Error analysis of a stochastic immersed boundary method incorporating thermal fluctuations

Mathematics and Computers in Simulation

Volumn 79, Issue 3, 2008, Pages 379-408

  Atzberger, Paul J ^a   Kramer, Peter R ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

Fluid dynamics; Immersed boundary method; Numerical analysis; Statistical mechanics; Stochastic analysis; Stochastic processes

Indexed keywords

BIOLOGICAL SYSTEMS; COMPUTATIONAL FLUID DYNAMICS; DIFFERENTIATION (CALCULUS); DYNAMICS; ERROR ANALYSIS; ERRORS; FLUID DYNAMICS; NUMERICAL ANALYSIS; NUMERICAL METHODS; STATISTICAL MECHANICS; TURBULENT FLOW;

DEGREES OF FREEDOMS; ELASTICA; FINITE DIFFERENCES; IMMERSED BOUNDARY METHOD; IMMERSED BOUNDARY METHODS; LARGE TIME STEPS; NUMERICAL ERRORS; NUMERICAL SCHEMES; STOCHASTIC ANALYSIS; STOCHASTIC CALCULUSES; STOCHASTIC PROCESSES; THERMAL FLUCTUATIONS; TIME SCALES; TIME STEPS;

MECHANICS;

EID: 55949103743     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.matcom.2008.01.004     Document Type: Article

References (44)

1. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walker, Molecular Biology of the Cell, Garland Publishing, 2002.
2. P.J. Atzberger, P.R. Kramer, C.S. Peskin, A stochastic immersed boundary method for fluid-structure dynamics at microscopic length scales, J. Comp. Phys. 224 (2007) 1255-1292.
3. Boal D. Mechanics of the Cell (2002), Cambridge University Press, Cambridge, UK
4. Brannigan G., and Brown F.L.H. A consistent model for thermal fluctuations and protein induced deformations in lipid bilayers. Biophys. J. 90 (2006) 1501-1520
5. Brannigan G., Philips P.F., and Brown F.L.H. Flexible lipid bilayers in implicit solvent. Phys. Rev. E 72 (2005) 011915
6. Champeney D.C. A Handbook of Fourier Theorems (1987), Cambridge University Press, Cambridge ISBN: 0-521-26503-7
7. Chorin A.J. Numerical Solution of the Navier-Stokes Equations. Ath. Comp. 22 (1968) 745
8. Corrsin S., Frenkiel F.N., and Shappard P.A. Atmospheric Diffusion and Air Pollution, vol. 6 (1960)
9. de Hoog L.C., and Mann M. Proteomics. Annu. Rev. Genomics Hum. Genet. 5 (2004) 267-293
10. C.P. Fall, E.S. Marland, J.M. Wagner, J.J. Tyson (Eds.), Computational cell biology, vol. 20, Interdisciplinary Applied Mathematics, Springer-Verlag, New York, 2002.
11. Farago O. Water-free Computer Model For Fluid Bilayer Membranes. J. Chem. Phys. 119 (2003) 596-605
12. Fauci L.J., and Fogelson A.L. Truncated Newton method and the modeling of complex immersed elastic structures. Commun. Pure Appl. Math. XLVI (1993) 787-818
13. Fradkin L. Comparison of Lagrangian and Eulerian approaches to turbulent diffusion. Plasma Phys. Controlled Fusion 33 (1991) 685-701
14. Gardiner C.W. Handbook of Stochastic Methods (1985), Springer Series in Synergetics
15. E. Givelberg, J. Bunn, Detailed simulation of the cochlea: recent progress using large shared memory parallel computers, CACR Technical Report CACR-190, 2001.
16. Gov N., and Safran S.A. Red-blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. Biophys. J. 88 (2005) 1859
17. Grimm H.P., Verkhovsky A.B., Mogilner A., and Meister J.J. Analysis of actin dynamics at the leading edge of crawling cells: implications for the shape of keratocyte lamellipodia. Eur. Biophys. J. 32 (2003) 563-577
18. M. Holmes, Introduction to Perturbation Methods, Springer-Verlag, New York, 1995.
19. Howard J. Mechanics of Motor Proteins and the Cytoskeleton (2001), Sinauer Associates, Sunderland, CN
20. Kloeden P.E., and Platen E. Numerical Solution of Stochastic Differential Equations (1992), Springer-Verlag
21. P.R. Kramer, A.J. Majda, Stochastic mode reduction for the immersed boundary method, SIAM J. Appl. Math. 64 (2003/2004) 369-400 (electronic).
22. Kramer P.R., and Peskin C.S. Incorporating thermal fluctuations into the immersed boundary method. In: Bathe K.K. (Ed). Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, vol. 2 (2003), Elsevier 1755-1758
23. Kubo R., Toda M., and Hashitsume N. Statistical physics. II. secon ed. (1991), Springer-Verlag, Berlin (Section 4)
24. Landau L.D., and Lifshitz E.M. Course of Theoretical Physics, vol. 9, Statistical Physics (1980), Pergamon Press, Oxford (Chapter IX)
25. Landau L.D., and Lifshitz E.M. Course of Theoretical Physics, vol. 6, Fluid Mechanics (1987), Butterworth-Heinemann, Oxford (Chapter II)
26. Lin L., and Brown F.L.H. Brownian dynamics in Fourier space: membrane simulations over long length and time scales. Phys. Rev. Lett. 93 (2004) 256001
27. Lin L.C.-L., Gov N.S., and Brown F.L.H. Nonequilibrium membrane fluctuations driven by active proteins. J. Chem. Phys. 124 (2006) 1
28. Lipowsky R. Statistical Mechanics of Biocomplexity (1999), Springer
29. X. Meng, A computational model of flow through porous media at the microscale, Ph.D. Thesis, Department of Mathematics, Tulane University, New Orleans, LA 70118, July 1998.
30. Miller L., and Peskin C. When vortices stick: an aerodynamic transition in tiny insect flight. J. Exp. Biol. 207 (2004) 3073-3088
31. K.C. Neuman, S.M. Block, Optical trapping, Rev. Sci. Instrum. 75 (9) (2004)
32. Oksendal B. Stochastic Differential Equations: An Introduction with Applications (2000), Springer
33. G. Oster, A. Mogilner, Force generation by cellular polymers, in: A. Ciferri (Ed.), Supramolecular Polymers, Marcel Dekker, New York, 2000.
34. Peskin C.S. The immersed boundary method. Acta Numer. 11 (2002) 1-39
35. Peskin C., and McQueen D. Shared-memory parallel vector implementation of the immersed boundary method for the computation of blood flow in the beating mammalian heart. J. Supercomput. 11 (1997) 213-236
36. Press W.H., Saul A., Teukolsky W.T., Vetterling B.P., and Flannery. Numerical Recipes (2002), Cambridge University Press
37. Reichl L.E. A Modern Course in Statistical Physics. second ed. (1998), John Wiley & Sons Inc., New York
38. Reimann P. Introduction to the physics of Brownian motors. Appl. Phys. A 75 (2002) 169-178
39. Robinson D.N., and Spudich J.A. Mechanics and regulation of cytokinesis. Curr. Opin. Cell Biol. 16 (2004) 182-188
40. Schlick T. Molecular Modeling and Simulation: An Interdisciplinary Guide, vol. 21, Interdisciplinary Applied Mathematics (2002), Springer-Verlag, Berlin
41. J.C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Chapman & Hall, New York, 1995.
42. H.J. Tanke, R.W. Dirks, T. Raap, FISH and immunocytochemistry: towards visualising single target molecules in living cells, Curr. Opin. Biotechnol. 16 (2005) 49-54.
43. Weinstock J. Lagrangian Eulerian relation and the independence approximation. Phys. Fluids 19 (1976) 1702-1711
44. Wittman T., Hyman A., and Desai A. The spindle: a dynamic assembly of microtubules and motors. Nat. Cell Biol. 3 (2001) E28-E34