2026-09-20T21:31:54Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/16923 2023-07-10 col_2142_5131 col_2142_14787 com_2142_5130 com_2142_9630 com_2142_234

Dankowicz, Harry Katzenbach, Michael T. 2010-08-20T18:02:03Z 2010-08-20T18:02:03Z 2010-08-20T18:02:03Z 2010-08 In this thesis, we study the dynamics near grazing for a model of an atomic force microscope in tapping mode and a model of cell cycle mitosis. In particular, period one behavior is studied near grazing points corresponding to tangential contact with the discontinuity surface used to initiate capillary interactions in a tapping mode AFM model. Two different discontinuity mapping analysis methods are developed and applied to this AFM model. The discontinuity mapping analysis predicts the existence of a branch of period one solutions emanating from the grazing point. In addition, the analysis predicts that one eigenvalue of a suitable Poincaré map approaches minus infinity as the varied parameter approaches its grazing value. The second, more general, method is then applied to a model of cell cycle mitosis at two grazing points corresponding to trajectories that have tangential contact with the discontinuity surface used to trigger a halving of the cell mass. Again, the analysis predicts a branch of period one solutions emanating from the grazing point, and an eigenvalue whose magnitude grows without bounds as the grazing point is approached in parameter space. In the case of both the AFM model and the cell cycle model, predictions produced using the discontinuity mapping analysis are shown to agree with results produced using numerical continuation. In addition, we remark on the limitations of the discontinuity mapping analysis and provide suggestions for future work. Specifically, we identify a family of attractors that exist for the AFM model and that warrant further investigation. Item withdrawn by Alexis Thompson (athmpsn1@illinois.edu) on 2010-06-17T15:51:19Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Katzenbach_Michael.pdf: 3885444 bytes, checksum: 11b5259a19ec4f52c4380301a92d28b5 (MD5) Made available in DSpace on 2010-08-20T18:02:03Z (GMT). No. of bitstreams: 3 Katzenbach_Michael.pdf: 3885444 bytes, checksum: 11b5259a19ec4f52c4380301a92d28b5 (MD5) 1_Katzenbach_Michael.pdf: 3885457 bytes, checksum: 8c7636e2abf819dc541141c76ce6e966 (MD5) license.txt: 4068 bytes, checksum: e16c17d5a788147a98a67d96f604e2e3 (MD5) http://hdl.handle.net/2142/16923 en © 2010 by MICHAEL KATZENBACH. All rights reserved. Atomic Force Microscopy (AFM) Grazing Atomic Force Discontinuity Capillary Dynamics near discontinuity events in systems with hysteresis and systems with finite state resets Mechanical Sci & Engineering 1917 Mechanical Engineering 0133 University of Illinois at Urbana-Champaign Thesis M.S. MS:Mechanical Engineerng -UIUC 10KS0133MS