Approximating the Three-Nucleon Continuum

Three-nucleon forces (3NFs) are necessary to accurately describe the properties of atomic nuclei. These forces arise naturally together with two-nucleon forces (2NFs) when constructing nuclear interactions using chiral effective field theories (χEFTs) of quantum chromodynamics. Unlike phenomenological nuclear interaction models, χEFT promises a handle on the theoretical uncertainty in our description of the nuclear interaction. Recently, methods from Bayesian statistics have emerged to quantify this theoretical truncation error in physical predictions based on chiral interactions. Alongside quantifying the truncation error, the low-energy constants (LECs) of the chiral interactions must be inferred using selected experimental data. In this regard, the abundant sets of experimentally measured nucleon-nucleon (NN) and nucleon-deuteron (Nd) scattering cross sections serve as natural starting points to condition such inferences on. Unfortunately, the high computational cost incurred when solving the Faddeev equations for Nd scattering has thus far hampered Bayesian parameter estimation of LECs from such data. In this thesis, I present the results from a two-part systematic investigation of the wave-packet continuum discretisation (WPCD) method for reliably approximating two- and three-nucleon (NNN) scattering states with an aim towards a quantitative Bayesian analysis in the NNN continuum. In the first part, I explore the possibilities of using graphics processing units to utilise the inherent parallelism of the WPCD method, focusing on solving the Lippmann-Schwinger equation. In the second part, I use the WPCD method to solve the Faddeev equations for Nd scattering and analyse the reliability of the approximations of the WPCD method. This allows me to quantify the posterior predictive distributions for a range of low-energy neutron-deuteron cross sections conditioned on NN scattering data and NN interactions up to fourth order in χEFT

Nucleon-Nucleon Scattering in a Wave-Packet Formalism

In this thesis I analyse the prospect of leveraging statistical analyses of the strong nuclear interaction by using the wave-packet continuum discretisation (WPCD) method to efficiently compute nucleon-nucleon (NN) scattering observables on a graphics processing unit (GPU). The WPCD method gives approximate solutions to the S-matrix at multiple scattering energies at the cost of a single eigendecomposition of the NN channel Hamiltonian. In particular, I demonstrate and analyse the accuracy and inherent parallelism of the WPCD method by computing the most common NN scattering observables using a chiral Hamiltonian at next-to-next-to-leading order. I present an in-depth numerical study of the WPCD method and the GPU acceleration thereof. Additionally, I discuss which windows of opportunity are open for studying the strong nuclear interaction using data from few-nucleon scattering experiments

AGCO Corporation Valuation

This paper will discuss the excellent growth potential that AGCO Corporation faces and the reason that this company\u27s stock is rated as a hold position. AGCO has seen tremendous progress and is in an industry that shows that a growing world population will continue to need food and more efficient ways to create food. However, based on sensitivities of assumptions in the models presented herein and on a current share price that is already close to my assumed fair value I do not issue a buy recommendation

ESTIMATING WILLINGNESS-TO-PAY USING A POLYCHOTOMOUS CHOICE FUNCTION: AN APPLICATION TO PORK PRODUCTS WITH ENVIRONMENTAL ATTRIBUTES

This paper utilizes a polychotomous choice function to investigate the relationship between socioeconomic characteristics and willingness-to-pay for embedded environmental attributes. Specifically, a two-stage estimation procedure with an ordered probit selection rule is used to predict the premium payers and the magnitude of the premium they are willing to pay.Research Methods/ Statistical Methods,

Estimating Willingness to Pay Using a Polychotomous Choice Function: An Application to Pork Products with Environmental Attributes

Bid data from a Vickrey auction for pork chops with embedded environmental attributes were analyzed. It was found that approximately 62% of the participants had a positive WTP for the most "environmentally friendly" package of pork. Thirty percent of the participants had no WTP, and 8% had a negative WTP. A polychotomous choice model was used to accommodate data having an anchoring point within the distribution of the data. Standard variables found in the WTP literature coupled with this model were used to predict participants who were premium payers and non-premium payers using an estimated ordered probit equation.anchoring points, environmental attributes, ordered probit, polychotomous choice functions, pork, Vickrey auction, willingness to pay, Consumer/Household Economics, Demand and Price Analysis,

The effect of realistic geometries on the susceptibility-weighted MR signal in white matter

Purpose: To investigate the effect of realistic microstructural geometry on the susceptibility-weighted magnetic resonance (MR) signal in white matter (WM), with application to demyelination. Methods: Previous work has modeled susceptibility-weighted signals under the assumption that axons are cylindrical. In this work, we explore the implications of this assumption by considering the effect of more realistic geometries. A three-compartment WM model incorporating relevant properties based on literature was used to predict the MR signal. Myelinated axons were modeled with several cross-sectional geometries of increasing realism: nested circles, warped/elliptical circles and measured axonal geometries from electron micrographs. Signal simulations from the different microstructural geometries were compared to measured signals from a Cuprizone mouse model with varying degrees of demyelination. Results: Results from simulation suggest that axonal geometry affects the MR signal. Predictions with realistic models were significantly different compared to circular models under the same microstructural tissue properties, for simulations with and without diffusion. Conclusion: The geometry of axons affects the MR signal significantly. Literature estimates of myelin susceptibility, which are based on fitting biophysical models to the MR signal, are likely to be biased by the assumed geometry, as will any derived microstructural properties.Comment: Accepted March 4 2017, in publication at Magnetic Resonance in Medicin

Flow Structure and Transport Characteristics of Feeding and Exchange Currents Generated by Upside-Down Cassiopea Jellyfish

Quantifying the flows generated by the pulsations of jellyfish bells is crucial for understanding the mechanics and efficiency of their swimming and feeding. Recent experimental and theoretical work has focused on the dynamics of vortices in the wakes of swimming jellyfish with relatively simple oral arms and tentacles. The significance of bell pulsations for generating feeding currents through elaborate oral arms and the consequences for particle capture are not as well understood. To isolate the generation of feeding currents from swimming, the pulsing kinematics and fluid flow around the benthic jellyfish Cassiopea spp. were investigated using a combination of videography, digital particle image velocimetry and direct numerical simulation. During the rapid contraction phase of the bell, fluid is pulled into a starting vortex ring that translates through the oral arms with peak velocities that can be of the order of 10 cm s–1. Strong shear flows are also generated across the top of the oral arms throughout the entire pulse cycle. A coherent train of vortex rings is not observed, unlike in the case of swimming oblate medusae such as Aurelia aurita. The phase-averaged flow generated by bell pulsations is similar to a vertical jet, with induced flow velocities averaged over the cycle of the order of 1–10 mm s–1. This introduces a strong near-horizontal entrainment of the fluid along the substrate and towards the oral arms. Continual flow along the substrate towards the jellyfish is reproduced by numerical simulations that model the oral arms as a porous Brinkman layer of finite thickness. This two-dimensional numerical model does not, however, capture the far-field flow above the medusa, suggesting that either the three-dimensionality or the complex structure of the oral arms helps to direct flow towards the central axis and up and away from the animal