4.1 結論
1. 從結果來看，外力頻率對棘輪運動也具有影響，但相對來說對流率的影響沒有外 力振幅來得大，就流率的區間來說，控制 a 對粒子分流的速率較快。
2. 結果顯示改變位能變化之振幅對具時變位能場之確定性棘輪會產生兩個較明顯 之逆流區段，而 a 與粒子的質量有關，此現象應能應用於粒子定向傳輸或分離不 同質量的粒子。
3. 文獻[33]之實驗並無解釋其逆流現象之原由，我們用具時變位能場之確定性棘輪 來簡化模擬此現象，希望此效應能用來當作解釋實驗中流場發生逆流現象的可能 原因之一。
4.2 未來研究與展望
我們用方程式來簡化模擬粒子運動行為，將粒子與流體的交互作用力以阻尼力來 表示，而非對稱電極週期性排列施以交流電壓，則以的粒子在非對稱、時間空間上具 週期性之位能力來表示。就模擬結果來看流場會因棘輪的效應而產生逆流的現象。若 要完整的模擬其運動行為，則需對粒子在流道內的作用、電場的效應、流場對粒子的 影響等進行模擬。
也就是對粒子在流場內的行為作詳細的分析，需要把粒子的運動方程式、電場的 Poisson 方程式、流場的 Navier-Stokes 方程式的耦合現象等都納入模擬的條件，而在 本論文中主要只對粒子的運動行為進行簡化的模擬，未來希望能把更多的條件加入以 期能完整的模擬出粒子的行為。
參考文獻
1. R. Feynman, The Feynman Lecture on Physics, Vol. I, Ch. 4, 1966.
2. M. O. Magnasco, “Forced Thermal Ratchets,” Physical Review Letters, Vol. 71, pp.
1477-1481, 1993.
3. R. D. Astumian, “Thermodynamics and Kinetics of a Brownian Motor,” Science, Vol.
276, pp. 917-922,1997.
4. R. D. Astumian and P. Hanggi, “Brownian motor,” Physics Today, Vol. 55, pp. 33-39, 2002.
5. P. Hanggi and F. Marchesoni, “Artificial Brownian motor: controlling transport on the nanoscale,” Review of Modern Physics, Vol. 81, pp. 387-442, 2009.
6. L. Daikhin and M. Urbakh, “Roughness effect on the frictional force in boundary lubrications,” Physical Review E, Vol. 49, pp. 1424-1429, 1994.
7. C. Daly and J. Krim, “Sliding friction of xenon monolayer and bilayers on Ag(111),”
Physical Review Letters, Vol. 76, pp. 803-806, 1996.
8. M. R. Ssorenseen, K. W. Jacobseen and P. Sstoltze, “Simulation of atomic scale sliding friction,” Physical Review B, Vol. 53, pp. 2101-2113, 1996.
9. A. L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth, Cambridge University Press, 1995.
10. I. Zapata, R. Bartussek, F. Sols and P. Hänggi, “Voltage rectification by a SQUID ratchet,” Physical Review Letters, Vol. 77, pp. 2292-2295, 1996.
11. L. Gorre-Talini, J. P. Sspatz and P. Silberzan, “Dielectrophoretic ratchets,” Chaos, Vol. 8, pp. 650-656,1998.
12. I. Derenyi and R. D. Astumian, “AC separation of particles by biased Brownian motion in a two dimensional sieve,” Physical Review E, Vol. 58, pp. 7781-7784, 1998.
13. D. Ertas, “Lateral separation of mcromolecules and polyelectrolytes in
microlithographic arrays,” Physical Review Letters, Vol. 80, pp. 1548-1551, 1998.
14. T. A. J. Duke and R. H. Austin, “Microfabricated sieve for the continuous sorting of macromolecules,” Physical Review Letters, Vol. 80, pp. 1552-1555, 1998.
15. R. D. Vale and R. A. Milligan, “The way things move: looking under the hood of molecular motor proteins,” Science, Vol. 288, pp. 88-95, 2000.
16. S. A. Endow and H. Higuchi, “A mutant of the motor protein kinesin that moves in both directions on microtubules,” Nature, Vol. 406, pp. 913-916, 2000.
17. I. Derenyi and T. Vicsek, “The kinesin walk: a dynamic model with elastically coupled heads,” Proceedings National Academic Science USA, Vol. 93, pp.
6775-6779, 1996.
18. Kevin Loutherback, Jason Puchalla, Robert H. Austin, and James C. Sturm,
“Deterministic Microfluidic Ratchet, ” Physical Review Letters, PRL 102, 045301,2009
19. S. I. Denisov, E. S. Denisova and P. Hanggi, “Ratchet transport for a chain of interacting charged particles,” Physical Review E, Vol. 71, pp. 016104, 2005.
20. D. Cubero, J. Casado Pascual, A. Alvarez, M. Morillo and P. Hanggi, “Overdamped deterministic ratchet driven by multifrequency forces,” Acta Physica Polonica B, Vol.
37, pp. 1467-1477, 2006.
21. P. Jung, J. G. Kissner and P. Hanggi, “Regular and chaotic transport in asymmetric periodic potential: inertia ratchets,” Physical Review Letters, Vol. 76, pp. 3436-3439, 1996.
22. T. Hondou and Y. Sawada, “Dynamical Behavior of Dissipative Particle in a periodic potential Subject to a Chaotic Noise;Retrieval of Chaotic Determinism with Broken Parity,” Physical Review Letters, Vol. 75, pp. 3269-3272, 1995.
23. J. L. Mateos, “Chaotic transport and current reversal in deterministic ratchets,”
Physical Review Letters, Vol. 84, pp. 256-261, 2000.
24. W. K. Son, I. Kim, Y. J. Park and C. M. Kim, “Current reversal with type-I intermittency in deterministic inertia ratchets,” Physical Reivew E, Vol. 68, pp.
067201, 2003.
25. C. M. Arizmendi, F. Family and A. L. Salas Brito, “Quenched disorder effects on deterministic inertia ratchets,” Physical Review E, Vol. 63, pp. 061104, 2001.
26. T. Harms and R. Lipowsky, “Driven ratchets with disordered tracks,” Physical Review Letters, Vol. 79, pp. 2895-2898, 1997.
27. F. Marchesoni, “Transport properties in disordered ratchet potentials,” Physical Review E, Vol. 56, pp. 2492-2495, 1997.
28. D. G. Zarlenga, H. A. Larrondo, C. M. Arizmendi and F. Family, “Trapping
mechanism in overdamped ratchets with quenched noise,” Physical Review E, Vol. 75, pp. 051101, 2007.
29. S. I. Denisov, T. V. Lyutyy, E. S. Denisova , P. Hanggi and H. Kantz, “Directed transport in periodically rocked random sawtooth potentials,” Physical Review E, Vol.
79, pp. 051102, 2009.
30. F. Family, H. A. Larrondo, D. G. Zarlenga and C. M. Arizmendi, “Chaotic dynamics and control of deterministic ratchets,” Journal of Physics: Condensed Matter, Vol. 17, pp. S3719-S3739, 2005.
31. F. Marchesoni, “Transport properties in disordered ratchet potentials,” Physical Review E, Vol. 56, pp. 2492-2495, 1997.
32. A. B. Kolten, “Transverse rectification of disordered-induced fluctuations in a driven system,” Physical Review B, Vol. 75, pp. 020201, 2007.