Microscopically-constrained Fock energy density functionals from chiral effective field theory. I. Two-nucleon interactions

The density matrix expansion (DME) of Negele and Vautherin is a convenient tool to map finite-range physics associated with vacuum two- and three-nucleon interactions into the form of a Skyme-like energy density functional (EDF) with density-dependent couplings. In this work, we apply the improved formulation of the DME proposed recently in arXiv:0910.4979 by Gebremariam {\it et al.} to the non-local Fock energy obtained from chiral effective field theory (EFT) two-nucleon (NN) interactions at next-to-next-to-leading-order (N$^2$LO). The structure of the chiral interactions is such that each coupling in the DME Fock functional can be decomposed into a cutoff-dependent coupling {\it constant} arising from zero-range contact interactions and a cutoff-independent coupling {\it function} of the density arising from the universal long-range pion exchanges. This motivates a new microscopically-guided Skyrme phenomenology where the density-dependent couplings associated with the underlying pion-exchange interactions are added to standard empirical Skyrme functionals, and the density-independent Skyrme parameters subsequently refit to data. A Mathematica notebook containing the novel density-dependent couplings is provided.Comment: 28 pages, 12 figures. Mathematica notebook provided with submission

Computer Tomograph Measurements in Shear and Gravity Particle Flows

The paper reports the recent results obtained on the applicability of cross-sectional digital imaging method to study particle flow characteristics in 3D particle beds forced to move by gravity or shear. X-ray CT imaging technique is widely used in medical diagnostics and, during the last decades, its spatial and temporal resolution has been improved significantly. In this study, an attempt was made to use this technique for engineering purposes. Two experimental set-ups with different types of particle flows were investigated using Siemens Somatom Plus type CT equipment. A series of trials were carried out in a small model hopper with flat bottom and almost cylindrical side wall slightly deviating from verticality. Non steady-state flow was studied during the outflow of particulate material from this vessel, through a central hole at the bottom. Further investigation was fulfilled in a modified Cuette-type shearing device to study steady-state shear flow. This equipment consisted of an almost cylindrical vessel identical to that used for gravity flow measurements, and a smaller inner cylinder rotating within this vessel concentrically, around its vertical axis. The surface of the inner cylinder was notched vertically, i.e. perpendicularly to the direction of rotation to increase wall friction between the particles and the cylinder. Almost spherical sucrose granules, also used for gravity flow measurements, were filled into the gap between the rotating cylinder and the outer wall of the equipment. Movement of particles took place due to shear, generated within the particle bed. By using X-ray CT technique, cross-sectional digital images were obtained in every two seconds for both types of particle flows. For this, the cross-sectional variation of the local Hounsfield density values were measured in a matrix of 0.1x0.1x2.0 mm space elements. It was proved that the applied non-invasive crosssectional imaging technique was suitable to distinguish the stationary and moving particle regions, and by this, to estimate the location of the boundary zone between them