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Numerical Methods for Transport Problems in Microdevices

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Book cover Large-Scale Scientific Computing (LSSC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3743))

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Abstract

Transport processes of large biomolecules in microdevices are of high interest for biological research and biomedical applications. Such devices have been proposed recently to address the problem of separating different components of macromolecules. From the mathematical point of view, such problems can be modeled by multiscale partial differential equations, which can be analyzed and numerically simulated. In this paper we propose a framework to model a class of transport problems which arise in microdevices and discuss their numerical simulation.

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References

  1. Abdulle, A., Medovikov, A.A.: Second order Chebyshev methods based on orthogonal polynomials. Numer. Math. 90, 1–18 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  2. Abdulle, A.: Fourth order Chebyshev methods with recurrence relation. SIAM SISC 23(6), 2041–2054 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Abdulle, A., Attinger, S.: Homogenization methods for Transport of DNA particles in Heterogeneous Arrays. Lecture Notes in Computer Science and Engineering, vol. 39, pp. 23–34 (2004)

    Google Scholar 

  4. Abdulle, A.: On a-priori error analysis of Fully Discrete Heterogeneous Multiscale FEM. SIAM Multiscale Model. Simul. 4, 447–459 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Abdulle, A.: Multiscale methods for advection-diffusion problems. AIMS Discrete and Continuous Dynamical Systems (2005) (to appear)

    Google Scholar 

  6. Austin, R.H., Darnton, N., Huang, R., Sturm, J., Bakajin, O., Duke, T.: Ratchets: the problems with boundary conditions in insulating fluids. Appl. Phys. A 75, 279–284 (2002)

    Article  Google Scholar 

  7. Bensoussan, A., Lions, J.-L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures. North Holland, Amsterdam (1978)

    Google Scholar 

  8. Chou, et al.: Sorting biomolecules with microdevices. Electrophoresis 21, 81–90 (2000)

    Article  Google Scholar 

  9. Duke, T.A., Austin, R.H.: Microfabricated Sieve for the Continuous Sorting of Macromolecules. Phys. Rev. Lett. 89(7), 1552–1555 (1998)

    Article  Google Scholar 

  10. Ertas, D.: Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays. Phys. Rev. Lett. 80(7), 1548–1551 (1998)

    Article  Google Scholar 

  11. Weinen, E., Engquist, B.: The Heterogeneous Multi-Scale Methods. Comm. Math. Sci. 1(1), 87–132 (2003)

    Google Scholar 

  12. Weinen, E., Ming, P., Zhang, P.: Analysis of the heterogeneous multi-scale method for elliptic homogenization problems. J. Amer. Math. Soc. 18, 121–156 (2004)

    Google Scholar 

  13. Kassegne, S.K., et al.: Numerical modeling of transport and accumulation of DNA on electronically active biochips. Sensors and Actuators B 94, 81–98 (2003)

    Article  Google Scholar 

  14. Majda, A.J., Kramer, P.R.: Simplified models for turbulent diffusion: Theory, numerical modelling and physical phenomena. Physics Reports 314, 237–574 (1999)

    Article  MathSciNet  Google Scholar 

  15. Radtkey, R., et al.: Rapid, high fidelity analysis of simple sequence repeats on an electronically active DNA microchip. Nucleic Acids Research 28(7) (2000)

    Google Scholar 

  16. Rickwood, D., Hames, B.D.: Gel electrophoresis of the nucleid Acids: A Practical Approach. Oxford University Press, Oxford (1990)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Abdulle, A., Attinger, S. (2006). Numerical Methods for Transport Problems in Microdevices. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2005. Lecture Notes in Computer Science, vol 3743. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11666806_6

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  • DOI: https://doi.org/10.1007/11666806_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31994-8

  • Online ISBN: 978-3-540-31995-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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