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Kosztołowicz, Tadeusz; Lewandowska, Katarzyna D.

doi:10.5506/aphyspolb.43.1043

Cited by 6 publications

(10 citation statements)

References 19 publications

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“…Numerical solutions to Eq. (43) for α ∈ (0 1) lead to ∈ (1/3 1) [23,24]. Thus, we have found three relations, namely, Eqs.…”

Section: The Agreement Conditionsmentioning

confidence: 81%

“…In order to interpret this, one uses the linear Langevin equation or the linear Fokker-Planck equation with specifically defined coefficients. We should mention here that we have recently proposed a new stochastic interpretation of subdiffusion described by nonlinear equations using a specific external Gamma type noise approach [11]. An important feature of subdiffusive systems is the occurrence of different relations similar to (1), namely…”

Section: Introductionmentioning

confidence: 99%

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Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

Kosztołowicz

Lewandowska

2012

Open Physics

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Abstract:We consider here two different models describing subdiffusion. One of them is derived from Continuous Time Random Walk formalism and utilizes a subdiffusion equation with a fractional time derivative. The second model is based on Sharma-Mittal nonadditive entropy formalism where the subdiffusive process is described by a nonlinear equation with ordinary derivatives. Using these two models we describe the process of a substance released from a thick membrane and we find functions which determine the time evolution of the amount of substance remaining inside this membrane. We then find 'the agreement conditions' under which these two models provide the same relation defining subdiffusion and give the same function characterizing the process of the released substance. These agreement conditions enable us to determine the relation between the parameters occuring in both models. PACS

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“…Numerical solutions to Eq. (43) for α ∈ (0 1) lead to ∈ (1/3 1) [23,24]. Thus, we have found three relations, namely, Eqs.…”

Section: The Agreement Conditionsmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

Kosztołowicz

Lewandowska

2012

Open Physics

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“…(14), D ∝ τ * − 1/2. The value of τ * max can now be chosen quite freely, e.g., based on accuracy, stability, or workload considerations for the problem.…”

Section: B Simulation Setupmentioning

confidence: 99%

“…[14], where a mesoscopic boundary condition corresponding to Eq. (1) was reported, and utilize this simple boundary condition for the implementation of a membrane in a lattice-Boltzmann scheme.…”

Section: Lattice-boltzmann Modeling Of Diffusion Across a Membranementioning

confidence: 99%

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Diffusion through thin membranes: Modeling across scales

et al. 2016

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From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.

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How to identify absorption in a subdiffusive medium

Kosztołowicz

Lewandowska

Klinkosz

2017

Math. Model. Nat. Phenom.

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We consider subdiffusion in a system which consists of two different media separated by a thin membrane. In one of the media particles' absorption can occur. Such systems can be studied experimentally but, due to technical reasons, it is not always possible to measure concentration profiles in the medium in which absorption can be present. We show the method which allows one to recognize whether absorption is present in such a medium knowing concentration profiles of diffusing substance in the other medium.

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Untitled

Cited by 6 publications

References 19 publications

Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

Conciliating the nonadditive entropy approach and the fractional model formulation when describing subdiffusion

Diffusion through thin membranes: Modeling across scales

How to identify absorption in a subdiffusive medium

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