2 research outputs found
Spin-spin correlations in the tt'-Hubbard model
No full textWe present calculations of the tt'-Hubbard model using Quantum Monte Carlo techniques. The parameters are chosen so that the van Hove Singularity in the density of states and the Fermi level coincide. We study the behaviour of the system with increasing Hubbard interaction U. Special emphasis is on the spin-spin correlation (SSC). Unusual behaviour for large U is observed there and in the momentum distribution function ( n(q))
Digital imaging characterisation of a granular hopper flow
No full textGranular flows in hoppers have been studied extensively in the past years. One way of approaching the problem is to focus on theoretical investigation of the bulk flow properties at the macroscopic scale: global flow pattern, wall pressure and strains (Brown et al., 2000), optimal design of hopper geometry and outlet size (Gremaud et al., 2000, Shang Jing et al., 1998), etc. Besides, theories have emerged (Drescher et al., 1995) to link the macroscale behaviour to the micro-scale phenomena acting on the particle level, like arching for example. This can be done by considering the granular matrix as a series of isolated structural members (referring to the so-called Structural Mechanics, SM) or as a continuum (Continuum Mechanics approach, CM). A different approach aims at modelling the inter-particle forces by statistical models (Coppersmith, 1997), or at describing the behaviour of individual particles as well as their interactions during collisions. This leads to computational models referred to as Discrete Elements Simulations (Mattutis et al., 2000) analogous to molecular simulations, which have proved their power but also their limits: due to their complexity, such models are constrained to deal only with simple systems containing a limited number of particles.
Resorting to experimental work is essential in order to compare such theories and models with reality at all levels. Tests on scale models have been carried out for a long time, where quantitative measurements of macroscopic parameters were possible. However, even if phenomena at the particle level were qualitatively observed or suspected, only few quantitative indications could be gained from them.
Recently, new investigation techniques have benefited from the rapid technological innovations. Among them, non-intrusive digital imaging and related image-processing techniques have increased tremendously the potential of traditional photography. Several authors have applied similar techniques for the experimental characterisation of granular flows in hoppers (Langston et al., 1997, Samadani et al., 1999) or in vibrated granular beds (Hsiau et al., 1998). They were initially limited to bulk observations, like deformations of the granular matrix within the silo, e.g. by tracking the shape of initially horizontal layers of coloured particles.
More recently a further step introduced a change of focus from the macroscopic to the microscopic scale, by tracking the movement of individual particles within the matrix. Such techniques, to the knowledge of the author, have always been restricted to the tracking of a small proportion of coloured tracer particles mixed in the dispersion (Hryciw et al., 1997, Losert et al., 1999) or to very large particles. The reason for this limitation is to be found in the characteristics of the particle tracking algorithms, whose robustness is a function of granular concentration and flow velocity: when the interframe particle displacement becomes of the order of magnitude of the particle interdistance (which is close to particle diameter for dense flows in hoppers), the available methods tend to fail quite rapidly, as well the simplest ones relying on minimum displacement matching as the more sophisticated ones, based on trajectory coherence.
In the present work, preliminary results are presented, where a novel particle-tracking method is applied to the
characterisation of granular flow in a wedge-shaped plane hopper. Derived from an original pattern-based
principle aimed at addressing the above shortcomings, the method (Capart et al., 2001) is able to resolve
individual grain motions even for rapid flows of dense, intensively sheared dispersions. Full automation is
achieved, allowing the derivation of accurate statistics from large sets of individual measurements, as well as the construction of complete sets of grain trajectories. This set of methods has recently been extended to the third dimension by resorting to stereoscopic imagery (Spinewine et al., 2000), allowing 3D measurements of free
surface topography, 3D particle tracking and velocimetry, as well as accurate estimation of volumetric granular
concentration
