Stratified Gradient Hamiltonian Vector Fields and Collective Integrable Systems

Let $X$ be a decomposed, quasi-projective complex algebraic variety that inherits a K\"ahler structure from an algebraic embedding into a smooth K\"ahler variety. We give a framework for constructing integrable systems on $X$ by toric degeneration. This generalizes a previous result of Harada and Kaveh in the case where $X$ is smooth and projective. We show how toric degenerations satisfying the assumptions of our framework can be produced from valuations when $X$ is affine. In this case, the image of the integrable system on $X$ is the cone generated by the value semigroup. For example, we show that every extended string cone is the image of a completely integrable system on base affine space. As an application, we show that every connected symplectic manifold $M$ equipped with a Hamiltonian action of a compact connected Lie group $K$ admits a Hamiltonian torus action of the same complexity on a connected, open, dense subset. The moment map of this torus action extends continuously to all of $M$. It is a collective integrable system since it factors through the moment map for the $K$ action. Moreover, it shares the convexity properties of the moment maps of Guillemin and Sternberg's Gelfand-Zeitlin collective integrable systems. We use these results to reduce a conjecture of Karshon and Tolman regarding the Gromov width of coadjoint orbits of compact simple Lie groups to an algebraic conjecture.Comment: This new version has been significantly edited down for length and clarity, and contains one new result about Gromov width of coadjoint orbit

Comparing Landsat 8-derived Surface Temperatures and Field-Collected Air Temperatures in the City of Richmond, VA.

Satellite data is a cost-effective and easily accessible information source that is widely used in a variety of applications. When it comes to temperature data, satellites receive thermal electromagnetic energy emitted by the earth’s surface from which surface temperature is empirically derived. Despite such data being a relatively accurate representation of surface temperature, it does not necessarily replicate the true air temperature patterns of a place. Depending on the type of data used, research studies can arrive at considerably different outcomes, and subsequently induce different public policies related to heat extremes, especially in cities. In this project, relations between surface temperature and air temperature during unusually hot summer days are examined for the City of Richmond, Virginia, a mid-sized city located in the Southeast Climate Region. This is achieved by comparing satellite-derived surface temperatures from Landsat 8 imagery retrieved on 22nd August 2017 to air temperatures collected in the field (from thermistors mounted on bicycles and cars) and modelled on 13th July 2017. Three types of comparisons are made, in which the 2 variables demonstrate considerable differences aiding understanding of the limitations of Landsat 8-derived temperatures. Subsequently, this will help further research seeking to inform the identification of populations vulnerable to the Urban Heat Island effect within the City of Richmond. This is an important contribution to the development of public policy responses to Urban Heat Island phenomena

Climate Resilience and Justice in Richmond

The author examines climate change inequity in Richmond and discusses strategies to deal with it in the long and short term in ways that would lead to climate resilience policy decisions that incorporate the values of community members, demonstrably improve community health and wellbeing, and bolster socioeconomic equity across the city.https://scholarscompass.vcu.edu/richmondracialequityessays_essays/1023/thumbnail.jp

Mechanical Properties of non-accreting Neutron Star Crusts

The mechanical properties of a neutron star crust, such as breaking strain and shear modulus, have implications for the detection of gravitational waves from a neutron star as well as bursts from Soft Gamma-ray Repeaters (SGRs). These properties are calculated here for three different crustal compositions for a non-accreting neutron star that results from three different cooling histories, as well as for a pure iron crust. A simple shear is simulated using molecular dynamics to the crustal compositions by deforming the simulation box. The breaking strain and shear modulus are found to be similar in the four cases, with a breaking strain of ~0.1 and a shear modulus of ~10^{30} dyne cm^{-2} at a density of \rho = 10^{14} g cm^{-3} for simulations with an initially perfect BCC lattice. With these crustal properties and the observed properties of {PSR J2124-3358} the predicted strain amplitude of gravitational waves for a maximally deformed crust is found to be greater than the observational upper limits from LIGO. This suggests that the neutron star crust in this case may not be maximally deformed or it may not have a perfect BCC lattice structure. The implications of the calculated crustal properties of bursts from SGRs are also explored. The mechanical properties found for a perfect BCC lattice structure find that crustal events alone can not be ruled out for triggering the energy in SGR bursts.Comment: 10 pages, 6 figures, accepted for publication in Monthly Notices of the Royal Astronomical Societ

Health Equity Impacts of Medical Tourism in the Caribbean: The Need to Provide Actionable Guidance Regarding Balancing Local and Foreign Interests

Medical tourism is a practice where individuals cross international borders with the intention of privately purchasing healthcare. Caribbean countries are increasingly entering into the medical tourism market, which presents both opportunities and dangers. Our previous fieldwork shows that medical tourism requires host countries to balance the interests of private developers and domestic actors, including those accessing healthcare locally. Discussions with stakeholders in Jamaica, Cayman Islands, Barbados and St Lucia demonstrate concrete instances of this problem. Firstly, medical tourism can enhance training and employment opportunities for domestic health-workers. In doing so, it may exacerbate the inequitable distribution of these workers between the public and private sectors. Secondly, the expansion of private medical services can provide locals with more care options. These facilities may also crowd out existing local operators and price out local consumers. Thirdly, medical tourism is hailed as potentially cross subsidizing and strengthening the local public health system. It may also heighten health inequities and distract local attention from the needs of the public health sector. Caribbean stakeholders are aware of the promise and dangers of medical tourism. However, they lack clear advice from medical tourism researchers about how to navigate these issues, and specifically balancing local and foreign interests. We call on researchers to shift focus from highlighting the theoretical problems associated with medical tourism to providing concrete guidance to stakeholders in a position to decide whether or not to pursue medical tourism development and to shape this development when it takes place

Pseudospectral methods for atoms in strong magnetic fields

We present a new pseudospectral algorithm for the calculation of the structure of atoms in strong magnetic fields. We have verified this technique for one, two and three-electron atoms in zero magnetic fields against laboratory results and find typically better than one-percent accuracy. We further verify this technique against the state-of-the-art calculations of hydrogen, helium and lithium in strong magnetic fields (up to about $2\times 10^{6}$ T) and find a similar level of agreement. The key enabling advantages of the algorithm are its simplicity (about 130 lines of commented code) and its speed (about $10^2-10^5$ times faster than finite-element methods to achieve similar accuracy).Comment: 10 pages, version accepted to MNRA