives numériques concernant la dynamique du voltage et des ions dans les dendrites. Notre objectif est de modéliser l'excitation neuronale dans les dendrites. Nous abordons la dynamique ionique suite à l'afflux de signaux nerveux. Pour les sim
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Cartailler, Jérôme. "Asymptotic of Poisson-Nernst-Planck equations and application to the voltage distribution in cellular micro-domains." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066297/document.

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Dans cette thèse j’étudie l’impact de la géométrie de micro et nano-domaines biologiques sur les propriétés d'électrodiffusion, ceci à l'aide des équations aux dérivées partielles de Poisson-Nernst-Planck. Je considère des domaines non-triviaux ayant une forme cuspide ou elliptique. Mon objectif est de développer des modèles ainsi que des méthodes mathématiques afin d'étudier les caractéristiques électriques de ces nano/micro-domaines, et ainsi mieux comprendre comment les signaux électriques sont modulés à ces échelles. Dans la première partie j’étudie le voltage à l'équilibre pour un électro
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Abdul, Samad Feras. "Polarisation provoquée : expérimentation, modélisation et applications géophysiques." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066049/document.

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Les mécanismes produisant les signaux observés par la méthode de Polarisation Provoquée (PP) sur une large gamme de fréquences (entre 1 mHz et 20 kHz) ne sont pas encore complètement identifiés. Deux sujets particuliers ont été abordés dans cette thèse. L'origine du signal observé à haute fréquence (>1 kHz) a été analysé en effectuant des mesures de la résistivité complexe sur de l'eau à différentes salinités. Les résultats montrent des écarts sur la phase par rapport à la réponse attendue à haute fréquence. Ils dépendent du type d'électrode de mesures et de la conductivité du milieu. Un mo
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Abdul, Samad Feras. "Polarisation provoquée : expérimentation, modélisation et applications géophysiques." Electronic Thesis or Diss., Paris 6, 2017. http://www.theses.fr/2017PA066049.

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Les mécanismes produisant les signaux observés par la méthode de Polarisation Provoquée (PP) sur une large gamme de fréquences (entre 1 mHz et 20 kHz) ne sont pas encore complètement identifiés. Deux sujets particuliers ont été abordés dans cette thèse. L'origine du signal observé à haute fréquence (>1 kHz) a été analysé en effectuant des mesures de la résistivité complexe sur de l'eau à différentes salinités. Les résultats montrent des écarts sur la phase par rapport à la réponse attendue à haute fréquence. Ils dépendent du type d'électrode de mesures et de la conductivité du milieu. Un mo
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Lefebvre, Xavier. "Etude des modèles de transfert en nanofiltration : application du modèle hybride basé sur les équations de Nernst-Planck étendues par le développement du logiciel de simulation "nanoflux"." Montpellier 2, 2003. http://www.theses.fr/2003MON20082.

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Moreau, Antoine. "Calcul des propriétés homogénéisées de transfert dans les matériaux poreux par des méthodes de réduction de modèle : Application aux matériaux cimentaires." Thesis, La Rochelle, 2022. http://www.theses.fr/2022LAROS024.

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Cette thèse propose de coupler deux outils préexistant pour la modélisation mathématique en mécanique : l’homogénéisation périodique et la réduction de modèle, afin de modéliser la corrosion des structures de béton armé exposées à la pollution atmosphérique et au sel marin. Cette dégradation est en effet difficile à simuler numériquement, eu égard la forte hétérogénéité des matériaux concernés, et la variabilité de leur microstructure. L’homogénéisation périodique fournit un modèle multi-échelle permettant de s’affranchir de la première de ces deux difficultés. Néanmoins, elle repose sur l’exi
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Herda, Maxime. "Analyse asymptotique et numérique de quelques modèles pour le transport de particules chargées." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1165/document.

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Cette thèse est consacrée à l'étude mathématique de quelques modèles d'équations aux dérivées partielles issues de la physique des plasmas. On s'intéresse principalement à l'analyse théorique de différents régimes asymptotiques de systèmes d'équations cinétiques de type Vlasov-Poisson-Fokker-Planck. Dans un premier temps, en présence d'un champ magnétique extérieur on se concentre sur l'approximation des électrons sans masse fournissant des modèles réduits lorsque le rapport me{mi entre la masse me d'un électron et la masse mi d'un ion tend vers 0 dans les modèles. Suivant le régime considéré,
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Minton, Geraint Philip. "Modelling the static and dynamic behaviour of electrolytes : a modified Poisson-Nernst-Planck approach." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/modelling-the-static-and-dynamic-behaviour-of-electrolytes-a-modified-poissonnernstplanck-approach(de9671fd-feb5-4870-b0a9-ad6a28ff953d).html.

