Micro-mechanical analysis of deformation characteristics of three-dimensional granular materials

The deformation characteristics of idealized granular materials have been studied from the micro-mechanical viewpoint, using Bagi’s three-dimensional micro-mechanical formulation for the strain tensor [Bagi, K., 1996. Mechanics of Materials 22, 165–177]. This formulation is based on the Delaunay tessellation of space into tetrahedra. The set of edges of the tetrahedra can be divided into physical contacts and virtual contacts between particles. Bagi’s formulation expresses the continuum, macro-scale strain as an average over all edges, of their relative displacements (between two successive states) and the complementary-area vectors. This latter vector is a geometrical quantity determined from the set of edges, i.e. from the structure of the particle packing.\ud \ud Results from Discrete Element Method simulations of isotropic and triaxial loading of a three-dimensional polydisperse packing of spheres have been used to investigate statistics of the branch vectors and complementary-area vectors of edges (subdivided into physical and virtual contacts) and of the relative displacements of edges. The investigated statistics are probability density functions and averages over groups of edges with the same orientation. It is shown that these averages can be represented by second-order Fourier series in edge orientation.\ud \ud Edge orientations are distributed isotropically, contrary to contact orientations. The average lengths of the branch vectors and the normal component of the complementary-area vectors are distributed isotropically (with respect to the edge orientation) and their average values are related to each other and to the volume fraction of the assembly. The other two components of the complementary-area vector are zero on average.\ud \ud The total deformation of the assembly, as given by the average of the relative displacements of the edges of the Delaunay tessellation follows the uniform-strain prediction. However, neither the deformation of the physical contact network nor of the virtual contact network has this property. The average relative displacement of physical edges in the normal direction (determined by the branch vector) is smaller than that according to the uniform-strain assumption, while that of virtual contacts is larger. This is caused by the high interparticle stiffness that hinders compression. The reverse observation holds for the tangential component of the relative displacement vector. The contribution of the deformation of the empty space between physical contacts to the continuum, macro-scale strain tensor is therefore very important for the understanding and the prediction of the macro-scale deformation of granular materials

Jamming in frictionless packings of spheres: determination of the critical volume fraction

The jamming transition in granular packings is characterized by a sudden change in the coordination number. In this work we investigate the evolution of coordination number as function of volume fraction for frictionless packings of spheres undergoing isotropic deformation. Using the results obtained from Discrete Element Method simulations, we confirm that the coordination number depends on volume fraction by a power law with exponent α≈0.5 above the critical volume fraction and up to rather high densities. We find that the system size and loading rate do not have an important effect on the evolution of the coordination number. Polydispersity of the packing seems to cause a shift in the critical volume fraction, i.e., more heterogeneous packings jam at higher volume fractions. Finally, we propose and evaluate alternative methods to determine the critical volume fraction based on the number of rattlers, the pressure and the ratio of kinetic and potential energies. The results are all consistent with the critical volume fractions obtained from the fits of the power law to the simulation data

Towards Generic Monitors for Object-Oriented Real-Time Maude Specifications

Non-Functional Properties (NFPs) are crucial in the design of software. Specification of systems is used in the very first phases of the software development process for the stakeholders to make decisions on which architecture or platform to use. These specifications may be an- alyzed using different formalisms and techniques, simulation being one of them. During a simulation, the relevant data involved in the anal- ysis of the NFPs of interest can be measured using monitors. In this work, we show how monitors can be parametrically specified so that the instrumentation of specifications to be monitored can be automatically performed. We prove that the original specification and the automati- cally obtained specification with monitors are bisimilar by construction. This means that the changes made on the original system by adding monitors do not affect its behavior. This approach allows us to have a library of possible monitors that can be safely added to analyze different properties, possibly on different objects of our systems, at will.Universidad de Málaga, Campus de Excelencia Internacional Andalucía Tech. Spanish MINECO/FEDER project TIN2014-52034-R, NSF Grant CNS 13-19109

Cross-diffusion systems for image processing: II. The nonlinear case

In this paper the use of nonlinear cross-diffu\-sion systems to model image restoration is investigated, theoretically and numerically. In the first case, well-posedness, scale-space properties and long time behaviour are analyzed. From a numerical point of view, a computational study of the performance of the models is carried out, suggesting their diversity and potentialities to treat image filtering problems. The present paper is a continuation of a previous work of the same authors, devoted to linear cross-diffusion models. \keywords{Cross-diffusion \and Complex diffusion \and Image restoration

A Statistical Study of Photospheric Magnetic Field Changes During 75 Solar Flares

Abrupt and permanent changes of photospheric magnetic fields have been observed during solar flares. The changes seem to be linked to the reconfiguration of magnetic fields, but their origin is still unclear. We carried out a statistical analysis of permanent line-of-sight magnetic field ($B_{\rm LOS}$) changes during 18 X-, 37 M-, 19 C- and 1 B-class flares using data from Solar Dynamics Observatory/Helioseismic and Magnetic Imager. We investigated the properties of permanent changes, such as frequency, areas, and locations. We detected changes of $B_{\rm LOS}$ in 59/75 flares. We find that strong flares are more likely to show changes, with all flares $\ge$ M1.6 exhibiting them. For weaker flares, permanent changes are observed in 6/17 C-flares. 34.3\% of the permanent changes occurred in the penumbra and 18.9\% in the umbra. Parts of the penumbra appeared or disappeared in 23/75 flares. The area where permanent changes occur is larger for stronger flares. Strong flares also show a larger change of flux, but there is no dependence of the magnetic flux change on the heliocentric angle. The mean rate of change of flare-related magnetic field changes is 20.7 Mx cm$^{-2}$ min$^{-1}$. The number of permanent changes decays exponentially with distance from the polarity inversion line. The frequency of the strength of permanent changes decreases exponentially, and permanent changes up to 750 Mx cm$^{-2}$ were observed. We conclude that permanent magnetic field changes are a common phenomenon during flares, and future studies will clarify their relation to accelerated electrons, white light emission, and sunquakes to further investigate their origin.Comment: Piblished in Ap