The Local Structure of Lie Bialgebroids

We study the local structure of Lie bialgebroids at regular points. In particular, we classify all transitive Lie bialgebroids. In special cases, they are connected to classical dynamical $r$-matrices and matched pairs induced by Poisson group actionsComment: 13 page

Manin Triples for Lie Bialgebroids

In his study of Dirac structures, a notion which includes both Poisson structures and closed 2-forms, T. Courant introduced a bracket on the direct sum of vector fields and 1-forms. This bracket does not satisfy the Jacobi identity except on certain subspaces. In this paper we systematize the properties of this bracket in the definition of a Courant algebroid. This structure on a vector bundle $E\rightarrow M$, consists of an antisymmetric bracket on the sections of $E$ whose ``Jacobi anomaly'' has an explicit expression in terms of a bundle map $E\rightarrow TM$ and a field of symmetric bilinear forms on $E$. When $M$ is a point, the definition reduces to that of a Lie algebra carrying an invariant nondegenerate symmetric bilinear form. For any Lie bialgebroid $(A,A^{*})$ over $M$ (a notion defined by Mackenzie and Xu), there is a natural Courant algebroid structure on $A\oplus A^{*}$ which is the Drinfel'd double of a Lie bialgebra when $M$ is a point. Conversely, if $A$ and $A^*$ are complementary isotropic subbundles of a Courant algebroid $E$, closed under the bracket (such a bundle, with dimension half that of $E$, is called a Dirac structure), there is a natural Lie bialgebroid structure on $(A,A^{*})$ whose double is isomorphic to $E$. The theory of Manin triples is thereby extended from Lie algebras to Lie algebroids. Our work gives a new approach to bihamiltonian structures and a new way of combining two Poisson structures to obtain a third one. We also take some tentative steps toward generalizing Drinfel'd's theory of Poisson homogeneous spaces from groups to groupoids.Comment: 24 pages, LaTeX2e (minor corrections, added section at end), final version of paper to appear in J. Diff. Geo

The Plasticity of Functional Traits in the Dipterocarps of Borneo

Plasticity plays an important role in the adaptation of sessile organisms like plants to the environment. Plants have been shown to respond plastically in heterogeneous environments, with plants originating from more resource-diverse environments thought to display greater plasticity. There is also evidence that fast-growing species show greater plasticity, as acquisition of resources from resource flushes is greatly aided by faster adaptations. We tested these theories in a Bornean tropical rain forest among three soil specialization groups (clay specialists, sandy loam specialists, and generalists) using two treatments of soil (clay versus sandy loam) and two treatments of light (high versus low). Here, I address four research questions: (1) Do tree species with different soil specializations exhibit differences in the plasticity of functional traits and growth rates? (2) Does the magnitude of plasticity depend on the type of resource? (3) Do functional traits and growth rates vary in the magnitude of plasticity exhibited? (4) Is plasticity in functional traits correlated with plasticity in growth rates? Overall the results show that clay specialists and generalists are more plastic than their sandy loam counterparts. Second, on average plasticity due to light was greater than plasticity due to soil. Third, growth rates were generally more plastic than functional traits. And finally, the plasticity of functional traits and growth rates were positively correlated. These finding add important insights to the plastic response of long-lived tree species to the environment, where much remains to be explored. Adviser: Sabrina E. Russ

The Plasticity of Functional Traits in the Dipterocarps of Borneo

Plasticity plays an important role in the adaptation of sessile organisms like plants to the environment. Plants have been shown to respond plastically in heterogeneous environments, with plants originating from more resource-diverse environments thought to display greater plasticity. There is also evidence that fast-growing species show greater plasticity, as acquisition of resources from resource flushes is greatly aided by faster adaptations. We tested these theories in a Bornean tropical rain forest among three soil specialization groups (clay specialists, sandy loam specialists, and generalists) using two treatments of soil (clay versus sandy loam) and two treatments of light (high versus low). Here, I address four research questions: (1) Do tree species with different soil specializations exhibit differences in the plasticity of functional traits and growth rates? (2) Does the magnitude of plasticity depend on the type of resource? (3) Do functional traits and growth rates vary in the magnitude of plasticity exhibited? (4) Is plasticity in functional traits correlated with plasticity in growth rates? Overall the results show that clay specialists and generalists are more plastic than their sandy loam counterparts. Second, on average plasticity due to light was greater than plasticity due to soil. Third, growth rates were generally more plastic than functional traits. And finally, the plasticity of functional traits and growth rates were positively correlated. These finding add important insights to the plastic response of long-lived tree species to the environment, where much remains to be explored. Adviser: Sabrina E. Russ

Administration Service for the Tourist Information System (TIP)

The modern day tourists do not want to deal with the hassle of using a large number of travel guides and paper maps while travelling. They would prefer to be able to access required information via their mobile phones or Personal Digital Assistants (PDAs). We realise that the delivered information may be originally available in numerous information formats. To support the administrator of the tourist guides the programme is required to help sorting information from these different sources and to help inserting them into a system. Our goal with this project is to develop a software support for processing information import via a graphical user interface, to support the administrator in identifying and extracting the appropriate sight information from various resources. The interface also helps in transferring and storing the structured and unstructured data into the TIP database

4,4′-(Propane-1,3-di­yl)dipyridinium tetra­chloridonickelate(II)

The title compound, (C13H16N2)[NiCl4] or (H2bpp)·NiCl4 [bpp is 1,3-bis­(4-pyrid­yl)propane], is isostructural with its already reported Cu, Zn and Hg analogues. The structure consists of a doubly charged (H2bpp)2+ cation and a tetra­hedral [NiCl4]2− dianion. Both pyridyl N atoms are protonated and form a (H2bpp)2+ cation which adopts an anti–anti conformation with a dihedral angle of 6.287 (7)° between the pyridyl rings. The two pyridyl N atoms are both involved in strong N—H⋯Cl hydrogen bonds, which link both units into a dimer

Breakup of spherical vesicles caused by spontaneous curvature change

We present our theoretical analysis and coarsegrained molecular dynamics (CGMD) simulation results to describe the mechanics of breakup of spherical vesicles driven by changes in spontaneous curvature. Systematic CGMD simulations reveal the phase diagrams for the breakup and show richness in breakup morphologies. A theoretical model based on Griffith fracture mechanics is developed and used to predict the breakup condition