scholarly journals DIFFUSIVE TRANSPORT IN PERIODIC POTENTIALS: UNDERDAMPED DYNAMICS

2008 ◽  
Vol 08 (02) ◽  
pp. L155-L173 ◽  
Author(s):  
G. A. Pavliotis ◽  
A. Vogiannou
Keyword(s):  
Diffusion Coefficient ◽  
Periodic Potential ◽  
Diffusion Tensor ◽  
Brownian Particle ◽  
One Dimension ◽  
Diffusive Transport ◽  
Periodic Potentials ◽  
Arbitrary Dimensions ◽  
Higher Order Corrections ◽  
Rigorous Method

In this paper we present a systematic and rigorous method for calculating the diffusion tensor for a Brownian particle moving in a periodic potential which is valid in arbitrary dimensions and for all values of the dissipation. We use this method to obtain an explicit formula for the diffusion coefficient in one dimension which is valid in the underdamped limit, and we also obtain higher order corrections to the Lifson-Jackson formula for the diffusion coefficient in the overdamped limit. A numerical method for calculating the diffusion coefficient is also developed and is shown to perform extremely well for all values of the dissipation.

OPTIMAL DIFFUSIVE TRANSPORT IN A TILTED PERIODIC POTENTIAL

2001 ◽  
Vol 01 (01) ◽  
pp. R25-R39 ◽  
Author(s):  
BENJAMIN LINDNER ◽  
MARCIN KOSTUR ◽  
LUTZ SCHIMANSKY-GEIER
Keyword(s):  
Diffusion Coefficient ◽  
Numerical Solution ◽  
Periodic Potential ◽  
Brownian Particle ◽  
Planck Equation ◽  
Diffusive Transport ◽  
Noise Strength ◽  
Diffusive Motion ◽  
Potential Mapping ◽  
Cumulative Process

We study the diffusive motion of an overdamped Brownian particle in a tilted periodic potential. Mapping the continuous dynamics onto a discrete cumulative process we find exact expressions for the diffusion coefficient and the Péclet number which characterize the transport. At a sufficiently strong but subcritical bias an optimized transport with respect to the noise strength is observed. These results are confirmed by numerical solution of the Fokker-Planck equation.

Enhanced Diffusion in a Model of Molecular Motors with Potential Switching

2019 ◽  
Vol 18 (02) ◽  
pp. 1940005 ◽  
Author(s):  
Ryota Shinagawa ◽  
Kazuo Sasaki
Keyword(s):  
Diffusion Coefficient ◽  
External Force ◽  
Molecular Motors ◽  
Periodic Potential ◽  
Brownian Particle ◽  
Molecular Motor ◽  
Free Diffusion ◽  
Enhanced Diffusion ◽  
Additional Peak ◽  
Diffusion Enhancement

Diffusion enhancement is a phenomenon in which the diffusion coefficient of a system is increased by an external force and it becomes larger than that of the force-free diffusion in thermal equilibrium. It is known that this phenomenon occurs for a Brownian particle in a periodic potential under a constant external force. Recently, it was found that diffusion enhancement also occurred in a biological molecular motor, whose moving part could move itself by switching the potentials generated by the other parts. It was shown that the diffusion coefficient exhibited peaks as a function of a constant external force. Here, we report the occurrence of an additional peak and investigate the condition governing its appearance.

Surface diffusion of a Brownian particle subjected to an external harmonic noise

2017 ◽  
Vol 31 (12) ◽  
pp. 1750082 ◽  
Author(s):  
Zhan-Wu Bai ◽  
Li-Ping Ding
Keyword(s):  
Diffusion Coefficient ◽  
Periodic Potential ◽  
Brownian Particle ◽  
Gaussian White Noise ◽  
Linear Functions ◽  
Potential Force ◽  
Negative Power ◽  
Absolute Value ◽  
Langevin Simulation ◽  
Harmonic Noise

Langevin simulation is performed to investigate the diffusion coefficient of a Brownian particle subjected to an external harmonic noise in a two-dimensional coupled periodic potential. Resonant diffusion phenomenon is observed as a result of the coupling between the central frequency of the spectral density of the harmonic noise and the frequency of the potential well bottom. The diffusion coefficient presents approximately linear functions of the strengths of the internal and external noises for low values of the strengths, these functions can be understood by the local linearization approximation of the potential force. The damping coefficient dependence of the diffusion coefficient in lower damping is well fitted by a negative power function, as an internal Gaussian white noise case does, but with a power whose absolute value is larger than 1.

