Taming the Inverse and Forward Problems in Density Functional Theory

The `forward problem' of ground-state density functional theory (DFT) constitutes finding the ground-state density $n(x)$ that minimises a Kohn-Sham total energy functional defined using some exchange-correlation (xc) functional $E_\text{xc}[n]$. Towards this end, the associated Euler-Lagrange equations, i.e. the Kohn-Sham equations, are often solved in practice, which demand a procedure that iterates an initial guess density to a \textit{self-consistent} density (the solution). A new framework is presented for evaluating the performance of self-consistent field methods in Kohn–Sham DFT. The aims of this work are two-fold. First, we explore the properties of Kohn–Sham DFT as it pertains to the convergence of self-consistent field iterations. Sources of inefficiencies and instabilities are identified, and methods to mitigate these difficulties are discussed. Second, we introduce a framework to assess the relative utility of algorithms, comprising a representative benchmark suite of over fifty Kohn–Sham simulation inputs, the \textsc{scf}-$x_n$ suite. This provides a new tool to develop, evaluate and compare new algorithms in a fair, well-defined and transparent manner. The `inverse problem' of time-dependent (ground-state) DFT constitutes finding the time-(in)dependent Kohn-Sham potential $v_\text{KS}(x,t)$ that yields a given reference density $n(x,t)$ upon solution of the time-(in)dependent Kohn-Sham equations. This inverse map can be unstable, particularly in the presence of low-density regions, and thus methods are designed to alleviate numerical difficulties in the present context. On the other hand, linear response time-dependent DFT centres around the first-order response of the xc potential due to perturbing densities -- the so-called xc kernel $f_\text{xc}(x,x',\omega)$. Computing exact xc kernels represents a linearised version of the previous inverse problem: this state of affairs, whilst still challenging, is more manageable. Methods to ensure the robustness of exact numerical $f_\text{xc}$ computations are set out. In the context of inhomogenous one-dimensional finite systems, these developments permit an improved understanding of $f_\text{xc}$ in itself, and in relation to various applications, such as the optical spectrum and ground-state correlation energies using the adiabatic connection fluctuation-dissipation theorem. We expect that certain key insights derived from this work will assist in the informed development of improved functional approximations

Semantic penumbra? Concept similarity in logic

It is widely accepted by formal and informal logicians alike that a formal logic which, by the lights of English, gets the connectives wrong, nevertheless conspires to get entailment right—right that is, modulo English. There is a vexing problem occasioned by this semantic alienation of formal logic. It is next to impossible for formal logic to meet the expectations of realism. What, then, of informal logic

Copepod Aggregations: Influences of Physics and Collective Behavior

Dense copepod aggregations form in Massachusetts Bay and provide an important resource for right whales. We re-examine the processes which might account for the high concentrations, investigating both horizontally convergent flow, which can increase the density of depth-keeping organisms, and social behavior. We argue that the two act in concert: social behavior creates small dense patches (on the scale of a few sensing radii); physical stirring brings them together so that they merge into aggregations with larger scales; it also moves them into areas of physical convergence which retain the increasingly large patch. But the turbulence can also break this apart, suggesting that the overall high density in the convergence zone will not be uniform but will instead be composed of multiple transient patches (which are still much larger than the sensing scale)

The Effects of Ethanol on the Pancreatic Cell Line Transcriptomes

Pancreatic Ductal Adenocarcinoma (PDAC) is a highly aggressive cancer that develops from cells in the pancreas. Currently, PDAC has a 5-year survival rate of only 10% and it makes up about 7% of all cancer deaths (1). Certain risk factors are associated with PDAC development, including family history of cancer, obesity, diabetes, pancreatitis, alcohol consumption, and smoking. While several studies have assessed alcohol consumption and its contribution to PDAC development, there is conflicting evidence to whether or not alcohol actually promotes PDAC. Work from our lab indicates that specific subtypes of pancreatic cancer are associated with a patient’s drinking status, which may influence treatment strategies and patient outcomes (2). This raises the question; How does alcohol affect cancerous and pre-cancerous pancreatic cells? In this study, we performed RNA-Sequencing on ethanol treated pancreatic cells in different stages of cancer progression may provide insight to the effects of ethanol on the etiology of this disease. We analyzed the protein coding genes that were differentially expressed between non-treated and ethanol treated cells and performed functional analysis to better understand the impact of ethanol on the biological processes in pancreatic cells.https://digitalcommons.unmc.edu/surp2020/1013/thumbnail.jp

