Shape Potential Effects on Transport and Diffusion Phenomena

2017 ◽  
Vol 16 (02) ◽  
pp. 1750011 ◽  
Author(s):  
A. M. Fopossi Mbemmo ◽  
G. Djuidjé Kenmoé ◽  
T. C. Kofané
Keyword(s):  
Diffusion Coefficient ◽  
Mean Square Displacement ◽  
Critical Force ◽  
Potential Shape ◽  
Brownian Particles ◽  
Normal Diffusion ◽  
Diffusion Phenomena ◽  
Transport And Diffusion ◽  
The Mean ◽  
And Diffusion

We investigate the diffusion of a particle subjected to a non-sinusoidal periodic potential and driven by an external constant force. To study the dynamic of the Brownian particles, we modify the shape of the potential as well as the temperature. This allows us to observe the dependence of the mean square displacement on the shape parameter as well as the diffusion coefficient. For a particular set of the system parameters, the dispersionless transport, normal diffusion and hyperdiffusion are generated in the system. We show that there exists a potential shape where some parameters of the system weakly affect the type of diffusion. The diffusion coefficient reaches its maximum around a critical value of the external field. This pronounced peak of the diffusion coefficient depends on the shape of the potential, so we have evaluated the critical force as a function of the potential features.

Non-Markovian effect of the fractional damping environment and Newton’s second law of motion

2018 ◽  
Vol 32 (19) ◽  
pp. 1850210
Author(s):  
Chun-Yang Wang ◽  
Zhao-Peng Sun ◽  
Ming Qin ◽  
Yu-Qing Xu ◽  
Shu-Qin Lv ◽  
...  
Keyword(s):  
Diffusion Process ◽  
Mean Square Displacement ◽  
Dynamical Analysis ◽  
Second Law ◽  
Mean Square ◽  
Fractional Damping ◽  
Dynamical Mechanism ◽  
Brownian Particles ◽  
The Mean ◽  
Dissipative Environments

We report, in this paper, a recent study on the dynamical mechanism of Brownian particles diffusing in the fractional damping environment, where several important quantities such as the mean square displacement (MSD) and mean square velocity are calculated for dynamical analysis. A particular type of backward motion is found in the diffusion process. The reason of it is analyzed intrinsically by comparing with the diffusion in various dissipative environments. Results show that the diffusion in the fractional damping environment obeys the Langevin dynamics which is quite different form what is expected.

scholarly journals Modeling Anomalous Diffusion by a Subordinated Integrated Brownian Motion

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Long Shi ◽  
Aiguo Xiao
Keyword(s):  
Brownian Motion ◽  
Continuous Time ◽  
Waiting Times ◽  
Mean Square Displacement ◽  
Mean Square ◽  
Weak Ergodicity ◽  
Normal Diffusion ◽  
Weak Ergodicity Breaking ◽  
The Mean ◽  
Ergodicity Breaking

We consider a particular type of continuous time random walk where the jump lengths between subsequent waiting times are correlated. In a continuum limit, the process can be defined by an integrated Brownian motion subordinated by an inverse α-stable subordinator. We compute the mean square displacement of the proposed process and show that the process exhibits subdiffusion when 0<α<1/3, normal diffusion when α=1/3, and superdiffusion when 1/3<α<1. The time-averaged mean square displacement is also employed to show weak ergodicity breaking occurring in the proposed process. An extension to the fractional case is also considered.

scholarly journals A molecular dynamics study on the diffusion and imprint ability of spectinomycin under different sizes of aniline oligomers

2022 ◽  
Author(s):  
Chanadan Douykhumklaw ◽  
Thana Sutthibutpong
Keyword(s):  
Molecular Dynamics ◽  
Diffusion Coefficient ◽  
Mean Square Displacement ◽  
Md Simulations ◽  
Template Molecule ◽  
Aniline Oligomers ◽  
The Mean ◽  
The Stability ◽  
Further Development ◽  
Aniline Oligomer

