Academic literature on the topic 'Équations de Poisson-Nernst Planck'
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Journal articles on the topic "Équations de Poisson-Nernst Planck"
Zheng, Qiong, and Guo-Wei Wei. "Poisson–Boltzmann–Nernst–Planck model." Journal of Chemical Physics 134, no. 19 (May 21, 2011): 194101. http://dx.doi.org/10.1063/1.3581031.
Full textXie, 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.
Full textYang, 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 (February 2013): 113–30. http://dx.doi.org/10.4208/aamm.11-m11184.
Full textHineman, 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.
Full textEisenberg, Bob, Tzyy-Leng Horng, Tai-Chia Lin, and Chun Liu. "Steric PNP (Poisson-Nernst-Planck): Ions in Channels." Biophysical Journal 104, no. 2 (January 2013): 509a. http://dx.doi.org/10.1016/j.bpj.2012.11.2809.
Full textGonzález Granada, José Rodrigo, and Victor A. Kovtunenko. "Entropy method for generalized Poisson–Nernst–Planck equations." Analysis and Mathematical Physics 8, no. 4 (November 2018): 603–19. http://dx.doi.org/10.1007/s13324-018-0257-1.
Full textProhl, Andreas, and Markus Schmuck. "Convergent discretizations for the Nernst–Planck–Poisson system." Numerische Mathematik 111, no. 4 (November 26, 2008): 591–630. http://dx.doi.org/10.1007/s00211-008-0194-2.
Full textKato, Masayuki. "Numerical analysis of the Nernst-Planck-Poisson system." Journal of Theoretical Biology 177, no. 3 (December 1995): 299–304. http://dx.doi.org/10.1006/jtbi.1995.0247.
Full textMeng, 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 (November 2014): 1298–322. http://dx.doi.org/10.4208/cicp.040913.120514a.
Full textChaudhry, 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 (January 2014): 93–125. http://dx.doi.org/10.4208/cicp.101112.100413a.
Full textDissertations / Theses on the topic "Équations de Poisson-Nernst Planck"
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.
Full textNeuroscientific questions about dendrites include understanding their structural plasticityin response to learning and how they integrate signals. Researchers aim to unravel these aspects to enhance our understanding of neural function and its complexities. This thesis aims at offering numerical insights concerning voltage and ionic dynamics in dendrites. Our primary focus is on modeling neuronal excitation, particularly in dendritic small compartments. We address ionic dynamics following the influx of nerve signals from synapses, including dendritic spines. To accurately represent their small scale, we solve the well-known Poisson-Nernst-Planck (PNP) system of equations, within this real application. The PNP system is widely recognized as the standard model for characterizing the electrodiffusion phenomenon of ions in electrolytes, including dendritic structures. This non-linear system presents challenges in both modeling and computation due to the presence of stiff boundary layers (BL). We begin by proposing numerical schemes based on the Discrete Duality Finite Volumes method (DDFV) to solve the PNP system. This method enables local mesh refinement at the BL, using general meshes. This approach facilitates solving the system on a 2D domain that represents the geometry of dendritic arborization. Additionally, we employ numerical schemes that preserve the positivity of ionic concentrations. Chapters 1 and 2 present the PNP system and the DDFV method along with its discrete operators. Chapter 2 presents a "linear" coupling of equations and investigate its associated numerical scheme. This coupling poses convergence challenges, where we demonstrate its limitations through numerical results. Chapter 3 introduces a "nonlinear" coupling, which enables accurate numerical resolution of the PNP system. Both of couplings are performed using DDFV method. However, in Chapter 3, we demonstrate the accuracy of the DDFV scheme, achieving second-order accuracy in space. Furthermore, we simulate a test case involving the BL. Finally, we apply the DDFV scheme to the geometry of dendritic spines and discuss our numerical simulations by comparing them with 1D existing simulations in the literature. Our approach considers the complexities of 2D dendritic structures. We also introduce two original configurations of dendrites, providing insights into how dendritic spines influence each other, revealing the extent of their mutual influence. Our simulations show the propagation distance of ionic influx during synaptic connections. In Chapter 4, we solve the PNP system over a 2D multi-domain consisting of a membrane, an internal and external medium. This approach allows the modeling of voltage dynamics in a more realistic way, and further helps checking consistency of the results in Chapter 3. To achieve this, we employ the FreeFem++ software to solve the PNP system within this 2D context. We present simulations that correspond to the results obtained in Chapter 3, demonstrating linear summation in a dendrite bifurcation. Furthermore, we investigate signal summation by adding inputs to the membrane of a dendritic branch. We identify an excitability threshold where the voltage dynamics are significantly influenced by the number of inputs. Finally, we also offer numerical illustrations of the BL within the intracellular medium, observing small fluctuations. These results are preliminary, aiming to provide insights into understanding dendritic dynamics. Chapter 5 presents collaborative work conducted during the Cemracs 2022. We focus on a composite finite volume scheme where we aim to derive the Euler equations with source terms on unstructured meshes
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.
