Semi-Global Exponential Stability of Augmented Primal-Dual Gradient Dynamics for Constrained Convex Optimization

Primal-dual gradient dynamics that find saddle points of a Lagrangian have been widely employed for handling constrained optimization problems. Building on existing methods, we extend the augmented primal-dual gradient dynamics (Aug-PDGD) to incorporate general convex and nonlinear inequality constraints, and we establish its semi-global exponential stability when the objective function is strongly convex. We also provide an example of a strongly convex quadratic program of which the Aug-PDGD fails to achieve global exponential stability. Numerical simulation also suggests that the exponential convergence rate could depend on the initial distance to the KKT point

フローダイバージョン術前後の脳動脈瘤におけるモデリングと血流解析

要約のみTohoku University太田信課

Adhesion of bituminous and cementitious materials using Particle-Probe Scanning Force Microscopy

As the most important materials in civil engineering, bituminous and cementitious materials have been used widely in pavements and constructions for many years. Accurate determination of adhesion is important to the bonding properties of bituminous and cementitious materials. In this work, we presented a novel approach to measure the adhesion between binders and aggregate mineral particles at microscopic scale. Particle probe scanning force microscopes (SFM) were used to study the adhesion between mineral microspheres representing the primary aggregate constituents (Al2O3, SiO2 and CaCO3) and various control (PG 64-22 and PG 58-22) and modified binders. Results showed that these modified SFM probes could effectively measure the adhesion between binders and aggregate minerals. Consistent adhesion measurements were obtained between different asphalt binders and aggregate mineral particles. Statistical analyses were performed to evaluate effects of different factors on the aggregate-modified binder adhesion, including aggregate constituents, binder types, modifier types and cantilever properties. Due to the stronger polarity of alumina particles, stronger interactions occur within alumina-binder pairs than within silica- and calcium carbonate-binder pairs. Meanwhile, morphologies of different modified binders clearly demonstrated microstructural variations in these binders. The adhesion between steel and different cement hydrated products was measured using particle probe SFM. Adhesive forces are collected between steel microspheres and new (four-week old) and old (six-month old) cement in air and saturated lime water. Mixed Gaussian models were applied to predict phase distributions in the cement paste, i.e., low density C-S-H, high density C-S-H, CH, other hydrated products and the unreacted components. For new cement in saturated lime water, adhesive forces between steel and low density C-S-H, high density C-S-H and other hydrated products are intermediate among all groups selected. The adhesive forces between steel and calcium hydroxide are smallest, whereas the adhesive forces between steel and the unreacted phases are largest. For the six-month old cement, the interweaving of calcium carbonate crystals and C-S-H during the carbonation produces greater adhesive forces to steel, consistent with the adhesive forces between steel and the control calcium carbonate specimen. CH turned into calcium carbonate by reacting with carbon dioxide in air. An increase in adhesive forces was found between steel and calcium carbonate in the old cement than those between steel and CH in the new cement. Particle probe SFM is able to measure the adhesion in bimaterials. For bituminous materials, this methodology provides opportunities to evaluate the effects of different processing methods and to generate quantitative information for the development of multi- scale asphalt mixture cracking models. For cementitious materials, these studies opened new avenues to study the interactions between steel and cement at microscale under a variety of environmental conditions and can be formulated as crack initiation and propagation criteria incorporated in multiscale models for reinforced concrete structures