Application of projection algorithms to differential equations: boundary value problems

The Douglas-Rachford method has been employed successfully to solve many kinds of non-convex feasibility problems. In particular, recent research has shown surprising stability for the method when it is applied to finding the intersections of hypersurfaces. Motivated by these discoveries, we reformulate a second order boundary valued problem (BVP) as a feasibility problem where the sets are hypersurfaces. We show that such a problem may always be reformulated as a feasibility problem on no more than three sets and is well-suited to parallelization. We explore the stability of the method by applying it to several examples of BVPs, including cases where the traditional Newton's method fails

The interrelationship of fertility, family maintenance and Mexico-U.S. Migration

This study examines the interrelationship between migration and marital fertility, using a bi-national sample of retrospective life histories collected in Mexican origin communities and U.S. destination areas. We treat couples as the unit of analysis and use discrete-time hazard models to examine: (1) how the timing and parity of births influence the occurrence of migration (to the U.S. or return to Mexico) and the type of migration (solo or couple), and (2) how current migration status and cumulative migration experience influence the likelihood of a birth. Examining the effects of fertility on migration, and the effects of migration on the timing of births, we are able to address how couples integrate migration opportunities and fertility goals into family building strategies in a context where international circular migration is pervasive.fertility, life course, Mexico, migration

A Study in GPS-Denied Navigation Using Synthetic Aperture Radar

In modern navigation systems, GPS is vital to accurately piloting a vehicle. This is especially true in autonomous vehicles, such as UAVs, which have no pilot. Unfortunately, GPS signals can be easily jammed or spoofed. For example, canyons and urban cities create an environment where the sky is obstructed and make GPS signals unreliable. Additionally, hostile individuals can transmit personal signals intended to block or spoof GPS signals. In these situations, it is important to find a means of navigation that doesn’t rely on GPS. Navigating without GPS means that other types of sensors or instruments must be used to replace the information lost from GPS. Some examples of additional sensors include cameras, altimeters, magnetometers, and radar. The work presented in this thesis shows how radar can be used to navigate without GPS. Specifically, synthetic aperture radar (SAR) is used, which is a method of processing radar data to form images of a landscape similar to images captured using a camera. SAR presents its own unique set of benefits and challenges. One major benefit of SAR is that it can produce images of an area even at night or through cloud cover. Additionally, SAR can image a wide swath of land at an angle that would be difficult for a camera to achieve. However, SAR is more computationally complex than other imaging sensors. Image quality is also highly dependent on the quality of navigation information available. In general, SAR requires that good navigation data be had in order to form SAR images. The research here explores the reverse problem where SAR images are formed without good navigation data and then good navigation data is inferred from the images. This thesis performs feasibility studies and real data implementations that show how SAR can be used in navigation without the presence of GPS. Derivations and background materials are provided. Validation methods and additional discussions are provided on the results of each portion of research

The deformed M2-brane

The superembedding formalism is used to study correction terms to the dynamics of the M2 brane in a flat background. This is done by deforming the standard embedding constraint. It is shown rigorously that the first such correction occurs at dimension four. Cohomological techniques are used to determine this correction explicitly. The action is derived to quadratic order in fermions, and the modified \k-symmetry transformations are given.Comment: 38 pages, 3 figure

Three personal barriers to teaching transformation

The benefits of active learning over traditional teaching methods have been well known for over a decade. Yet, uptake in courses taught by lecturers not familiar with the literature is very slow. Existing research has highlighted several institutional and structural barriers to change, but few go into the personal experience of the lecturer undergoing this transformation. In 2021, a second-year course on quantum mechanics was transformed to a flipped classroom style course employing constructive alignment. The lecturer (Micolich) had taught the course with good student feedback for several years and was not previously experienced with modern teaching methods before collaborating with a Physics Education Research academic (Lindstrøm). All meetings were recorded, and all written communication and notes were collated, resulting in a large data set capturing the process. In this talk, we will focus on three clear barriers to transformation faced by the lecturer: 1) being convinced of the research evidence for active teaching methods; 2) being convinced that the research literature was relevant to the lecturer’s specific context; and 3) as a late career researcher accustomed to being the expert, fundamentally changing his teaching approach required moving outside his comfort zone and having the courage to be a novice again

Data report for the Siple Coast (Antarctica) project

This report presents data collected during three field seasons of glaciological studies in the Antarctica and describes the methods employed. The region investigated covers the mouths of Ice Streams B and C (the Siple Coast) and Crary Ice Rise on the Ross Ice Shelf. Measurements included in the report are as follows: surface velocity and deformation from repeated satellite geoceiver positions; surface topography from optical levelling; radar sounding of ice thickness; accumulation rates; near-surface densities and temperature profiles; and mapping from aerial photography

Kappa-symmetric non-abelian Born-Infeld actions in three dimensions

A superembedding construction of general non-abelian Born-Infeld actions in three dimensions is described. These actions have rigid target space and local worldvolume supersymmetry(i.e. kappa symmetry). The standard abelian Born-Infeld gauge multiplet is augmented with an additional worldvolume SU(N) gauge supermultiplet. It is shown how to construct single-trace actions and in particular a kappa-supersymmetric extension of the symmetrised trace action.Comment: 14 page

Triangulation Made Easy

We describe a simple and efficient algorithm for two-view triangulation of 3D points from approximate 2D matches based on minimizing the L2 reprojection error. Our iterative algorithm improves on the one by Kanatani et al. by ensuring that in each iteration the epipolar constraint is satisfied. In the case where the two cameras are pointed in the same direction, the method provably converges to an optimal solution in exactly two iterations. For more general camera poses, two iterations are sufficient to achieve convergence to machine precision, which we exploit to devise a fast, non-iterative method. The resulting algorithm amounts to little more than solving a quadratic equation, and involves a fixed, small number of simple matrixvector operations and no conditional branches. We demonstrate that the method computes solutions that agree to very high precision with those of Hartley and Sturm's original polynomial method, though achieves higher numerical stability and 1-4 orders of magnitude greater speed

Implications of new measurements of O-16 + p + C-12,13, N-14,15 for the abundances of C, N isotopes at the cosmic ray source

The fragmentation of a 225 MeV/n O-16 beam was investigated at the Bevalac. Preliminary cross sections for mass = 13, 14, 15 fragments are used to constrain the nuclear excitation functions employed in galactic propagation calculations. Comparison to cosmic ray isotonic data at low energies shows that in the cosmic ray source C-13/C approximately 2% and N-14/0=3-6%. No source abundance of N-15 is required with the current experimental results