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Equilibrium Constraints (equilibrium + constraint)

Distribution by Scientific Domains
Engineering80%

Selected Abstracts

Phase Equilibria Constraints on Relations of Ore-bearing Intrusions with Flood Basalts in the Panxi Region, Southwestern China

ACTA GEOLOGICA SINICA (ENGLISH EDITION), Issue 2 2009
Zhaochong ZHANG
Abstract: There are two types of temporally and spatially associated intrusions within the Emeishan large igneous province (LIP); namely, small ultramafic subvolcanic sills that host magmatic Cu-Ni-Platinum Group Element (PGE)-bearing sulfide deposits and large mafic layered intrusions that host giant Ti-V magnetite deposits in the Panxi region. However, except for their coeval ages, the genetic relations between the ore-bearing intrusions and extrusive rocks are poorly understood. Phase equilibria analysis (Q-Pl-Ol-Opx-Cpx system) has been carried out to elucidate whether ore-bearing Panzhihua, Xinjie and Limahe intrusions are co-magmatic with the picrites and flood basalts (including high-Ti, low-Ti and alkali basalts), respectively. In this system, the parental magma can be classified as silica-undersaturated olivine basalt and silica-saturated tholeiite. The equivalents of the parental magma of the Xinjie and Limahe peridotites and picrites and low-Ti basalts are silica-undersaturated, whereas the Limahe gabbro-diorites and high-Ti basalts are silica-saturated. In contrast, the Panzhihua intrusion appears to be alkali character. Phase equilibria relations clearly show that the magmas that formed the Panzhihua intrusion and high-Ti basalts cannot be co-magmatic as there is no way to derive one liquid from another by fractional crystallization. On the other hand, the Panzhihua intrusion appears to be related to Permian alkali intrusions in the region, but does not appear to be related to the alkali basalts recognized in the Longzhoushan lava stratigraphy. Comparably, the Limahe intrusion appears to be a genetic relation to the picrites, whereas the Xinjie intrusion may be genetically related to be low-Ti basalts. Additionally, the gabbro-diorites and peridotites of the Limahe intrusion are not co-magmatic, and the former appears to be derived liquid from high-Ti basalts. [source]

On the convergence of stationary sequences in topology optimization

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005
Anton Evgrafov
Abstract We consider structural topology optimization problems including unilateral constraints arising from non-penetration conditions in contact mechanics. The resulting non-convex non-smooth problems are instances of mathematical programs with equilibrium constraints (MPEC), or bi-level programs. Applying nested (implicit programming) algorithms to this class of problems is problematic owing to the singularity of the feasible set. We propose a perturbation strategy combining the relaxation of the equilibrium constraint with the restriction of the design domain to its regular part only. This strategy allows us to attack the problem numerically using standard non-linear programming algorithms. We rigorously study the optimality conditions for the original singular problem as well as the convergence of stationary points and globally optimal solutions to approximating problems towards respective stationary points and globally optimal solutions to the original problem. A limited numerical benchmarking of the algorithm is performed. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Private road competition and equilibrium with traffic equilibrium constraints

JOURNAL OF ADVANCED TRANSPORTATION, Issue 1 2009
Hai Yang
Abstract Toll road competition is one of the important issues under a build-operate-transfer (BOT) scheme, which is being encountered nowadays in many cities. When there are two or more competing firms and each firm operates a competitive toll road, their profits are interrelated due to the competitors' choices and demand inter-dependence in the network. In this paper we develop game-theoretic approaches to the study of the road network, on which multiple toll roads are operated by competitive private firms. The strategic interactions and market equilibria among the private firms are analyzed both in determining their supply (road capacity) and price (toll level) over the network. The toll road competition problems in general traffic equilibrium networks are formulated as an equilibrium program with equilibrium constraints or bi-level variational inequalities. Heuristic solution methods are proposed and their convergences are demonstrated with simple network examples. It is shown that private pricing and competition can be both profitable and welfare-improving. [source]