Specific Features of the Simulation of the Particle Diffusion Processes in Spatially Periodic Fields
This paper is devoted to the studies of the specific features of the simulation of the particle diffusion processes in space – periodic potentials using Langevin equations. Different methods used for the presetting of initial conditions and their effect on the obtained solutions have been analyzed. It is shown that the system is nonequilibrium for all the methods of the presetting of initial conditions during a certain time interval of ttrm. This interval is increased as 1/γ with a decrease in the friction coefficient. A reasonable description of the transient processes of particle transport and diffusion requires a preliminary system thermalization procedure. A new method of the presetting of initial conditions that provides the most accurate description of equilibrium system has been suggested. It consists in the generation of the initial particle coordinates and velocities that correspond to the equilibrium distribution of harmonic oscillators with a specified temperature. The use of such initial conditions enables the computations with a good accuracy using no thermalization procedure at T < 0.1. The classic method of the determination of diffusion coefficients D as a limit limt→ꝏ (σ2/t) has been analyzed. It was shown that the use of it for computer-aided calculations is limited by the restricted computational time. It results in that the computation of D under certain conditions becomes impossible. A new method was suggested for the determination of the diffusion coefficient using the linear approximation of the dependence of dispersion on time. This approximation can only be possible after the kinetic temperature attains its stationary value. The suggested method requires several orders of magnitude less time in comparison to the classic method. As a result, it enables the computation of the diffusion coefficient even in the cases of total previous failure. The obtained data are of great importance for correct simulation computations of diffusion processes and for the appropriate physical interpretations of obtained data.
H. Risken, The Fokker-Planck Equation and Methods of Solution and Applications (Springer, 1989), pp. 485.
P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 287 (2009), https://doi.org/10.1103/RevModPhys.81.387
R.H. Koch, and D.J. Van Harlingen, J. Clarke, Phys. Rev. B 26, 74 (1982), https://doi.org/10.1103/PhysRevB.26.74
K. Siraj, Past, International Journal of Nano and Material Sciences, 1, 1 (2012), https://bit.ly/3rXzTO1
M. Beck, E. Goldobin, M. Neuhaus, M. Siegel, R. Kleiner, and D. Koelle, Phys. Rev. Lett. 95, 090603 (2005), https://doi.org/10.1103/PhysRevLett.95.090603
G. Grüner, A. Zawadowski, and P.M. Chaikin, Phys. Rev. Lett. 46, 511 (1981), https://doi.org/10.1103/PhysRevLett.46.511
P. Tierno, P. Reiman, T.H. Johansen, and F. Sagués, Phys. Rev. Let. 105, 230602 (2010), https://doi.org/10.1103/PhysRevLett.105.230602
P. Eshuis, K. van der Weele, D. Lohse, and D. van der Meer, Phys. Rev. Let. 104, 248001 (2010), https://doi.org/10.1103/PhysRevLett.104.248001
M. Zarshenas, V. Gervilla, D.G. Sangiovanni, and K. Sarakinos, Phys. Chem. Chem. Phys. 23, 13087 (2021), https://doi.org/10.1039/D1CP00522G
