Hamiltonian G-Spaces with Regular Momenta

Let G be a compact connected non-Abelian Lie group and let (P, w, G, J) be a Hamiltonian G-space. Call this space a G-space with regular momenta if J(P) ⊂ g*reg, here g*reg⊂g* denotes the regular points of the co-adjoint action of G. Here problems involving a G-space with regular momenta are reduced to problems in an associated lower dimensional Hamiltonian T-space, where T ⊂ G is a maximal torus. For example two such G-spaces are shown to be equivalent if and only if they have equivalent associated T-spaces. We also give a new construction of a normal form due to Marle (1983), for integrable G-spaces with regular momenta. We show that this construction, which is a kind of non-Abelian generalization of action-angle coordinates, can be reduced to constructing conventional action-angle coordinates in the associated T-space. In particular the normal form applies globally if the action-angle coordinates can be constructed globally. We illustrate our results in concrete examples from mechanics, including the rigid body. We also indicate applications to Hamiltonian perturbation theory

Pseudogroups via pseudoactions: Unifying local, global, and infinitesimal symmetry

A multiplicatively closed, horizontal foliation on a Lie groupoid may be viewed as a "pseudoaction" on the base manifold $M$. A pseudoaction generates a pseudogroup of transformations of $M$ in the same way an ordinary Lie group action generates a transformation group. Infinitesimalizing a pseudoaction, one obtains the action of a Lie algebra on $M$, possibly twisted. A global converse to Lie's third theorem proven here states that every twisted Lie algebra action is integrated by a pseudoaction. When the twisted Lie algebra action is complete it integrates to a twisted Lie group action, according to a generalization of Palais' global integrability theorem.Comment: 31 pages; minor revision

Rude and crude?: When teens in your library respond negatively to you, think back to how you approached them

Skaters, taggers, gang members, and other groups of young people are being identified all over America as problems for libraries. However, these teens respond negatively to librarians because of the way that they are approached and because they experience so much discrimination. If teen behavior needs to be changed, there needs to be a change in the way they are approached and an appeal toward their code of ethics

Simulations of submonolayer Xe on Pt(111)(111): the case for a chaotic low temperature phase

Molecular Dynamics simulations are reported for the structural and thermodynamic properties of submonolayer xenon adsorbed on the $(111)$ surface of platinum for temperatures up to the (apparently incipient) triple point and beyond. While the motion of the atoms in the surface plane is treated with a standard two-dimensional molecular dynamics simulation, the model takes into consideration the thermal excitation of quantum states associated with surface-normal dynamics in an attempt to describe the apparent smoothing of the corrugation with increasing temperature. We examine the importance of this thermal smoothing to the relative stability of several observed and proposed low-temperature structures. Structure factor calculations are compared to experimental results in an attempt to determine the low temperature structure of this system. These calculations provide strong evidence that, at very low temperatures, the domain wall structure of a xenon monolayer adsorbed on a Pt$(111)$ substrate possesses a chaotic-like nature, exhibiting long-lived meta-stable states with pinned domain walls, these walls having narrow widths and irregular shapes. This result is contrary to the standard wisdom regarding this system, namely that the very low temperature phase of this system is a striped incommensurate phase. We present the case for further experimental investigation of this and similar systems as possible examples of chaotic low temperature phases in two dimensions.Comment: 13+9 pages, 6+6 figures. Change in the title, closer to published versio

New Hybrid Protected Lands Layer for Vermont Conservation Design Analysis (February 2019)

This shapefile (.shp) is a hybrid of the March 2017 Edition of the Vermont Center for Geographic Information\u27s (VCGI) Vermont Protected Lands Database (VPLD), the Vermont Land Trust\u27s February 2019 Protected Lands database, and The Nature Conservancy\u27s Secured Areas (SA 2018+) database. The VLT and SA 2018+ datasets were used as the scaffolding for the hybrid protected lands layer, with some VCGI VPLD polygons retained if they contained unique contributions. These datasets were combined by C.D. Loeb because each input dataset was missing some protected lands polygons in the state of Vermont. Additionally, the VCGI VPLD dataset contained many overlapping polygons, making it unusable for the area calculations of interest to our study on the overlap between formally protected lands and Vermont Conservation Design landscape-level targets (see publication reference). This hybrid protected lands layer creates a more complete snapshot of Vermont’s protected lands for our study’s purposes than any other known, publicly available dataset as of February 2019, and also corrects for all improperly overlapping polygons. However, we know that this hybrid product still does not capture all of Vermont\u27s protected lands. Specifically, some Upper Valley Land Trust-protected parcels are missing from this hybrid protected lands layer, and there are probably other protected parcels that could not be captured by the input datasets. Thus, our hybrid product will likely underrepresent actual protections. This layer was created to intersect with Vermont Conservation Design targets for input into the software Tableau. Its purpose was to perform cross tabulations to compare Vermont Conservation Design targets with protected lands in Vermont to-date, and to calculate acreages of protected lands that are also design targets by primary protecting agency. All parcel attributes and delineations in the hybrid output are only as good as the parent datasets. In areas where parcels were digitized differently between parent datasets, “slivers” may have been generated by merging them. Our study objectives originally included an analysis of the GAP Status of protected lands in Vermont (reflected in this layer\u27s metadata); however, some serious errors were detected in parent datasets with regards to GAP Status, so GAP Status was discarded as an analysis object. Please note author-identified GAP Status issues if using this dataset. Please see the shapefile\u27s metadata for detailed creation steps. The user implies knowledge of the limitations of this dataset. This dataset should not be used to ascertain boundaries or legal acreages for any parcels. Note: This version of the hybrid protected lands layer does not have county boundaries embedded in it nor waterbodies excluded from it, since it was created to capture all formally protected lands in the state of Vermont to the best of the authors’ abilities. Prior to use in our analysis, this layer was modified to exclude waterbodies and to introduce county boundaries. To obtain the same hybrid protected lands layer with county boundaries embedded in it and waterbodies excluded from it, please contact C. D. Loeb at [email protected]