Compaction of anisotropic granular materials : experiments and simulations

We present both experimental and numerical investigations of compaction in granular materials composed of rods. As a function of the aspect ratio of the particles, we have observed large variations of the asymptotic packing volume fraction in vertical tubes. The relevant parameter is the ratio between the rod length $\ell$ and the tube diameter $D$. Even the compaction dynamics remains unchanged for various particle lengths, a 3d/2d phase transition for grain orientations is observed for $\ell/D = 1$. A toy model for the compaction of needles on a lattice is also proposed. This toy model gives a complementary view of our experimental results and leads to behaviors similar to experimental ones.Comment: 5 pages, 10 figure

On the existence of bounded solutions for a nonlinear elliptic system

This work deals with the system $(-\Delta)^m u= a(x) v^p$, $(-\Delta)^m v=b(x) u^q$ with Dirichlet boundary condition in a domain \Omega\subset\RR^n, where $\Omega$ is a ball if $n\ge 3$ or a smooth perturbation of a ball when $n=2$. We prove that, under appropriate conditions on the parameters ($a,b,p,q,m,n$), any non-negative solution $(u,v)$ of the system is bounded by a constant independent of $(u,v)$. Moreover, we prove that the conditions are sharp in the sense that, up to some border case, the relation on the parameters are also necessary. The case $m=1$ was considered by Souplet in \cite{PS}. Our paper generalize to $m\ge 1$ the results of that paper

Experimental study of the compaction dynamics for 2D anisotropic granular materials

We present an experimental study of the compaction dynamics for two-dimensional anisotropic granular systems. Compaction dynamics is measured at three different scales : (i) the macroscopic scale through the packing fraction $\rho$, (ii) the mesoscopic scale through both fractions of aligned grains $\phi_{a}$ and ideally ordered grains $\phi_{io}$, and (iii) the microscopic scale through both rotational and translational grain mobilities $\mu_{r,t}$. The effect of the grain rotations on the compaction dynamics has been measured. At the macroscopic scale, we have observed a discontinuity in the late stages of the compaction curve. At the mesoscopic scale, we have observed the formation and the growth of domains made of aligned grains. From a microscopic point of view, measurements reveal that the beginning of the compaction process is essentially related to translational motion of the grains. The grains rotations drive mainly the process during the latest stages of compaction.Comment: 8pages, 11 figure

Test fixture insures high degree of accuracy in flexure tests

Modified die set improves accuracy in load application, minimizes problems of parallelism, and eliminates testing errors normally encountered during flexure tests. Test results are given for a comparison test of the old and new fixtures

On the average Gamma-Ray Burst X-ray flaring activity

Gamma-ray burst X-ray flares are believed to mark the late time activity of the central engine. We compute the temporal evolution of the average flare luminosity $$ in the common rest frame energy band of 44 GRBs taken from the large \emph{Swift} 5-years data base. Our work highlights the importance of a proper consideration of the threshold of detection of flares against the contemporaneous continuous X-ray emission. In the time interval $30 \rm{s}\propto t^{-2.7\pm 0.1}$; this implies that the flare isotropic energy scaling is $E_{\rm{iso,flare}}\propto t^{-1.7}$. The decay of the continuum underlying the flare emission closely tracks the average flare luminosity evolution, with a typical flare to steep-decay luminosity ratio which is $L_{\rm{flare}}/L_{\rm{steep}}=4.7$: this suggests that flares and continuum emission are deeply related to one another. We infer on the progenitor properties considering different models. According to the hyper-accreting black hole scenario, the average flare luminosity scaling can be obtained in the case of rapid accretion ($t_{\rm{acc}}\ll t$) or when the last \sim 0.5 M_{\sun} of the original 14 M_{\sun} progenitor star are accreted. Alternatively, the steep $\propto t^{-2.7}$ behaviour could be triggered by a rapid outward expansion of an accretion shock in the material feeding a convective disk. If instead we assume the engine to be a rapidly spinning magnetar, then its rotational energy can be extracted to power a jet whose luminosity is likely to be between the monopole ($L\propto e^{-2t}$) and dipole ($L\propto t^{-2}$) cases. In both scenarios we suggest the variability, which is the main signature of the flaring activity, to be established as a consequence of different kinds of instabilities.Comment: MNRAS accepte

Efficient vasculature investment in tissues can be determined without global information

Cells are the fundamental building blocks of organs and tissues. Information and mass flow through cellular contacts in these structures is vital for the orchestration of organ function. Constraints imposed by packing and cell immobility limit intercellular communication, particularly as organs and organisms scale up to greater sizes. In order to transcend transport limitations, delivery systems including vascular and respiratory systems evolved to facilitate the movement of matter and information. The construction of these delivery systems has an associated cost, as vascular elements do not perform the metabolic functions of the organs they are part of. This study investigates a fundamental trade-off in vascularization in multicellular tissues: the reduction of path lengths for communication versus the cost associated with producing vasculature. Biologically realistic generative models, using multicellular templates of different dimensionalities, revealed a limited advantage to the vascularization of two-dimensional tissues. Strikingly, scale-free improvements in transport efficiency can be achieved even in the absence of global knowledge of tissue organization. A point of diminishing returns in the investment of additional vascular tissue to the increased reduction of path length in 2.5- and three-dimensional tissues was identified. Applying this theory to experimentally determined biological tissue structures, we show the possibility of a co-dependency between the method used to limit path length and the organization of cells it acts upon. These results provide insight as to why tissues are or are not vascularized in nature, the robustness of developmental generative mechanisms and the extent to which vasculature is advantageous in the support of organ function

Radial Solutions for Hamiltonian Elliptic Systems with Weights

We prove the existence of infinitely many radial solutions for elliptic systems in Rn with power weights. A key tool for the proof will be a weighted imbedding theorem for fractional-order Sobolev spaces, that could be of independent interest.Comment: 13 page

Diffusion of a granular pulse in a rotating drum

The diffusion of a pulse of small grains in an horizontal rotating drum is studied through discrete elements methods simulations. We present a theoretical analysis of the diffusion process in a one-dimensional confined space in order to elucidate the effect of the confining end-plate of the drum. We then show that the diffusion is neither subdiffusive nor superdiffusive but normal. This is demonstrated by rescaling the concentration profiles obtained at various stages and by studying the time evolution of the mean squared deviation. Finally we study the self-diffusion of both large and small grains and we show that it is normal and that the diffusion coefficient is independent of the grain size