File dynamics information

The term file dynamics is the motion of many particles in a narrow channel.

In science: in chemistry, physics, mathematics and related fields, file dynamics (sometimes called, single file dynamics) is the diffusion of N (N → ∞) identical Brownian hard spheres in a quasi-one-dimensional channel of length L (L → ∞), such that the spheres do not jump one on top of the other, and the average particle's density is approximately fixed. The most famous statistical properties of this process is that the mean squared displacement (MSD) of a particle in the file follows, $\mathrm {MSD} \approx t^{\frac {1}{2}}$ , and its probability density function (PDF) is Gaussian in position with a variance MSD.^[1]^[2]^[3]

Results in files that generalize the basic file include:

In files with a density law that is not fixed, but decays as a power law with an exponent a with the distance from the origin, the particle in the origin has a MSD that scales like, $MSD\approx t^{\frac {1+a}{2}}$ , with a Gaussian PDF.^[4]
When, in addition, the particles' diffusion coefficients are distributed like a power law with exponent γ (around the origin), the MSD follows, $MSD\approx t^{\frac {1-\gamma }{2/(1+a)-\gamma }}$ , with a Gaussian PDF.^[5]
In anomalous files that are renewal, namely, when all particles attempt a jump together, yet, with jumping times taken from a distribution that decays as a power law with an exponent, −1 − α, the MSD scales like the MSD of the corresponding normal file, in the power of α.^[6]
In anomalous files of independent particles, the MSD is very slow and scales like, $MSD\approx log^{2}(t)$ . Even more exciting, the particles form clusters in such files, defining a dynamical phase transition. This depends on the anomaly power α: the percentage of particles in clusters ξ follows, $\xi \approx {\sqrt {1-\alpha ^{3}}}$ .^[7]
Other generalizations include: when the particles can bypass each other with a constant probability upon encounter, an enhanced diffusion is seen.^[8] When the particles interact with the channel, a slower diffusion is observed.^[9] Files in embedded in two-dimensions show similar characteristics of files in one dimension.^[7]

Generalizations of the basic file are important since these models represent reality much more accurately than the basic file. Indeed, file dynamics are used in modeling numerous microscopic processes:^[10]^[11]^[12]^[13]^[14]^[15]^[16] the diffusion within biological and synthetic pores and porous material, the diffusion along 1D objects, such as in biological roads, the dynamics of a monomer in a polymer, etc.

^ Harris T. E. (1965) "Diffusion with 'Collisions' between Particles", Journal of Applied Probability, 2 (2), 323-338 JSTOR 3212197
^ Jepsen, D. W. (1965). "Dynamics of a Simple Many‐Body System of Hard Rods". Journal of Mathematical Physics. 6 (3). AIP Publishing: 405–413. Bibcode:1965JMP.....6..405J. doi:10.1063/1.1704288. ISSN 0022-2488.
^ Lebowitz, J. L.; Percus, J. K. (1967-03-05). "Kinetic Equations and Density Expansions: Exactly Solvable One-Dimensional System". Physical Review. 155 (1). American Physical Society (APS): 122–138. Bibcode:1967PhRv..155..122L. doi:10.1103/physrev.155.122. ISSN 0031-899X.
^ Cite error: The named reference OF_2008EPL was invoked but never defined (see the help page).
^ Cite error: The named reference OF_2010PRE was invoked but never defined (see the help page).
^ Cite error: The named reference OF_2010PLA was invoked but never defined (see the help page).
^ ^a ^b Cite error: The named reference OF_2011EPL was invoked but never defined (see the help page).
^ Cite error: The named reference mon was invoked but never defined (see the help page).
^ Cite error: The named reference taloni was invoked but never defined (see the help page).
^ Kärger J. and Ruthven D. M. (1992) Diffusion in Zeolites and Other Microscopic Solids (Wiley, NY).
^ Wei, Q.; Bechinger, C.; Leiderer, P. (2000-01-28). "Single-File Diffusion of Colloids in One-Dimensional Channels". Science. 287 (5453). American Association for the Advancement of Science (AAAS): 625–627. Bibcode:2000Sci...287..625W. doi:10.1126/science.287.5453.625. ISSN 0036-8075. PMID 10649990.
^ de Gennes, P. G. (1971-07-15). "Reptation of a Polymer Chain in the Presence of Fixed Obstacles". The Journal of Chemical Physics. 55 (2). AIP Publishing: 572–579. Bibcode:1971JChPh..55..572D. doi:10.1063/1.1675789. ISSN 0021-9606.
^ Richards, Peter M. (1977-08-15). "Theory of one-dimensional hopping conductivity and diffusion". Physical Review B. 16 (4). American Physical Society (APS): 1393–1409. Bibcode:1977PhRvB..16.1393R. doi:10.1103/physrevb.16.1393. ISSN 0556-2805.
^ Maxfield, Frederick R (2002). "Plasma membrane microdomains". Current Opinion in Cell Biology. 14 (4). Elsevier BV: 483–487. doi:10.1016/s0955-0674(02)00351-4. ISSN 0955-0674. PMID 12383800.
^ Biological Membrane Ion Channels: Dynamics, Structure, And Applications, Chung S-h., Anderson O. S. and Krishnamurthy V. V., editors (Springer-verlag) 2006.
^ Howard J., Mechanics of Motor Proteins and the Cytoskeleton (Sinauer associates Inc. Sunderland, MA) 2001.

