Calculating the Fickian diffusivity for a lattice-based random walk with agents and obstacles of different shapes and sizes

Random walk models are often used to interpret experimental observations of the motion of biological cells and molecules. A key aim in applying a random walk model to mimic an in vitro experiment is to estimate the Fickian diffusivity (or Fickian diffusion coefficient),D. However, many in vivo experiments are complicated by the fact that the motion of cells and molecules is hindered by the presence of obstacles. Crowded transport processes have been modeled using repeated stochastic simulations in which a motile agent undergoes a random walk on a lattice that is populated by immobile obstacles. Early studies considered the most straightforward case in which the motile agent and the obstacles are the same size. More recent studies considered stochastic random walk simulations describing the motion of an agent through an environment populated by obstacles of different shapes and sizes. Here, we build on previous simulation studies by analyzing a general class of lattice-based random walk models with agents and obstacles of various shapes and sizes. Our analysis provides exact calculations of the Fickian diffusivity, allowing us to draw conclusions about the role of the size, shape and density of the obstacles, as well as examining the role of the size and shape of the motile agent. Since our analysis is exact, we calculateDdirectly without the need for random walk simulations. In summary, we find that the shape, size and density of obstacles has a major influence on the exact Fickian diffusivity. Furthermore, our results indicate that the difference in diffusivity for symmetric and asymmetric obstacles is significant.

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Laboratory Test Methods For The Evaluation Of Flammability Of Polymers

Combustion is a complex phenomena involving a multiplicity of variables. Some important variables measured in flame tests follow [1]. In order to characterize ignition, such related parameters as ignition time, ease of ignition, flash ignition temperature, and self-ignition temperature are measured. For studying the propagation of the flame, parameters such as distance burned or charred, area of flame spread, time of flame spread, burning rate, charred or melted area, and fire endurance are measured. Smoke characteristics are studied by determining such parameters as specific optical density, maximum specific optical density, time of occurrence of the densities, maximum rate of density increase, visual obscuration time, and smoke obscuration index. In addition to the above variables, there are a number of specific properties of the combustible system which could be measured. These are soot formation, toxicity of combustion gases, heat of combustion, dripping phenomena during the burning of thermoplastics, afterglow, flame intensity, fuel contribution, visual characteristics, limiting oxygen concentration (OI), products of pyrolysis and combustion, and so forth. A multitude of flammability tests measuring one or more of these properties have been developed [2]. Admittedly, no one small scale test is adequate to mimic or assess the performance of a plastic in a real fire situation. The conditions are much too complicated [3, 4]. Some conceptual problems associated with flammability testing of polymers have been reviewed [5, 6].

Size effect on the lattice parameter of KCl during mechanical milling

The size effect on the lattice parameter of ionic KCl nanocrystals was studied systematically during mechanical milling of Pure KCl powder under vacuum. The results suggest anomalous lattice expansion, with the lattice parameter increasing from 6.278 angstrom at d = 6 mu m to 6.30307 angstrom at d = 85 mn. The defects generated during ball milling of KCl and surface stress are deemed to be responsible for this lattice parameter expansion. (C) 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

A simple and inexpensive technique to study the flammability of polymers

A simple and inexpensive technique is described for the study of flammability of polymers, wherein the samples can be weighed continuously during their combustion in controlled atmosphere. The mass versus time curves for burning and quenching process in polystyrene samples are discussed. The experimental data indicates the efficiency of Monoammonium phosphate and ammonium halides in quenching of polystyrene.

Proton Spin-Lattice Relaxation in Sodium Ammonium Selenate Dihydrate:NaNHaSeOa.2He0

Proton spin-lattice relaxation studies in sodium ammonium selenate dihydrate carried out in the temperature range 130 to 300 K at 10 MHz show a continuous change in T, at T, indicating a second order phase transition. This compound is a typical case of a highly hindered solid wherein the thermally activated reorientations of ammonium ions freeze well above 77 K, as seen by NMR.Untersuchimgen der Protonen-Spin-Gitter-Relaxation in Natriuni-Ammoniumselenat-Dihydrat bei 10 MHz im Temperaturbereich 130 bis 300 K zeigen eine kontinuierliche Andernng in TI bei T, und ergeben einen Phasenubergang zweiter Art. Diese Verbindung ist ein typischer Fall eines stark ,,behinderten" Festkarpers, in dein die thermisch aktivierten Reorientierungen der Ammoniumionen weit oberhalb 77 H einfrieren, wie die NMR-Ergebnisse zeigen.

