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.

Modeling transport through an environment crowded by a mixture of obstacles of different shapes and sizes

Many biological environments are crowded by macromolecules, organelles and cells which can impede the transport of other cells and molecules. Previous studies have sought to describe these effects using either random walk models or fractional order diffusion equations. Here we examine the transport of both a single agent and a population of agents through an environment containing obstacles of varying size and shape, whose relative densities are drawn from a specified distribution. Our simulation results for a single agent indicate that smaller obstacles are more effective at retarding transport than larger obstacles; these findings are consistent with our simulations of the collective motion of populations of agents. In an attempt to explore whether these kinds of stochastic random walk simulations can be described using a fractional order diffusion equation framework, we calibrate the solution of such a differential equation to our averaged agent density information. Our approach suggests that these kinds of commonly used differential equation models ought to be used with care since we are unable to match the solution of a fractional order diffusion equation to our data in a consistent fashion over a finite time period.

Different energy sources for three symbiont-dependent bivalve molluscs at the Lagatchve hydrothermal site (Mid Atlantic Ridge)

The vent mussel Bathymodiolus puteoserpentis, a large vesicomyid clam and a smaller thyasirid were collected from an area of sediment subject to diffuse hydrothermal flow. The mussels live on the surface, the vesicomyids are partly buried and the thyasirids burrow in the sediment. The fine structure of the gills differs in the three bivalves. Bathymodiolus puteoserpentis hosts two types of bacterial symbiont, one methanotrophic, and another probably thiotrophic. The other two bivalves have single types of symbiont of different shapes. Stable isotope ratios of carbon and nitrogen indicate thiotrophy in the vesicomyid and thyasirid, but a predominance of methanotrophy in the mussel. This is the first time that such an assemblage has been found at a hydrothermal site on the Mid-Atlantic Ridge (MAR), with the different faunistic elements exploiting different energy resources

Effect of different surfactants on the shape, growth and photoluminescence behavior of MnWO4 crystals synthesized by the microwave-hydrothermal method

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effect of different surfactants on the shape, growth and photoluminescence behavior of MnWO4 crystals synthesized by the microwave-hydrothermal method

In this communication, we report the effect of different surfactants [cetyltrimethylammonium bromide (CTAB), sodium dodecyl sulfate (SDS) and sodium bis(2-ethylhexyl)sulfosuccinate (AOT)] on the shape, growth and photoluminescence (PL) behavior of manganese tungstate (MnWO4) crystals synthesized by the microwave-hydrothermal (MH) method at 413 K for 45 min. These crystals were characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), ultraviolet-visible (UV-vis) absorption spectroscopy and PL measurements. XRD patterns proved that these crystals have a monoclinic structure. FE-SEM images showed that MnWO4 crystals exhibit different shapes and growth mechanisms depending on the surfactant employed. The CTAB cationic surfactant promotes the hindrance of small nuclei that leads to the formation of flake-like nanocrystals, while SDS and AOT anionic surfactants promote a growth of crystals to plate-like and leaf-like crystals due to considerable size effect of counter-ions (RSO4- and RSO2O-) and an increase in Na+ ion remnants. UV-vis absorption spectroscopy revealed different optical band gap values due to modifications in the shape, surface and crystal size. Finally, the effect of surfactants on the crystal shapes and average crystal size distribution causing changes in the PL behavior of MnWO4 crystals was explained. (C) 2011 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.

(Table 1, page 400) Metal content of different manganese nodules from cruise VA-04 (R/V Valdivia) in the Pacific Ocean

Deep sea manganese nodules are considered as important natural resources for the future because of their Ni, Cu and Co contents. Their different shapes cannot be correlated clearly with their chemical composition. Surface constitution, however, can be associated with the metal contents. A classification of the nodules is suggested on the basis of these results. The iron content of the nodules strikingly shows relations to the physical properties (e.g. density and porosity). The method of density-measurement is the reason for this covariance. The investigation of freeze-dried nodular substance does not give this result. The Fe-rich nodules lose more hydration water than the Fe-poor ones during heat drying. The reason for this effect is the different crystallinity, respectively the particle size. The mean particle size is calculated on the basis of geometrical models. The X-ray-diffraction analysis proves the variation of crystallinity in connection with the Fe-content, too. The internal nodular textures also show characteristic distinctions.

