Basis adaptation for the stochastic nonlinear Poisson–Boltzmann equation
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A basis-adaptation method based on polynomial chaos expansion is used for the stochastic nonlinear Poisson–Boltzmann equation. The uncertainty in this numerical approach is motivated by the quantification of noise and fluctuations in nanoscale field-effect sensors. The method used here takes advantage of the properties of the nonlinear Poisson–Boltzmann equation and shows an exact and efficient approximation of the real solution. Numerical examples are motivated by the quantification of noise and fluctuations in nanowire field-effect sensors as a concrete example. Basis adaptation is validated by comparison with the full solution, and it is compared to optimized multi-level Monte-Carlo method, and the model equations are validated by comparison with experiments. Finally, various design parameters of the field-effect sensors are investigated in order to maximize the signal-to-noise ratio.
KeywordsPoisson–Boltzmann equation Current Biological noise Polynomial chaos expansion Biosensor
The authors acknowledge the support by FWF (Austrian Science Fund) START Project No. Y660 PDE Models for Nanotechnology. The authors also would like to appreciate Prof. Roger Ghanem (University of Southern California) for useful discussions about polynomial chaos expansion.
- 13.Eldred, M., Burkardt, J.: Comparison of non-intrusive polynomial chaos and stochastic collocation methods for uncertainty quantification. In: Proc. 47th AIAA Aerospace Sciences Meeting, vol. 976, pp. 1–20 (2009)Google Scholar
- 14.Giles, M.: Improved multilevel Monte Carlo convergence using the Milstein scheme. Monte Carlo and Quasi-Monte Carlo Methods 2006, pp. 243–258. Springer, Berlin (2008)Google Scholar
- 24.Liu, Y., Lilja, K., Heitzinger, C., Dutton, R.W.: Overcoming the screening-induced performance limits of nanowire biosensors: a simulation study on the effect of electro-diffusion flow. In: IEDM 2008 Technical Digest, pp. 491–494. San Francisco, CA (2008). doi: 10.1109/IEDM.2008.4796733
- 28.Pittino, F., Selmi, L.: Use and comparative assessment of the CVFEM method for Poisson–Boltzmann and Poisson–Nernst–Planck three dimensional simulations of impedimetric nano-biosensors operated in the DC and AC small signal regimes. Comput. Methods Appl. Mech. Eng. 278, 902–923 (2014)MathSciNetCrossRefGoogle Scholar
- 38.Tulzer, G., Heitzinger, C.: Fluctuations due to association and dissociation processes at nanowire-biosensor surfaces and their optimal design. Nanotechnology 26(2), 025502 (2015). doi: 10.1088/0957-4484/26/2/025502