Molecular kinetics of solid and liquid CHCl3_3

We present a detailed analysis of the molecular kinetics of CHCl$_3$ in a range of temperatures covering the solid and liquid phases. Using nuclear quadrupolar resonance we determine the relaxation times for the molecular rotations in solid at pre-melting conditions. Molecular dynamics simulations are used to characterize the rotational dynamics in the solid and liquid phases and to study the local structure of the liquid in terms of the molecular relative orientations. We find that in the pre-melting regime the molecules rotate about the C-H bond, but the rotations are isotropic in the liquid, even at supercooled conditions.Comment: Chemical Physics Letter (in press). 14 pages, 7 figure

A matéria do património

Este texto é formado pelas notas tomadas no decurso da preparação de uma aula, ou melhor, de um conjunto de aulas. Não se trata de um ensaio, mas de materiais seleccionados pelo docente em função de um ponto do programa: comentários à bibliografia recomendada, apontamentos de natureza explicativa, reflexões destinadas a suscitar e informar o debate intelectual. O tema da aula é a atitude patrimonial e seus significados. Em sociedades que se caracterizam pela predação da natureza e, portanto, da história, a patrimonialização funciona num contexto contraditório: legitima-se num dever de preservação de manifestações do passado numa sociedade de generalizada velocidade que perdeu o sentido da história, sobretudo da história dos tempos longos. O património é convocado pelos processos de afirmação de identidade e até por estratégias de turismo e animação, mas a descontextualização a que é submetido oculta o seu significado original e sublinha a sua reificação

On the asymptotic spectrum of finite element matrix sequences

We derive a new formula for the asymptotic eigenvalue distribution of stiffness matrices obtained by applying Fi finite elements with standard mesh refinement to the semielliptic PDE of second order in divergence form -\u25bd(\u39a\u25bdTu) = f on \u3a9, u = g on 02\u3a9. Here \u3a9 82 \u211d2, and K is supposed to be piecewise continuous and point wise symmetric semipositive definite. The symbol describing this asymptotic eigenvalue distribution depends on the PDE, but also both on the numerical scheme for approaching the underlying bilinear form and on the geometry of triangulation of the domain. Our work is motivated by recent results on the superlinear convergence behavior of the conjugate gradient method, which requires the knowledge of such asymptotic eigenvalue distributions for sequences of matrices depending on a discretization parameter h when h \u2192 0. We compare our findings with similar results for the finite difference method which were published in recent years. In particular we observe that our sequence of stiffness matrices is part of the class of generalized locally Toeplitz sequences for which many theoretical tools are available. This enables us to derive some results on the conditioning and preconditioning of such stiffness matrices