Leonardo Dagdug

Communications: Drift and diffusion in a tube of periodically varying diameter. Driving force induced intermittency

We show that the effect of driving force F on the effective mobility and diffusion coefficient of a particle in a tube formed by identical compartments may be qualitatively different depending on the compartment shape. In tubes formed by cylindrical (spherical) compartments the mobility monotonically decreases (increases) with F and the diffusion coefficient diverges (remains finite) as F tends to infinity. In tubes formed by cylindrical compartments, at large F there is intermittency in the particle transitions between openings connecting neighboring compartments.

Projection of two-dimensional diffusion in a curved midline and narrow varying width channel onto the longitudinal dimension

This study focuses on the derivation of a general effective diffusion coefficient to describe the two-dimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width, in the simple diffusional motion of noninteracting pointlike particles under no external field. We present a generalization to the case of an asymmetric channel using the projection method introduced earlier by Kalinay and Percus [J. Chem. Phys. 122, 204701 (2005); and Phys. Rev. E 74, 041203 (2006)] to project the 2D diffusion equation into an effective one-dimensional generalized Fick-Jacobs equation. The expression for the diffusion coefficient given in Eq. (23) is our main result. This expression is a more general effective diffusion coefficient for narrow channels in 2D, which contains the well-known previous results as special cases, namely, those obtained by Bradley [Phys. Rev. E 80, 061142 (2009)], and more recently by Berezhkovskii and Szabo [J. Chem. Phys. 135, 074108 (2011)]. Finally, we study some specific 2D asymmetric channel configurations to test and show the broader applicability of Eq. (23).

Effects of anisotropic optical properties on photon migration in structured tissues

It is often adequate to model photon migration in human tissue in terms of isotropic diffusion or random walk models. A nearly universal assumption in earlier analyses is that anisotropic tissue optical properties are satisfactorily modelled by using a transport-corrected scattering coefficient which then allows one to use isotropic diffusion-like models. In the present paper we introduce a formalism, based on the continuous-time random walk, which explicitly allows the diffusion coefficients to differ along the three axes. The corrections necessitated by this form of anisotropy are analysed in the case of continuous-wave and time-resolved measurements and for both reflectance and transmission modes. An alternate model can be developed in terms of a continuous-time random walk in which the times between successive jumps differ along the three axes, but is not included here.

TRANSIENT DIFFUSION IN A TUBE WITH DEAD ENDS

A particle diffusing in a tube with dead ends, from time to time enters a dead end, spends some time in the dead end, and then comes back to the tube. As a result, the particle spends in the tube only a part of the entire observation time that leads to slowdown of its diffusion along the tube. We study the transient diffusion in a tube with periodic identical dead ends formed by cavities of volume V(cav) connected to the tube by cylindrical channels of length L and radius a, which is assumed to be much smaller than the tube radius R and the distance l between neighboring dead ends. Assuming that the particle initial position is uniformly distributed over the tube, we analyze the monotonic decrease of the particle diffusion coefficient D(t) from its initial value D(0)=D, which characterizes diffusion in the tube without dead ends, to its asymptotic long-time value D(infinity)=D(eff)<D. We derive an expression for the Laplace transform of D(t), denoted by D(s), where s is the Laplace parameter. Although the expression is too complicated to be inverted analytically, we use it to find the relaxation time of the process as a function of the geometric parameters of the system mentioned above. To check the accuracy of our results, we ran Brownian dynamics simulations and found the mean squared displacement of the particle as a function of time by averaging over 5x10(4) realizations of the particle trajectory. The time-dependent mean squared displacement found in simulations is compared with that obtained by numerically inverting the Laplace transform of the mean squared displacement predicted by the theory, which is given by 2D(s)/s. Comparison shows excellent agreement between the two time dependences that support the approximations used when developing the theory.

Communication: Turnover behavior of effective mobility in a tube with periodic entropy potential

Using Brownian dynamics simulations, we study the effective mobility and diffusion coefficient of a point particle in a tube formed from identical compartments of varying diameter, as functions of the driving force applied along the tube axis. Our primary focus is on how the driving force dependences of these transport coefficients are modified by the changes in the compartment shape. In addition to monotonically increasing or decreasing behavior of the effective mobility in periodic entropy potentials reported earlier, we now show that the effective mobility can even be nonmonotonic in the driving force.

Unbiased diffusion in tubes with corrugated walls

This study is devoted to unbiased motion of a point Brownian particle in a tube with corrugated walls made of conical sections of a varying length. Effective one-dimensional description in terms of the generalized Fick-Jacobs equation is used to derive a formula which gives the effective diffusion coefficient of the particle as a function of the geometric parameters of the tube. Comparison with the results of Brownian dynamics simulations allows us to establish the domain of applicability of both the one-dimensional description and the formula for the effective diffusion coefficient.

Biased diffusion in tubes formed by spherical compartments

We study the effect of the driving force on brownian motion of a point particle in a tube formed by identical spherical compartments, which create periodic entropy potential for the motion along the tube axis. The focus is on (i) the effective mobility and diffusion coefficient of the particle as functions of the driving force, (ii) localization of the particle in the central part of the tube induced by the driving force, and (iii) transit time of the particle between the openings connecting neighboring compartments. Some of the results at very small and large driving force are obtained analytically, while the majority of the results are obtained from brownian dynamics simulations.

Discriminating between anomalous diffusion and transient behavior in microheterogeneous environments.

Diffusion in macrohomogeneous and microheterogeneous media can be described as effective free diffusion only at sufficiently long times. At intermediate times, the mean-square displacement of a diffusing object shows a transient behavior that can be misinterpreted as anomalous subdiffusion. We discuss how to discriminate between the two.

Diffusion in the presence of cylindrical obstacles arranged in a square lattice analyzed with generalized Fick-Jacobs equation

The generalized Fick-Jacobs equation is widely used to study diffusion of Brownian particles in three-dimensional tubes and quasi-two-dimensional channels of varying constraint geometry. We show how this equation can be applied to study the slowdown of unconstrained diffusion in the presence of obstacles. Specifically, we study diffusion of a point Brownian particle in the presence of identical cylindrical obstacles arranged in a square lattice. The focus is on the effective diffusion coefficient of the particle in the plane perpendicular to the cylinder axes, as a function of the cylinder radii. As radii vary from zero to one half of the lattice period, the effective diffusion coefficient decreases from its value in the obstacle free space to zero. Using different versions of the generalized Fick-Jacobs equation, we derive simple approximate formulas, which give the effective diffusion coefficient as a function of the cylinder radii, and compare their predictions with the values of the effective diffusion coefficient obtained from Brownian dynamics simulations. We find that both Reguera-Rubi and Kalinay-Percus versions of the generalized Fick-Jacobs equation lead to quite accurate predictions of the effective diffusion coefficient (with maximum relative errors below 4% and 7%, respectively) over the entire range of the cylinder radii from zero to one half of the lattice period.

Diffusion in periodic two-dimensional channels formed by overlapping circles: Comparison of analytical and numerical results

We study two-dimensional diffusion in a channel formed by periodic overlapping circles. Periodic variation of the channel width leads to the slowdown of diffusion along the channel axis. There are several approximate approaches, which allow one to analyze the slowdown. We use these approaches to derive five expressions for the effective diffusion coefficient of a point Brownian particle in the channel. To check the accuracy of the expressions we compare their predictions with the effective diffusion coefficient obtained from Brownian dynamics simulations.