Filtration problems in porous media are important for studying the movement of groundwater in porous formations and the spreading of liquid concrete injected into porous soil. Deep bed filtration of a monodisperse suspension in a homogeneous porous medium with two simultaneously acting particle capture mechanisms is considered. A mathematical model of suspension flow through porous medium with pore blocking by size-exclusion and arched bridging is developed. Exact solutions are obtained on the concentration front and at the porous medium inlet. For the linear filtration function, exact and asymptotic solutions are constructed.
We prove that any compact manifold whose fundamental group contains an abelian normal subgroup of positive rank can be represented as a leaf of a structurally stable suspended foliation on a compact manifold. In this case, the role of a transversal manifold can be played by an arbitrary manifold. We construct examples of structurally stable foliations that have a compact leaf with infinite solvable fundamental group which is not nilpotent. We also distinguish a class of structurally stable foliations each of whose leaves is compact and locally stable in sense of Ehresmann and Reeb.
Filtering the suspension in porous media is important for long-term assessment of the strength of soil in the construction of underground and hydraulic engineering structures. The geometrical and mechanical model of filtering is considered: solid particles pass freely through the larger pores, and get stuck at the entrance of tiny pores smaller than the diameter of the particles. The asymptotics of the suspended and retained particle concentrations in the suspension is constructed on the assumption of small deposit.
It speaks in God, in translation, in violence, apparently everywhere and in everything. There is, however, somewhere that language does not speak, or in which it speaks without speaking, but only implies - that is the realm of intimacy, where we imply that which we cannot say, but about which we also cannot remain silent. The question then becomes: Can we tolerate the suspension of language implied by intimation? And by intimacy?
A group G acts infinitely transitively on a set Y if for every positive integer m, its action is m-transitive on Y. Given a real affine algebraic variety Y of dimension greater than or equal to 2, we show that, under a mild restriction, if the special automorphism group of Y (the group generated by one-parameter unipotent subgroups) is infinitely transitive on each connected component of the smooth locus Yreg , then for any real affine suspension X over Y, the special automorphism group of X is infinitely transitive on each connected component of Xreg . This generalizes a recent result given by Arzhantsev, Kuyumzhiyan, and Zaidenberg over the field of real numbers.