Trimmed Serendipity Finite Element Differential Forms

We introduce the family of trimmed serendipity finite element differential form spaces, defined on cubical meshes in any number of dimensions, for any polynomial degree, and for any form order. The relation between the trimmed serendipity family and the (non-trimmed) serendipity family developed by Arnold and Awanou [Math. Comp. 83(288) 2014] is analogous to the relation between the trimmed and (non-trimmed) polynomial finite element differential form families on simplicial meshes from finite element exterior calculus. We provide degrees of freedom in the general setting and prove that they are unisolvent for the trimmed serendipity spaces. The sequence of trimmed serendipity spaces with a fixed polynomial order r provides an explicit example of a system described by Christiansen and Gillette [ESAIM:M2AN 50(3) 2016], namely, a minimal compatible finite element system on squares or cubes containing order r-1 polynomial differential forms.Comment: Improved results, detailed comparison to prior and contemporary work, and further explanation of computational benefits have been added since the original version. This version has been accepted for publication in Mathematics of Computatio

Solar Furnace: Heliostat and Concentrator Design

In recent decades, solar energy has been shown as a viable, clean, and abundant alternative to fossil fuels. Many methods of solar energy collection are being researched, with solar thermal electrochemistry being one of the most promising. Solar thermal electrochemistry uses sunlight to heat a furnace to temperatures nearing 2000 K. At these temperatures, metallic oxides can be decomposed to metals and oxygen with minimal electrical work. Achieving these high temperatures requires a solar furnace that consists of a heliostat to track and reflect the sun’s rays into a concentrator, which then focuses the sunlight to a single point in a solar thermal chemical reactor. A system of louvers regulates the amount of sunlight entering the system. Our research focuses on the design and development of the solar furnace components; specifically, the design and construction of the heliostat structure, the heliostat control system, and the concentrator

Land Grant Application- Tyler, Andrew (Frankfort)

Land grant application submitted to the Maine Land Office for Andrew Tyler for service in the Revolutionary War.https://digitalmaine.com/revolutionary_war_me_land_office/1917/thumbnail.jp

The Eroding Artificial/Natural Distinction: Some Consequences for Ecology and Economics

Since Thomas Kuhn’s The Structure of Scientific Revolutions (1962), historians and philosophers of science have paid increasing attention to the implications of disciplinarity. In this chapter we consider restrictions posed to interdisciplinary exchange between ecology and economics that result from a particular kind of commitment to the ideal of disciplinary purity, that is, that each discipline is defined by an appropriate, unique set of objects, methods, theories, and aims. We argue that, when it comes to the objects of study in ecology and economics, ideas of disciplinary purity have been underwritten by the artificial-natural distinction. We then problematize this distinction, and thus disciplinary purity, both conceptually and empirically. Conceptually, the distinction is no longer tenable. Empirically, recent interdisciplinary research has shown the epistemological and policy-oriented benefits of dealing with models which explicitly link anthropogenic (i.e., “artificial”) and non-anthropogenic factors (i.e., “natural”). We conclude that, in the current age of the Anthropocene, it is to be expected that without interdisciplinary exchange, ecology and economics may relinquish global relevance because the distinct and separate systems to which each “pure” science was originally made to apply will only diminish over time

Steric and electronic control of an ultrafast isomerization.

Synthetic control of the influence of steric and electronic factors on the ultrafast (picosecond) isomerization of penta-coordinate ruthenium dithietene complexes (Ru((CF3)2C2S2)(CO)(L)2, where L = a monodentate phosphine ligand) is reported. Seven new ruthenium dithietene complexes were prepared and characterized by single crystal X-ray diffraction. The complexes are all square pyramidal and differ only in the axial vs. equatorial coordination of the carbonyl ligand. Fourier Transform Infrared (FTIR) spectroscopy was used to study the ν(CO) bandshapes of the complexes in solution, and these reveal rapid exchange between two or three isomers of each complex. Isomerization is proposed to follow a Berry psuedorotation-like mechanism where a metastable, trigonal bipyramidal (TBP) intermediate is observed spectroscopically. Electronic tuning of the phosphine ligands L = PPh3, P((p-Me)Ph)3, ((p-Cl)Ph)3, at constant cone angle is found to have little effect on the kinetics or thermodynamic stabilities of the axial, equatorial and TBP isomers of the differently substituted complexes. Steric tuning of the phosphine ligands over a range of phosphine cone angles (135 < θ < 165°) has a profound impact on the isomerization process, and in the limit of greatest steric bulk, the axial isomer is not observable. Temperature dependence of the FTIR spectra was used to obtain the relative thermodynamic stabilities of the different isomers of each of the seven ruthenium dithietene complexes. This study details how ligand steric effects can be used to direct the solution state dynamics on the picosecond time scale of discrete isomers energetically separated by <2.2 kcal mol-1. This work provides the most detailed description to date of ultrafast isomerization in the ground states of transition metal complexes

The Distribution and Reactivity of Organochlorines in Estuaries

In February 1997, the Governing Council of the United Nations Environment Programme initiated a protocol to reduce the risks to human health and the environment arising from persistent organic pollutants. The initial list of 12 families of organochlorine pollutants included polychlorinated biphenyls (PCBs), polychlorinated dibenzo-p-dioxins (PCDDs) and polychlorinated dibenzofurans (PCDFs) selected for their persistence, bioaccumulation capacity and toxicity. The aim of this work was to further understanding of the behaviour of these organochlorines (OCs) in estuarine systems. Field surveys were conducted at UK estuarine (Humber, Clyde and Dee) and coastal locations. Sediments were analysed for OCs and a range of chemical and physicochemical properties (trace metals, organic carbon content, specific surface area). Hydrographic measurements were also made to assist in defining the estuarine environment. Concentrations of PCDD/DF on a dry weight basis ranged from non-detectable (n.d.) to 11100 pg g"^ and PCB from n.d. to 3000 ng g Estuarine OC contamination was generally elevated above coastal waters concentrations. The distribution of OCs was studied to determine the extent of source, compound physicochemical, and particulate geochemical influences. In the Clyde estuary some source-related effects were observed but in the Humber estuary, characterised by highly dynamic conditions, these were masked by mixing of sediments. The characteristics of the sorbent were found to be of key importance with the content and nature of particulate organic carbon being the major control. To further understand the sorption behaviour of OCs, partitioning experiments were conducted with ^"C analogues of the compounds under realistic estuarine gradient conditions (K^ range from 2.4 x 10** to 49.4 x 10"* for TCB and 23.1 x 10Mo 313 x 10^ for TCDD). Particle concentration was found to be of key importance and it was concluded that this effect was transferable to environmental situations. Salinity was found to be a minor influence on partitioning behaviour. Development of sorption sub-models and their incorporation into an integrated estuarine contaminant transport model was demonstrated. A particle interaction-based sorption model was shown to only partially account for the observed partitioning behaviour; inclusion of an irreversibly adsorbed fraction may more adequately represent estuarine partitioning. Riverine and outfall discharges were simulated in the integrated contaminant transport model to demonstrate the influence of tidal hydrodynamics, sediment dynamics and variable partitioning applied to the Humber estuary.Department of Environmental Sciences Faculty of Science University of Plymout