Internal states of model isotropic granular packings. III. Elastic properties

In this third and final paper of a series, elastic properties of numerically simulated isotropic packings of spherical beads assembled by different procedures and subjected to a varying confining pressure P are investigated. In addition P, which determines the stiffness of contacts by Hertz's law, elastic moduli are chiefly sensitive to the coordination number, the possible values of which are not necessarily correlated with the density. Comparisons of numerical and experimental results for glass beads in the 10kPa-10MPa range reveal similar differences between dry samples compacted by vibrations and lubricated packings. The greater stiffness of the latter, in spite of their lower density, can hence be attributed to a larger coordination number. Voigt and Reuss bounds bracket bulk modulus B accurately, but simple estimation schemes fail for shear modulus G, especially in poorly coordinated configurations under low P. Tenuous, fragile networks respond differently to changes in load direction, as compared to load intensity. The shear modulus, in poorly coordinated packings, tends to vary proportionally to the degree of force indeterminacy per unit volume. The elastic range extends to small strain intervals, in agreement with experimental observations. The origins of nonelastic response are discussed. We conclude that elastic moduli provide access to mechanically important information about coordination numbers, which escape direct measurement techniques, and indicate further perspectives.Comment: Published in Physical Review E 25 page

Mobile particles in an immobile environment: Molecular Dynamics simulation of a binary Yukawa mixture

Molecular dynamics computer simulations are used to investigate thedynamics of a binary mixture of charged (Yukawa) particles with a size-ratio of 1:5. We find that the system undergoes a phase transition where the large particles crystallize while the small particles remain in a fluid-like (delocalized) phase. Upon decreasing temperature below the transition, the small particles become increasingly localized on intermediate time scales. This is reflected in the incoherent intermediate scattering functions by the appearance of a plateau with a growing height. At long times, the small particles show a diffusive hopping motion. We find that these transport properties are related to structural correlations and the single-particle potential energy distribution of the small particles.Comment: 7 pages, 5 figure

Defect-mediated turbulence in systems with local deterministic chaos

We show that defect-mediated turbulence can exist in media where the underlying local dynamics is deterministically chaotic. While many of the characteristics of defect-mediated turbulence, such as the exponential decay of correlations and a squared Poissonian distribution for the number of defects, are identical to those seen in oscillatory media, the fluctuations in the number of defects differ significantly. The power spectra suggest the existence of underlying correlations that lead to a different and non-universal scaling structure in chaotic media.Comment: 4 pages, 5 figure

Conformal Mapping on Rough Boundaries II: Applications to bi-harmonic problems

We use a conformal mapping method introduced in a companion paper to study the properties of bi-harmonic fields in the vicinity of rough boundaries. We focus our analysis on two different situations where such bi-harmonic problems are encountered: a Stokes flow near a rough wall and the stress distribution on the rough interface of a material in uni-axial tension. We perform a complete numerical solution of these two-dimensional problems for any univalued rough surfaces. We present results for sinusoidal and self-affine surface whose slope can locally reach 2.5. Beyond the numerical solution we present perturbative solutions of these problems. We show in particular that at first order in roughness amplitude, the surface stress of a material in uni-axial tension can be directly obtained from the Hilbert transform of the local slope. In case of self-affine surfaces, we show that the stress distribution presents, for large stresses, a power law tail whose exponent continuously depends on the roughness amplitude

Occurrence and extent of hybridisation between the invasive Mallard Duck and native Yellow-billed Duck in South Africa

Hybridisation between invasive and native species represents a significant threat to biodiversity. The Mallard Duck (Anas platyrhynchos) is known to hybridise with numerous closely related Anas species in regions where they have been introduced, threatening the genetic integrity of native ducks and in some instances contributing to their extinction risk. Mallard Ducks were introduced into South Africa in the 1940s and are now naturalised and widespread in the country. It has been speculated that Mallard Ducks are hybridising with native Yellow-billed Ducks (A. undulata) in South Africa, but evidence for this remains observational or purely anecdotal. Here we use data from nuclear microsatellite markers and mitochondrial DNA sequencing to show that hybridisation is indeed occuring between these two species. We found evidence for the occurance of hybridisation, mostly as crosses between Mallard Duck hens and Yellow-billed Duck drakes. Surprisingly, our results suggest that introgressive hybridisation is primarily occuring into the invasive Mallard Duck population (mostly Mallard Duck backcrosses were detected), evidenced by directionally-skewed gene flow and sex-biased mating. Whether these findings reflect true assortative mating or a case of Haldane’s rule remains unknown. We also found evidence of high connectivity between Yellow-billed Duck populations, as far as 1000 km apart, in South Africa. Taken together these results suggest that hybrid genotypes can disperse over vast distances between populations and lead to genetic pollution, even in the absence of invasive Mallard Ducks. Active management of Mallard Duck populations has been met by public resistance in some areas in South Africa, partly because of a lack of evidence showing clear impacts by these birds. This study provides some of the first scientifically-documented evidence for such impacts

The consumption response to positive and negative income shocks

A set of newly added questions in the 2011 to 2014 Bank of England/NMG Consulting Survey reveals that British households tend to change their consumption by significantly more in reaction to temporary and unanticipated falls in income than to rises of the same size. Household balance sheet characteristics such as high debt-to-income ratios and small liquidity buffers, concerns about credit market access and higher subjective risk of lower future income account for a sizable share of this spending asymmetry. Our findings have important implications for predicting the response of aggregate consumption to expansionary and contractionary macroeconomic policies

Experiences with HPTN 067/ADAPT Study-Provided Open-Label PrEP Among Women in Cape Town: Facilitators and Barriers Within a Mutuality Framework.

