Stress inhomogeneity effect on fluid-induced fracture behavior into weakly consolidated granular systems.

We study the effect of stress inhomogeneity on the behavior of fluid-driven fracture development in weakly consolidated granular systems. Using numerical models we investigate the change in fracture growth rate and fracture pattern structure in unconsolidated granular packs (also referred to as soft-sands) as a function of the change in the confining stresses applied to the system. Soft-sands do not usually behave like brittle, linear elastic materials, and as a consequence, poroelastic models are often not applicable to describe their behavior. By making a distinction between "cohesive" and "compressive" grain-grain contact forces depending on their magnitude, we propose an expression that describes the fluid opening pressure as a function of the mean value and the standard deviation of the "compressive stress" distribution. We also show that the standard deviation of this distribution can be related with the extent to which fracture "branches" reach into the material.BP International Centre for Advanced Materials (BP-ICAM

High intensity tapping regime in a frustrated lattice gas model of granular compaction

In the frame of a well established lattice gas model for granular compaction, we investigate the high intensity tapping regime where a pile expands significantly during external excitation. We find that this model shows the same general trends as more sophisticated models based on molecular dynamic type simulations. In particular, a minimum in packing fraction as a function of tapping strength is observed in the reversible branch of an annealed tapping protocol.Comment: 5 pages, 4 figure

Investigating participation in Advanced level mathematics: a study of student drop out

There has for some years been a growing concern about participation in university-entrance level mathematics in England and across the developed world. Extensive statistical analyses present the decline but offer little to help us understand the causes. In this paper we explore a concern which cannot be explored through national datasets, namely the retention of mathematics students on Advanced level mathematics courses. Drawing on survey data from fifteen secondary schools in the Midlands of England, we examine subject differences in decisions to study, withdraw from, and continue in a range of A level subjects. Not only is the rate of attrition from mathematics higher than most other subjects, but there are substantial differences between schools. In order to explore this high rate of attrition further we consider one school – Queensbury Park - in which a large proportion of students decided not to continue with their study of mathematics from year 12 to 13. Drawing on performance data and focus group interviews we explore some of the reasons for the students’ decisions

Relevance of system size to the steady-state properties of tapped granular systems

We investigate the steady-state packing fraction ϕ and force moment tensor Σ of quasi-two-dimensional granular columns subjected to tapping. Systems of different height h and width L are considered. We find that ϕ and Σ, which describe the macroscopic state of the system, are insensitive to L for L>50d (with d the grain diameter). However, results for granular columns of different heights cannot be conciliated. This suggests that comparison between results of different laboratories on this type of experiments can be done only for systems of same height. We show that a parameter ɛ=1+(Aω)^{2}/(2gh), with A and ω the amplitude and frequency of the tap and g the acceleration of gravity, can be defined to characterize the tap intensity. This parameter is based on the effective flight of the granular bed, which takes into account the h dependency. When ϕ is plotted as a function of ɛ, the data collapses for systems of different h. However, this parameter alone is unable to determine the steady state to be reached since different Σ can be observed for a given ɛ if different column heights are considered

Towards a relevant set of state variables to describe static granular packings

We analyze, experimentally and numerically, the steady states, obtained by tapping, of a two-dimensional granular layer. Contrary to the usual assumption, we show that the reversible (steady state branch) of the density-acceleration curve is nonmonotonous. Accordingly, steady states with the same mean volume can be reached by tapping the system with very different intensities. Simulations of dissipative frictional disks show that equal volume steady states have different values of the force moment tensor. Additionally, we find that steady states of equal stress can be obtained by changing the duration of the taps; however, these states present distinct mean volumes. These results confirm previous speculations that the volume and the force moment tensor are both needed to describe univocally equilibrium states in static granular assemblies

Managing learning trajectories: the case of 14-19 mathematics

In this paper we explore how mathematics department leaders manage curriculum (what is taught), teaching (how it is taught) and learner progression (what results) for 14-19 year olds. The background to the study is a range of national, and international, concerns about participation rates in university entrance level mathematics. Given the recommendation of the Smith Report (2004) that new pathways models be developed for 14-19 mathematics, this paper explores some of the strategies employed, and issues faced, by schools as they seek to maximise attainment and participation in mathematics. Following a thematic analysis of data from interviews with heads of department in fifteen schools we look in more depth at one school to see how it manages the mathematics learning trajectories of young people. The theme of performativity is all pervasive

Air-sea CO2 fluxes in the Atlantic as measured during the FICARAM cruises

A total of fourteen hydrographic cruises spanning from 2000 to 2008 were conducted during the spring and autumn seasons between Spain and the Southern Ocean, under the framework of the Spanish research project FICARAM. The performed underway measurements are processed and analysed to describe the meridional air-sea CO2 fluxes (F CO2) along the Atlantic Ocean. The data was organised into different biogeochemical oceanographic provinces, according mainly to the thermohaline characteristics. The obtained spatial and temporal distributions of F CO2 follow the generally expected patterns and annual trends. The Subtropical regions in both hemispheres alternated the CO2 source and sink nature from autumn to spring, respectively. On the other hand, Tropical waters and the Patagonian Sea clearly behaved as sinks of atmospheric CO2 like the waters of the Drake Passage during autumn. The obtained results during the cruises also revealed significant long-term trends, such as the warming of equatorial waters (0.11±0.03 Cyr−1) and the decrease of surface salinity (−0.16±0.01 yr−1) in tropical waters caused by the influence of the Amazon River plume. This reduction in surface salinity appears to have a direct influence over the CO2 storage rates, fostering the uptake capacity of atmospheric CO2 (−0.09±0.03 molm−2 yr−1). An analysis of the biogeochemical forcing on the CO2 fugacity (fCO2) variability performed from an empirical algorithm highlighted the major role of the Amazon River input in the tropical North Atlantic fluxes. In addition, it has provided a quantitative measure of the importance of the thermodynamic control of F CO2 at temperate latitudes