Brownian particle motion in a system with absorbing boundaries

Usenko, A. S.; Zagorodny, A. G.

doi:10.1080/00268978700101751

Cited by 4 publications

(3 citation statements)

References 10 publications

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“…The last piece of the kinetic framework is the distribution Pr 3→2 (τ), which is mathematically equivalent to the first passage time distribution of a 1-D Brownian motion that starts at z 3 and ends at z 2 . The solution is Pr 3 → 2 ( τ ) = 1 2 ∂ ∂ τ .25em ∑ n = − ∞ ∞ .25em false( prefix− 1 false) n f n ( τ ) where f n ( τ ) = prefix− erf [ α false( 2 n L − z ′ false) ] + erf { α false[ ( 2 n + 1 ) L − z ′ false] } + erf [ α false( 2 n L + z ′ false) ] − erf { α false[ ( 2 n + 1 ) L + z ′ false] } erf( x ) = 2π –1/2 ∫ 0 x d x exp(− x 2 ) represents the error function, α = (4 D τ) −1/2 , z ′ = z 3 – z 2 , and L = z max – z 2 , and z max is a reflecting boundary representing the upper bound of the desorbed state (i.e., the surface of the fluid). In the limit z max → ∞, eq reduces to <...…”

Section: Theoretical Methodsmentioning

confidence: 99%

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Insights into Microscopic Diffusion Processes at a Solid/Fluid Interface under Supercritical Conditions: A Study of the Aqueous Calcite (101̅4) Surface

Pérez

Hickmott

et al. 2012

J. Phys. Chem. C

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The diffusion of adsorbed molecules at a solid/ fluid interface is a phenomenon of great fundamental interest and technological importance. We use molecular dynamics and kinetic Monte Carlo simulations to investigate the diffusion processes at an aqueous calcite (101̅ 4) interface under various geologically relevant supercritical conditions [101.3 MPa (1000 atm), 300−800 K]. Between 600 and 700 K, the adsorption configuration changes from an outer-to inner-sphere surface complex, and the desorption free energy barrier, ΔG d , increases greatly. The ratio ΔG d /k B T takes a minimum value at 600 K, making it the temperature with the greatest desorption tendency. Consequently, the temperature dependence of the mean lateral diffusivity of a finite bulk system reverses at 600 K. More interestingly, the system exhibits typical characteristics of bulk fluidmediated surface diffusion. For example, the mean-squared displacement shows different scaling properties with changes in temperature or bulk thickness. The optimized bulk thickness which maximizes the effective surface diffusivity was also found to vary with temperature.

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Section: Theoretical Methodsmentioning

confidence: 99%

Section: Theoretical Methodsmentioning

confidence: 99%

Insights into Microscopic Diffusion Processes at a Solid/Fluid Interface under Supercritical Conditions: A Study of the Aqueous Calcite (101̅4) Surface

Pérez

Hickmott

et al. 2012

J. Phys. Chem. C

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“…Taking into account that not all extracellular auxin molecules are protonated and hence able to penetrate the membrane we assume the probability to enter a cell to be of 10% [31,8]. Considering these assumptions already 97% of all auxin molecules have reentered any cell including the one they were delivered from after a time duration of one millisecond [33]. flow only.…”

Section: Modelmentioning

confidence: 99%

Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

Alim

Frey

2010

Eur. Phys. J. E

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The dynamic patterning of the plant hormone auxin and its efflux facilitator the PIN protein are the key regulators for the spatial and temporal organization of plant development. In particular auxin induces the polar localization of its own efflux facilitator. Due to this positive feedback, auxin flow is directed and patterns of auxin and PIN arise. During the earliest stage of vein initiation in leaves auxin accumulates in a single cell in a rim of epidermal cells from which it flows into the ground meristem tissue of the leaf blade. There the localized auxin supply yields the successive polarization of PIN distribution along a strand of cells. We model the auxin and PIN dynamics within cells with a minimal canalization model. Solving the model analytically we uncover an excitable polarization front that triggers a polar distribution of PIN proteins in cells. As polarization fronts may extend to opposing directions from their initiation site, we suggest a possible resolution to the puzzling occurrence of bipolar cells, thus we offer an explanation for the development of closed, looped veins. Employing non-linear analysis, we identify the role of the contributing microscopic processes during polarization. Furthermore, we deduce quantitative predictions on polarization fronts establishing a route to determine the up to now largely unknown kinetic rates of auxin and PIN dynamics.

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Incoherent scattering of electromagnetic waves by a weakly ionized plasma layer

Zagorodnii¹,

Usenko²

1990

Radiophys Quantum Electron

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Brownian particle motion in a system with absorbing boundaries

Cited by 4 publications

References 10 publications

Insights into Microscopic Diffusion Processes at a Solid/Fluid Interface under Supercritical Conditions: A Study of the Aqueous Calcite (101̅4) Surface

Insights into Microscopic Diffusion Processes at a Solid/Fluid Interface under Supercritical Conditions: A Study of the Aqueous Calcite (101̅4) Surface

Quantitative predictions on auxin-induced polar distribution of PIN proteins during vein formation in leaves

Incoherent scattering of electromagnetic waves by a weakly ionized plasma layer

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