New calculations of P(b) curves for 1s_\sigma excitation in low-Z (Z\le10) ion-atom scattering

Ab initio fully relativistic SCF molecular calculations of energy eigenvalues as well as coupling-matrix elements are used to calculate the 1s_\sigma excitation differential cross section for Ne-Ne and Ne-O in ion-atom collisions. A relativistic perturbation treatment which allows a direct comparison with analogous non-relativistic calculations is also performed.

Statistical treatment of grain-size curves and empirical distributions: densities as compositions?

The preceding two editions of CoDaWork included talks on the possible consideration of densities as infinite compositions: Egozcue and D´ıaz-Barrero (2003) extended the Euclidean structure of the simplex to a Hilbert space structure of the set of densities within a bounded interval, and van den Boogaart (2005) generalized this to the set of densities bounded by an arbitrary reference density. From the many variations of the Hilbert structures available, we work with three cases. For bounded variables, a basis derived from Legendre polynomials is used. For variables with a lower bound, we standardize them with respect to an exponential distribution and express their densities as coordinates in a basis derived from Laguerre polynomials. Finally, for unbounded variables, a normal distribution is used as reference, and coordinates are obtained with respect to a Hermite-polynomials-based basis. To get the coordinates, several approaches can be considered. A numerical accuracy problem occurs if one estimates the coordinates directly by using discretized scalar products. Thus we propose to use a weighted linear regression approach, where all k- order polynomials are used as predictand variables and weights are proportional to the reference density. Finally, for the case of 2-order Hermite polinomials (normal reference) and 1-order Laguerre polinomials (exponential), one can also derive the coordinates from their relationships to the classical mean and variance. Apart of these theoretical issues, this contribution focuses on the application of this theory to two main problems in sedimentary geology: the comparison of several grain size distributions, and the comparison among different rocks of the empirical distribution of a property measured on a batch of individual grains from the same rock or sediment, like their composition

Vector functions and curves

Exercises and solutions about vector functions and curves.

Corticosterone plasma concentrations in Carioca High- and Low-Conditioned freezing rats after a fear conditioned task

Our group in the Psychology Department at Pontifícia Universidade Católica do Rio de Janeiro (PUC-Rio) developed a rat genetic model of extreme freezing in response to contextual cues in an experimental chamber previously associated with footshock. One of the lines, Carioca High Freezing (CHF), exhibits an enhanced conditioned freezing response, whereas the other line, Carioca Low Freezing (CLF), shows the opposite response. The present study investigated corticosterone concentration between these two lines of animals and a random (RND) line of rats both under basal conditions and test condition after an emotional challenge using a contextual fear conditioning protocol. Comparisons between basal and test plasma corticosterone concentrations suggested differential basal and fear-induced differences between the two lines. The differences between basal conditions is an important and relevant aspect to be considered in behavioral experiments using or assessing stress and could help to understand variability in naïve populations.

Influence of freezable/non-freezable water and sucrose on the viability of Theobroma cacao somatic embryos following desiccation and freezing

Encapsulated cocoa (Theobroma cacao L.) somatic embryos subjected to 0.08-1.25 M sucrose treatments were analyzed for embryo soluble sugar content, non-freezable water content, moisture level after desiccation and viability after desiccation and freezing. Results indicated that the higher the sucrose concentration in the treatment medium, the greater was the extent of sucrose accumulation in the embryos. Sucrose treatment greatly assisted embryo post-desiccation recovery since only 40% of the control embryos survived desiccation, whereas a survival rate of 60-95% was recorded for embryos exposed to 0.5-1.25 M sucrose. The non-freezable water content of the embryos was estimated at between 0.26 and 0.61 g H2O g(-1)dw depending on the sucrose treatment, and no obvious relationship could be found between the endogenous sucrose level and the amount of non-freezable water in the embryos. Cocoa somatic embryos could withstand the loss of a fraction of their non-freezable water without losing viability following desiccation. Nevertheless, the complete removal of potentially freezable water was not sufficient for most embryos to survive freezing.

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Finding the point on Bezier Curves with the normal vector passing an external point

Two algorithms for finding the point on non-rational/rational Bezier curves of which the normal vector passes through a given external point are presented. The algorithms are based on Bezier curves generation algorithms of de Casteljau's algorithm for non-rational Bezier curve or Farin's recursion for rational Bezier curve, respectively. Orthogonal projections from the external point are used to guide the directional search used in the proposed iterative algorithms. Using Lyapunov's method, it is shown that each algorithm is able to converge to a local minimum for each case of non-rational/rational Bezier curves. It is also shown that on convergence the distance between the point on curves to the external point reaches a local minimum for both approaches. Illustrative examples are included to demonstrate the effectiveness of the proposed approaches.

The elasticity of demand is about occupancy, not prices: building European demand curves based on occupancy elasticity

The peak congestion of the European grid may create significant impacts on system costs because of the need for higher marginal cost generation, higher cost system balancing and increasing grid reinforcement investment. The use of time of use rates, incentives, real time pricing and other programmes, usually defined as Demand Side Management (DSM), could bring about significant reductions in prices, limit carbon emissions from dirty power plants, and improve the integration of renewable sources of energy. Unlike previous studies on elasticity of residential electricity demand under flat tariffs, the aim of this study is not to investigate the known relatively inelastic relationship between demand and prices. Rather, the aim is to assess how occupancy levels vary in different European countries. This reflects the reality of demand loads, which are predominantly determined by the timing of human activities (e.g. travelling to work, taking children to school) rather than prices. To this end, two types of occupancy elasticity are estimated: baseline occupancy elasticity and peak occupancy elasticity. These represent the intrinsic elasticity associated with human activities of single residential end-users in 15 European countries. This study makes use of occupancy time-series data from the Harmonised European Time Use Survey database to build European occupancy curves; identify peak occupancy periods; draw time use demand curves for video and TV watching activity; and estimate national occupancy elasticity levels of single-occupant households. Findings on occupancy elasticities provide an indication of possible DSM strategies based on occupancy levels and not prices.