A Computational Procedure to Detect a New Type of High Dimensional Chaotic Saddle and its Application to the 3-D Hill's Problem

A computational procedure that allows the detection of a new type of high-dimensional chaotic saddle in Hamiltonian systems with three degrees of freedom is presented. The chaotic saddle is associated with a so-called normally hyperbolic invariant manifold (NHIM). The procedure allows to compute appropriate homoclinic orbits to the NHIM from which we can infer the existence a chaotic saddle. NHIMs control the phase space transport across an equilibrium point of saddle-centre-...-centre stability type, which is a fundamental mechanism for chemical reactions, capture and escape, scattering, and, more generally, ``transformation'' in many different areas of physics. Consequently, the presented methods and results are of broad interest. The procedure is illustrated for the spatial Hill's problem which is a well known model in celestial mechanics and which gained much interest e.g. in the study of the formation of binaries in the Kuiper belt.Comment: 12 pages, 6 figures, pdflatex, submitted to JPhys

Strong flows of dilute suspensions of microstructure

We consider dilute suspensions that have a microstructure that may be characterized by an axial state vector. Examples include axisymmetric particles, line elements of the fluid itself, or, as an approximation, droplets of fluid or polymer molecules. Past studies, in which sufficient conditions for stretch or coherent orientation of the microstructure are obtained for steady flows with homogeneous velocity gradient tensors are shown not to apply to the general situation. Instead, a careful analysis of the microdynamical equations reveals that stretching and orientation of the microstructure by the flow must be analyzed over a time interval. Using techniques from the theory of dynamical systems, a quantitative measure is developed to determine orientations and/or stretched lengths of the microstructure, that are robust and attractive to nearby states. This leads to a strong flow criterion for unsteady flows with inhomogeneous velocity gradient tensors in which the effects of history dependence are apparent. A particular model system is treated in the case of general two-dimensional flow. The sensitivity of the results to changes in the modeling assumptions is investigated

Death on a Whim: Jury Discretion and Especially Heinous Crimes - Maynard v. Cartwright

Note

The Search for Balance: Understanding and Implementing Yoga, Peace, and Democratic Education

Peace, yoga and democracy share a vision of freedom, truth, and justice to promote both individual and societal transformation. Barack Obama created a vision of hope in 2008; students should be allowed to carry out that vision of freedom and democracy in their homes, schools and communities with curricular implementation across the content areas. Allowing the community and the school to interact and makes strides for change are essential if peace is ever to be a possibility

THE INFLUENCE OF TREE HEIGHT ON LIDAR’S ABILITY TO ACCURATELY CHARACTERIZE FOREST STRUCTURE AND SPATIAL PATTERN ACROSS REFERENCE LANDSCAPES

Successful restoration of degraded forest landscapes requires reference models that adequately capture structural heterogeneity at multiple spatial scales. Field-based methods for assessing variation in forest structure are costly and inherently suffer from limited replication and spatial coverage. LiDAR is a more cost-effective approach for generating landscape-scale data, but it has a limited ability to detect understory trees. Increased understanding of appropriate height cut-offs for trees to be reliably included in LiDAR-based analysis could improve applications of LiDAR to assessments of landscape-scale forest structure. Toward that end, I investigated the effect of varying tree-height criterion (minimum height cutoffs of 6, 9, 12, 15, and 18 m) on the accuracy of LiDAR for estimating forest structure and spatial pattern in forests of the Sierra de San Pedro Martir National Park, Baja, Mexico. In order to increase the utility of the analysis, LiDAR trees were identified using a widely-available processing tool (FUSION’s TreeSeg). Accuracy was measured as the similarity between field-measured and LiDAR-detected tree datasets and was assessed for overall number of trees, spatial tree density maps, and a set of variables related to forest structure and spatial pattern. I found that removing trees less than 12 m in height increased correlation between LiDAR- and field-based spatial maps of tree density and strongly reduced differences in estimates of forest structure and spatial pattern. Although the frequency of small, medium, and large tree clumps was always underestimated by LiDAR-detected trees, the 12 m minimum height cutoff detected more of the large tree clumps than taller height cutoffs and provided estimates of forest structure and spatial pattern that were more similar to those derived from field data. The 12 m height cutoff also successfully captured structural variation across the study landscape: canyons, shallow northerly, and shallow southerly slopes were structurally similar, having larger and more abundant trees than steep northerly slopes, steep southerly slopes, and ridges. Methods developed here should be useful to managers interested in using LiDAR to characterize distributions of large, overstory trees without the need for extensive complementary field data and specifically for the development of landscape-scale reference models for forest management and restoration