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In this thesis a method is presented for the modelling the effects of the excluded volume (ion-ion) and ion excess polarisability (ion-solvent) interactions in an electrolyte at a smooth planar electrode. The impact of these interactions is studied in terms of the equilibrium state of single and mixed electrolytes, the dynamic response of single electrolytes to a time-dependent applied potential, and their effect on the reaction rate, for both steady and time-dependent applied potentials. For reacting systems, the reaction rate is modelled using a modified form of the Frumkin-Butler-Volmer equ
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Lim, Jong Il. "Transient finite element analysis of electric double layer using Nernst-Planck-Poisson equations with a modified stern layer." Texas A&M University, 2006. http://hdl.handle.net/1969.1/4703.

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Finite element analysis of electric double layer capacitors using a transient nonlinear Nernst-Planck-Poisson (NPP) model and Nernst-Planck-Poisson-modified Stern layer (NPPMS) model are presented in 1D and 2D. The NPP model provided unrealistic ion concentrations for high electrode surface potential. The NPPMS model uses a modified Stern layer to account for finite ion size, resulting in realistic ion concentrations even at high surface potential. The finite element solution algorithm uses the Newton-Raphson method to solve the nonlinear problem and the alpha family approximation for time int
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Neuen, Christian P. T. [Verfasser]. "Numerical Simulation of Ion Migration with Particle Dynamics and the Heat-Poisson-Nernst-Planck System / Christian P. T. Neuen." Bonn : Universitäts- und Landesbibliothek Bonn, 2016. http://d-nb.info/1124540164/34.

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Book chapters on the topic "Équations de Poisson-Nernst Planck"

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Lu, Benzhuo. "Poisson-Nernst-Planck Equation." In Encyclopedia of Applied and Computational Mathematics. Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_276.

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Horgmo Jæger, Karoline, and Aslak Tveito. "The Poisson-Nernst-Planck (PNP) Model." In Differential Equations for Studies in Computational Electrophysiology. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_12.

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AbstractIn these notes, we have considered models of electrophysiology across several scales. The first was the membrane model. It assumes that the action potential is similar across the whole cell membrane, and the model represents the action potential as a function of time alone. No spatial variable is involved in the pure membrane models, so a length scale of these models does not make sense.
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Holcman, David, and Zeev Schuss. "The Poisson–Nernst–Planck Equations in a Ball." In Applied Mathematical Sciences. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76895-3_10.

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Zubkova, Anna V. "The Generalized Poisson–Nernst–Planck System with Nonlinear Interface Conditions." In Trends in Mathematics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01153-6_18.

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Fuhrmann, Jürgen. "Activity Based Finite Volume Methods for Generalised Nernst-Planck-Poisson Systems." In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05591-6_59.

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Lefraich, H. "Computational Modeling of Membrane Blockage via Precipitation: A 2D Extended Poisson-Nernst-Planck Model." In Trends in Biomathematics: Modeling Epidemiological, Neuronal, and Social Dynamics. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33050-6_21.

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Kovtunenko, Victor A., and Anna V. Zubkova. "Solvability and Lyapunov Stability of a Two-component System of Generalized Poisson–Nernst–Planck Equations." In Recent Trends in Operator Theory and Partial Differential Equations. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-47079-5_9.

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Cancès, Clément, Maxime Herda, and Annamaria Massimini. "Finite Volumes for a Generalized Poisson-Nernst-Planck System with Cross-Diffusion and Size Exclusion." In Springer Proceedings in Mathematics & Statistics. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-40864-9_4.

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Fuhrmann, Jürgen, Benoît Gaudeul, and Christine Keller. "Two Entropic Finite Volume Schemes for a Nernst–Planck–Poisson System with Ion Volume Constraints." In Springer Proceedings in Mathematics & Statistics. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-40864-9_23.

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Fuhrmann, Jürgen, and Clemens Guhlke. "A Finite Volume Scheme for Nernst-Planck-Poisson Systems with Ion Size and Solvation Effects." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57394-6_52.

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Conference papers on the topic "Équations de Poisson-Nernst Planck"

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Zhu, Zhenjin, Nima Tajallipour, Sina Fardisi, and Patrick J. Teevens. "Interaction between Two Pre-Existing Micro Pits on Pitting Propagation." In CORROSION 2012. NACE International, 2012. https://doi.org/10.5006/c2012-01470.

