Dynamics of charged gibbsite platelets in the isotropic phase

We report on depolarized and non-depolarized dynamic light scattering, static light scattering, and static viscosity measurements on interacting charged gibbsite platelets suspended in dimethyl sulfoxide (DMSO). The average collective and (long-time) translational self-diffusion coefficients, and the rotational diffusion coefficient, have been measured as functions of the platelet volume fraction \phi, up to the isotropic-liquid crystal (I/LC) transition. The non-depolarized intensity autocorrelation function, measured at low scattering wavenumbers, consists of a fast and a slowly decaying mode which we interpret as the orientationally averaged collective and translational self-diffusion coefficients, respectively. Both the rotational and the long-time self-diffusion coefficients decrease very strongly, by more than two orders of magnitude, in going from the very dilute limit to the I/LC transition concentration. A similarly strong decrease, with increasing \phi, is observed for the inverse zero-strain limiting static shear viscosity. With increasing \phi, increasingly strong shear-thinning is observed, accompanied by a shrinking of the low shear-rate Newtonian plateau. The measured diffusion coefficients are interpreted theoretically in terms of a simple model of effective charged spheres interacting by a screened Coulomb potential, with hydrodynamic interactions included. The disk-like particle shape, and the measured particle radius and thickness polydispersities, enter into the model calculations via the scattering amplitudes. The interaction-induced enhancement of the collective diffusion coefficient by more than a factor of 20 at larger volume fractions is well captured in the effective sphere model, whereas the strong declines both of the experimental translational and rotational self-diffusion coefficients are underestimated

The Friedrichs Extension of Singular Differential Operators

AbstractThe Friedrichs extension of singular ordinary differential operators of order 2n is characterized in terms of singular boundary conditions. These are given in terms of principal solutions

Counting and computing eigenvalues of left-definite Sturm–Liouville problems

AbstractFor left-definite regular self-adjoint Sturm–Liouville problems we construct a function N(λ) which counts the number of positive eigenvalues less than λ when λ is positive and the number of negative eigenvalues greater than λ when λ is negative. Based on this function we construct a code for the numerical computation of the eigenvalues and illustrate its use with examples. The boundary conditions can be separated or coupled.The code is available from www.mcs.le.ac.uk/~mmarletta/programs.html

Remanufacturing approaches contributing to sustainable engineering Abordagens de remanufatura - uma contribuição para engenharia sustentável

Increasing use of resources by an increasing population with unequally distributed wealth make sustainability an urgent topic to pay attention to. A reference model for sustainability in engineering is presented referring to education and research, management, technology, processes and products as the relevant issues for a global change to sustainability. The European environmental laws for sustainable development are an attempt to cope with this challenge by legislative means. The provocative reality of practical implementation in dealing with electric and electronic products after their usage phases in Europe is illustrated. Laboratory developments in disassembly and testing demonstrate the feasibility of remanufacturing. In addition, approaches to increase the efficiency of remanufacturing by improving the product design are introduced.O crescente uso de recursos gerado pelo contínuo crescimento populacional inserido em um cenário de distribuição desigual de riqueza faz do termo sustentabilidade um tópico urgente para discussão. Neste artigo, apresenta-se um modelo de referência para sustentabilidade em engenharia que aborda questões relevantes para uma mudança global no caminho para a sustentabilidade, priorizando os seguintes elementos: educação e pesquisa; gestão, tecnologia, processos e produtos. As leis ambientais da União Européia esforçam-se para tratar com responsabilidade esse desafio de desenvolvimento sustentável. A realidade de implementações práticas em consideração a produtos eletro-eletrônicos depois de sua fase de uso é ilustrada no artigo. Desenvolvimentos em laboratório de desmontagens e testes demonstram a viabilidade da remanufatura. Além disso, abordagens para aumentar a eficiência do processo de remanufatura a partir de melhorias no processo de desenvolvimento do produto são também sugeridas

Fabrication of magnetic force microscopy probes via localized electrochemical deposition of cobalt

Magnetic force microscopy probes were obtained via the solution phase electrochemical deposition of cobalt nanostructures at the probe apexes. Single tips were fabricated in an atomic force microscope fluid cell. Multiple tips were produced in a single batch with an alternating potential in an electrochemical cell. The probes achieve 50 nm spatial resolution

Fabrication of magnetic force microscopy probes via localized electrochemical deposition of cobalt

Magnetic force microscopy probes were obtained via the solution phase electrochemical deposition of cobalt nanostructures at the probe apexes. Single tips were fabricated in an atomic force microscope fluid cell. Multiple tips were produced in a single batch with an alternating potential in an electrochemical cell. The probes achieve 50 nm spatial resolution