Placebo-controlled trials of pre-exposure prophylaxis (PrEP) have reported challenges with study-product uptake and use, with the greatest challenges reported in studies with young women in sub-Saharan Africa. We conducted a qualitative sub-study to explore experiences with open-label PrEP among young women in Cape Town, South Africa participating in HTPN 067/Alternative Dosing to Augment Pre-Exposure Prophylaxis Pill Taking (ADAPT). HPTN 067/ADAPT provided open label oral FTC/TDF PrEP to young women in Cape Town, South Africa who were randomized to daily and non-daily PrEP regimens. Following completion of study participation, women were invited into a qualitative sub-study including focus groups and in-depth interviews. Interviews and groups followed a semi-structured guide, were recorded, transcribed, and translated to English from isiXhosa, and coded using framework analysis. Sixty of the 179 women enrolled in HPTN 067/ADAPT participated in either a focus group (six groups for a total of 42 participants) or an in-depth interview (n = 18). This sample of mostly young, unmarried women identified facilitators of and barriers to PrEP use, as well as factors influencing study participation. Cross-cutting themes characterizing discourse suggested that women placed high value on contributing to the well-being of one's community (Ubuntu), experienced a degree of skepticism towards PrEP and the study more generally, and reported a wide range of approaches towards PrEP (ranging from active avoidance to high levels of persistence and adherence). A Mutuality Framework is proposed that identifies four dynamics (distrust, uncertainty, alignment, and mutuality) that represent distinct interactions between self, community and study and serve to contextualize women's experiences. Implications for better understanding PrEP use, and non-use, and intervention opportunities are discussed. In this sample of women, PrEP use in the context of an open-label research trial was heavily influenced by underlying beliefs about safety, reciprocity of contributions to community, and trust in transparency and integrity of the research. Greater attention to factors positioning women in the different dynamics of the proposed Mutuality Framework could direct intervention approaches in clinical trials, as well as open-label PrEP scale-up

Frictionless bead packs have macroscopic friction, but no dilatancy

The statement of the title is shown by numerical simulation of homogeneously sheared packings of frictionless, nearly rigid beads in the quasistatic limit. Results coincide for steady flows at constant shear rate γ in the limit of small γ and static approaches, in which packings are equilibrated under growing deviator stresses. The internal friction angle ϕ, equal to 5.76 $\pm$ 0.22 degrees in simple shear, is independent on the average pressure P in the rigid limit. It is shown to stem from the ability of stable frictionless contact networks to form stress-induced anisotropic fabrics. No enduring strain localization is observed. Dissipation at the macroscopic level results from repeated network rearrangements, like the effective friction of a frictionless slider on a bumpy surface. Solid fraction Φ remains equal to the random close packing value ≃ 0.64 in slowly or statically sheared systems. Fluctuations of stresses and volume are observed to regress in the large system limit, and we conclude that the same friction law for simple shear applies in the large psystem limit if normal stress or density is externally controlled. Defining the inertia number as I = γ m/(aP), with m the grain mass and a its diameter, both internal friction coefficient $\mu$∗ = tan ϕ and volume 1/Φ increase as powers of I in the quasistatic limit of vanishing I, in which all mechanical properties are determined by contact network geometry. The microstructure of the sheared material is characterized with a suitable parametrization of the fabric tensor and measurements of connectivity and coordination numbers associated with contacts and near neighbors.Comment: 19 pages. Additional technical details may be found in v

Roughness of fracture surfaces

We study the fracture surface of three dimensional samples through a model for quasi-static fractures known as Born Model. We find for the roughness exponent a value of 0.5 expected for ``small length scales'' in microfracturing experiments. Our simulations confirm that at small length scales the fracture can be considered as quasi-static. The isotropy of the roughness exponent on the crack surface is also shown. Finally, considering the crack front, we compute the roughness exponents for longitudinal and transverse fluctuations of the crack line (both 0.5). They result in agreement with experimental data, and supports the possible application of the model of line depinning in the case of long-range interactions.Comment: 10 pages, 5 figures, Late

Internal states of model isotropic granular packings. I. Assembling process, geometry and contact networks

This is the first paper of a series of three, reporting on numerical simulation studies of geometric and mechanical properties of static assemblies of spherical beads under an isotropic pressure. Frictionless systems assemble in the unique random close packing (RCP) state in the low pressure limit if the compression process is fast enough, slower processes inducing traces of crystallization, and exhibit specific properties directly related to isostaticity of the force-carrying structure. The different structures of frictional packings assembled by various methods cannot be classified by the sole density. While lubricated systems approach RCP densities and coordination number z^*~=6 on the backbone in the rigid limit, an idealized "vibration" procedure results in equally dense configurations with z^*~=4.5. Near neighbor correlations on various scales are computed and compared to available laboratory data, although z^* values remain experimentally inaccessible. Low coordination packings have many rattlers (more than 10% of the grains carry no force), which should be accounted for on studying position correlations, and a small proportion of harmless "floppy modes" associated with divalent grains. Frictional packings, however slowly assembled under low pressure, retain a finite level of force indeterminacy, except in the limit of infinite friction.Comment: 29 pages. Published in Physical Review