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Molecular motors, Brownian ratchets, and reflected diffusions
1.  Department of Statistics & Operations Research, University of North Carolina, Chapel Hill, NC 275993250, 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 & Continuous Dynamical Systems  B, 2011, 16 (3) : 963971. 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 & Continuous Dynamical Systems  B, 2002, 2 (2) : 153167. doi: 10.3934/dcdsb.2002.2.153 
[3] 
Fabrice Baudoin, Camille Tardif. Hypocoercive estimates on foliations and velocity spherical Brownian motion. Kinetic & Related Models, 2018, 11 (1) : 123. doi: 10.3934/krm.2018001 
[4] 
Monia Karouf. Reflected solutions of backward doubly SDEs driven by Brownian motion and Poisson random measure. Discrete & Continuous Dynamical Systems  A, 2019, 39 (10) : 55715601. doi: 10.3934/dcds.2019245 
[5] 
TzongYow Lee. Asymptotic results for superBrownian motions and semilinear differential equations. Electronic Research Announcements, 1998, 4: 5662. 
[6] 
Jasmina Djordjević, Svetlana Janković. Reflected backward stochastic differential equations with perturbations. Discrete & Continuous Dynamical Systems  A, 2018, 38 (4) : 18331848. doi: 10.3934/dcds.2018075 
[7] 
Hongyong Zhao, Qianjin Zhang, Linhe Zhu. The spatial dynamics of a zebrafish model with crossdiffusions. Mathematical Biosciences & Engineering, 2017, 14 (4) : 10351054. doi: 10.3934/mbe.2017054 
[8] 
Yaozhong Hu, Yanghui Liu, David Nualart. Taylor schemes for rough differential equations and fractional diffusions. Discrete & Continuous Dynamical Systems  B, 2016, 21 (9) : 31153162. doi: 10.3934/dcdsb.2016090 
[9] 
Le Li, Lihong Huang, Jianhong Wu. Flocking and invariance of velocity angles. Mathematical Biosciences & Engineering, 2016, 13 (2) : 369380. doi: 10.3934/mbe.2015007 
[10] 
Han Wu, Changfan Zhang, Jing He, Kaihui Zhao. Distributed faulttolerant consensus tracking for networked nonidentical motors. Journal of Industrial & Management Optimization, 2017, 13 (2) : 917929. doi: 10.3934/jimo.2016053 
[11] 
Irina Berezovik, Carlos GarcíaAzpeitia, Wieslaw Krawcewicz. Symmetries of nonlinear vibrations in tetrahedral molecular configurations. Discrete & Continuous Dynamical Systems  B, 2019, 24 (6) : 24732491. doi: 10.3934/dcdsb.2018261 
[12] 
Hirotada Honda. On a model of target detection in molecular communication networks. Networks & Heterogeneous Media, 2019, 14 (4) : 633657. doi: 10.3934/nhm.2019025 
[13] 
Howard A. Levine, YeonJung Seo, Marit NilsenHamilton. A discrete dynamical system arising in molecular biology. Discrete & Continuous Dynamical Systems  B, 2012, 17 (6) : 20912151. doi: 10.3934/dcdsb.2012.17.2091 
[14] 
G. Wei, P. Clifford. Analysis and numerical approximation of a class of twoway diffusions. Communications on Pure & Applied Analysis, 2003, 2 (1) : 9199. doi: 10.3934/cpaa.2003.2.91 
[15] 
Atsushi Yagi. Exponential attractors for competing species model with crossdiffusions. Discrete & Continuous Dynamical Systems  A, 2008, 22 (4) : 10911120. doi: 10.3934/dcds.2008.22.1091 
[16] 
Kimun Ryu, Inkyung Ahn. On certain elliptic systems with nonlinear selfcross diffusions. Conference Publications, 2003, 2003 (Special) : 752759. doi: 10.3934/proc.2003.2003.752 
[17] 
Changbing Hu. Stability of undercompressive waves with second and fourth order diffusions. Discrete & Continuous Dynamical Systems  A, 2008, 22 (3) : 629662. doi: 10.3934/dcds.2008.22.629 
[18] 
Patrick Guidotti. A family of nonlinear diffusions connecting PeronaMalik to standard diffusion. Discrete & Continuous Dynamical Systems  S, 2012, 5 (3) : 581590. doi: 10.3934/dcdss.2012.5.581 
[19] 
Takashi Suzuki. Brownian point vortices and ddmodel. Discrete & Continuous Dynamical Systems  S, 2014, 7 (1) : 161176. doi: 10.3934/dcdss.2014.7.161 
[20] 
Elena Kosygina. Brownian flow on a finite interval with jump boundary conditions. Discrete & Continuous Dynamical Systems  B, 2006, 6 (4) : 867880. doi: 10.3934/dcdsb.2006.6.867 
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