Shapes and Dynamics of Blood Cells in Poiseuille and Shear Flows

The dynamics, shape, deformation, and orientation of red blood cells in microcirculation affect the rheology, flow resistance and transport properties of whole blood. This leads to important correlations of cellular and continuum scales. Furthermore, the dynamics of RBCs subject to different flow conditions and vessel geometries is relevant for both fundamental research and biomedical applications (e.g drug delivery). In this thesis, the behaviour of RBCs is investigated for different flow conditions via computer simulations. We use a combination of two mesoscopic particle-based simulation techniques, dissipative particle dynamics and smoothed dissipative particle dynamics. We focus on the microcapillary scale of several μm. At this scale, blood cannot be considered at the continuum but has to be studied at the cellular level. The connection between cellular motion and overall blood rheology will be investigated. Red blood cells are modelled as viscoelastic objects interacting hydrodynamically with a viscous fluid environment. The properties of the membrane, such as resistance against bending or shearing, are set to correspond to experimental values. Furthermore, thermal fluctuations are considered via random forces. Analyses corresponding to light scattering measurements are performed in order to compare to experiments and suggest for which situations this method is suitable. Static light scattering by red blood cells characterises their shape and allows comparison to objects such as spheres or cylinders, whose scattering signals have analytical solutions, in contrast to those of red blood cells. Dynamic light scattering by red blood cells is studied concerning its suitability to detect and analyse motion, deformation and membrane fluctuations. Dynamic light scattering analysis is performed for both diffusing and flowing cells. We find that scattering signals depend on various cell properties, thus allowing to distinguish different cells. The scattering of diffusing cells allows to draw conclusions on their bending rigidity via the effective diffusion coefficient. The scattering of flowing cells allows to draw conclusions on the shear rate via the scattering amplitude correlation. In flow, a RBC shows different shapes and dynamic states, depending on conditions such as confinement, physiological/pathological state and cell age. Here, two essential flow conditions are studied: simple shear flow and tube flow. Simple shear flow as a basic flow condition is part of any more complex flow. The velocity profile is linear and shear stress is homogeneous. In simple shear flow, we find a sequence of different cell shapes by increasing the shear rate. With increasing shear rate, we find rolling cells with cup shapes, trilobe shapes and quadrulobe shapes. This agrees with recent experiments. Furthermore, the impact of the initial orientation on the dynamics is studied. To study crowding and collective effects, systems with higher haematocrit are set up. Tube flow is an idealised model for the flow through cylindric microvessels. Without cell, a parabolic flow profile prevails. A single red blood cell is placed into the tube and subject to a Poiseuille profile. In tube flow, we find different cell shapes and dynamics depending on confinement, shear rate and cell properties. For strong confinements and high shear rates, we find parachute-like shapes. Although not perfectly symmetric, they are adjusted to the flow profile and maintain a stationary shape and orientation. For weak confinements and low shear rates, we find tumbling slippers that rotate and moderately change their shape. For weak confinements and high shear rates, we find tank-treading slippers that oscillate in a limited range of inclination angles and strongly change their shape. For the lowest shear rates, we find cells performing a snaking motion. Due to cell properties and resultant deformations, all shapes differ from hitherto descriptions, such as steady tank-treading or symmetric parachutes. We introduce phase diagrams to identify flow regimes for the different shapes and dynamics. Changing cell properties, the regime borders in the phase diagrams change. In both flow types, both the viscosity contrast and the choice of stress-free shape are important. For in vitro experiments, the solvent viscosity has often been higher than the cytosol viscosity, leading to a different pattern of dynamics, such as steady tank-treading. The stress-free state of a RBC, which is the state at zero shear stress, is still controversial, and computer simulations enable direct comparisons of possible candidates in equivalent flow conditions.

Primary students’ spatial visualization and spatial orientation : an evidence base for instruction

This paper reports on the performance of 58 11 to 12-year-olds on a spatial visualization task and a spatial orientation task. The students completed these tasks and explained their thinking during individual interviews. The qualitative data were analysed to inform pedagogical content knowledge for spatial activities. The study revealed that “matching” or “matching and eliminating” were the typical strategies that students employed on these spatial tasks. However, errors in making associations between parts of the same or different shapes were noted. Students also experienced general difficulties with visual memory and language use to explain their thinking. The students’ specific difficulties in spatial visualization related to obscured items, the perspective used, and the placement and orientation of shapes.

Feminist contributions to understanding woman abuse: Myths, controversies, and realities

Woman abuse in intimate heterosexual relationships takes different shapes and forms and is a worldwide public health problem. Many journalists, activists, and researchers, however, minimize the extent of woman abuse, sharply criticize feminist empirical, theoretical, and policy work on this issue, and disseminate myths about feminism. A key objective of this paper is to challenge these myths and respond to criticisms of feminist scholarship. Another goal is to show that some feminists use quantitative methods and that feminist techniques influence some types of conventional research, such as large-scale surveys conducted in Canada and the United States.

