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This study focuses on the derivation of a general effective diffusion coefficient to describe the twodimensional (2D) diffusion in a narrow and smoothly asymmetric channel of varying width that lies on a curved surface, in the simple diffusional motion of noninteracting point-like particles under no external field. To this end we extend the generalization of the Kalinay-Percus’ projection method [J. Chem. Phys. 122, 204701 (2005); Phys. Rev. E 74, 041203 (2006)] for the asymmetric channels introduced in [J. Chem. Phys. 137, 024107 (2012)], to project the anisotropic 2D diffusion equation on a smooth curved manifold into an effective one-dimensional generalized Fick-Jacobs equation which is modified due to the curvature of the surface. The lowest order in the perturbation parameter, corresponding to the Fick-Jacobs equation, contains an extra term that accounts for the curvature of the surface. We found explicitly the first order correction for the invariant effective concentration, which is defined as the correct marginal concentration in one variable, and we obtain the first approximation to the effective diffusion coefficient analogous to Bradley’s coefficient [Phys. Rev. E 80, 061142 (2009)] as a function of metric elements of the surface. Straightforwardly we study the perturbation series up to the n-th order, and we derive the full effective diffusion coefficient for 2D diffusion in a narrow asymmetric channel, which have modifications due to the curved metric. Finally, as an example we show how to use our formula to calculate the effective diffusion coefficient considering the case of an asymmetric conical channel embedded on a torus.

We numerically investigate random walks (RWs) and self-avoiding random walks (SAWs) on critical percolation clusters, basic models for diffusion and flexible polymers in disordered media. While this can be easily done for RWs using a simple enumeration method, it is difficult for long SAWs due to the long-range correlations. We employed a sophisticated algorithm that makes use of the self-similar structure of the critical clusters and allows exact enumeration of several thousand SAW steps. We also investigate a kinetic version of the SAW, the so-called kinetic growth (self-avoiding) walk (KGW), as well static averaging over all RW conformations, which describes the so-called ideal chain. For the KGW, we use a chain-growth Monte Carlo method which is inspired by the pruned-enriched Rosenbluth method. The four walk types are found to be affected in different ways by the fractal, disordered structure of the critical clusters. The simulations were carried out in two and three dimensions.

A method for rapid characterization of emulsions is presented. From the proposed setup we are able to measure the droplet size distribution of brine or water droplets confined by an oil phase, even though there is complete overlap in relaxation times and/or molecular mobility between the water and the oil phases. A PFG-NMR sequence is presented that applies the spoiler recovery method for significant reduction in acquisition time, and the method is used for rapid characterization of emulsions.

Traditional bead-spring models of the polymer dynamics are based on the Einstein theory of the Brownian motion (BM), valid only at the times much larger than the particle´s relaxation time. The reason is in neglecting the inertial and memory effects in the dynamics. In the present work we use a generalized theory of the BM to build models of the dynamics of flexible polymers in dilute solution. The equations of motion for the polymer segments include the friction force that follows from the linearized Navier-Stokes hydrodynamics. It has a form of a memory integral. To get a correct description of the short-time dynamics, inertial effects are included into the consideration. For negligible hydrodynamic interactions (HI) between the beads the motion of the polymer center of mass is not influenced by internal forces within the chain and has been considered exactly. Then we include the HI int the description of motion of chains, which are assumed Gaussian in equilibrium. Analytical solutions for the observable time correlation functions describing the movement of the polymer coils significantly differ from the classical results showing, in particular, algebraic long-time tails and ballistic motion at short times.

The paper analyses afresh the data of Russell and Hastings on the changes in lattice parameter during post-irradiation annealing of copper-boron alloy in the temperature range 823-923 K. The changes in lattice parameter are brought about by the generation of helium during irradiation through (n, α) reaction and its subsequent behavior during annealing. The new analytical procedure adopted here follows chemical kinetics route to determine the appropriate activation energies associated with the rate processes controlling the changes in lattice parameter. During the first stage of annealing, the lattice parameter decreases to a value which is below the equilibrium one. The second stage involves the recovery of lattice parameter to the equilibrium value. The diffusion of monovacancy and the jump of helium atom to vacancy on its nearest neighbor site are identified as the unit processes for the first and second stages of annealing respectively. Finally, it is suggested that a helium–monovacancy complex may act as nucleus for the formation of helium gas bubbles.

The present paper involves application of nondestructive radioactive tracer technique in characterization of Dowex 550A LC and Indion-820 anion exchange resins. The characterization study was based on kinetic of exchange reactions between inactive iodide/bromide ions on the resins with radioactive iodide/bromide ions in the solution. During iodide exchange reaction performed at a constant temperature of 40.00C, using 1.000 g of ion exchange resins and labeled iodide ion solution of concentration 0.003 mol/L, for Dowex 550A LC resin the specific reaction rate and initial rate of ion exchange was 0.271 min-1 and 0.141 mmol/min respectively, while the amount of iodide ions exchanged was 0.522 mmol, and log Kd was calculated to be 12.1. The above values calculated for Dowex 550A LC resin was higher than the respective values of 0.108, 0.330, 0.036 and 6.0 as obtained for Indion-820 resins. Similar results were obtained for the two resins during bromide exchange reactions, thereby indicating superior performance of Dowex 550A LC resin over Indion-820 resins.

The estimation of axon radius provides insights into brain function [1] and could provide progression and classification biomarkers for a number of white matter diseases [2-4]. A recent in silico study [5] has shown that optimised gradient waveforms (GEN) and oscillating gradient waveform spin echo (OGSE) have increased sensitivity to small axon radius compared to pulsed gradient spin echo (PGSE) diffusion MR sequences. In a follow-up study [6], experiments with glass capillaries show the practical feasibility of GEN sequences and verify improved pore-size estimates. Here, we compare PGSE with sine, sine with arbitrary phase, and square wave OGSE (SNOGSE, SPOGSE, SWOGSE, respectively) for axon radius mapping in the corpus callosum of a rat, ex-vivo. Our results suggest improvements in pore size estimates from OGSE over PGSE, with greatest improvement from SWOGSE, supporting theoretical results from [5] and other studies [7-9].