Probability distribution of eigenspectra and eigendirections of a twodimensional,symmetric rank two random tensor

Let there be given a twodimensional symmetric rank two tensor of random type (examples:strain, stress) which is either directly observed or indirectly estimated from observations by an adjustment procedure. Under the assumption of normalityof tensor components we compute the joint probability density functionas well as the marginal probability density functionsof its eigenspectra (eigenvalues) and eigendirections (orientation parameters). Due to the nonlinearity of the relation between eigenspectra-eigendirections and the random tensor components, via the inverse nonlinear error propagationbiases and aliases of their first and centralized second moments (mean value, variance-covariance) are expressed in terms of Jacobianand Hessianmatrices. The joint probability density function and the first and second moments thus form the fundamental of hypothesis testing and qualify control of eigenspectra (eigenvalues, principal components) and eigendirections (orientation parameters, eigenvectors, principial direction) of a twodimensional, symmetric rank two random tensor.     

Economic gains of liberalising access to fishing quotas within the European Union

This paper analyses the extent to which specialisation gains can be achieved by liberalising access to fishing quotas within the European Union (EU). Fishing quotas are today exchanged between EU member states at a rate of 4% of total turnover in EU fisheries. Germany, Belgium, Denmark and the Netherlands are the most active. Only one fourth of these exchanges are permanent. With the management systems in EU fisheries differing among countries, comparative advantages in fisheries exist in member states with the best management practices. Hence, although positive but small specialisation gains exist in EU fisheries today, these gains might potentially be increased by liberalising access to fishing quotas and allowing transferability of quotas between individuals from different countries on a permanent basis. Increasing the gains might, however, affect relative stability.     

Low-speed impacts between rubble piles modeled as collections of polyhedra

We present results of modeling rubble piles as collections of polyhedra. The use of polyhedra allows more realistic (irregular) shapes and interactions (e.g. collisions), particularly for objects of different sizes. Rotational degrees of freedom are included in the modeling, which may be important components of the motion. We solved the equations of rigid-body dynamics, including frictional/inelastic collisions, for collections of up to several hundred elements. As a demonstration of the methods and to compare with previous work by other researchers, we simulated low-speed collisions between km-scale bodies with the same general parameters as those simulated by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151]. High-speed collisions appropriate to present-day asteroid encounters require additional treatment of shock effects and fragmentation and are the subject of future work; here we study regimes appropriate to planetesimal accretion and re-accretion in the aftermath of catastrophic events. Collisions between equal-mass objects at low speeds () were simulated for both head-on and off-center collisions between rubble piles made of a power-law mass spectrum of sub-elements. Very low-speed head-on collisions produce single objects from the coalescence of the impactors. For slightly higher speeds, extensive disruption occurs, but re-accretion produces a single object with most of the total mass. For increasingly higher speeds, the re-accreted object has smaller mass, finally resulting in complete catastrophic disruption with all sub-elements on escape trajectories and only small amounts of mass in re-accreted bodies. Off-center collisions at moderately low speeds produce two re-accreted objects of approximately equal mass, separating at greater than escape speed. At high speed, complete disruption occurs as with the high-speed head-on collisions. Head-on collisions at low to moderate speeds result in objects of mostly oblate shape, while higher speed collisions produce mostly prolate objects, as do off-center collisions at moderate and high speeds. Collisions carried out with the same dissipative coefficients (coefficient of restitution ?n=0.8, zero friction) as used by Leinhardt et al. [Leinhardt, Z.M., Richardson, D.C., Quinn, T., 2000. Icarus 146, 133-151] result in a value for specific energy for disruption , somewhat lower than the value of 2 J/kg found by them, while collisions with a lower coefficient of restitution and friction [?n=0.5, ?t=0, μ=0.5, similar to those used by Michel, et al. [Michel, P., Benz, W., Richardson, D.C., 2004. Planet. Space Sci. 52, 1109-1117] for SPH + N-body calculations] yield .     

Volatile retention from cometary impacts on the Moon

Impacts of comets and asteroids play an important role in volatile delivery on the Moon. We use a novel method for tracking vapor masses that reach escape velocity in hydrocode simulations of cometary impacts to explore the effects of volatile retention. We model impacts on the Moon to find the mass of vapor plume gravitationally trapped on the Moon as a function of impact velocity. We apply this result to the impactor velocity distribution and find that the total impactor mass retained on the Moon is approximately 6.5% of the impactor mass flux. Making reasonable assumptions about water content of comets and the comet size-frequency distribution, we derive a water flux for the Moon. After accounting for migration and stability of water ice at the poles, we estimate a total 1.3×10⁸-4.3×10⁹ metric tons of water is delivered to the Moon and remains stable at the poles over 1 Ga. A factor of 30 uncertainty in the estimated cometary impact flux is primarily responsible for this large range of values. The calculated mass of water is sufficient to account for the neutron fluxes poleward of 75° observed by Lunar Prospector. A similar analysis for water delivery to the Moon via asteroid impacts shows that asteroids provide six times more water mass via impacts than comets.     

The role of palaeolimnology in assessing eutrophication and its impact on lakes

Eutrophication is perhaps the most pervasive form of pollution. Here we first review its effects on lake ecosystems based largely on modern ecological investigation. The longer time scale afforded by palaeolimnological investigation has seen an increase in the number of the publications since 1990 with a disproportionate increase in citations demonstrating the increasing use and usefulness of palaeolimnology to help understand lakes ecosystems and their response to eutrophication. We summarise briefly the history and origins of palaeolimnological investigation into eutrophication and its impacts in lakes. Then we review quantitative and qualitative palaeolimnological methods for tracking change in nutrient concentrations, algal community and abundance, macrophyte community composition and abundance and zooplanktivorous fish density. The usefulness of stable isotope analysis on sediment organic matter to track eutrophication is assessed and alternative methods discussed. A current challenge is to determine the effects of recent climate change on lake ecosystems. The impacts of climate change and eutrophication on the ecology of lakes have many similarities making it difficult to disentangle the impact of one from the other, in particular where the eutrophication impacts are greatest. We review a number of recent palaeolimnological studies, in particular those integrating long term monitoring data, which have gone some way to identifying when nutrients or climate may be having the greatest impact. Finally, we discuss possible future directions for the discipline, such as the greater integration of studies of evolutionary change using molecular techniques.