In this article, we investigate the spectrum of the Neumann-Poincaré operator associated to a periodic distribution of small inclusions with size ε, and its asymptotic behavior as the parameter ε vanishes. Combining techniques pertaining to the fields of homogenization and potential theory, we prove that the limit spectrum is composed of the ‘trivial’ eigenvalues 0 and 1, and of a subset which ...

The study of diffusion in macromolecular solutions is important in many biomedical applications such as separations, drug delivery, and cell encapsulation, and key for many biological processes such as protein assembly and interstitial transport. Not surprisingly, multiple models for the a-priori prediction of diffusion in macromolecular environments have been proposed. However, most models inc...

We give some examples of existing mathematical methods for homogenizing partial differential equations (PDEs). In particular we will explore homogenization in Fourier space. The Maxwell equations are homogenized as an example of the method. INTRODUCTION Homogenization of PDEs is a mathematical method in which one find homogeneous material approximations of heterogeneous materials. That is, for ...

objective(s): in the current study, sunscreen and moisturizing properties of solid lipid nanoparticle (sln)-safranal formulations were evaluated. materials and methods:series of sln were prepared using glyceryl monostearate, tween 80 and different amounts of safranal by high shear homogenization, and ultrasound and high-pressure homogenization (hph) methods. sln formulations were characterized ...

Studying the patterns in which local extinctions occur is critical to understanding how extinctions affect biodiversity at local, regional and global spatial scales. To understand the importance of patterns of extinction at a regional spatial scale, we use data from extirpations associated with a widespread pathogenic agent of amphibian decline, Batrachochytrium dendrobatidis (Bd) as a model sy...

Human-induced biotic homogenization resulting from landscape change and increased competition from widespread generalists or 'winners', is widely recognized as a global threat to biodiversity. However, it remains unclear what aspects of landscape structure influence homogenization. This paper tests the importance of interspecific competition and landscape structure, for the spatial homogeneity ...

Two milk protein concentrates powders with 80% protein content (MPC80) were reconstituted with either water or permeate at 4C or 37C to contain 3.5% protein content. Samples were homogenized at 0 or 13800 kPa. The objective of this research was to determine how different solubility measures such as solubility index, soluble solids and particle size were affected by powder source, reconstitution...