One important issue associated with the complexity of dynamically evolving material interface is the scale-dependent dynamics which implies very different physical phenomena depending on the resolvability of the material interface. In this work we present a concept of multi-scale modeling where the interface interaction is modeled as being in mechanical non-equilibrium or in equilibrium, depend...

1. Introduction Resolvable designs, though introduced in the combinatorial context, have found their utility in field experiments. The concept of resolvability is due to Bose (1942) who defined this for a balanced incomplete block (BIB) design. A BIB design is an arrangement of v treatments into b blocks such that each block contains k (< v) distinct treatments, each treatment appears in r bloc...

The minimum complexity or minimum description-length criterion developed by Kolmogorov, Rissanen, Wallace, So&in, and others leads to consistent probability density estimators. These density estimators are defined to achieve the best compromise between likelihood and simplicity. A related issue is the compromise between accuracy of approximations and complexity relative to the sample size. An i...

In this paper we examine the resolvability of infinite designs. We show that in stark contrast to the finite case, resolvability for infinite designs is fairly commonplace. We prove that every t-(v, k,Λ) design with t finite, v infinite and k, λ < v is resolvable and, in fact, has α orthogonal resolutions for each α < v. We also show that, while a t-(v, k,Λ) design with t and λ finite, v infini...