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Abstract In the petroleum industry, pipeline failures are mostly the result of localized pitting corrosion which demonstrates the worst-case scenario for leaks as compared to metal loss due to uniform corrosion. When pitting nucleation occurs, numerous pits are generated within a short interval. Growth of pits leads to inevitable pit-to-pit interaction. Depending on the surrounding corrosive environment, the ultimate consequence of a competitive interaction between nearby active pits can be: Firstly, all initiated pits are passivated, resulting in uniform corrosion; Secondly, tiny pits merge i
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Zhu, Zhenjin, Nima Tajallipour, Patrick J. Teevens, Huibin Xue, and Frank Y. F. Cheng. "A Mechanistic Model for Predicting Localized Pitting Corrosion in a Brine Water-CO2 System." In CORROSION 2011. NACE International, 2011. https://doi.org/10.5006/c2011-11256.

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Abstract This paper proposes a Finite-Element-Analysis-based mechanistic model to predict internal localized pitting corrosion rates of petroleum pipelines in sweet (CO2) production environments. In this model, the computational domain consisted of a hemispherical pit and a thin boundary layer of an electrolyte solution. The mesh was generated using quadratic triangular elements in the Cartesian coordinate system whereas a moving mesh method was utilized to track the dynamic pitting propagation. The flux rate of each participating chemical ionic species was computed by solving the Nernst-Planc
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Shi, XiaoMin, JiaChun Le, KaiRong Qin, and YuFan Zheng. "The singular perturbation analysis for one-dimensional poisson-nernst-planck equation." In 2010 8th IEEE International Conference on Control and Automation (ICCA). IEEE, 2010. http://dx.doi.org/10.1109/icca.2010.5524264.

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Tano, M., S. Walker, and A. Abou-Jaoude. "Flow-Informed Corrosion in Molten Salts Using the Poisson-Nernst-Planck Model." In 20th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-20). American Nuclear Society, 2023. http://dx.doi.org/10.13182/nureth20-40838.

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Mathur, Sanjay R., and Jayathi Y. Murthy. "A Multigrid Method for the Solution of Ion Transport Using the Poisson Nernst Planck Equations." In ASME 2007 InterPACK Conference collocated with the ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ipack2007-33410.

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Recently there has been much interest in simulating ion transport in biological and synthetic ion channels using the Poisson-Nernst-Planck (PNP) equations. However, many published methods exhibit poor convergence rates, particularly at high driving voltages, and for long-aspect ratio channels. The paper addresses the development of a fast and efficient coupled multigrid method for the solution of the PNP equations. An unstructured cell-centered finite volume method is used to discretize the governing equations. An iterative procedure, based on a Newton-Raphson linearization accounting for the
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Furini, S., F. Zerbetto, and S. Cavalcanti. "A numerical solver of 3D Poisson Nernst Planck equations for functional studies of ion channels." In BIOMEDICINE 2005. WIT Press, 2005. http://dx.doi.org/10.2495/bio050111.

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Wang, Yiwei, Lijun Zhang, and Mingji Zhang. "A special case study of boundary layer effects via Poisson-Nernst-Planck systems with permanent charges." In 2020 International Conference on Information Technology and Nanotechnology (ITNT). IEEE, 2020. http://dx.doi.org/10.1109/itnt49337.2020.9253312.

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Aureli, Matteo, and Maurizio Porfiri. "On a Physics-Based Model for Nonlinear Sensing in Ionic Polymer Metal Composites." In ASME 2012 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/smasis2012-7983.

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In this paper, we propose a physics-based model of ionic polymer metal composites (IPMCs) charge dynamics in response to dynamic mechanical deformation by developing a perturbation solution of a particular form of the Poisson-Nernst-Planck equations. We derive an equivalent nonlinear circuit model whose components are directly controlled by the imposed mechanical deformation. We show results for a variety of loading scenarios to gather insight on the nonlinear characteristics of IPMC electrical response and its potential application in sensors and energy harvesting devices.
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Kovtunenko, Victor A., and Anna V. Zubkova (Buchynskaja). "Homogenization of the generalized Poisson–Nernst–Planck problem in two-phase medium: The corrector due to nonlinear interface condition." In MODERN TREATMENT OF SYMMETRIES, DIFFERENTIAL EQUATIONS AND APPLICATIONS (Symmetry 2019). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5125075.

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Tang, G. Y., C. Yang, C. J. Chai, and H. Q. Gong. "Joule Heating Induced Thermal and Hydrodynamic Development in Microfluidic Electroosmotic Flow." In ASME 2004 2nd International Conference on Microchannels and Minichannels. ASMEDC, 2004. http://dx.doi.org/10.1115/icmm2004-2442.

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Joule heating is present in electrokinetically driven flow and mass transport in microfluidic systems. Specifically, in the cases of high applied voltages and concentrated buffer solutions, the thermal management may become a problem. In this study, a mathematical model is developed to describe the Joule heating and its effects on electroosmotic flow and mass species transport in microchannels. The proposed model includes the Poisson equation, the modified Navier-Stokes equation, and the conjugate energy equation (for the liquid solution and the capillary wall). Specifically, the ionic concent
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