Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem

We study stochastic integer programming models for assigning delays to flights that are destined for an airport whose capacity has been impacted by poor weather or some other exogenous factor. In the existing literature, empirical evidence seemed to suggest that a proposed integer programming model had a strong formulation, but no existing theoretical results explained the observation. We apply recent results concerning the polyhedra of stochastic network flow problems to explain the strength of the existing model, and we propose a model whose size scales better with the number of flights in the problem and that preserves the strength of the existing model. Computational results are provided that demonstrate the benefits of the proposed model. Finally, we define a type of equity property that is satisfied by both models.

A note on the Hausdorff dimension of the singular set of solutions to elasticity type systems

We prove partial regularity for minimizers to elasticity type energies with [Formula: see text]-growth, [Formula: see text], in a geometrically linear framework in dimension [Formula: see text]. Therefore, the energies we consider depend on the symmetrized gradient of the displacement field. It is an open problem in such a setting either to establish full regularity or to provide counterexamples. In particular, we give an estimate on the Hausdorff dimension of the potential singular set by proving that is strictly less than [Formula: see text], and actually [Formula: see text] in the autonomous case (full regularity is well-known in dimension [Formula: see text]). The latter result is instrumental to establish existence for the strong formulation of Griffith type models in brittle fracture with nonlinear constitutive relations, accounting for damage and plasticity in space dimensions [Formula: see text] and [Formula: see text].

Some Novel Numerical Applications of Cosserat Continua

Cosserat continua demonstrated to have peculiar mechanical properties, with respect to classic Cauchy continua, because they are able to more accurately describe heterogeneous materials, as particle composites and masonry-like material, taking into account size effects. Many studies have been devoted to their numerical implementation. In this paper, some reference benchmarks, referred to an isotropic heterogeneous sample, are shown by comparing the solutions provided by strong and weak formulations. The strong formulation finite element method (SFEM), implemented in MATLAB®, is compared to the finite element method (FEM), given by COMSOL® Multiphysics, and the advantages of the two approaches are highlighted and discussed.