Stresses in isostatic granular systems and emergence of force chains

Progress is reported on several questions that bedevil understanding of granular systems: (i) are the stress equations elliptic, parabolic or hyperbolic? (ii) how can the often-observed force chains be predicted from a first-principles continuous theory? (iii) How to relate insight from isostatic systems to general packings? Explicit equations are derived for the stress components in two dimensions including the dependence on the local structure. The equations are shown to be hyperbolic and their general solutions, as well as the Green function, are found. It is shown that the solutions give rise to force chains and the explicit dependence of the force chains trajectories and magnitudes on the local geometry is predicted. Direct experimental tests of the predictions are proposed. Finally, a framework is proposed to relate the analysis to non-isostatic and more realistic granular assemblies.Comment: 4 pages, 2 figures, Corrected typos and clkearer text, submitted to Phys. Rev. Let

Development of Stresses in Cohesionless Poured Sand

The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9

Standardizing estimates of the Plasmodium falciparum parasite rate

<p>Abstract</p> <p>Background</p> <p>The <it>Plasmodium falciparum </it>parasite rate (PfPR) is a commonly reported index of malaria transmission intensity. PfPR rises after birth to a plateau before declining in older children and adults. Studies of populations with different age ranges generally report average PfPR, so age is an important source of heterogeneity in reported PfPR data. This confounds simple comparisons of PfPR surveys conducted at different times or places.</p> <p>Methods</p> <p>Several algorithms for standardizing PfPR were developed using 21 studies that stratify in detail PfPR by age. An additional 121 studies were found that recorded PfPR from the same population over at least two different age ranges; these paired estimates were used to evaluate these algorithms. The best algorithm was judged to be the one that described most of the variance when converting the PfPR pairs from one age-range to another.</p> <p>Results</p> <p>The analysis suggests that the relationship between PfPR and age is predictable across the observed range of malaria endemicity. PfPR reaches a peak after about two years and remains fairly constant in older children until age ten before declining throughout adolescence and adulthood. The PfPR pairs were poorly correlated; using one to predict the other would explain only 5% of the total variance. By contrast, the PfPR predicted by the best algorithm explained 72% of the variance.</p> <p>Conclusion</p> <p>The PfPR in older children is useful for standardization because it has good biological, epidemiological and statistical properties. It is also historically consistent with the classical categories of hypoendemic, mesoendemic and hyperendemic malaria. This algorithm provides a reliable method for standardizing PfPR for the purposes of comparing studies and mapping malaria endemicity. The scripts for doing so are freely available to all.</p

Segregation of binary mixtures of particles during the filling of a two-dimensional representation of a hopper

This paper contains a summary of results obtained from experiments carried out at The Wolfson Centre for Bulk Solids Handling Technology at the University of Greenwich on the segregation of dry binary particle mixtures of the same material when they fill a hopper. A test facility has been built which represents a two-dimensional segment of a hopper. Binary mixtures were fed into this container using amplitude feedback-controlled vibratory feeders via a static in-line mixer and one of two different feed chute designs; one curved and the other straight. 'Thieving' probes were used to sample the segregated heap of material from the hopper. The contents of each probe then underwent size analysis to ascertain the change in the size distribution from that of the original mixture. It is shown that a mechanism, termed embedment, caused by the vertical component of the feed velocity on impact with the forming heap, has a dramatic effect on the segregation process. A detailed discussion of the relationship between the possible mechanisms occurring in the heap formation process in the light of the segregation patterns observed is given. This paper contains a summary of results obtained from experiments carried out at The Wolfson Centre for Bulk Solids Handling Technology at the University of Greenwich on the segregation of dry binary particle mixtures of the same material when they fill a hopper. A test facility has been built which represents a two-dimensional segment of a hopper. Binary mixtures were fed into this container using amplitude feedback-controlled vibratory feeders via a static in-line mixer and one of two different feed chute designs; one curved and the other straight. 'Thieving' probes were used to sample the segregated heap of material from the hopper. The contents of each probe then underwent size analysis to ascertain the change in the size distribution from that of the original mixture. It is shown that a mechanism, termed embedment, caused by the vertical component of the feed velocity on impact with the forming heap, has a dramatic effect on the segregation process. A detailed discussion of the relationship between the possible mechanisms occurring in the heap formation process in the light of the segregation patterns observed is given

Effects of cell density and biomacromolecule addition on the flow behavior of concentrated mesenchymal cell suspensions

With the rapidly growing interest in the use of mesenchymal stromal cells (MSCs) for cell therapy and regenerative medicine applications, either alone as an injected suspension, or dispersed within injectable hydrogel delivery systems, greater understanding of the structure-function-property characteristics of suspensions of adhesion-dependent mesenchymal cells is required. In this paper, we present the results of an experimental study into the flow behavior of concentrated suspensions of living cells of mesenchymal origin (fibroblasts) over a wide range of cell concentrations, with and without the addition of hyaluronic acid (HA), a commonly utilized biomolecule in injectable hydrogel formulations. We characterize the change in the shear viscosity as a function of shear stress and shear rate for cell volume fractions varying from 20 to 60%. We show that high volume fraction suspensions of living mesenchymal cells, known to be capable of homotypic interactions, exhibit highly complex but reproducible rheological footprints, including yield stress, shear thinning and shear-induced fracture behaviors. We show that with the addition of HA, we can significantly modify and tailor the rheology of these cell suspensions at all volume fractions. Using FACS and confocal imaging, we show that the observed effect of HA addition is due to a significantly modulation in the formation of cellular aggregates in these suspensions, and thus the resultant volume spanning network. Considering the aggregates as fractal structures, we show that by taking into account the changes in volume fractions with shear, we are able to plot a master curve for the range of conditions investigated and extract from it the average adhesion force between individual cells, across a population of millions of cells. The outcomes of this study not only provide new insight into the complexity of the flow behaviors of concentrated, adhesive mesenchymal cell suspensions, and their sensitivity to associative biomacromolecule addition, but also a novel, rapid method by which to measure the average adhesion force between individual cells, and the impacts of biomacromolecules on this important parameter