In this paper we explore the algorithmic space in which stripification, simplification and geometric compression of triangulated 2-manifolds overlap. Edge-collase/uncollapse based geometric simplification algorithms develop a hierarchy of collapses such that during uncollapse the reverse order has to be maintained. We show that restricting the simplification and refinement operations only to, w...

Abstract Collapsible soils have caused infrastructural damages resulting in several economic losses and loss of lives certain cases. The prerequisite for collapse occurring is an open metastable structure; capable developing any soil type given the right placement or aging conditions. Natural anthropogenic (engineered non-engineered) collapsible exist many regions world. In their unsaturated st...

Loess is very widely distributed, and the unsaturated hydraulic conductivity of loess related to many engineering issues. To determine remoulded more conveniently at a lower cost, filter paper test soil column seepage were carried out. The results indicate that in one-dimensional process, increases with increase volumetric water content, as time continues, from top depth 40 cm gradually becomes...

The microstructure can have an important impact on the hydraulic and mechanical behaviors of unsaturated soil; therefore, it must be considered in constitutive models to enable accurate predictions soil behavior. This paper focused modeling soils that exhibited a dual porosity structure. Based assumption macro micropores contained double structure had different influences behaviors, effective d...

Let ∆(Πn) denote the order complex of the partition lattice. The natural Sn-action on the set [n] induces an Sn-action on ∆(Πn). We show that the regular CW complex ∆(Πn)/Sn is collapsible. Even more, we show that ∆(Πn)/Sn is collapsible, where Π∆ is a suitable type selection of the partition lattice. This allows us to generalize and reprove in a conceptual way several previous results regardin...

A graph G is collapsible if for every even subset X ~ V(G), G has a subgraph r such that G E(J ') is connected and the set of odd-degree vertices of J' is X. A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the reduction of G. In this paper. we characterize graphs of diameter two in terms of collapsible subgraphs and investigate the relationship between t...

Non-evasiveness is a further strengthening of collapsibility, emerged in theoretical computer science and later studied by Kahn, Saks and Sturtevant [9] and Welker [11]. A 0-dimensional complex is non-evasive if and only if it consists of a single point. Recursively, a d-dimensional simplicial complex (d > 0) is non-evasive if and only if there is some vertex v whose link and deletion are both ...

Higher-order recursion schemes are systems of rewrite rules on typed non-terminal symbols, which can be used to define infinite trees. The Global Modal Mu-Calculus Model Checking Problem takes as input such a recursion scheme together with a modal μ-calculus sentence and asks for a finite representation of the set of nodes in the tree generated by the scheme at which the sentence holds. Using a...

We present a combined theoretical and computational analysis of three-dimensional unsteady finite-Reynolds-number flows in collapsible tubes whose walls perform prescribed high-frequency oscillations which resemble those typically observed in experiments with a Starling resistor. Following an analysis of the flow fields, we investigate the system’s overall energy budget and establish the critic...

In 1975 Wegner conjectured that the nerve of every finite good cover in R is d-collapsible. We disprove this conjecture. A good cover is a collection of open sets in R such that the intersection of every subcollection is either empty or homeomorphic to an open d-ball. A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing a face of dimension at mos...