Publication: Low-Cost Optimization for Fast-Microfluidic-Mixer Shape Design
Full text at PDC
Advisors (or tutors)
We give an unified formulation for deterministic and stochastic global optimization algorithms via initial and boundary value problems for different first and second order dynamic systems. The ensemble is applied to the design of a fast-micro-mixer. The aim is to optimize a given mixer shape in order to reduce its mixing time. The algorithms are compared from their complexity and optimization efficiency. In order to reduce computational time approximate state and sensitivity evaluations are introduced during optimization
 E. Hertzog, X. Michalet, M. Jager, X. Kong, J. Santiago, J. Weiss, and O. Bakajin. Femtomole mixer for microsecond kinetic studies of protein folding. Proceedings of the National Academy of Sciences of the USA, page Accepted, 2005.  Roder H. Proceedings of the National Academy of Sciences of the United States of America, 101:1793–1794, 2004.  C. M. Jones, E. R. Henry, Y. Hu, C.-K. Chan, S. D. Luck, A. Bhuyan, H. Roder, J. Hofrichter, and W. A. Eaton. Proceedings of the National Academy of Sciences of the USA, pages 11860–11864, 1993.  S. J. Hagen and W. A. Eaton. Journal of Molecular Biology, 301:1037–1045.  K. M. Pryse, T. G. Bruckman, B. W. Maxfield, and E. L. Elson. Biochemistry, 31:5127–5136, 1992.  M. Jacob, G. Holtermann, D. Perl, J. Reinstein, T. Schindler, M. A. Geeves, and F. X. Schmid. Biochemistry, 38:2882–2891, 1999.  C.K. Chan, Y. Hu, S. Takahashi, D. L. Rousseau, and W. A. Eaton. Proceedings of the National Academy of Sciences of the United States of America, 94:1779–1784, 1997.  Pollack L., M. W. Tate, N. C. Darnton, J. B. Knight, S. M. Gruner, W. A. Eaton, and R. H. Austin. Proceedings of the National Academy of Sciences of the USA, 96:10115–10117, 1999.  S.-H. Park, M. C. R. Shastry, and H. Roder. Nature, structural Biology, 6:943–947, 1999.  J. P. Brody, P. Yager, R.E. Goldstein, and R.H. Austin. Biophysical Journal, 71:3430–3441, 1996.  R. Russell, S. Ian, M. W. T. Millett, W. Lisa, Kwok, Bradley, Nakatani, M. Sol, S. G. J. Gruner, V. P. S. Mochrie, D. H. Doniach, and Pollack Lois. Proceedings of the National Academy of Sciences of the United States of America, 99:4266–4271, 2002.  J. B. Knight, A. Vishwanath, J. P. Brody, and R. H. Austin. Physical Review Letters, pages 3863–3866, 1998.  M. C. R. Shastry, S. D. Luck, and H. Roder. Biophysical Journal, 74:2714–2721, 1998.  B. Mohammadi, J. Santiago, and J. Molho. Incomplete sensitivities in the design of minimal dispersion fluidic channels. Computers and Fluids, 192,2003.  B. Mohammadi, R. Bharadwadj, and J. Santiago. Design and optimization of on-chip capillary electrophoresis. Electrophoresis Journa, 23(16), 2002.  B. Mohammadi, J. Molho, A. Herr, J. Santiago, T. Kenny, R. Brennen, and Gordon G. Optimization of turn geometries for on-chip electrophoresis. Analytical Chemestry, 73(6), 2001.  B. Mohammadi, E. Leclerc, and P. Sagaut. Optimal shape design of coastal structures. Computers and Fluids, 12(5), 2003.  L. Dumas, V. Herbert, and F. Muyl. Hybrid method for aerodynamic shape optimization in automotive industry. Computers and Fluids, 33(5):849–858, 2004.  D. Goldberg. Genetic algorithms in search, optimization and machine learning. Addison Wesley, 1989.  B. Ivorra. Semi-deterministic global optimization. PhD. University of Montpellier 2, 2006.  H. Attouch and R. Cominetti. A dynamical approach to convex minimization coupling approximation with the steepest descent method. J. Differential Equations, 128(2):519–540, 1996.  B. Mohammadi and O. Pironneau. Applied Shape Optimization for Fluids. Oxford University Press, 2001.  B. Mohammadi and J-H. Saiac. Pratique de la simulation numerique. Dunod, 2002.  G.N. Vanderplaats. Numerical optimization techniques for engineering design. Mc Graw-Hill., 1990.  B. Ivorra, B. Mohammadi, and P. Redont. Low-complexity global optimization by solution of bvp. Optimal Control and Applied Mathematics, submitted, 2005.  D. Isebe, B. Mohammadi, P. Azerad, B. Ivorra, and F. Bouchette. Optimal shape design of coastal structures. Proceeding of Siam on Mathematical & Computational Issues in the Geosciences, 2005  L. Debiane, B. Ivorra, B. Mohammadi, F. Nicoud, A. Ern, T. Poinsot, and H. Pitsch. Temperature and pollution control in flames. In Proceeding of the Summer Program, pages 367–375, Center for Turbulence Research, NASA AMES/Stanford University, USA, 2004.  B. Ivorra, B. Mohammadi, L. Dumas, Y. Moreau, G. Pille, and O. Durand. Apodisation de fibres `a réseaux de bragg pour la synthèse de codes cdma spectral. IEEE Lasers and Electro-Optics Society French Chapter, Conference COSTO04, 2004.  B. Mohammadi and O. Pironneau. Shape optimization in fluid mechanics. Annual Review of Fluid Mechanics., 36:255–279, 2004.  N. Darnton, O. Bakajin, R. Huang, B. North, J. Tegenfeldt, E. Cox, J. Sturn, and R. H. Austin. Condensed matter. Journal of Physics, 13:4891–4902, 2001.  T. Hughes and A. Brooks. A multi-dimensional upwind scheme with no crosswind diffusion, in t. hughes, ed., finite element methods for convection dominated flows. ASME, New York, 34:19–35, 1979.  P. Deuflhard. A modified newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting. Numer. Math., 32:289–315, 1974.