Abstract Molecularly imprinted polymers (MIP) are the polymers created by molecular imprinting techniques that leave cavities for the specific interactions with a template molecule, and have been applied in molecular selectivity tasks. In this study, the molecular dynamics (MD) simulation technique was used to demonstrate that aniline oligomer could be developed as a potential MIP for detection and separation of the spectinomycin drug molecule for gonorrhoea treatment. MD simulations were performed for the systems of a spectinomycin within aniline oligomers of different sizes. The mean square displacement (MSD) and the diffusivity calculated from MD simulations showed that the diffusion coefficient was significantly dropped when the length of aniline oligomer was greater than two. The diffusion coefficient of spectinomycin became the lowest within aniline trimers, corresponded to the highest atomic distribution of MIP around the template. Then, the specific cavity in MIP systems with and without spectinomycin were calculated to assess the stability of the cavity created by the template. The volume of a cavity created within the trimer system was closest to the spectinomycin volume, and therefore became the optimal oligomer size for further development of MIP.

scholarly journals Unbiased Diffusion through a Linear Porous Media with Periodic Entropy Barriers: A Tube Formed by Contacting Ellipses

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yoshua Chávez ◽  
Marco-Vinicio Vázquez ◽  
Leonardo Dagdug
Keyword(s):  
Diffusion Coefficient ◽  
Cross Section ◽  
Effective Diffusion Coefficient ◽  
Effective Diffusion ◽  
Radial Symmetry ◽  
Computational Simulations ◽  
One Dimensional ◽  
Brownian Particles ◽  
Mathematical Expressions ◽  
The Mean

This work is devoted to the study of unbiased diffusion of point-like Brownian particles through channels with radial symmetry of varying cross-section and elliptic shape. The effective one-dimensional reduction is used with distinct forms of a position-dependent diffusion coefficient,D(x), found in literature, to obtain expressions for (I) narrow escape times from a single open-ended tube, (II) its correspondent effective diffusion coefficient, both as functions of the eccentricity of the tube,ε, whereε= 0 returns the system to a spherical vesicle with two open opposite sides, and (III) finally, Lifson-Jackson formula that is used to compute expressions to assess the mean effective diffusion coefficient for a periodic elliptic channel formed by contacting ellipses, also as a function of the eccentricity. Mathematical expressions are presented and contrasted against computational simulations to validate them.

Transport and diffusion of Brownian particles in a tilted deformable potential

2020 ◽  
Vol 541 ◽  
pp. 123284
Author(s):  
M.F. Kepnang Pebeu ◽  
R.L. Woulaché ◽  
C.B. Tabi ◽  
T.C. Kofane
Keyword(s):  
Brownian Particles ◽  
Transport And Diffusion ◽  
And Diffusion

ON GENERATING RANDOM POTENTIALS

2012 ◽  
Vol 11 (04) ◽  
pp. 1250026 ◽  
Author(s):  
M. SUÑÉ SIMON ◽  
J. M. SANCHO ◽  
A. M. LACASTA
Keyword(s):  
Real Space ◽  
Fourier Space ◽  
Random Potentials ◽  
Practical Applications ◽  
Gaussian Potential ◽  
Brownian Particles ◽  
Straightforward Method ◽  
Transport And Diffusion ◽  
Potential Landscape ◽  
And Diffusion

The study of transport and diffusion of Brownian particles in disorder media needs the generation of random potentials with well prescribed statistical properties. Here we present a straightforward method to build a Gaussian potential landscape with an arbitrary spatial correlation with the only requirement of isotropy. The method has the particularity that, although it uses the Fourier space, all its constraints and information are in real space. As practical applications we construct three types of Gaussian disordered correlations: Normal, exponential and power-law. These three cases cover a variety of physical situations.

