-
Previous Article
Existence of traveling wavefront for discrete bistable competition model
- DCDS-B Home
- This Issue
-
Next Article
Tikhonov's theorem and quasi-steady state
The flashing ratchet and unidirectional transport of matter
1. | CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, 3001-454 Coimbra, Portugal |
References:
[1] |
P. Amengual, A. Allison, R. Toral and D. Abbott, Discrete-time ratchets, the Fokker-Planck equation and Parrondo's paradox, Proc. Royal Society London A, 460 (2004), 2269-2284.
doi: 10.1098/rspa.2004.1283. |
[2] |
R. D. Astumian, Thermodynamics and kinetics of a Brownian motor, Science, 276, (1997), 917-922.
doi: 10.1126/science.276.5314.917. |
[3] |
D. Astumian and P. Hänggi, Brownian motors, Phys. Today, 55 (2002), 33-39.
doi: 10.1063/1.1535005. |
[4] |
J. Dolbeault, D. Kinderlehrer and M. Kowalczyk, Remarks about the flashing rachet, in: "Partial Differential Equations and Inverse Problems," (2004), 167-175, Contemporary Mathematics, 362, American Mathematical Society, Providence, RI. |
[5] |
D. Heath, D. Kinderlehrer and M. Kowalczyk, Discrete and continuous ratchets: from coin toss to molecular motor, Discr. Cont. Dyn. Sys. Ser. B, 2 (2002), 1-15. |
[6] |
R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation, SIAM J. Math. Anal., 29 (1998), 1-17.
doi: 10.1137/S0036141096303359. |
[7] |
D. Kinderlehrer and M. Kowalczyk, Diffusion-mediated transport and the flashing ratchet, Arch. Rat. Mech. Anal., 161 (2002), 149-179.
doi: 10.1007/s002050100173. |
[8] |
P. Palffy-Muhoray, T. Kosa and W. E, Brownian ratchets and the photoalignment of liquid crystals, Braz. J. Phys., 32 (2002), 552-563.
doi: 10.1590/S0103-97332002000300016. |
[9] |
B. Perthame and P. E. Souganidis, Asymmetric potentials and motor effect: a large deviation approach, Arch. Rat. Mech. Anal., 193 (2009), 153-169.
doi: 10.1007/s00205-008-0198-1. |
[10] |
A. D. Polyanin and A. V. Manzhirov, "Handbook of Mathematics for Engineers and Scientists," Chapman & Hall/CRC, Boca Raton, FL, 2007. |
[11] |
P. Reimann and P. Hänggi, Introduction to the physics of Brownian motors, Appl. Phys. A, 75 (2002), 169-178.
doi: 10.1007/s003390201331. |
show all references
References:
[1] |
P. Amengual, A. Allison, R. Toral and D. Abbott, Discrete-time ratchets, the Fokker-Planck equation and Parrondo's paradox, Proc. Royal Society London A, 460 (2004), 2269-2284.
doi: 10.1098/rspa.2004.1283. |
[2] |
R. D. Astumian, Thermodynamics and kinetics of a Brownian motor, Science, 276, (1997), 917-922.
doi: 10.1126/science.276.5314.917. |
[3] |
D. Astumian and P. Hänggi, Brownian motors, Phys. Today, 55 (2002), 33-39.
doi: 10.1063/1.1535005. |
[4] |
J. Dolbeault, D. Kinderlehrer and M. Kowalczyk, Remarks about the flashing rachet, in: "Partial Differential Equations and Inverse Problems," (2004), 167-175, Contemporary Mathematics, 362, American Mathematical Society, Providence, RI. |
[5] |
D. Heath, D. Kinderlehrer and M. Kowalczyk, Discrete and continuous ratchets: from coin toss to molecular motor, Discr. Cont. Dyn. Sys. Ser. B, 2 (2002), 1-15. |
[6] |
R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation, SIAM J. Math. Anal., 29 (1998), 1-17.
doi: 10.1137/S0036141096303359. |
[7] |
D. Kinderlehrer and M. Kowalczyk, Diffusion-mediated transport and the flashing ratchet, Arch. Rat. Mech. Anal., 161 (2002), 149-179.
doi: 10.1007/s002050100173. |
[8] |
P. Palffy-Muhoray, T. Kosa and W. E, Brownian ratchets and the photoalignment of liquid crystals, Braz. J. Phys., 32 (2002), 552-563.
doi: 10.1590/S0103-97332002000300016. |
[9] |
B. Perthame and P. E. Souganidis, Asymmetric potentials and motor effect: a large deviation approach, Arch. Rat. Mech. Anal., 193 (2009), 153-169.
