New poisson-boltzmann type equations: One-dimensional solutions

Nonlinearity

Volumn 24, Issue 2, 2011, Pages 431-458

  Lee, Chiun Chang ^a   Lee, Hijin ^b   Hyon, Yun Kyong ^c   Lin, Tai Chia ^a   Liu, Chun ^d,e  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^b Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

^c UNIVERSITY OF NEVADA   (United States)

^d UNIVERSITY OF MINNESOTA   (United States)

^e PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79251607124     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/24/2/004     Document Type: Article

References (46)

1. Barcilon V, Chen D P and Eisenberg R S 1992 Ion flow through narrow membrane channels: II. SIAM J. Appl. Math. 52 1405-25 (Pubitemid 23589679)
2. Barcilon V, Chen D P, Eisenberg R S and Jerome J W 1997 Qualitative properties of steady-state Poisson-Nernst-Planck systems: perturbation and simulation study SIAM J. Appl. Math. 57 631-48
3. Bard A J and Faulkner L R 2001 Electrochemical Methods (New York: Wiley)
4. Brett C M A and Brett A A O 1993 Electrochemistry. Principles, Methods, and Applications (Oxford: Oxford Science Publications)
5. Chu K T 2005 PhD Thesis Asymptotic analysis of extreme electrochemical transport, MIT
6. Gilbarg D and Trudinger N S 2001 Elliptic Partial Differential Equations of Second Order (Classics in Mathematics) (Berlin: Springer)
7. Grochowski P and Trylska J 2008 Continuum molecular electrostatics, salt effects and counterion binding a review of the Poisson-Boltzmann model and its modifications Biopolymers 89 93-113
8. Hille B 2001 Ion Channels of Excitable Membranes 3rd edn (Sunderland, MA: Sinauer Associates, Inc.)
9. Hsu J P and Liu B T 1997 Current efficiency of ion-selective membranes: effects of local electroneutrality and donnan equilibrium J. Phys. Chem. B 101 7928-32
10. Lacoste D, Menon G I, Bazant M Z and Joanny J F 2009 Electrostatic and electrokinetic contributions to the elastic moduli of a driven membrane Eur. Phys. J. E 28 243-64
11. Li B 2009 Continuum electrostatics for ionic solutions with non-uniform ionic sizes Nonlinearity 22 811-33
12. Li B 2009 Minimization of electrostatic free energy and the Poisson-Boltzmann equation for molecular solvation with implicit solvent SIAM J. Math. Anal. 40 2536-66
13. Lee C C, Lee H, Hyon Y, Lin T C and Liu C 2010 A new Poisson-Boltzmann type of equations for multi-species ions, in preparation
14. Lee C C, Lin T C and Liu C 2010 Steady-state solutions of the Poisson-Nernst-Planck equations with N spatial dimension, in preparation
15. Lee M and Chan K Y 1997 Non-neutrality in a charged slit pore Chem. Phys. Lett. 275 56-62
16. Liu W 2005 Geometric singular perturbation approach to steady-state Poisson-Nernst-Planck systems SIAM J. Appl. Math. 65 754-66
17. Luchinsky D G, Tindjong R, Kaufman I, McClintock P V E and Eisenberg R S 2008 Ion channels as electrostatic amplifiers of charge fluctuations J. Phys.: Conf. Ser. 142 012049
18. Marsden J E and Chorin A J 1993 A Mathematical Introduction to Fluid Mechanics (Berlin: Springer)
19. Newman J 1991 Electrochemical Systems 2nd edn (Englewood Cliffs, NJ: Prentice-Hall)
20. Park J H and Jerome J W 1997 Qualitative properties of steady-state Poisson-Nernst-Planck systems: mathematical study SIAM J. Appl. Math. 57 609-30
21. Riccardi E,Wang J C and Liapis A I 2009 Porous polymer absorbent media constructed by molecular dynamics modeling and simulations: the immobilization of charged ligands and their effect on pore structure and local nonelectroneutrality J. Phys. Chem. B 113 2317-27
