Primer for the algebraic geometry of sandpiles

The Abelian Sandpile Model (ASM) is a game played on a graph realizing the dynamics implicit in the discrete Laplacian matrix of the graph. The purpose of this primer is to apply the theory of lattice ideals from algebraic geometry to the Laplacian matrix, drawing out connections with the ASM. An extended summary of the ASM and of the required algebraic geometry is provided. New results include a characterization of graphs whose Laplacian lattice ideals are complete intersection ideals; a new construction of arithmetically Gorenstein ideals; a generalization to directed multigraphs of a duality theorem between elements of the sandpile group of a graph and the graph's superstable configurations (parking functions); and a characterization of the top Betti number of the minimal free resolution of the Laplacian lattice ideal as the number of elements of the sandpile group of least degree. A characterization of all the Betti numbers is conjectured.Comment: 45 pages, 14 figures. v2: corrected typo

Loop measures and the Gaussian free field

Loop measures and their associated loop soups are generally viewed as arising from finite state Markov chains. We generalize several results to loop measures arising from potentially complex edge weights. We discuss two applications: Wilson's algorithm to produce uniform spanning trees and an isomorphism theorem due to Le Jan.Comment: 20 page

The Warped Nuclear Disk of Radio Galaxy 3C 449

Among radio galaxies containing nuclear dust disks, the bipolar jet axis is generally observed to be perpendicular to the disk major axis. The FR I radio source 3C 449 is an outlier to this statistical majority, as it possesses a nearly parallel jet/disk orientation on the sky. We examine the 600 pc dusty disk in this galaxy with images from the Hubble Space Telescope. We find that a colormap of the disk exhibits a twist in its isocolor contours (isochromes). We model the colormap by integrating galactic starlight through an absorptive disk, and find that the anomalous twist in the isochromes can be reproduced in the model with a vertically thin, warped disk. The model predicts that the disk is nearly perpendicular to the jet axis within 100 pc of the nucleus. We discuss physical mechanisms capable of causing such a warp. We show that precessional models or a torque on the disk arising from a possible binary black hole in the AGN causes precession on a timescale that is too long to account for the predicted disk morphology. However, we estimate that the pressure in the X-ray emitting interstellar medium is large enough to perturb the disk, and argue that jet-driven anisotropy in the excited ISM may be the cause of the warp. In this way, the warped disk in 3C 449 may be a new manifestation of feedback from an active galactic nucleus.Comment: Accepted for publication in Ap

AN ASSESSMENT OF MUNICIPAL WATER RIGHTS AND WATER SYSTEMS IN THE CLARK FORK RIVER BASIN

In the semi-arid Inland Northwest, water is undoubtedly the most important natural resource. Western Montana’s Clark Fork River basin is no exception. As the population of western Montana continues to grow, the Clark Fork River basin below the Flathead Indian Reservation is largely in de facto closure to the establishment of new water rights. Communities face a great amount of uncertainty with respect to their ability to establish new water rights to accommodate future growth due to the de facto closure, along with the ongoing adjudication process and the inability for communities to grow into their claimed water rights established before July 1, 1973. It is therefore essential for communities, and water resources planners and managers, to know their legal and physical entitlements to water. This assessment of municipal water rights and systems in the Clark Fork River basin was conducted by ascertaining the volumes and maximum flows of each community’s water right, analyzing the volume of water used annually, and projecting future water consumption amounts for the next 20 years based on projected county population growth rates. Other information gathered includes water conservation measures, water-related infrastructure, and metering. Interviews of water system managers and operators were conducted to gauge their level of understanding of water resource issues and policies that might play a significant role in each community’s ability to provide water to its residents. It appears that while the vast majority of communities in the Clark Fork River basin will have sufficient water right amounts for the next 20 years, other communities, e.g., Seeley Lake, Hamilton, and Missoula are more likely to experience difficulties in meeting future population growth with their current rights. Some communities, e.g., Butte, Columbia Falls, Superior, and Thompson Falls, may be limited in using their water rights due to water quality issues, while others, e.g., Hamilton, Missoula, and Stevensville, will be limited due to the Montana Department of Natural Resources and Conservation’s rules regarding where water rights are able to be used

