No abstract

No abstract

Many studies originally made in the field of statistical physics have led to results which are directly related to different features of random packings of granular materials. This review outlines some of these recent developments: geometrical properties of packings, electrical transport in the pore or the grain space, mechanics of granular arrays. We mainly focus on the following points:(i) The geometrical properties of random close packings of grains which can be studied using the tools of stereology.(ii) The distribution of contacts which controls the transport characteristics in the grain phase.(iii) The rigidity of granular structures which can be mapped onto a lattice model and which can be approached by a central-force percolation model.(iv) The non-linear properties due to the asymmetry of the contact behaviour between two grains, which can be studied on randomly depleted lattice models. Such properties, which come from the existence of non-linear local laws, are extended to the strong irreversible behaviour of fractured structures.(v) Finally, we consider some minimal structure approaches which model the distribution of stresses along a granular system.Without trying to be exhaustive, we want to show that these different approaches, which are not commonly used in classical descriptions of granular matter, may bring a new impetus to its physics. Together with a physical approach we also introduce a presentation of some mathematical developments of the problem of rigidity of triangular plane grids, which is closely related to the present problem and is a classical subject of applied mathematics mostly ignored by physicists. However, in order to ensure more coherence in the presentation and style of this particular treatment, this last part is presented separately.

No abstract

(No ve mbe r 16, 1964) Extensions of matroid s to se ts co ntaining on e additional ele me nt are c ha rac te ri ze d in te rm s or mod ular cuts of the latti ce or closed s ubse ts. An equival e nt c harac teri za ti o n is give n in term s or lin ear subclasse s or the se t or c irc uit s or bonds or th e matroid . A sc heme for the cons tru c ti o n o r finit e geo· me tri c lattice s is deri ved a nd th e ex is te nce of a t leas t 2" no ni so morphi c matroid s on an II-ele me nt se t is established.