ACCELERATION OF DIFFUSION IN SUBCRITICALLY TILTED PERIODIC POTENTIALS

2005 ◽  
Vol 05 (02) ◽  
pp. L283-L290 ◽  
Author(s):  
NIKOLAY AGUDOV ◽  
ALEXEY SAFONOV
Keyword(s):  
Diffusion Coefficient ◽  
Brownian Particle ◽  
Effective Diffusion ◽  
Potential Profile ◽  
Linear Potential ◽  
Potential Wells ◽  
Potential Barriers ◽  
Periodic Potentials ◽  
Independent Variation ◽  
Shape Of Potential

We study the enhancement of effective diffusion coefficient of an overdamped Brownian particle in tilted periodical potential profile. For analysis we use the model piece-wise linear potential, where independent variation of the potential profile parameters (such as height and width of potential barriers, width of potential wells and period of potential profile) is possible. This approach allows to investigate the influence of potential profile shape on the conditions for the diffusion acceleration, maximal value of the diffusion coefficient, values of noise intensity and the tilt for which the maximum occurs. For the large barriers and subcritical tilt the results are generalized for arbitrary shape of potential profile.

Directed Transport in Symmetrically Periodic Potentials Induced by Cross-Correlation among Colored Gaussian Noises

2019 ◽  
Vol 20 (2) ◽  
pp. 105-114
Author(s):  
Igor Alexandrovich Knyaz’
Keyword(s):  
Correlation Time ◽  
Cross Correlation ◽  
Periodic Potential ◽  
Brownian Particle ◽  
System Parameters ◽  
Directed Transport ◽  
Periodic Potentials ◽  
Spatially Periodic ◽  
Correlation Parameters

AbstractWe study the noise induced directed transport of an inertial Brownian particle moving in a symmetric spatially periodic potential and is subjected to correlated colored noises. Under the assumption of small correlation times of colored fluctuations we obtain an analytical expression for resulting current in overdamped systems. Our analytical and numerical calculations indicate the directed current is controlled by the correlation parameters. It has been pointed out that the nonzero correlation time makes an important contribution to current only at large enough values of noise intensities. The role of other system parameters is investigated from the viewpoint of optimization the current amplitude.

Diffusion tensor imaging reveals microstructural differences between subtypes of trigeminal neuralgia

2020 ◽  
Vol 133 (2) ◽  
pp. 573-579 ◽  
Author(s):  
Matthew S. Willsey ◽  
Kelly L. Collins ◽  
Erin C. Conrad ◽  
Heather A. Chubb ◽  
Parag G. Patil
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Tensor Imaging ◽  
Trigeminal Neuralgia ◽  
Apparent Diffusion Coefficient ◽  
Diffusion Tensor ◽  
Statistical Significance ◽  
Region Of Interest ◽  
Pain Syndrome ◽  
Radial Diffusivity ◽  
Apparent Diffusion

OBJECTIVETrigeminal neuralgia (TN) is an uncommon idiopathic facial pain syndrome. To assist in diagnosis, treatment, and research, TN is often classified as type 1 (TN1) when pain is primarily paroxysmal and episodic or type 2 (TN2) when pain is primarily constant in character. Recently, diffusion tensor imaging (DTI) has revealed microstructural changes in the symptomatic trigeminal root and root entry zone of patients with unilateral TN. In this study, the authors explored the differences in DTI parameters between subcategories of TN, specifically TN1 and TN2, in the pontine segment of the trigeminal tract.METHODSThe authors enrolled 8 patients with unilateral TN1, 7 patients with unilateral TN2, and 23 asymptomatic controls. Patients underwent DTI with parameter measurements in a region of interest within the pontine segment of the trigeminal tract. DTI parameters were compared between groups.RESULTSIn the pontine segment, the radial diffusivity (p = 0.0049) and apparent diffusion coefficient (p = 0.023) values in TN1 patients were increased compared to the values in TN2 patients and controls. The DTI measures in TN2 were not statistically significant from those in controls. When comparing the symptomatic to asymptomatic sides in TN1 patients, radial diffusivity was increased (p = 0.025) and fractional anisotropy was decreased (p = 0.044) in the symptomatic sides. The apparent diffusion coefficient was increased, with a trend toward statistical significance (p = 0.066).CONCLUSIONSNoninvasive DTI analysis of patients with TN may lead to improved diagnosis of TN subtypes (e.g., TN1 and TN2) and improve patient selection for surgical intervention. DTI measurements may also provide insights into prognosis after intervention, as TN1 patients are known to have better surgical outcomes than TN2 patients.

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