On Effective Constraints for the Riemann-Lanczos System of Equations

There have been conflicting points of view concerning the Riemann--Lanczos problem in 3 and 4 dimensions. Using direct differentiation on the defining partial differential equations, Massa and Pagani (in 4 dimensions) and Edgar (in dimensions n > 2) have argued that there are effective constraints so that not all Riemann tensors can have Lanczos potentials; using Cartan's criteria of integrability of ideals of differential forms Bampi and Caviglia have argued that there are no such constraints in dimensions n < 5, and that, in these dimensions, all Riemann tensors can have Lanczos potentials. In this paper we give a simple direct derivation of a constraint equation, confirm explicitly that known exact solutions of the Riemann-Lanczos problem satisfy it, and argue that the Bampi and Caviglia conclusion must therefore be flawed. In support of this, we refer to the recent work of Dolan and Gerber on the three dimensional problem; by a method closely related to that of Bampi and Caviglia, they have found an 'internal identity' which we demonstrate is precisely the three dimensional version of the effective constraint originally found by Massa and Pagani, and Edgar.Comment: 9pages, Te

The Lanczos potential for Weyl-candidate tensors exists only in four dimensions

We prove that a Lanczos potential L_abc for the Weyl candidate tensor W_abcd does not generally exist for dimensions higher than four. The technique is simply to assume the existence of such a potential in dimension n, and then check the integrability conditions for the assumed system of differential equations; if the integrability conditions yield another non-trivial differential system for L_abc and W_abcd, then this system's integrability conditions should be checked; and so on. When we find a non-trivial condition involving only W_abcd and its derivatives, then clearly Weyl candidate tensors failing to satisfy that condition cannot be written in terms of a Lanczos potential L_abc.Comment: 11 pages, LaTeX, Heavily revised April 200

Behavior of shell-model configuration moments

An important input into reaction theory is the density of states or the level density. Spectral distribution theory (also known as nuclear statistical spectroscopy) characterizes the secular behavior of the density of states through moments of the Hamiltonian. One particular approach is to partition the model space into subspaces and find the moments in those subspaces; a convenient choice of subspaces are spherical shell-model configurations. We revisit these configuration moments and find, for complete $0\hbar\omega$ many-body spaces, the following behaviors: (a) the configuration width is nearly constant for all configurations; (b) the configuration asymmetry or third moment is strongly correlated with the configuration centroid; (c) the configuration fourth moment, or excess is linearly related to the square to the configuration asymmetry. Such universal behavior may allow for more efficient modeling of the density of states in a shell-model framework.Comment: 12 pages, 8 figure

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late

Symbiont 'bleaching' in planktic foraminifera during the Middle Eocene Climatic Optimum

Many genera of modern planktic foraminifera are adapted to nutrient-poor (oligotrophic) surface waters by hosting photosynthetic symbionts, but it is unknown how they will respond to future changes in ocean temperature and acidity. Here we show that ca. 40 Ma, some fossil photosymbiont-bearing planktic foraminifera were temporarily 'bleached' of their symbionts coincident with transient global warming during the Middle Eocene Climatic Optimum (MECO). At Ocean Drilling Program (ODP) Sites 748 and 1051 (Southern Ocean and mid-latitude North Atlantic, respectively), the typically positive relationship between the size of photosymbiont-bearing planktic foraminifer tests and their carbon isotope ratios (δ13C) was temporarily reduced for ∼100 k.y. during the peak of the MECO. At the same time, the typically photosymbiont-bearing planktic foraminifera Acarinina suffered transient reductions in test size and relative abundance, indicating ecological stress. The coincidence of minimum δ18O values and reduction in test size–δ13C gradients suggests a link between increased sea-surface temperatures and bleaching during the MECO, although changes in pH and nutrient availability may also have played a role. Our findings show that host-photosymbiont interactions are not constant through geological time, with implications for both the evolution of trophic strategies in marine plankton and the reliability of geochemical proxy records generated from symbiont-bearing planktic foraminifera

A Sleepy Little Village : Where The Dixie Cotton Grows

https://digitalcommons.library.umaine.edu/mmb-vp/6045/thumbnail.jp