In this article, the homogenization process of periodic structures is analyzed using Bloch waves in the case of system of linear elasticity in three dimensions. The Bloch wave method for homogenization relies on the regularity of the lower Bloch spectrum. For the three dimensional linear elasticity system, the first eigenvalue is degenerate of multiplicity three and hence existence of such a re...

The widespread replacement of native species with cosmopolitan, nonnative species is homogenizing the global fauna and flora. While the empirical study of biotic homogenization is substantial and growing, theoretical aspects have yet to be explored. Consequently, the breadth of possible ecological mechanisms that can shape current and future patterns and rates of homogenization remain largely u...

Species homogenization or floristic differentiation are two possible consequences of the fragmentation process in plant communities. Despite the few studies, it seems clear that fragments with low forest cover inserted in anthropogenic matrices are more likely to experience floristic homogenization. However, the homogenization process has two other components, genetic and functional, which have...

Abstract. Homogenization of integral functionals is studied under the constraint that admissible maps have to take their values into a given smooth manifold. The notion of tangential homogenization is defined by analogy with the tangential quasiconvexity introduced by Dacorogna, Fonseca, Malý & Trivisa [18]. For energies with superlinear or linear growth, a Γ-convergence result is established i...

Human population and urbanization is unprecedented in its rate of growth and geographic scope. With the help of humans, exotic species have piggybacked their way to distant lands, which in combination with the loss of endemic native species, has led to the convergence of biological communities toward common and ubiquitous forms. However, the extent to which this ‘‘biotic homogenization’’ varies...

Considerable reshuffling of biotas has occurred in recent decades, largely through the gradual replacement of once spatially distinct, native communities with locally expanding and cosmopolitan, non-native ones, in a process coined biotic homogenization (McKinney & Lockwood 1999; Rahel 2000; Olden & Poff 2003; Rooney et al. 2004). Implications of biotic homogenization surfaced recently within t...

Quantitative studies of biotic homogenization can provide useful insights into conservation problems when used appropriately, but can be dangerously misleading when they are not. By separating the concept of biotic homogenization at the global scale from the study of biotic homogenization at spatiallyand temporally-explicit scales, researchers can avoid many of the subtle pitfalls inherent in h...

We prove a general convergence result for singular perturbations with an arbitrary number of scales of fully nonlinear degenerate parabolic PDEs. As a special case we cover the iterated homogenization for such equations with oscillating initial data. Explicit examples, among others, are the two-scale homogenization of quasilinear equations driven by a general hypoelliptic operator and the n-sca...

—Widespread introduction of common species coupled with extirpation of endemic species can cause fish assemblages to lose much of their regional uniqueness. This process of biotic homogenization contrasts with biotic differentiation, whereby initially similar fish faunas diverge due to introductions of different species. The relative importance of homogenization and differentiation in altering ...

 In this work, effects of homogenization time of 3 to 13 h at 1200 °C on the grain refinement of as-cast AISI 301 stainless steel after different hot rolling conditions were investigated. The results showed that the minimum grain size of 16±7 mm was achieved when homogenization took place at 1200 °C for 9 h followed by hot rolling at temperature range of 1000–1200 °C with strain of 0.8 and stra...