Full textIn this PhD I study how electro-diffusion within biological micro and nano-domains is affected by their shapes using the Poisson-Nernst-Planck (PNP) partial differential equations. I consider non-trivial shapes such as domains with cusp and ellipses. Our goal is to develop models, as well as mathematical tools, to study the electrical properties of micro and nano-domains, to understand better how electrical neuronal signaling is regulated at those scales. In the first part I estimate the steady-state voltage inside an electrolyte confined in a bounded domain, within which we assume an excess of positive charge. I show the mean first passage time in a charged ball depends on the surface and not on the volume. I further study a geometry composed of a ball with an attached cusp-shaped domain. I construct an asymptotic solution for the voltage in 2D and 3D and I show that to leading order expressions for the voltage in 2D and 3D are identical. Finally, I obtain similar conclusion considering an elliptical-shaped domain for which I construct an asymptotic solution for the voltage in 2D and 3D. In the second part, I model the electrical compartmentalization in dendritic spines. Based on numerical simulations, I show how spines non-cylindrical geometry leads to concentration polarization effects. I then compare my model to experimental data of microscopy imaging. I develop a deconvolution method to recover the fast voltage dynamic from the data. I estimate the neck resistance, and we found that, contrary to Ohm's law, the spine neck resistance can be inversely proportional to its radius
Abdul, Samad Feras. "Polarisation provoquée : expérimentation, modélisation et applications géophysiques." Thesis, Paris 6, 2017. http://www.theses.fr/2017PA066049/document.
Full textThe physical mechanisms responsible for the induced polarization response over the frequency range (from 1 mHz to 20 kHz) are not completely understood. In particular, within the framework of this thesis, two subjects have been addressed. The origin of the signal observed at high frequency (HF) (>1 kHz) was analyzed by carrying out Spectral IP measurements on tap water samples. A phase deviation from the expected response has been observed at HF. The resulted deviation in phase appears to be dependent on the measuring electrode type (potential electrodes) and conductivity of the medium. A model based on an equivalent electrical circuit and designed to represent HF response, has been proposed to correct these effects. The mechanism responsible for the polarization in a medium containing semi-conductor grains has been investigated by analyzing the dependence of the relaxation time. We carried out experimental measurements on a sand medium containing different types of semi-conductors. The spectral response was studied by varying the concentration and type of the electrolyte, the size and content of semi-conductor grains. By using the finite element method, a 2D numerical simulation based on Poisson-Nernst-Planck equations was performed in time and frequency domains. The experimental results are qualitatively in accordance with numerical simulation. It showed a comparable decrease in the relaxation time when increasing the electrolyte concentration. Finally, field measurements on a paleo-mining site containing semi-conductor grains have been acquired. Time-domain IP measurements allowed us to define the zones of slag in the site and led to estimate the slag volume
Abdul, Samad Feras. "Polarisation provoquée : expérimentation, modélisation et applications géophysiques." Electronic Thesis or Diss., Paris 6, 2017. http://www.theses.fr/2017PA066049.
Full textThe physical mechanisms responsible for the induced polarization response over the frequency range (from 1 mHz to 20 kHz) are not completely understood. In particular, within the framework of this thesis, two subjects have been addressed. The origin of the signal observed at high frequency (HF) (>1 kHz) was analyzed by carrying out Spectral IP measurements on tap water samples. A phase deviation from the expected response has been observed at HF. The resulted deviation in phase appears to be dependent on the measuring electrode type (potential electrodes) and conductivity of the medium. A model based on an equivalent electrical circuit and designed to represent HF response, has been proposed to correct these effects. The mechanism responsible for the polarization in a medium containing semi-conductor grains has been investigated by analyzing the dependence of the relaxation time. We carried out experimental measurements on a sand medium containing different types of semi-conductors. The spectral response was studied by varying the concentration and type of the electrolyte, the size and content of semi-conductor grains. By using the finite element method, a 2D numerical simulation based on Poisson-Nernst-Planck equations was performed in time and frequency domains. The experimental results are qualitatively in accordance with numerical simulation. It showed a comparable decrease in the relaxation time when increasing the electrolyte concentration. Finally, field measurements on a paleo-mining site containing semi-conductor grains have been acquired. Time-domain IP measurements allowed us to define the zones of slag in the site and led to estimate the slag volume
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.
Full textMoreau, 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.
