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In this paper, we study several spatially multidimensional initial-boundary value problems modelling sedimentation-consolidation processes of a flocculated suspension. This solid-fluid mixture is considered as two superimposed continuous media differing in density and viscosity. The phenomenological foundation and derivation of the mathematical model are based on the previous work by R. Bürger et al. (2000, Z. Angew. Math. Mech. 80, 79-92). We study the full coupling of the conservation of mass equation and the conservation of linear momentum equation. For different types of regularization, we establish energy estimates. The dissipative nature of the whole system assures the existence as well as the stability (long time asymptotics) of a solution of the system (provided that the viscosities of the fluid are large enough). Moreover, the energy estimates might serve as the foundation for the design of numerical algorithms to simulate the system.  2001 Elsevier Science

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques.

Localized corrosion phenomena, including pitting corrosion, stress corrosion cracking, and corrosion fatigue, are the principal causes of corrosion-induced damage in electric power-generating facilities and typically result in more than 50 percent of the unscheduled outages. In this paper, we describe a deterministic method for predicting localized corrosion damage in low-pressure steam turbine disks downstream of the Wilson line, where a condensed, thin electrolyte layer exists on the steel disk surfaces. Our calculations show that the initiation and propagation of stress corrosion cracking (SCC) is not very sensitive to the oxygen content of the steam, but is sensitive to the conductivity of the condensed liquid layer and the stresses (residual and operational) that the disk experiences in service.

Abstract-In this paper, we study sensor enabled landmine networks by formulating a minimum-cost mine selection problem. The problem arises in a target defence scenario, where the objective is to destroy the intruding targets using the minimumcost pre-deployed mines. Due to the problem complexity, we first transform it using a novel bucket-tub model, and then propose several approximation algorithms. Among them, it is shown that the layering algorithm can achieve an approximation ratio of α · f , where α ≥ 1 is the tunable relaxation factor and f is the maximum number of mines that a target is associated with, and that the greedy algorithm has an approximation ratio of P j Rj, where Rj is the coefficient in the related integer program. We also present a localized greedy algorithm which is shown to produce the same solution set as the global greedy algorithm. Theoretical analysis and extensive simulations demonstrate the effectiveness of the proposed algorithms.