On natural resource substitution

We present a simple dynamic model to get some key insights about the substitution of renewable for nonrenewable resources in production and the consequences for sustainability. We highlight the role of the elasticity of substitution (technological component) to determine the adjustment of every sector as a response to scarcity and growing ability of resources (environmental component). Sometimes, the model predicts a smooth substitution of renewable resources for nonrenewables, but this process could work in the opposite direction if renewable resources are temporarily beyond their maximum sustainable yield, so that their marginal natural growth is negative. If substitution possibilities are high enough, it may be optimal to suspend the extraction of a resource, for example, to allow for regeneration of the biomass. We show analytically that a production process is more likely to be sustainable the more heavily it depends on renewable, rather than nonrenewable resources.Renewable resources, Nonrenewable resources, Production, Optimal control.

OPTIMAL SUBSTITUTION OF RENEWABLE AND NONRENEWABLE NATURAL RESOURCES IN PRODUCTION

A theoretical model is presented in order to study the optimal combination of natural resources, used as inputs, taking into account their natural growth ability and the technical possibilities of input substitution. The model enables us to consider renewable resources, nonrenewable, or both. The relative use of resources evolves through time according to the difference between both resources' natural growth and technological flexibility, as measured by the elasticity of substitution of the production function. Output evolves according to a version of the traditional Keynes-Ramsey rule, where the marginal productivity of capital is substituted by the ''marginal productivity of natural capital'', that is a combination of both resources' marginal growth weighted by each resource return in production.Renewable Resources, Nonrenewable Resources, Production, Optimal Control.

A unified approach for commutators theorems in interpolation theory, a survey

Sin resume

Tuning surface metallicity and ferromagnetism by hydrogen adsorption at the polar ZnO(0001) surface

The adsorption of hydrogen on the polar Zn-ended ZnO(0001) surface has been investigated by density functional {\it ab-initio} calculations. An on top H(1x1) ordered overlayer with genuine H-Zn chemical bonds is shown to be energetically favorable. The H covered surface is metallic and spin-polarized, with a noticeable magnetic moment at the surface region. Lower hydrogen coverages lead to strengthening of the H-Zn bonds, corrugation of the surface layer and to an insulating surface. Our results explain experimental observations of hydrogen adsorption on this surface, and not only predict a metal-insulator transition, but primarily provide a method to reversible switch surface magnetism by varying the hydrogen density on the surface.Comment: 4 pages, 3 figure

Magnetism and half-metallicity at the O surfaces of ceramic oxides

The occurence of spin-polarization at ZrO$_{2}$, Al$_{2}$O$_{3}$ and MgO surfaces is proved by means of \textit{ab-initio} calculations within the density functional theory. Large spin moments, as high as 1.56 $\mu_B$, develop at O-ended polar terminations, transforming the non-magnetic insulator into a half-metal. The magnetic moments mainly reside in the surface oxygen atoms and their origin is related to the existence of $2p$ holes of well-defined spin polarization at the valence band of the ionic oxide. The direct relation between magnetization and local loss of donor charge makes possible to extend the magnetization mechanism beyond surface properties

Coadsorption phases of CO and oxygen on Pd(111) studied by scanning tunneling microscopy

The adsorption of CO on an oxygen precovered Pd(111) surface was investigated between 60 and 300 K. Applied methods were variable temperature scanning tunneling microscopy (STM) and video STM to analyze the coadsorption structures. The STM data are compared with simulated STM images for the various surface phases in order to identify the appropiate structural model for each case. Low-energy electron diffraction and reaction isotherms by means of mass spectrometry were used to correlate the phases with the reaction yielding CO2. The video-STM data recorded during CO adsorption at 300 K on the (2x2)O phase show a fast phase transition into the (√3x√3)R30°O structure, followed by reaction to CO2. The reaction only starts after completion of the phase transition, indicating that the (√3x√3)R30°O structure plays a crucial role for the reaction. At temperatures between 170 and 190 K the phase transition is slow enough to be monitored with STM. The experimental images of both the (2x2)O and the (√3x√3)R30°O structures are well reproduced by the simulations. Further CO adsorption caused a second phase transition into a p(2x1)O structure. The STM simulations strongly support a pure oxygen p(2x1) structure, rather than a mixed O + CO structure, in contrast to previous experimental work. The CO molecules form the same structures between the O islands that are known from the pure Pd(111)/CO system. At lower temperatures, between 110 and 60 K, a so far unknown (2x2) phase was observed. The formation of this structure, and its imaging by the STM, show that it constitutes a mixed p(2x2)O+CO structure, where the oxygen atoms remain unchanged, and the CO molecules occupy hcp sites between the O atoms

Towards relativistic simulations of magneto-rotational core collapse

We present a new general relativistic hydrodynamics code specifically designed to study magneto-rotational, relativistic, stellar core collapse. The code is an extension of an existing (and thoroughly tested) hydrodynamics code, which has been applied in the recent past to study relativistic rotational core collapse. It is based on the conformally-flat approximation of Einstein's field equations and conservative formulations for the magneto-hydrodynamics equations. As a first step towards magneto-rotational core collapse simulations the code assumes a passive (test) magnetic field. The paper is focused on the description of the technical details of the numerical implementation, with emphasis on the magnetic field module. A number of code tests are presented and discussed, along with a representative core collapse simulation