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Molecular motors, Brownian ratchets, and reflected diffusions
1. | Department of Statistics & Operations Research, University of North Carolina, Chapel Hill, NC 27599-3250, United States |
2. | Department of Mathematics, University of North Carolina, Chapel Hill, NC 27514, United States |
[1] |
Dmitry Vorotnikov. The flashing ratchet and unidirectional transport of matter. Discrete and Continuous Dynamical Systems - B, 2011, 16 (3) : 963-971. doi: 10.3934/dcdsb.2011.16.963 |
[2] |
David Heath, David Kinderlehrer, Michal Kowalczyk. Discrete and continuous ratchets: from coin toss to molecular motor. Discrete and Continuous Dynamical Systems - B, 2002, 2 (2) : 153-167. doi: 10.3934/dcdsb.2002.2.153 |
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Fabrice Baudoin, Camille Tardif. Hypocoercive estimates on foliations and velocity spherical Brownian motion. Kinetic and Related Models, 2018, 11 (1) : 1-23. doi: 10.3934/krm.2018001 |
[4] |
Monia Karouf. Reflected solutions of backward doubly SDEs driven by Brownian motion and Poisson random measure. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5571-5601. doi: 10.3934/dcds.2019245 |
[5] |
Tzong-Yow Lee. Asymptotic results for super-Brownian motions and semilinear differential equations. Electronic Research Announcements, 1998, 4: 56-62. |
[6] |
Giovanni Colombo, Paolo Gidoni, Emilio Vilches. Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction. Discrete and Continuous Dynamical Systems, 2022, 42 (2) : 737-757. doi: 10.3934/dcds.2021135 |
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Jasmina Djordjević, Svetlana Janković. Reflected backward stochastic differential equations with perturbations. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1833-1848. doi: 10.3934/dcds.2018075 |
[8] |
Muhammad Aamer Rashid, Sarfraz Ahmad, Muhammad Kamran Siddiqui, Juan L. G. Guirao, Najma Abdul Rehman. Topological indices of discrete molecular structure. Discrete and Continuous Dynamical Systems - S, 2021, 14 (7) : 2487-2495. doi: 10.3934/dcdss.2020418 |
[9] |
Hongyong Zhao, Qianjin Zhang, Linhe Zhu. The spatial dynamics of a zebrafish model with cross-diffusions. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1035-1054. doi: 10.3934/mbe.2017054 |
[10] |
Yaozhong Hu, Yanghui Liu, David Nualart. Taylor schemes for rough differential equations and fractional diffusions. Discrete and Continuous Dynamical Systems - B, 2016, 21 (9) : 3115-3162. doi: 10.3934/dcdsb.2016090 |
[11] |
Han Wu, Changfan Zhang, Jing He, Kaihui Zhao. Distributed fault-tolerant consensus tracking for networked non-identical motors. Journal of Industrial and Management Optimization, 2017, 13 (2) : 917-929. doi: 10.3934/jimo.2016053 |
[12] |
Yinggu Chen, Said HamadÈne, Tingshu Mu. Mean-field doubly reflected backward stochastic differential equations. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022012 |
[13] |
Le Li, Lihong Huang, Jianhong Wu. Flocking and invariance of velocity angles. Mathematical Biosciences & Engineering, 2016, 13 (2) : 369-380. doi: 10.3934/mbe.2015007 |
[14] |
Irina Berezovik, Carlos García-Azpeitia, Wieslaw Krawcewicz. Symmetries of nonlinear vibrations in tetrahedral molecular configurations. Discrete and Continuous Dynamical Systems - B, 2019, 24 (6) : 2473-2491. doi: 10.3934/dcdsb.2018261 |
[15] |
Hirotada Honda. On a model of target detection in molecular communication networks. Networks and Heterogeneous Media, 2019, 14 (4) : 633-657. doi: 10.3934/nhm.2019025 |
[16] |
Howard A. Levine, Yeon-Jung Seo, Marit Nilsen-Hamilton. A discrete dynamical system arising in molecular biology. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 2091-2151. doi: 10.3934/dcdsb.2012.17.2091 |
[17] |
G. Wei, P. Clifford. Analysis and numerical approximation of a class of two-way diffusions. Communications on Pure and Applied Analysis, 2003, 2 (1) : 91-99. doi: 10.3934/cpaa.2003.2.91 |
[18] |
Atsushi Yagi. Exponential attractors for competing species model with cross-diffusions. Discrete and Continuous Dynamical Systems, 2008, 22 (4) : 1091-1120. doi: 10.3934/dcds.2008.22.1091 |
[19] |
Kimun Ryu, Inkyung Ahn. On certain elliptic systems with nonlinear self-cross diffusions. Conference Publications, 2003, 2003 (Special) : 752-759. doi: 10.3934/proc.2003.2003.752 |
[20] |
Changbing Hu. Stability of under-compressive waves with second and fourth order diffusions. Discrete and Continuous Dynamical Systems, 2008, 22 (3) : 629-662. doi: 10.3934/dcds.2008.22.629 |
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