Up-converted Emissions of Er3+ Doped Gd2(WO4)3 Phosphors

In this work, the up-conversion (UC) emissions of Er3+ in a gadolinium tungstate host was investigated to analyze the possible processes of up-conversion by 1500 nm and 980 nm excitation. Studies were conducted to see how the 4S3/2 -\u3e 4I15/2 transition changed with varying current through the excitation source, varying excitation wavelength, and doping concentration. Power dependent studies revealed that under 1500 nm excitation the 4S3/2 -\u3e 4I15/2 transition needed 3 photons, while 980 nm excitation could do the same transition with 2 photons. It was found that 1500 nm could produce more efficient red emission due to the 4I9/2 -\u3e 4I15/2 transition only needing 2 photons. Concentration dependence studies revealed many trends of how up-conversion processes varied with erbium ion separation. The number of photons used to UC 980 nm decreases as concentration increases, meaning that the mechanism depends on energy transfer UC and the inefficiency of green emissions at higher concentration is due to concentration quenching. UC of 1500 nm also uses less photons as concentration increases; red and green emissions are not as dependent on energy transfer UC as 980 nm UC. Also, as concentration increases past the point least photon use, the erbium ions start cross relaxing causing the number of photons used to increase rapidly. It was found that even after cross relaxation becomes the dominant UC process, the intensity still increases as concentration increases until a point where quenching starts to take effect

How Palestinian Aid Organizations Adapt to the Possibility of Further Annexation and Rights Abuses in the Wake of The Deal of the Century

This research explores the question, “To what extent has the ‘Deal of the Century’ impacted Palestinian aid organizations, and how might it impact them in the future?” The significance of this question lies in the fact that the “Deal of the Century” claims to solve one of the longest and most complex conflicts, yet it has not been sufficiently analyzed from a Palestinian perspective nor a humanitarian perspective. Furthermore, by presenting scholarly critiques of the deal and aid worker’s concerns, my hope is that an American audience may be convinced of the complicity of our government in devising a failed and harmful plan, develop empathy for peacebuilding in the region, and support a more inclusive approach when our government negotiates peace deals in the future. To answer my research question, I interviewed ten people involved with organizations who give aid to Palestinians. I asked them questions regarding potential changes in their missions and objectives, their feelings about the deal, their knowledge of its details, and how it relates to Palestinian refugees. By grouping their responses into common themes, I present a small case study of what elements of this deal worried Palestinian aid workers, what they all agreed and disagreed upon, and what they speculated about. My findings showed that all participants were opposed to the deal and generally tried to ignore its implications for their beneficiaries, operating according to international law instead. They all hope that this deal is not realized after the removal of U.S. President Trump from office. In contrast, my participants could not agree on how severely the mere proposal of the deal had impacted their work. However, I believe that there is enough evidence to conclude that their mentality and cause have been harmed since the deal was proposed almost a year ago. Lastly, this research found there is an overall need for a more inclusive peace deal, which can incorporate lessons learned from past peace deal failures and listen to aid organizations who represent the Palestinian cause. All participants proved to have great insight into the needs of refugees, the requirements for peace, and the roots of the conflict. I learned from them that, to even begin to create peace, a successful deal needs to involve the parties who represent the people involved, can advocate for their people’s needs, and are willing to make compromises

Reflective Reactions: Learning What It Means to Read and Reread Self Within a 6th Grade Social Action Project

This article focuses on the ways in which social action can be read and reread through one white female teacher’s experience. More specifically, how I read my actions and how I was read by them illustrates the compelling need to consistently reevaluate our perception of what we believe aligns with the ideals of building socially just and safe communities and what could subvert the very causes we are trying to help. This article originally started as a tribute to the success of my sixth-grade students writing letters to the mayor about the problems with drugs, gangs, and homeless people in their local park. However, as I revisited their letters, our exchanges about this project, and then a letter by the local neighborhood association, I realized that my actions as the teacher could be read in a variety of ways. How people read their actions and how they are read by others can be revealing, intimidating, and quite complicated. Displacing critical fixed spaces of what social justice is and how it is perceived by the actor and the one acted upon is open to a variety of complex and reflexive readings