doi: 10.1007/s00205-008-0198-1. |
[10] |
A. D. Polyanin and A. V. Manzhirov, "Handbook of Mathematics for Engineers and Scientists," Chapman & Hall/CRC, Boca Raton, FL, 2007. |
[11] |
P. Reimann and P. Hänggi, Introduction to the physics of Brownian motors, Appl. Phys. A, 75 (2002), 169-178.
doi: 10.1007/s003390201331. |
[1] |
Sylvain De Moor, Luis Miguel Rodrigues, Julien Vovelle. Invariant measures for a stochastic Fokker-Planck equation. Kinetic and Related Models, 2018, 11 (2) : 357-395. doi: 10.3934/krm.2018017 |
[2] |
Marco Torregrossa, Giuseppe Toscani. On a Fokker-Planck equation for wealth distribution. Kinetic and Related Models, 2018, 11 (2) : 337-355. doi: 10.3934/krm.2018016 |
[3] |
Michael Herty, Christian Jörres, Albert N. Sandjo. Optimization of a model Fokker-Planck equation. Kinetic and Related Models, 2012, 5 (3) : 485-503. doi: 10.3934/krm.2012.5.485 |
[4] |
José Antonio Alcántara, Simone Calogero. On a relativistic Fokker-Planck equation in kinetic theory. Kinetic and Related Models, 2011, 4 (2) : 401-426. doi: 10.3934/krm.2011.4.401 |
[5] |
Helge Dietert, Josephine Evans, Thomas Holding. Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus. Kinetic and Related Models, 2018, 11 (6) : 1427-1441. doi: 10.3934/krm.2018056 |
[6] |
Andreas Denner, Oliver Junge, Daniel Matthes. Computing coherent sets using the Fokker-Planck equation. Journal of Computational Dynamics, 2016, 3 (2) : 163-177. doi: 10.3934/jcd.2016008 |
[7] |
Ioannis Markou. Hydrodynamic limit for a Fokker-Planck equation with coefficients in Sobolev spaces. Networks and Heterogeneous Media, 2017, 12 (4) : 683-705. doi: 10.3934/nhm.2017028 |
[8] |
Manh Hong Duong, Yulong Lu. An operator splitting scheme for the fractional kinetic Fokker-Planck equation. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5707-5727. doi: 10.3934/dcds.2019250 |
[9] |
Giuseppe Toscani. A Rosenau-type approach to the approximation of the linear Fokker-Planck equation. Kinetic and Related Models, 2018, 11 (4) : 697-714. doi: 10.3934/krm.2018028 |
[10] |
Shui-Nee Chow, Wuchen Li, Haomin Zhou. Entropy dissipation of Fokker-Planck equations on graphs. Discrete and Continuous Dynamical Systems, 2018, 38 (10) : 4929-4950. doi: 10.3934/dcds.2018215 |
[11] |
Martin Burger, Ina Humpert, Jan-Frederik Pietschmann. On Fokker-Planck equations with In- and Outflow of Mass. Kinetic and Related Models, 2020, 13 (2) : 249-277. doi: 10.3934/krm.2020009 |
[12] |
Michael Herty, Lorenzo Pareschi. Fokker-Planck asymptotics for traffic flow models. Kinetic and Related Models, 2010, 3 (1) : 165-179. doi: 10.3934/krm.2010.3.165 |
[13] |
Ludovic Dan Lemle. $L^1(R^d,dx)$-uniqueness of weak solutions for the Fokker-Planck equation associated with a class of Dirichlet operators. Electronic Research Announcements, 2008, 15: 65-70. doi: 10.3934/era.2008.15.65 |
[14] |
Joseph G. Conlon, André Schlichting. A non-local problem for the Fokker-Planck equation related to the Becker-Döring model. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 1821-1889. doi: 10.3934/dcds.2019079 |
[15] |
Simon Plazotta. A BDF2-approach for the non-linear Fokker-Planck equation. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 2893-2913. doi: 10.3934/dcds.2019120 |
[16] |
Patrick Cattiaux, Elissar Nasreddine, Marjolaine Puel. Diffusion limit for kinetic Fokker-Planck equation with heavy tails equilibria: The critical case. Kinetic and Related Models, 2019, 12 (4) : 727-748. doi: 10.3934/krm.2019028 |
[17] |
Fabio Camilli, Serikbolsyn Duisembay, Qing Tang. Approximation of an optimal control problem for the time-fractional Fokker-Planck equation. Journal of Dynamics and Games, 2021, 8 (4) : 381-402. doi: 10.3934/jdg.2021013 |
[18] |
Anton Arnold, Beatrice Signorello. Optimal non-symmetric Fokker-Planck equation for the convergence to a given equilibrium. Kinetic and Related Models, , () : -. doi: 10.3934/krm.2022009 |
[19] |
Florian Schneider, Andreas Roth, Jochen Kall. First-order quarter-and mixed-moment realizability theory and Kershaw closures for a Fokker-Planck equation in two space dimensions. Kinetic and Related Models, 2017, 10 (4) : 1127-1161. doi: 10.3934/krm.2017044 |
[20] |
Zeinab Karaki. Trend to the equilibrium for the Fokker-Planck system with an external magnetic field. Kinetic and Related Models, 2020, 13 (2) : 309-344. doi: 10.3934/krm.2020011 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]