New analytical solution for nonlinear adsorption and diffusion in a single particle

Abstract We numerically investigate the resonance of the underdamped scaled Brownian motion in a bistable system for both cases of a single particle and interacting particles. Through the velocity autocorrelation function (VACF) and mean squared displacement (MSD) of a single particle, we ﬁnd that for the steady state, diﬀusions are ballistic at short times and then become normal for most of parameter regimes. However, for certain parameter regimes, both VACF and MSD suggest that the transition between superdiﬀusion and subdiﬀusion takes place at intermediate times, and diﬀusion becomes normal at long times. Via the power spectrum density corresponding to the transitions, we ﬁnd that there exists a nontrivial resonance. For interacting particles, we ﬁnd that the interaction between the probe particle and other particles can lead to the resonance, too. Thus we theoretically propose the system with the Brownian particle as a probe, which can detect the temperature of the system and identify the number of the particles or the types of diﬀerent coupling strengths in the system. The probe is potentially useful for detecting microscopic and nanometer-scale particles and for identifying cancer cells or healthy ones.

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Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium

Journal of the Taiwan Institute of Chemical Engineers ◽

10.1016/j.jtice.2009.04.011 ◽

2010 ◽

Vol 41 (1) ◽

pp. 22-28 ◽

Cited By ~ 42

Author(s):

Z. Ziabakhsh ◽

G. Domairry ◽

H. Bararnia ◽

H. Babazadeh

Keyword(s):

Porous Medium ◽

Analytical Solution ◽

Stretching Sheet ◽

Reactive Species ◽

Nonlinearly Stretching Sheet ◽

Chemically Reactive Species ◽

And Diffusion

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Formal Analytical Solution to a Regional Blood Flow and Diffusion Based Urea Kinetic Model

ASAIO Journal ◽

10.1097/00002480-199407000-00082 ◽

1994 ◽

Vol 40 (3) ◽

pp. M667-M673 ◽

Cited By ~ 37

Author(s):

Daniel Schneditz ◽

John T. Daugirdas

Keyword(s):

Blood Flow ◽

Kinetic Model ◽

Analytical Solution ◽

Regional Blood Flow ◽

And Diffusion

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Modeling of Tau Protein Transport in Axons

Volume 3B: Biomedical and Biotechnology Engineering ◽

10.1115/imece2013-62430 ◽

2013 ◽

Author(s):

Ivan A. Kuznetsov ◽

Andrey V. Kuznetsov

Keyword(s):

Analytical Solution ◽

Axonal Transport ◽

Tau Protein ◽

Protein Transport ◽

State Model ◽

Tau Proteins ◽

Transition Rates ◽

Slow Axonal Transport ◽

Transport Velocity ◽

And Diffusion

This paper develops a simplified analytical solution for the slow axonal transport of tau proteins. A six kinetic state model developed in Jung and Brown [1] was used to simulate transport of tau. The model was extended by accounting for tau degradation and diffusion in the off-track kinetic states. The analytical solution was obtained by assuming that transitions between anterograde and retrograde states are infrequent. This assumption was validated through an analysis of the sensitivity of the solution to changes in the values of the two kinetic constants that describe the transition rates between the anterograde and retrograde states, and by a comparison with the experimentally measured tau distributions reported in Konzack et al. [2]. The predicted average transport velocity of tau was also in the experimentally reported range.

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Analytical and Numerical Study of Soret and Dufour Effects on Thermosolutal Convection in a Horizontal Brinkman Porous Layer with a Stress-Free Upper Boundary

Mathematical Problems in Engineering ◽

10.1155/2020/4046570 ◽

2020 ◽

Vol 2020 ◽

pp. 1-17

Author(s):

Ismail Filahi ◽

Mohamed Bourich ◽

Mohammed Hasnaoui ◽

Abdelkhalek Amahmid

Keyword(s):

Mass Transfer ◽

Analytical Solution ◽

Heat And Mass Transfer ◽

Porous Layer ◽

Parallel Flow ◽

Thermosolutal Convection ◽

Flow Intensity ◽

And Diffusion ◽

Buoyancy Ratio ◽

Upper Boundary

In this paper, thermo-diffusion (Soret effect) and diffusion-thermo (Dufour effect) effects on double-diffusive natural convection induced in a horizontal Brinkman porous layer with a stress-free upper boundary are investigated. The cavity is filled with a binary fluid and subjected to uniform fluxes of heat and mass on its long sides. An analytical solution based on the parallel flow approximation is developed for the problem considered in order to allow prompt determination of the thresholds of stationary and finite amplitude solutions and also heat and mass transfer characteristics. The analytical solution is validated numerically by using a finite difference method. The combined effects of the Soret and Dufour parameters, the thermal Rayleigh number, the buoyancy ratio, and the Darcy number on the flow intensity and heat and mass transfer are illustrated graphically, and some particular behaviors observed are discussed. The analytical solution proves the existence of different regions in the buoyancy ratio-Dufour parameter plane, corresponding to different parallel flow behaviors. The number, the location, and the extent of these regions, which are impossible to predict numerically, depend strongly on Soret and Dufour parameters. The effect of thermo-diffusion and diffusion-thermo on flow intensity and heat and mass transfer is found to be important.

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