Superhydrophobic Polymers

Superhydrophobic polymers are particularly attractive materials, as they combine low cost, ease of processing, and compatibility with a variety of applications. Surfaces that display the Cassie–Baxter wetting state are particularly attractive for their self-cleaning properties. In this chapter, a brief overview of the wetting principles will be followed by an account of several techniques currently used to impart superhydrophobicity onto polymer surfaces. Surface roughness and surface structure will be the focus of this chapter, with an emphasis on topographies that exhibit microscale or nanoscale features arranged in hierarchical order.

Pyrrolidine ring conformations in prolyl peptides from 13C spin-lattice relaxation times

A method was developed in the framework of a bistable jump model to obtain the pyrrolidine ring conformations in proline peptides from 13C spin-lattice relaxation times. Equations are presented expressing the ring torsions in terms of the 13C spin-lattice relaxation times of the ring carbons. This method was applied to 26 pyrrolidine ring systems and acceptable conformations were obtained.

Effect of Molecular Weight on the Thermal and Impact Sensitivity of Polymers in Propellants

Abstract is not available.

Synthesis, characterization, thermal degradation, and comparative chain dynamics studies of weak-link polysulfide polymers

Synthesis, spectroscopic and thermal characterization of two new classes of polysulfide polymers: poly[1(phenoxymethyl) ethylene polysulfide] (PPMEP), and poly [1-(phenoxy) ethylene polysulfide] (PPEP) is presented. The direct pyrolysis mass spectrometry (DP-MS) technique, used to study the thermal degradation behavior of these polysulfide polymers, indicated that the polymers underwent degradation through the weak-links scission. The thermal stability of the polysulfide polymers decreased as the ``rank'' (number of sulfur atoms in the polysulfide linkage; n=1, 2, 4) increased. The main-chain flexibility of these polysulfide polymers in terms of their C-13 NMR spinlattice relaxation time (T-1) measurements on the backbone methine (-CH-) and methylene (-CH2-) carbons are reported here for the first time. A comparative study of the solution chain dynamics indicated that it increased as ``rank'' of the polysulfide linkages decreased as well as by introducing side chain spacers such as, ether (-O-) or methyleneoxy (-CH2O-) groups.

Large Low-Frequency Fluctuations in the Velocity of a Driven Vortex Lattice in a Single Crystal of 2H-NbSe2 Superconductor

The driven state of a well-ordered flux line lattice in a single crystal of 2H-NbSe2 in the time domain has revealed the presence of substantial fluctuations in velocity, with large and distinct time periods (similar to seconds). A superposition of a periodic drive in the driven vortex lattice causes distinct changes in these fluctuations. We propose that prior to the onset of the peak effect there exists a heretofore unexplored regime of coherent dynamics, with unexpected behavior in velocity fluctuations.

Origin of activation of Lattice Oxygen and Synergistic Interaction in Bimetal-Ionic Ce0.89Fe0.1Pd0.01O2-delta Catalyst

Flourite-type nanocrystalline Ce0.9Fe0.1O2-delta and Ce0.89Fe0.1Pd0.01O2-delta solid solutions have been synthesized by solution combustion method,'.which show higher oxygen storage/release property (OSC) compared to CeO2 and Ce0.8Zr0.2O2. Temperature programmed reduction an XPS study reveal that the presence of Pd ion in Ce0.9Fe0.1O2-delta facilitates complete reduction of Fe3+ to Fe2+ state and partial reduction of Ce4+ to Ce3+ state at.temperatures as low as 105 degrees C compared to 400 degrees C for monometal-ionic Ce0.9Fe0.1O2-delta. Fe3+ ion is reduced to Fe2+ and not to Feo due to favorable redox potential for Ce4+ + Fe2+ -> Ce3+ + Fe3+ reaction. Using first-principles density functional theory calculation we determine M-O (M = Pd, Fe, Ce) bond lengths, and find that bond lengths vary from shorter (2.16 angstrom) to longer (2.9 angstrom) bond distances compared to mean Ce-O bond distance of 2.34 angstrom. for CeO2. Using these results in bond valence analysis, we show that oxygen with bond valences as low as -1.55 are created, leading to activation of lattice oxygen in the bimetal ionic catalyst. Temperatures of CO oxidation and NO reduction by CO/H-2 are lower with the bimetalionic Ce0.89Fe0.1Pd0.01O2-delta catalyst compared to monometal-ionic Ce0.9Fe0.1O2-delta and Ce0.99Pd0.01O2-delta catalysts. From XPS studies of Pd impregnated on CeO2 and Fe2O3 oxides, we show that the synergism leading to low temperature activation of lattice oxygen in bimetal-ionic catalyst Ce0.89Fe0.1Pd0.01O2-delta is due to low-temperature reduction of Pd2+ to Pd-0, followed by Pd-0 + 2Fe(3+) -> Pd2+ + 2Fe(2+), Pd-0 + 2Ce(4+) -> Pd2+ + 2Ce(3+) redox reaction.