Search results for "Compact"
showing 10 items of 531 documents
On the Analysis of a Random Interleaving Walk–Jump Process with Applications to Testing
2011
Abstract Although random walks (RWs) with single-step transitions have been extensively studied for almost a century as seen in Feller (1968), problems involving the analysis of RWs that contain interleaving random steps and random “jumps” are intrinsically hard. In this article, we consider the analysis of one such fascinating RW, where every step is paired with its counterpart random jump. In addition to this RW being conceptually interesting, it has applications in testing of entities (components or personnel), where the entity is never allowed to make more than a prespecified number of consecutive failures. The article contains the analysis of the chain, some fascinating limiting proper…
Resuming Shapes with Applications
2004
Many image processing tasks need some kind of average of different shapes. Frequently, different shapes obtained from several images have to be summarized. If these shapes can be considered as different realizations of a given random compact set, then the natural summaries are the different mean sets proposed in the literature. In this paper, new mean sets are defined by using the basic transformations of Mathematical Morphology (dilation, erosion, opening and closing). These new definitions can be considered, under some additional assumptions, as particular cases of the distance average of Baddeley and Molchanov. The use of the former and new mean sets as summary descriptors of shapes is i…
Contact formation in random networks of elongated objects
2014
The effect of steric hindrance is an important aspect of granular packings as it gives rise to, e.g., limitations on the densities of ordered and disordered packings, both of which are essentially defined by the geometry of the constituents. Here we focus on the random packing of rods via deposition and their distributions of contact number and segment length. Such statistical properties are relevant for mechanical properties of the structures, but the (quite large) steric effects on them have not been addressed in previous studies. We therefore develop a theory that describes the statistical properties of rod packings, while taking into account that the deposited rods cannot overlap and th…
Shear strength of a compacted scaly clay in variable saturation conditions
2015
Scaly clays are stiff and highly fissured clays often used as construction materials. This paper presents the results of triaxial compression tests carried out on saturated and unsaturated samples of a compacted scaly clay. Complementary investigation on the microstructural features and their evolution with the amount of water stored into the material are also presented in order to shed light on the evolution of the micro- and macroporosity with suction. The water retention behaviour of the compacted scaly clay is also addressed. The results from the controlled suction triaxial tests are used to discuss the applicability of a single-shear strength criterion to compacted double-structured cl…
Stylolite interfaces and surrounding matrix material: Nature and role of heterogeneities in roughness and microstructural development
2010
Rough pressure solution interfaces, like stylolites, are one of the most evident features of localized slow deformation in rocks of the upper crust. There is a general consensus that the development of these rough structures is a result of localized, stress enhanced, dissolution of material along a fluid filled interface, but little is known on the initiation of this roughness. The aim of this article is to reveal the role of heterogeneities initially present in the host-rock on roughness initiation. This should give insights on whether stylolite roughness is generated by a stress-induced instability or by the presence of disorder in the material (i.e. quenched noise). We use a microstructu…
Volumetric Behaviour of Lime Treated High Plasticity Clay Subjected to Suction Controlled Drying and Wetting Cycles
2017
The paper presents some experimental results collected on samples recovered from an experimental embankment obtained by compacting a lime-treated clay. Samples were collected soon after the in situ compaction and they were cured in controlled environmental conditions for at least 18 months. Mercury intrusion porosimetry tests (MIP) were carried out on freeze-dried specimens to characterize the microstructure of the material. In order to assess the durability of the improved material, laboratory tests focused on the effects of cyclic variations of the degree of saturation on the water retention properties and the volumetric behaviour of the stabilized clay. Collected results show that the li…
Stress path dependence of hydromechanical behaviour of compacted scaly clay in wetting and drying suction controlled oedometer tests at constant vert…
2008
The results are presented of an experimental programme devoted to investigating the volumetric strain and water ratio (volume of water to volume of solids) evolution of a compacted scaly clay stressed by wetting and drying cycles in suction-controlled oedometer tests. The stress paths applied included loading and unloading cycles at constant matric suction and suction controlled wetting-drying cycles at constant vertical net stress. The test results show that during wetting and drying cycles the samples experienced irreversible shrinkage or swelling strains depending on the stress path applied. Irreversible water ratio increases were always observed in these cycles. However, a quasi-reversi…
Volume change behaviour of a compacted scaly clay during cyclic suction changes
2010
The research presented in this paper focuses on the investigation and modelling of the volume change response of compacted tectonised clay samples subjected to several wetting and drying cycles in controlled-suction oedometers. Oedometer tests were carried out under different values of constant vertical net stress, and wetting and drying cycles were performed varying applied matric suction between 10 and 800 kPa. The investigation was complemented with a study of the material microstructure to support the interpretation of the overall mechanical response. At a microscopic level, the material is characterized by different types of particle assemblages, scales, and clay aggregates. One of th…
Computation of the topological type of a real Riemann surface
2014
We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution τ \tau , namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the A \mathcal {A} -cycles are invariant under the anti-holomorphic involution τ \tau .
Surfaces with Boundary
2012
One of the objectives of this book is to obtain a rigorous proof of a version of Green’s formula for compact subsets of \(\mathbb{R}^2\) whose topological boundary is a regular curve of class C 2. These sets are typical examples of what we will call regular 2-surfaces with boundary in \(\mathbb{R}^2\). The analogous three-dimensional example would consist of a compact set of \(\mathbb{R}^3\) whose topological boundary is a regular surface of class C 2. The following example is perhaps instructive.