Tactically-driven nonmonotone travelling waves

Models of cell invasion incorporating directed cell movement up a gradient of an external substance and carrying capacity-limited proliferation give rise to travelling wave solutions. Travelling wave profiles with various shapes, including smooth monotonically decreasing, shock-fronted monotonically decreasing and shock-fronted nonmonotone shapes, have been reported previously in the literature. The existence of tacticallydriven shock-fronted nonmonotone travelling wave solutions is analysed for the first time. We develop a necessary condition for nonmonotone shock-fronted solutions. This condition shows that some of the previously reported shock-fronted nonmonotone solutions are genuine while others are a consequence of numerical error. Our results demonstrate that, for certain conditions, travelling wave solutions can be either smooth and monotone, smooth and nonmonotone or discontinuous and nonmonotone. These different shapes correspond to different invasion speeds. A necessary and sufficient condition for the travelling wave with minimum wave speed to be nonmonotone is presented. Several common forms of the tactic sensitivity function have the potential to satisfy the newly developed condition for nonmonotone shock-fronted solutions developed in this work.

Lattice-free models of cell invasion : discrete simulations and travelling waves

Invasion waves of cells play an important role in development, disease and repair. Standard discrete models of such processes typically involve simulating cell motility, cell proliferation and cell-to-cell crowding effects in a lattice-based framework. The continuum-limit description is often given by a reaction–diffusion equation that is related to the Fisher–Kolmogorov equation. One of the limitations of a standard lattice-based approach is that real cells move and proliferate in continuous space and are not restricted to a predefined lattice structure. We present a lattice-free model of cell motility and proliferation, with cell-to-cell crowding effects, and we use the model to replicate invasion wave-type behaviour. The continuum-limit description of the discrete model is a reaction–diffusion equation with a proliferation term that is different from lattice-based models. Comparing lattice based and lattice-free simulations indicates that both models lead to invasion fronts that are similar at the leading edge, where the cell density is low. Conversely, the two models make different predictions in the high density region of the domain, well behind the leading edge. We analyse the continuum-limit description of the lattice based and lattice-free models to show that both give rise to invasion wave type solutions that move with the same speed but have very different shapes. We explore the significance of these differences by calibrating the parameters in the standard Fisher–Kolmogorov equation using data from the lattice-free model. We conclude that estimating parameters using this kind of standard procedure can produce misleading results.

Synthesis and study of conductivity behaviour of blended conducting polymer films irradiated with swift heavy ions of silicon

In recent times, blended polymers have shown a lot of promise in terms of easy processability in different shapes and forms. In the present work, polyaniline emeraldine base (PANi-EB) was doped with camphor sulfonic acid (CSA) and combined with the conducting polymer polyfluorene (PF) as well as the insulating polymer polyvinyl chloride (PVC) to synthesize CSA doped PANi-PF and PANi-PVC blended polymers. It is well known that PANi when doped with CSA becomes highly conducting. However, its poor mechanical properties, such as low tensile, compressive, and flexural strength render PANi a non-ideal material to be processed for its various practical applications, such as electromagnetic shielding, anti-corrosion shielding, photolithography and microelectronic devices etc. Thus the search for polymers which are easily processable and are capable of showing high conductivity still continues. PANi-PVC blend was prepared, which showed low conductivity which is limiting factor for certain applications. Therefore, another processable polymer PF was chosen as conducting matrix. Conducting PF can be easily processed into various shapes and forms. Therefore, a blend mixture was prepared by using PANi and PF through the use of CSA as a counter ion which forms a "bridge" between the two polymeric components of the inter-polymer complex. Two blended polymers have been synthesized and investigated for their conductivity behaviour. It was observed that the blended film of CSA doped PANi-PVC showed a room temperature electrical conductivity of 2.8 × 10-7 S/cm where as the blended film made by CSA doped PANi with conducting polymer PF showed a room temperature conductivity of 1.3 × 10-5 S/cm. Blended films were irradiated with 100 MeV silicon ions with a view to increase their conductivity with a fluence ranging from 1011 ions to 1013 per cm2 from 15 UD Pelletron accelerator at NSC, New Delhi.

Interacting motile agents : taking a mean-field approach beyond monomers and nearest-neighbor steps

We consider a discrete agent-based model on a one-dimensional lattice, where each agent occupies L sites and attempts movements over a distance of d lattice sites. Agents obey a strict simple exclusion rule. A discrete-time master equation is derived using a mean-field approximation and careful probability arguments. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy are obtained. Averaged discrete simulation data are generated and shown to compare very well with the solution to the derived nonlinear diffusion equations. This framework allows us to approach a lattice-free result using all the advantages of lattice methods. Since different cell types have different shapes and speeds of movement, this work offers insight into population-level behavior of collective cellular motion.

Wear lip formation during dry sliding

A pin-on-disc test configuration has been used to examine the formation of the strain-hardened projection, or wear lips, especially at the trailing edge of the pin during dry sliding of aluminium alloys against steel discs. The mechanism of formation of such wear lips is studied with the aid of optical and electron microscopes. The plastic deformation of the pin, growth and eventual removal of the wear lip as wear debris are elucidated. The size and shape of the wear lips in pins of different shapes, i.e. square, rectangular, triangular and circular cross-sections, are described.