S.-H. Lee, and D.G. Grier, Phys. Rev. Let. 96, 190601 (2006), https://doi.org/10.1103/PhysRevLett.96.190601
S. Pagliara, C. Schwall, and U.F. Keyser, Advanc. Mat. 25, 844 (2013), https://doi.org/10.1002/adma.201203500
P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J.M. Rubí, and A. Pérez-Madrid, Phys. Rev. E 65, 031104 (2002), https://doi.org/10.1103/PhysRevE.65.031104
R. Salgado-García, Phys. Rev. E 90, 032105 (2014), https://doi.org/10.1103/PhysRevE.90.032105
G. Costantini, and F. Marchesoni, Europhys. Lett. 48, 491 (1999), https://doi.org/10.1209/epl/i1999-00510-7
J.M. Sancho, A.M. Lacasta, K. Lindenberg, I.M. Sokolov, and A.H. Romero, Phys. Rev. Lett. 92, 250601 (2004), https://doi.org/10.1103/PhysRevLett.92.250601
B. Lindner, and I.M. Sokolov, Phys. Rev. E93, 042106 (2016), https://doi.org/10.1103/PhysRevE.93.042106
J. Spiechowicz, and J. Łuczka, Phys. Rev. E 104, 034104 (2021), https://doi.org/10.1103/PhysRevE.104.034104
I.G. Marchenko, I.I. Marchenko, and V.I. Tkachenko, JETP Letters 109 №10, 671 (2019), https://doi.org/10.1134/S0021364019100126
J. Spiechowicz, and J. Łuczka, Phys. Rev. E 101, 032123 (2020), https://doi.org/10.1103/PhysRevE.101.032123
P. Siegle, I. Goychuk, and P. Hänggi Phys. Rev. Lett. 105, 100602 (2010), https://doi.org/10.1103/PhysRevLett.105.100602
D. Garcia-Alvarez, arXiv:1102.4401v1 [physics.comp-ph] (2011), https://doi.org/10.48550/arXiv.1102.4401
A.M. Lacasta, J.M. Sancho, A.H. Romero, I.M. Sokolov, and K. Lindenberg, Phys. Rev. E 70, 051104 (2004), https://doi.org/10.1103/PhysRevE.70.051104
J. Spiechowicz, P Talkner, P Hänggi, and J. Luczka, New J. Phys. 18, 123029 (2016), https://doi.org/10.1088/1367 2630/aa529f
J. Spiechowicz, M. Kostur, and J. Łuczka, Chaos 27, 023111 (2017), https://doi.org/10.1063/1.4976586
I. Goychuk, Phys. Rev. Lett. 123, 180603 (2019), https://doi.org/10.1103/PhysRevLett.123.180603
I.G. Marchenko, I.I. Marchenko, and A.V. Zhiglo, Phys. Rev. E 97, 012121 (2018), https://doi.org/10.1103/PhysRevE.97.012121
B. Lindner, M. Kostur, and L. Schimansky-Geier, Fluctuation and Noise Letters 01 №01, R25 (2001), https://doi.org/10.1142/S0219477501000056
D. Speer, R. Eichhorn, and P. Reimann, EPL 97, 60004 (2012), https://doi.org/10.1209/0295-5075/97/60004
I.G. Marchenko ,V.Yu. Aksenova, I.I. Marchenko, and A.V. Zhiglo, J. Phys. A: Math. Theor. 55, 155005 (2022), https://doi.org/10.1088/1751-8121/ac57d1
K. Lindenberg, J.M. Sancho, A.M. Lacasta, and I.M. Sokolov, Phys. Rev. Lett. 98, 020602 (2007), https://doi.org/10.1103/PhysRevLett.98.020602
J.M. Sancho, and A.M. Lacasta, Eur. Phys. J. Special Topics 187, 49 (2010), https://doi.org/10.1140/epjst/e2010-01270-7
R.D.L. Hanes, M. Schmiedeberg, and S.U. Egelhaaf, Phys. Rev. E 88, 062133 (2013), https://doi.org/10.1103/PhysRevE.88.062133
F. Evers, C. Zunke, R.D.L. Hanes, J. Bewerunge, and I. Ladadwa, Phys. Rev. E 88, 022125 (2013), https://doi.org/10.1103/PhysRevE.88.022125
J. Wolberg, Data Analysis Using the Method of Least Squares: Extracting the Most Information from Experiments (Springer, 2005), pp. 250.
I.G. Marchenko, V.Yu. Аksenova, and I.I. Marchenko, East Eur. J. Phys. 3, 27 (2021), https://doi.org/10.26565/2312-4334-2021-3-03
I.G. Marchenko, I.I. Marchenko, and V.I. Tkachenko, JETP Letters, 109(10), 694 (2019), https://doi.org/10.1134/S0021364019100126
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