Anisotropic constitutive modeling for nickel base single crystal superalloy Rene N4 at 982 C

A back stress/drag stress constitutive model based on a crystallographic approach to model single crystal anisotropy is presented. Experimental results demonstrated the need for the back stress variable in the inelastic flow equations. Experimental findings suggested that back stress is orientation dependent and controls both strain hardening and recovery characteristics. Due to the observed stable fatigue loops at 1800 F, drag stress is considered constant for this temperature. The constitutive model operated with constraints determined only from tensile data was extensively tested from simple tensile and fatigue to complicated strain hold tests. The model predicted very well under those conditions

Finiteness of the Fixed Point Set for the Simple Genetic Algorithm

The infinite population simple genetic algorithm is a discrete dynamical system model of a genetic algorithm. It is conjectured that trajectories in the model always converge to fixed points. This paper shows that an arbitrarily small perturbation of the fitness will result in a model with a finite number of fixed points. Moreover, every sufficiently small perturbation of fimess preserves the finiteness of the fixed point set. These results allow proofs and constructions that require finiteness of the fixed point set. For example, applying the stable manifold theorem to a fixed point requires the hyperbolicity of the differential of the transition map of the genetic algorithm, which requires (among other things) that the fixed point be isolated

Reinterpreting No Free Lunch

Since it’s inception, the “No Free Lunch theorem” has concerned the application of symmetry results rather than the symmetries themselves. In our view, the conflation of result and application obscures the simplicity, generality, and power of the symmetries involved. This paper separates result from application, focusing on and clarifying the nature of underlying symmetries. The result is a general set-theoretic version of NFL which speaks to symmetries when arbitrary domains and co-domains are involved. Although our framework is deterministic, we note situations where our deterministic set-theoretic results speak nevertheless to stochastic algorithms

Group Properties of Crossover and Mutation

It is supposed that the finite search space Ω has certain symmetries that can be described in terms of a group of permutations acting upon it. If crossover and mutation respect these symmetries, then these operators can be described in terms of a mixing matrix and a group of permutation matrices. Conditions under which certain subsets of Ω are invariant under crossover are investigated, leading to a generalization of the term schema. Finally, it is sometimes possible for the group acting on Ω to induce a group structure on Ω itself