Physical controls on copepod aggregations in the Gulf of Maine

Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences; and the Woods Hole Oceanographic Institution), 2013.Cataloged from PDF version of thesis.Includes bibliographical references (p. 297-213).This thesis explores the role that the circulation in the Gulf of Maine (GOM) plays in determining the distribution of dense aggregations of copepods. These aggregations are an important part of the marine ecosystem, especially for endangered North Atlantic right whales. Certain ocean processes may generate dense copepod aggregations, while others may destroy them; this thesis looks at how different characteristics of the GOM circulation fit into these two categories. The first part of the thesis investigates a hypothetical aggregation mechanism in which frontal circulation interacts with copepod behavior to generate a dense patch of copepods. The first two chapters of this thesis address this mechanism in the context of coastal river plumes and salinity fronts. One chapter describes the characteristics and variability of coastal freshwater and salinity fronts using a historical dataset and a realistic numerical model. The seasonal variability of freshwater is tied in part to seasonality in river discharge, while variability on shorter time scales in the frontal position is related to wind stress. Another chapter applies the hypothetical mechanism to idealized river plumes using a suite of numerical models. The structure of the plume and plume-relative circulation change the resulting copepod aggregation from what is expected from the hypothetical mechanism. The second part of the thesis discusses the GOM circulation and how it may eliminate copepod patches. The summertime mean surface circulation and eddy kinetic energy are computed from a Lagrangian drifter dataset and an adaptive technique that allows for higher spatial resolution while also keeping uncertainty low. Eddy diffusivity is also computed over different regions of the GOM in an attempt to quantify the spreading of a patch of copepods, and is found to be lower near the coast where right whales are often found feeding on copepod patches. In the next chapter, a numerical drifter dataset is used to understand how the results of the previous chapter depend upon the quantity of observations. It is found that the uncertainty in estimating eddy diffusivity is tightly coupled to the number of drifters in the calculation.by Nicholas W. WoodsPh.D

Modeling Supermassive Primordial Stars with MESA

Supermassive stars forming at $z \sim$ 15 - 20 are one of the leading contenders for the origin of the first quasars, over 200 of which have now been discovered at $z >$ 6. These stars likely form in pristine, atomically cooled haloes immersed in strong Lyman-Werner UV backgrounds or in highly supersonic baryon streaming flows. Atomic cooling triggers catastrophic baryon collapse capable of building up stars at rates of up to $\sim$1 M$_{\odot}$ yr$^{-1}$. Here we examine the evolution of supermassive stars with a much larger and finer grid of accretion rates than in previous studies with the \texttt{MESA} stellar evolution code. We find that their final masses range from 3.5 $\times$ 10$^3$ M$_{\odot}$ - 3.7 $\times$ 10$^5$ M$_{\odot}$ at accretion rates of 0.001 M$_{\odot}$ yr$^{-1}$ - 1 M$_{\odot}$ yr$^{-1}$, respectively. We also find that supermassive star evolution diverges at accretion rates of 0.01 M$_{\odot}$ yr$^{-1}$ - 0.02 M$_{\odot}$ yr$^{-1}$, above which they evolve as cool red hypergiants along the Hayashi track and collapse via the general relativistic instability during central hydrogen burning, and below which they evolve as hot blue supergiants and collapse at the end of their nuclear burning lifetimes after exiting the main sequence.Comment: 11 pages, 10 figures, accepted by MNRA

Detecting Differences in Communication During Two Types of Patient Handovers: A Linguistic Construct Categorization Approach

Health Professions - Clinical: 4th Place, Honorable Mention (The Ohio State University Denman Undergraduate Research Forum)Patient handovers are a critical point in the patient care process. Software to identify differences in communication content and strategies across different types of patient handovers could be helpful in customizing physician training programs. To determine whether there were differences, Linguistic Inquiry and Word Count (LIWC) software was used. The primary measure was the LIWC output score, which is the frequency of mention of words in a construct category divided by the total number of words in the handover transcript. Two types of constructs were investigated: 1) content, which included name/age, care plan, prognosis, and family, and 2) strategy, which included questioning and collaborative cross-checks. We hypothesized that the Emergency Department (ED) to hospital transfer compared to Intensive Care Unit (ICU) sign-outs would have more discussion of family and less of the patient’s prognosis, as well as more collaborative cross-checks. A two-tailed t-test was used to detect differences. One hypothesis was confirmed, that there was less discussion of prognosis in the ED as compared to the ICU handover. Unexpected findings were less discussion of the care plan and more questioning in the ED as compared to the ICU handover. Findings confirm that both communication content and strategies are different for the two types of patient handovers and that an automated analysis approach can detect differences across a set of handover transcripts.Academic Major: Neuroscienc