14,418 research outputs found
Applying GSH to a Wide Range of Experiments in Granular Media
Granular solid hydrodynamics (GSH) is a continuum-mechanical theory for
granular media, the range of which is shown in this paper. Simple, frequently
analytic solutions are related to classic observations at different shear
rates, including: (i)~static stress distribution, clogging; (ii)~elasto-plastic
motion: loading and unloading, approach to the critical state, angle of
stability and repose; (iii)~rapid dense flow: the -rheology, Bagnold
scaling and the stress minimum; (iv)~elastic waves, compaction, wide and narrow
shear band. Less conventional experiments have also been considered: shear
jamming, creep flow, visco-elastic behavior and nonlocal fluidization. With all
these phenomena ordered, related, explained and accounted for, though
frequently qualitatively, we believe that GSH may be taken as a unifying
framework, providing the appropriate macroscopic vocabulary and mindset that
help one coming to terms with the breadth of granular physics.Comment: arXiv admin note: substantial text overlap with arXiv:1207.128
Nonlinear Generalized Functions: their origin, some developments and recent advances
We expose some simple facts at the interplay between mathematics and the real
world, putting in evidence mathematical objects " nonlinear generalized
functions" that are needed to model the real world, which appear to have been
generally neglected up to now by mathematicians. Then we describe how a
"nonlinear theory of generalized functions" was obtained inside the Leopoldo
Nachbin group of infinite dimensional holomorphy between 1980 and 1985. This
new theory permits to multiply arbitrary distributions and contains the above
mathematical objects, which shows that the features of this theory are natural
and unavoidable for a mathematical description of the real world. Finally we
present direct applications of the theory such as existence-uniqueness for
systems of PDEs without classical solutions and calculations of shock waves for
systems in non-divergence form done between 1985 and 1995, for which we give
three examples of different nature: elasticity, cosmology, multifluid flows.Comment: 42 pages, 4 figure
- …