Full textIn this thesis, we manage to combine two existing tools in mechanics: periodic homogenization, and reduced-order modelling, to modelize corrosion of reinforced concrete structures. Indeed, chloride and carbonate diffusion take place their pores and eventually oxydate their steel skeleton. The simulation of this degradation is difficult to afford because of both the material heterogenenity, and its microstructure variability. Periodic homogenization provides a multiscale model which takes care of the first of these issues. Nevertheless, it assumes the existence of a representative elementary volume (REV) of the material at the microscopical scale. I order to afford the microstructure variability, we must solve the equations which arise from periodic homogenization in a reduced time. This motivates the use of model order reduction, and especially the POD. In this work we design geometrical transformations that transport the original homogenization equations on the fluid domain of a unique REV. Indeed, the POD method can’t be directly performed on a variable geometrical space like the material pore network. Secondly, we adapt model order reduction to the Poisson-Boltzmann equation, which is strongly nonlinear, and which rules ionic electro diffusion at the Debye length scale. Finally, we combine these new methods to other existing tools in model order reduction (ITSGM interpolatin, MPS method), in order to couple the micro- and macroscopic components of periodic homogenization
Herda, Maxime. "Analyse asymptotique et numérique de quelques modèles pour le transport de particules chargées." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1165/document.
Full textThis thesis is devoted to the mathematical study of some models of partial differential equations from plasma physics. We are mainly interested in the theoretical study of various asymptotic regimes of Vlasov-Poisson-Fokker-Planck systems. First, in the presence of an external magnetic field, we focus on the approximation of massless electrons providing reduced models when the ratio me{mi between the mass me of an electron and the mass mi of an ion tends to 0 in the equations. Depending on the scaling, it is shown that, at the limit, solutions satisfy hydrodynamic models of convection-diffusion type or are given by Maxwell-Boltzmann-Gibbs densities depending on the intensity of collisions. Using hypocoercive and hypoelliptic properties of the equations, we are able to obtain convergence rates as a function of the mass ratio. In a second step, by similar methods, we show exponential convergence of solutions of the Vlasov-Poisson-Fokker-Planck system without magnetic field towards the steady state, with explicit rates depending on the parameters of the model. Finally, we design a new type of finite volume scheme for a class of nonlinear convection-diffusion equations ensuring the satisfying long-time behavior of discrete solutions. These properties are verified numerically on several models including the Fokker-Planck equation with magnetic field
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.
Full textLim, 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.
Full textNeuen, 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.
Full textBook chapters on the topic "Équations de Poisson-Nernst Planck"
Lu, Benzhuo. "Poisson-Nernst-Planck Equation." In Encyclopedia of Applied and Computational Mathematics, 1159–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-540-70529-1_276.
Full textHorgmo Jæger, Karoline, and Aslak Tveito. "The Poisson-Nernst-Planck (PNP) Model." In Differential Equations for Studies in Computational Electrophysiology, 119–25. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30852-9_12.
Full textHolcman, David, and Zeev Schuss. "The Poisson–Nernst–Planck Equations in a Ball." In Applied Mathematical Sciences, 341–83. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-76895-3_10.
Full textZubkova, Anna V. "The Generalized Poisson–Nernst–Planck System with Nonlinear Interface Conditions." In Trends in Mathematics, 101–6. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01153-6_18.
Full textFuhrmann, Jürgen. "Activity Based Finite Volume Methods for Generalised Nernst-Planck-Poisson Systems." In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, 597–605. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-05591-6_59.
Full textLefraich, 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, 375–88. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-33050-6_21.
Full textKovtunenko, 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, 173–91. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-47079-5_9.
Full textFuhrmann, 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, 497–505. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57394-6_52.
Full textCancès, 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, 57–73. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-40864-9_4.
Full textFuhrmann, 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, 285–94. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-40864-9_23.
Full textConference papers on the topic "Équations de Poisson-Nernst Planck"
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.
Full textTano, 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). Illinois: American Nuclear Society, 2023. http://dx.doi.org/10.13182/nureth20-40838.
Full textMathur, 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.
Full textFurini, S., F. Zerbetto, and S. Cavalcanti. "A numerical solver of 3D Poisson Nernst Planck equations for functional studies of ion channels." In BIOMEDICINE 2005. Southampton, UK: WIT Press, 2005. http://dx.doi.org/10.2495/bio050111.
Full textWang, 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.
Full textAureli, 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.
Full textKovtunenko, 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.
Full textTang, 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.
Full textBanerjee, A., and A. K. Nayak. "Electroosmotic Flow Separation in a Corrugated Micro-Channel: A Numerical Study." In ASME 2018 5th Joint US-European Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/fedsm2018-83026.
Full textChein, Reiyu, and Baogan Chung. "Electrokinetic Transport in Micro-Nanofluidic Systems With Sudden-Expansion and Contraction Cross Sections." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18120.
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