Explicit Construction of the Brownian Self-Transport Operator

Applying the technique of characteristic functions developped for one-dimensional regular surfaces (curves) with compact support, we obtain the distribution of hitting probabilities for a wide class of finite membranes on square lattice. Then we generalize it to multi-dimensional finite membranes on hypercubic lattice. Basing on these distributions, we explicitly construct the Brownian self-transport operator which governs the Laplacian transfer. In order to verify the accuracy of the distribution of hitting probabilities, numerical analysis is carried out for some particular membranes.Comment: 30 pages, 9 figures, 1 tabl

A free boundary problem for the localization of eigenfunctions

We study a variant of the Alt, Caffarelli, and Friedman free boundary problem with many phases and a slightly different volume term, which we originally designed to guess the localization of eigenfunctions of a Schr\"odinger operator in a domain. We prove Lipschitz bounds for the functions and some nondegeneracy and regularity properties for the domains.Comment: 174 page

Diffusion-Reorganized Aggregates: Attractors in Diffusion Processes?

A process based on particle evaporation, diffusion and redeposition is applied iteratively to a two-dimensional object of arbitrary shape. The evolution spontaneously transforms the object morphology, converging to branched structures. Independently of initial geometry, the structures found after long time present fractal geometry with a fractal dimension around 1.75. The final morphology, which constantly evolves in time, can be considered as the dynamic attractor of this evaporation-diffusion-redeposition operator. The ensemble of these fractal shapes can be considered to be the {\em dynamical equilibrium} geometry of a diffusion controlled self-transformation process.Comment: 4 pages, 5 figure

Transfer across Random versus Deterministic Fractal Interfaces

A numerical study of the transfer across random fractal surfaces shows that their responses are very close to the response of deterministic model geometries with the same fractal dimension. The simulations of several interfaces with prefractal geometries show that, within very good approximation, the flux depends only on a few characteristic features of the interface geometry: the lower and higher cut-offs and the fractal dimension. Although the active zones are different for different geometries, the electrode reponses are very nearly the same. In that sense, the fractal dimension is the essential "universal" exponent which determines the net transfer.Comment: 4 pages, 6 figure

The Nagoya Protocol on the use of genetic resources : one embodiment of an endless discussion

O objetivo deste artigo é destacar o processo de negociação do Protocolo de Nagoya sobre a utilização dos recursos genéticos, adotado em outubro de 2010. Ao abordar os mitos e realidades associados à exploração da biodiversidade em uma perspectiva mais ampla, busca-se discutir como e por que os argumentos utilizados por países desenvolvidos e em desenvolvimento foram finalmente conciliados, resultando em um novo quadro jurídico internacional. O artigo demonstra em que medida este Protocolo permite aplicar o disposto na Convenção sobre a Diversidade Biológica de forma coerente à legislação internacional pertinente (por exemplo, referente à propriedade intelectual). Também pretende avaliar se o protocolo permitirá reduzir a sempre existente lacuna entre os conceitos jurídicos construídos pela «biodiplomacia» e as necessidades reais e práticas de cientistas e empresas. Por último, procura estimar o impacto deste documento e sua aplicação sobre as estruturas já existentes, com foco na experiência brasileira