[1] Harris T. E. (1965) "Diffusion with 'Collisions' between Particles", Journal of Applied Probability, 2 (2), 323-338 JSTOR 3212197

[2] Jepsen, D. W. (1965). "Dynamics of a Simple Many‐Body System of Hard Rods". Journal of Mathematical Physics. 6 (3). AIP Publishing: 405–413. Bibcode:1965JMP.....6..405J. doi:10.1063/1.1704288. ISSN 0022-2488.

[3] Lebowitz, J. L.; Percus, J. K. (1967-03-05). "Kinetic Equations and Density Expansions: Exactly Solvable One-Dimensional System". Physical Review. 155 (1). American Physical Society (APS): 122–138. Bibcode:1967PhRv..155..122L. doi:10.1103/physrev.155.122. ISSN 0031-899X.

[OF_2008EPL-4] Cite error: The named reference OF_2008EPL was invoked but never defined (see the help page).

[OF_2010PRE-5] Cite error: The named reference OF_2010PRE was invoked but never defined (see the help page).

[OF_2010PLA-6] Cite error: The named reference OF_2010PLA was invoked but never defined (see the help page).

[OF_2011EPL-7] Cite error: The named reference OF_2011EPL was invoked but never defined (see the help page).

[mon-8] Cite error: The named reference mon was invoked but never defined (see the help page).

[taloni-9] Cite error: The named reference taloni was invoked but never defined (see the help page).

[10] Kärger J. and Ruthven D. M. (1992) Diffusion in Zeolites and Other Microscopic Solids (Wiley, NY).

[11] Wei, Q.; Bechinger, C.; Leiderer, P. (2000-01-28). "Single-File Diffusion of Colloids in One-Dimensional Channels". Science. 287 (5453). American Association for the Advancement of Science (AAAS): 625–627. Bibcode:2000Sci...287..625W. doi:10.1126/science.287.5453.625. ISSN 0036-8075. PMID 10649990.

[12] Gennes, P. G. (1971-07-15). "Reptation of a Polymer Chain in the Presence of Fixed Obstacles". The Journal of Chemical Physics. 55 (2). AIP Publishing: 572–579. Bibcode:1971JChPh..55..572D. doi:10.1063/1.1675789. ISSN 0021-9606.

[13] Richards, Peter M. (1977-08-15). "Theory of one-dimensional hopping conductivity and diffusion". Physical Review B. 16 (4). American Physical Society (APS): 1393–1409. Bibcode:1977PhRvB..16.1393R. doi:10.1103/physrevb.16.1393. ISSN 0556-2805.

[14] Maxfield, Frederick R (2002). "Plasma membrane microdomains". Current Opinion in Cell Biology. 14 (4). Elsevier BV: 483–487. doi:10.1016/s0955-0674(02)00351-4. ISSN 0955-0674. PMID 12383800.

[15] Biological Membrane Ion Channels: Dynamics, Structure, And Applications, Chung S-h., Anderson O. S. and Krishnamurthy V. V., editors (Springer-verlag) 2006.

[16] Howard J., Mechanics of Motor Proteins and the Cytoskeleton (Sinauer associates Inc. Sunderland, MA) 2001.

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