22. Schumaker M F and Kentler C J 1998 Far-field analysis of coupled bulk and boundary layer diffusion toward an ion channel entrance Biophys. J. 74 2235-48
23. Mori Y, Jerome J W and Peskin C S 2007 A three-dimensional model of cellular electrical activity Bull. Inst. Math. Acad. Sin. 2 367-90
24. Mori Y 2007 A three-dimensional model of cellular electrical activity PhD Thesis New York University
25. Hyon Y, Eisenberg R, Liu C and Mori Y 2010 A mathematical model for electrical activity in cell membrane: energetic variational approach, in preparation
26. Hodgkin A L, and Huxley A F 1952 A qualitative description of the membrane current and its application to conduction and excitation nerve J. Physiol. 117 500-44
27. Keener J P and Sneyd J 1998 Mathematical Physiology (New York: Springer)
28. Koch C 1999 Biophysics of Computation (New York: Oxford University Press)
29. Rabier P J and Rheinbolt W C 2002 Theoretical and Numerical Analysis of Differential-Algebraic Equations (Handbook of Numerical Analysis vol VIII) pp 183-540 (Amsterdam: North-Holland)
30. Carl S and Jerome J 2002 Trapping region for discontinuous quasilinear elliptic systems of mixed monotone type Nonlinear Anal. 51 843-63
31. Aidley D J 1998 The Physiology of Excitable Cells 4th edn (New York: Cambridge University Press)
32. Zhang J, Gong X, Liu C,WenWand Sheng P 2008 Electrorheological fluid dynamics Phys. Rev. Lett. 101 194503
33. Eisenberg B 1998 Ionic channels in biological membranes: natural nanotubes Acc. Chem. Res. 31 117-23
34. Nonner W, Chen D P and Eisenberg B 1999 Progress and prospects in permeation J. Gen. Physiol. 113 773-82
35. Marcowich P A 1986 The Stationary Semiconductor Device Equations (Vienna: Springer)
36. Riveros O J, Croxton T L and Armstrong W M 1989 Liquid junction potentials calculated from numerical solutions of the Nernst-Planck and Poisson equations J. Theor. Biol. 140 221-30
37. Ryham R 2006 An energetic variational approach to mathematical modeling of charged fluids: charge phases, simulation and well posedness Thesis Pennsylvania State University
38. Ryham R, Liu C and Zikatanov L 2007 Mathematical models for the deformation of electrolyte droplets Discrete Contin Dyn. Syst. B 8 649-61
39. Ryham R, Liu C and Wang Z Q 2006 On electro-kinetic fluids: one dimensional configurations Discrete Contin. Dyn. Syst. B 6 357-71
40. Hyon Y, Kwak D Y and Liu C 2010 Energetic variational approach in complex fluids: maximum dissipation principle DCDS-A 26 129-304
41. Gummel H K 1964 A self-consistent iterative scheme for one-dimensional steady state transistor calculations IEEE Trans. Electron Devices ED-11 455-65
42. Scharfetter D L and Gummel H K 1969 Large-signal analysis of a silicon read diode oscillator IEEE Trans. Electron Devices ED-16 64-77
43. Bova S W and Carey G F 1996 Iterative solution of the semiconductor device equations Copper Mountain Conference on Iterative Methods
44. Ziebert F, Bazant M Z and Lacoste D 2010 Effective zero-thickness model for a conductive membrane driven by an electric field Phys. Rev. E 81 031912
45. Ziebert F and Lacoste D 2010 A Poisson-Boltzmann approach for a lipid membrane in an electric field New J. Phys. 12 095002
46. Bazant M Z, Chu K T and Bayly B J 2005 Current-voltage relations for electrochemical thin films SIAM J. Appl. Math. 65 1463-84