Durability study of eleven years old cement-bentonite cut-off wall material

Comprehensive understanding of the long-term performance of cement-bentonite slurry trench cut-off walls is essential as these mixes may degrade when exposed to aggressive environments or when subjected to prolonged drying. A series of wetting-drying and immersion experiments was carried out to evaluate the durability characteristics of laboratory mixed samples and block field samples from 40 days to 11 years of age. For the wetting-drying tests, the samples buried in medium graded sand were subjected to periodical flooding and drying cycles. They were then used for permeability testing and unconfined compressive strength (UCS) testing. For the immersion tests, the samples confined in perforated molds were submerged in magnesium sulfate solution for 16 weeks and their microstructures were then analyzed using X-ray diffraction (XRD) technique. This paper identifies the effects of contaminant exposure on durability of cement-bentonite and the effects of aging by comparing 11 years old samples to younger samples. Test results showed that young or previously contaminated cement-bentonite mixes are more susceptible to sulfate attack than old or less contaminated mixes. Copyright ASCE 2008.

Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Low-rank optimization on the cone of positive semidefinite matrices

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a low-rank solution. The factorization X = Y Y T leads to a reformulation of the original problem as an optimization on a particular quotient manifold. The present paper discusses the geometry of that manifold and derives a second-order optimization method with guaranteed quadratic convergence. It furthermore provides some conditions on the rank of the factorization to ensure equivalence with the original problem. In contrast to existing methods, the proposed algorithm converges monotonically to the sought solution. Its numerical efficiency is evaluated on two applications: the maximal cut of a graph and the problem of sparse principal component analysis. © 2010 Society for Industrial and Applied Mathematics.