scholarly journals Exact Universal Excitation Waveform for Optimal Enhancement of Directed Ratchet Transport

2021 ◽  
Vol 31 (07) ◽  
pp. 2150109
Author(s):  
Ricardo Chacón ◽  
Pedro J. Martínez
Keyword(s):  
Numerical Experiments ◽  
Average Velocity ◽  
Periodic Potential ◽  
Brownian Particle ◽  
Half Period ◽  
Time Integral ◽  
Excitation Waveform

We show the existence and properties of an exact universal excitation waveform for optimal enhancement of directed ratchet transport (in the sense of the average velocity) by providing three alternative derivations. Specifically, it is deduced from the criticality scenario giving rise to ratchet universality as well as from an approach based on Fokker–Planck’s equation. Numerical experiments confirmed the existence of such exact universal excitation waveform in the context of a driven overdamped Brownian particle subjected to a periodic potential. While the universality scenario holds regardless of the waveform of the periodic vibratory excitations involved, it is shown that the enhancement of directed ratchet transport is optimal when the impulse transmitted by those excitations (time integral over a half-period) is maximum.

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.

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.

scholarly journals Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

2013 ◽  
Vol 13 (2) ◽  
pp. 502-525 ◽  
Author(s):  
Adérito Araújo ◽  
Amal K. Das ◽  
Cidália Neves ◽  
Ercília Sousa
Keyword(s):  
Diffusion Equation ◽  
Periodic Potential ◽  
Space Dimension ◽  
Numerical Solutions ◽  
Brownian Particle ◽  
Particle Density ◽  
Mean Square Displacement ◽  
Hyperbolic Type ◽  
Fickian Diffusion ◽  
Spatial Shape

AbstractNumerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and mean-square-displacement (covering both inertial and diffusive regimes) are presented.

Phase induced transport of a Brownian particle in a periodic potential in the presence of an external noise: A semiclassical treatment

2011 ◽  
Vol 52 (7) ◽  
pp. 073302 ◽  
Author(s):  
Satyabrata Bhattacharya ◽  
Sudip Chattopadhyay ◽  
Pinaki Chaudhury ◽  
Jyotipratim Ray Chaudhuri
Keyword(s):  
Periodic Potential ◽  
Brownian Particle ◽  
External Noise

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.

scholarly journals Nonlinear noninertial response of a Brownian particle in a tilted periodic potential to a strong ac force

2000 ◽  
Vol 61 (4) ◽  
pp. 4599-4602 ◽  
Author(s):  
W. T. Coffey ◽  
J. L. Déjardin ◽  
Yu. P. Kalmykov
Keyword(s):  
Periodic Potential ◽  
Brownian Particle
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