Effect of the porosity on the fracture surface roughness of sintered materials: From anisotropic to isotropic self-affine scaling

To unravel how the microstructure affects the fracture surface roughness in heterogeneous brittle solids like rocks or ceramics, we characterized the roughness statistics of post-mortem fracture surfaces in home-made materials of adjustable microstructure length-scale and porosity, obtained by sintering monodisperse polystyrene beads. Beyond the characteristic size of disorder, the roughness profiles are found to exhibit self-affine scaling features evolving with porosity. Starting from a null value and increasing the porosity, we quantitatively modify the self-affine scaling properties from anisotropic (at low porosity) to isotropic (for porosity larger than 10 %).Comment: 10 pages, 10 figures, Physical Review E in Jan 2015, Vol. 91 Issue

Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming

In this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm. Compared to other primal--dual affine scaling algorithms for semidefinite programming, our algorithm enjoys the lowest computational complexity

Polynomial Primal-Dual Cone Affine Scaling for Semidefinite Programming

In this paper we generalize the primal--dual cone affine scaling algorithm of Sturm and Zhang to semidefinite programming. We show in this paper that the underlying ideas of the cone affine scaling algorithm can be naturely applied to semidefinite programming, resulting in a new algorithm. Compared to other primal--dual affine scaling algorithms for semidefinite programming, our algorithm enjoys the lowest computational complexity.semidefinite programming;affine scaling;primal--dual Interior point methods

On affine scaling inexact dogleg methods for bound-constrained nonlinear systems

Within the framework of affine scaling trust-region methods for bound constrained problems, we discuss the use of a inexact dogleg method as a tool for simultaneously handling the trust-region and the bound constraints while seeking for an approximate minimizer of the model. Focusing on bound-constrained systems of nonlinear equations, an inexact affine scaling method for large scale problems, employing the inexact dogleg procedure, is described. Global convergence results are established without any Lipschitz assumption on the Jacobian matrix, and locally fast convergence is shown under standard assumptions. Convergence analysis is performed without specifying the scaling matrix used to handle the bounds, and a rather general class of scaling matrices is allowed in actual algorithms. Numerical results showing the performance of the method are also given

Generalized Kruithof approach for traffic matrix estimation

[Abstract]: In this paper, the traffic matrix estimation problem is formulated as an nonlinear optimization problem based on the generalized Kruithof approach which uses the Kullback distance to measure the probabilistic distance between two traffic matrices. In addition, an algorithm using the affine scaling method is provided to solve the constraint optimization problem