Multi-physics modeling and finite element approximation of charge flow in ionic channels

7th International Conference on Thermal, Mechanical and Multiphysics Simulation and Experiments in Micro-Electronics and Micro-Systems, EuroSimE 2006

Volumn 2006, Issue , 2006, Pages

  Chini, Bice ^a   Jerome, Joseph W ^b   Sacco, Riccardo ^c  

^a CNR   (Italy)

^b NORTHWESTERN UNIVERSITY   (United States)

^c POLITECNICO DI MILANO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; ELECTRIC BATTERIES; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; NAVIER STOKES EQUATIONS; NUMERICAL METHODS;

CHARGE FLOW; CHARGE TRANSPORT; IONIC CHANNELS; MULTI PHYSICS MODELING;

ELECTRIC CHARGE;

EID: 33847161303     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ESIME.2006.1643975     Document Type: Conference Paper

References (23)

1. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter, Molecular Biology of the Cell, 4th ed. New York, Garland Publishing (2002).
2. V. Barcilon, D. Chen, R. Eisenberg, J.W. Jerome, Qualitative properties of steady-state Poisson-Nernst-Planck systems: perturbation and simulation study, SIAM J. Appl. Math., 57 (3), 631-648 (1997).
3. F. Brezzi, L.D. Marini, S. Micheletti, P. Pietra, R. Sacco, Stability and Error Analysis of Mixed Finite Volume Methods for Advective-Diffusive Problems, 1-PV I.M.A.T.I.-C.N.R. (2003), 1-18. In press in Computers and Mathematics with Applications (2005).
4. F. Brezzi, L. D. Marini, S. Micheletti, P. Pietra, R. Sacco, S. Wang, Discretization of Semiconductor Device Problems (I), pp. 317-441, Handbook of Numerical Analysis, Vol. XIII, P.G. Ciarlet Ed., W.H.A. Schilders, E.J.W. ter Maten, Guest Eds., Elsevier North-Holland, Amsterdam (2005).
5. P. Causin, R. Sacco, A discontinuous Petrov-Galerkin method with Lagrangian multipliers for second order elliptic problems, SIAM J. Numer. Anal., 43 (1), 280-302 (2005).
6. P. Causin, M. Restelli, R. Sacco, A simulation system based on mixed-hybrid finite elements for thermal oxidation in semiconductor technology, Comput. Methods Appl. Mech. Engrg., 193, 3687-3710 (2004).
7. D. Chen, R. Eisenberg, J.W. Jerome, C.-W. Shu, A hydrodynamic model of temperature change in open ionic channels, Biophysical Journal, 69, 2304-2322 (1995).
8. B. Chini, Basi molecolari dell'eterogeneità funzionale e delle relazioni struttura-funzione del canali ionici. In: Approcci molecolari allo studio del canali ionici, A. Volterra and G. Racagni Eds., Pythagora Press, Milano, 15-23 (1992).
9. B. Chini, F. Clementi, N. Hukovic, E. Sher, Neuronal type α-Bungarotoxin receptors and the as nicotinic receptor subunit gene are expressed in neuronal and non neuronal human cell lines, Prot. Natl. Acad. Sci. USA, 89, 1572-1576 (1992).
10. B. Cockburn, G.E. Karniadakis, C.W. Shu, The development of Discontinuous Galerkin Methods, in Discontinuous Galerkin Methods, B. Cockburn, G.E. Karniadakis, C.W. Shu, eds., Lecture Notes in Computational Science and Engineering, Springer-Verlag, 11, 3-50 (2000).
11. C. de Falco, A. L. Lacaita, E. Gatti, R. Sacco, Quantum-Corrected Drift-Diffusion Models for Transport in Semiconductor Devices, J. Comp. Phys., 204 (2), 533-561 (2005).
12. B. Hille, Ionic channels of excitable membranes, Second Ed., Sinauer Associates, Inc., Sunderland, Mass. (1992).
13. J.W. Jerome, Analysis of charge transport: A mathematical study of semiconductor devices, Springer-Verlag, New York (1996).
14. G. Karniadakis, A. Beskok, N. Aluru, Microflows and nanoflows. Fundamentals and simulation, Interdisciplinary Applied Mathematics, 29, Springer-Verlag, New York (2005).
15. J. Keener, J. Sneyd, Mathematical physiology, Interdisciplinary Applied Mathematics, 8, Springer-Verlag, New York (1998).
16. L.D. Landau, E.M. Lifshitz, Fluid Mechanics, Second Ed., Butterworth-Heinemann, Oxford (2000).
17. R. MacKinnon, Potassium Channels and the Atomic Basis of Selective Ion Conduction, Bioscience Reports, 24 (2), 75-100 (2004).
18. S. Micheletti, R. Sacco, F. Saleri, On Some Mixed Finite Element Methods with Numerical Integration, SIAM J. Sci. Comput., 23 (1), 245-270 (2001).
19. E. Neher, Molecular biology meets microelectronics, Nature Biotechnology, 19, 114 (2001).
20. J.H. Park, J.W. Jerome, Qualitative properties of steady-state Poisson-Nernst-Planck systems: mathematical study, SIAM J. Appl. Math., 57 (3), 609-630 (1997).
21. A. Quarteroni, A. Valli, Domain Decomposition Methods for Partial Differential Equations, Clarendon Press, Oxford (1999).
22. I. Rubinstein, Electro-Diffusion of Ions, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, PA (1990).
23. B. Straub, E. Meyer, P. Fromherz, Recombinant maxi-K channels on transistor, a prototype of iono-electronic interfacing, Nature Biotechnology, 19, 121-124 (2001).