WEAK DISORDER IN PERIODIC POTENTIALS: ANOMALOUS TRANSPORT AND DIFFUSION

2012 ◽  
Vol 11 (01) ◽  
pp. 1240004 ◽  
Author(s):  
KATJA LINDENBERG ◽  
J. M. SANCHO ◽  
M. KHOURY ◽  
A. M. LACASTA
Keyword(s):  
Periodic Potential ◽  
Model Parameters ◽  
Weak Disorder ◽  
Periodic Potentials ◽  
Normal Diffusion ◽  
Random Components ◽  
Transport And Diffusion ◽  
And Diffusion ◽  
Deterministic Force ◽  
Pronounced Peak

Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around the critical deterministic force that defines the transition between locked and running states. It has recently been shown both experimentally and numerically that this peak is greatly enhanced if some amount of spatial disorder is superimposed on the periodic potential. Here, we show that this enhancement is a fingerprint of a broad phenomenology that goes well beyond a simple augmentation. For some values of the model parameters, including the characteristic distances associated with the periodic and random components of the potential, the magnitude of the external force, and the temperature, the system can exhibit a rich variety of regimes from normal diffusion to superdiffusion, subdiffusion and even subtransport.

scholarly journals VIRIAL THEOREM FOR ROTATING SELF-GRAVITATING BROWNIAN PARTICLES AND TWO-DIMENSIONAL POINT VORTICES

2012 ◽  
Vol 26 (12) ◽  
pp. 1241002 ◽  
Author(s):  
PIERRE-HENRI CHAVANIS
Keyword(s):  
Virial Theorem ◽  
Mean Square Displacement ◽  
Point Vortices ◽  
Mean Square ◽  
Two Dimensional ◽  
Exact Analytical Expression ◽  
Brownian Particles ◽  
The Mean ◽  
Gravitating Systems ◽  
Interacting Brownian Particles

We derive the virial theorem for an overdamped system of rotating self-gravitating Brownian particles. We show that, in the two-dimensional case, it takes a closed form that can be used to obtain general results about the dynamics without being required to solve the Smoluchowski–Poisson system explicitly. In particular, we obtain the exact analytical expression of the mean square displacement 〈r2〉(t) of the interacting Brownian particles. We exhibit a critical temperature below which the system collapses, and above which it evaporates, and we determine how this temperature is affected by a solid rotation. We also develop an analogy between self-gravitating systems and two-dimensional point vortices. We derive a virial-like relation for point vortices at statistical equilibrium relating the angular velocity to the angular momentum and the temperature.

THE EFFECTS OF QUENCHED DISORDER ON THE CHAOTIC DIFFUSION FOR SIMPLE MAPS

1999 ◽  
Vol 13 (01) ◽  
pp. 83-95 ◽  
Author(s):  
HSEN-CHE TSENG ◽  
HUNG-JUNG CHEN
Keyword(s):  
Initial Conditions ◽  
Mean Square Displacement ◽  
Quenched Disorder ◽  
Mean Square ◽  
Numerical Errors ◽  
Limited Sampling ◽  
Chaotic Diffusion ◽  
Normal Diffusion ◽  
The Mean ◽  
Diffusive Processes

That both normal and anomalous chaotic diffusions are suppressed by the presence of quenched disorder for a large class of maps was established by G. Radons.1 In this paper, we consider simple maps (which exhibit normal diffusion) modified by discrete disorder. By decomposing the mean square displacement (MSD) σ2(t) of the system into three terms, namely, [Formula: see text], we find that the MSD of the random walk which corresponds to disorder, [Formula: see text], enhances that of the original unmodified map, [Formula: see text] and that the term 2σ01(t), which describes the correlation between the diffusion fronts of the previous two diffusive processes, just essentially cancels the sum of [Formula: see text] and [Formula: see text]. In consequence, the trajectories of the system are effectively localized. In this formalism, exact numerical calculations without any round-off error can be achieved, the numerical errors coming only from the limited sampling of the initial conditions.

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