An Environmental-Economic Measure of Sustainable Development

A central issue in the study of sustainable development is the interplay of growth and sacrifice in a dynamic economy. This paper investigates the relationship among current consumption, growth, and sustained consumption in two canonical, stylized economies and in a more general context. It is found that the maximin value measures what is sustainable and provides the limit to growth. Maximin value is interpreted as an environmental-economic carrying capacity and current consumption or utility as an environmental-economic footprint. The time derivative of maximin value is interpreted as net investment in sustainability improvement. It is called durable savings to distinguish it from genuine savings, usually computed with discounted utilitarian prices.sustained development, growth, maximin, sustainability indicator

Chains of rotational tori and filamentary structures close to high multiplicity periodic orbits in a 3D galactic potential

This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis and Zachilas 1994] in order to visualize them. As examples we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.Comment: 12 pages,22 figures, Accepted for publication in the International Journal of Bifurcation and Chao

Disc galaxies with multiple triaxial structures. II. JHK surface photometry and numerical simulations

We present detailed JHK surface photometry with ellipse fits of 13 galaxies selected from previous optical observations as likely candidates for having a secondary bar or a triaxial bulge within the primary bar. We have found 7 double-barred galaxies, 3 double-barred galaxies with an additional intermediate structure with twisted isophotes, and 3 galaxies with a bar and central twisted isophotes. A global analysis of the structural parameter characteristics in the I- and K-bands is presented. Various numerical models of galaxies with bars within bars are also analysed using the ellipse fitting technique and compared to the observations. A thorough review of the possible hypotheses able to explain this phenomenon is given with emphasis on the most likely ones.Comment: 12 pages, AATEX. Accepted for publication in A&A. Large color postscript figures omitted (Figs. 1), figures 2-9 included; gzip'ed postscript files of the paper and Figs. 1 available via anonymous ftp at ftp://obsftp.unige.ch/pub/fri/aasjhk/ , files fri_aasjhk.ps.gz and ngc*.ps.g

Sustainability of an Economy Relying on Two Reproducible Assets

Evaluating the sustainability of a society requires a system of shadow or accounting values derived from the sustainability objective. As a first step toward the derivation of such shadow values for a maximin objective, this paper studies an economy composed of two reproducible assets, each producing one of two consumption goods. The effect of the substitutability between goods in utility is studied by postulating, in turn, neoclassical diminishing marginal substitutability, perfect substitutability and perfect complementarity. The degree of substitutability has strong effects on the maximin solution, affecting the regularity or non-regularity of the program, and on the accounting values. This has important consequences for the computation of genuine savings and the sustainability prospects of future generations

Central Mass Concentration and Bar Dissolution in Nearby Spiral Galaxies

We use data from the BIMA Survey of Nearby Galaxies (SONG) to investigate the relationship between ellipticity and central mass concentration in barred spirals. Existing simulations predict that bar ellipticity decreases as inflowing mass driven by the bar accumulates in the central regions, ultimately destroying the bar. Using the ratio of the bulge mass to the mass within the bar radius as an estimate of the central mass concentration, we obtain dynamical mass estimates from SONG CO 1-0 rotation curve data. We find an inverse correlation between bar ellipticity and central mass concentration, consistent with simulations of bar dissolution.Comment: 10 pages, 2 figures and 2 tables, accepted for publication in the Astrophysical Journa

Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory

We study Chern-Simons theory on 3-manifolds $M$ that are circle-bundles over 2-dimensional surfaces $\Sigma$ and show that the method of Abelianisation, previously employed for trivial bundles $\Sigma \times S^1$, can be adapted to this case. This reduces the non-Abelian theory on $M$ to a 2-dimensional Abelian theory on $\Sigma$ which we identify with q-deformed Yang-Mills theory, as anticipated by Vafa et al. We compare and contrast our results with those obtained by Beasley and Witten using the method of non-Abelian localisation, and determine the surgery and framing presecription implicit in this path integral evaluation. We also comment on the extension of these methods to BF theory and other generalisations.Comment: 37 pages; v2: references adde