HST/ACS Emission Line Imaging of Low Redshift 3CR Radio Galaxies I: The Data

We present 19 nearby (z<0.3) 3CR radio galaxies imaged at low- and high-excitation as part of a Cycle 15 Hubble Space Telescope snapshot survey with the Advanced Camera for Surveys. These images consist of exposures of the H-alpha (6563 \AA, plus [NII] contamination) and [OIII] 5007 \AA emission lines using narrow-band linear ramp filters adjusted according to the redshift of the target. To facilitate continuum subtraction, a single-pointing 60 s line-free exposure was taken with a medium-band filter appropriate for the target's redshift. We discuss the steps taken to reduce these images independently of the automated recalibration pipeline so as to use more recent ACS flat-field data as well as to better reject cosmic rays. We describe the method used to produce continuum-free (pure line-emission) images, and present these images along with qualitative descriptions of the narrow-line region morphologies we observe. We present H-alpha+[NII] and [OIII] line fluxes from aperture photometry, finding the values to fall expectedly on the redshift-luminosity trend from a past HST/WFPC2 emission line study of a larger, generally higher redshift subset of the 3CR. We also find expected trends between emission line luminosity and total radio power, as well as a positive correlation between the size of the emission line region and redshift. We discuss the associated interpretation of these results, and conclude with a summary of future work enabled by this dataset.Comment: 18 pages, 12 figures, accepted for publication in ApJ

Mechanisms of cooperation for states' construction of large-scale water infrastructure projects in transboundary river basins

How does transboundary water cooperation begin at the initial stages? Countries in many transboundary basins either do not cooperate at all or have ceased cooperation altogether. Yet cooperation does often prevail, resulting in 688 water-related treaties signed between 1820 and 2007. The question we address here is, by which practices can development partners best design and implement collaborative projects in the earliest stages? This paper identifies lessons and strategies for the initiation of cooperation drawing from global experience. We also identify the impact of securitization framing on initiating cooperation. We completed the following: 1) We culled from the Oregon State University Transboundary Freshwater Dispute Database (TFDD) a compilation of all transboundary water resources projects over the last decade that have multinational participation (official or unofficial). 2) We further refined our culling to include only projects that fit filtering criteria which included: a) Funding exclusively or primarily from outside sources b) Inclusion of non-official (Track II) stakeholders in project design and implementation c) Absence of formal relations around water resources, in the form of a treaty or River Basin Organization (RBO), between or among the riparian countries in advance of the project discussed d) Project design including at least the possibility of enhancing hydropolitical relations. Using the above filtering criteria, we selected 10 case studies. Findings suggest that it is best to focus on project designs that respect the autonomy of participating riparians, create basinwide networks of scientists, allow for each partner to garner responsibility for project activities, and consult a diverse group of stakeholders. Although the costs and benefits of dam construction are generally borne by one country in national basins, absence or softness of legal frameworks in many international basins may increase the incentive for riparian countries to build dams since certain riparians may enjoy the benefits of dam construction while externalizing many of the costs. To determine whether the transboundary nature of river basins is associated with increased dam construction, and whether the existence of transboundary institutions offsets any such increase, this paper analyzes the extent to which i) the large dam construction rate in international watersheds differs from that of national watersheds, and ii) the rate and distribution of large dam construction differs between transboundary waters with and without agreements. Data on large dam locations, river basin boundaries, and international borders were collected, mapped in GIS and analyzed to determine dam construction rates in national and transboundary basins, and in transboundary basins with and without an agreement. The results indicate that large dam construction rates in national basins exceeds that of transboundary basins, and construction rates in areas covered by a transboundary water agreement exceed construction rates in areas not covered by an agreement. Further, it appears that agreement formation in transboundary basins enables relatively greater and more distributed development. These results indicate that dynamics of transboundary waters may be at odds with experiences in other common pool natural resources, and the existence of cooperative institutional frameworks on transboundary river basins may be linked to more equitable, mutually beneficial outcomes. Projecting future hotspots of hydropolitical tension in river basins across the world may allow countries to take measures to prevent hydropolitical conflict. The Zambezi River Basin has been identified as a basin at risk of future hydropolitical conflict. This paper analyzes the hydropolitical resilience of the Zambezi River Basin using two approaches: i) a global analysis of factors that indicate change and a basin’s institutional capacity, and ii) an in-depth examination of the basin's hydropolitical history and its present-day status using interviews with basin stakeholders, academics, NGOs, and policy makers. Results of the global analysis indicate that the Zambezi River Basin on the whole has comparatively higher institutional capacity, lower to medium rates of new dam development, lower human development and security values, lower water scarcity, yet higher projected water variability. When examining the basin’s hydropolitical history results show that the values of the global indicators only tell a partial story. This paper argues that while global analyses of hydropolitical resilience are valid for indicating areas of possible tension over shared water resources, analyzing a basin’s hydropolitical resilience on the basin scale through tracing its hydropolitical history and interviews puts the global results into context and adds nuance that is crucial to identify specific aspects of the basin that may push the basin into a state of conflict

Gaylord Produce Removal Machine

This Final Design Review Report outlines the senior design project that began Winter Quarter of 2021 at California Polytechnic State University. Our team consists of three mechanical engineers and a general engineer, working together to design, build, and test a product for Alameda County Food Bank. The goal of the final product is to relieve volunteers and employees of tedious manual labor and increase efficiency during the removal of produce from large Gaylord containers. This document describes background research, the objectives of the project, chosen concept design, analysis and initial prototyping of said concept, the final design, and verification prototype and testing