Beyond the blur: Construction and characterization of the first autonomous AO system and An AO survey of magnetar proper motions

Adaptive optics (AO) corrects distortions created by atmospheric turbulence and delivers diffraction-limited images on ground-based telescopes. The vastly improved spatial resolution and sensitivity has been utilized for studying everything from the magnetic fields of sunspots upto the internal dynamics of high-redshift galaxies. This thesis about AO science from small and large telescopes is divided into two parts: Robo-AO and magnetar kinematics.

In the first part, I discuss the construction and performance of the world’s first fully autonomous visible light AO system, Robo-AO, at the Palomar 60-inch telescope. Robo-AO operates extremely efficiently with an overhead < 50s, typically observing about 22 targets every hour. We have performed large AO programs observing a total of over 7,500 targets since May 2012. In the visible band, the images have a Strehl ratio of about 10% and achieve a contrast of upto 6 magnitudes at a separation of 1′′. The full-width at half maximum achieved is 110–130 milli-arcsecond. I describe how Robo-AO is used to constrain the evolutionary models of low-mass pre-main-sequence stars by measuring resolved spectral energy distributions of stellar multiples in the visible band, more than doubling the current sample. I conclude this part with a discussion of possible future improvements to the Robo-AO system.

In the second part, I describe a study of magnetar kinematics using high-resolution near-infrared (NIR) AO imaging from the 10-meter Keck II telescope. Measuring the proper motions of five magnetars with a precision of upto 0.7 milli-arcsecond/yr, we have more than tripled the previously known sample of magnetar proper motions and proved that magnetar kinematics are equivalent to those of radio pulsars. We conclusively showed that SGR 1900+14 and SGR 1806-20 were ejected from the stellar clusters with which they were traditionally associated. The inferred kinematic ages of these two magnetars are 6±1.8 kyr and 650±300 yr respectively. These ages are a factor of three to four times greater than their respective characteristic ages. The calculated braking index is close to unity as compared to three for the vacuum dipole model and 2.5-2.8 as measured for young pulsars. I conclude this section by describing a search for NIR counterparts of new magnetars and a future promise of polarimetric investigation of a magnetars’ NIR emission mechanism.

Crystals that count! Physical principles and experimental investigations of DNA tile self-assembly

Algorithmic DNA tiles systems are fascinating. From a theoretical perspective, they can result in simple systems that assemble themselves into beautiful, complex structures through fundamental interactions and logical rules. As an experimental technique, they provide a promising method for programmably assembling complex, precise crystals that can grow to considerable size while retaining nanoscale resolution. In the journey from theoretical abstractions to experimental demonstrations, however, lie numerous challenges and complications.

In this thesis, to examine these challenges, we consider the physical principles behind DNA tile self-assembly. We survey recent progress in experimental algorithmic self-assembly, and explain the simple physical models behind this progress. Using direct observation of individual tile attachments and detachments with an atomic force microscope, we test some of the fundamental assumptions of the widely-used kinetic Tile Assembly Model, obtaining results that fit the model to within error. We then depart from the simplest form of that model, examining the effects of DNA sticky end sequence energetics on tile system behavior. We develop theoretical models, sequence assignment algorithms, and a software package, StickyDesign, for sticky end sequence design.

As a demonstration of a specific tile system, we design a binary counting ribbon that can accurately count from a programmable starting value and stop growing after overflowing, resulting in a single system that can construct ribbons of precise and programmable length. In the process of designing the system, we explain numerous considerations that provide insight into more general tile system design, particularly with regards to tile concentrations, facet nucleation, the construction of finite assemblies, and design beyond the abstract Tile Assembly Model.

Finally, we present our crystals that count: experimental results with our binary counting system that represent a significant improvement in the accuracy of experimental algorithmic self-assembly, including crystals that count perfectly with 5 bits from 0 to 31. We show some preliminary experimental results on the construction of our capping system to stop growth after counters overflow, and offer some speculation on potential future directions of the field.

On the Construction of Higher étale Regulators

We present three approaches to define the higher étale regulator maps Φ^r,n_et : H^r_et(X,Z(n)) → H^r_D(X,Z(n)) for regular arithmetic schemes. The first two approaches construct the maps on the cohomology level, while the third construction provides a morphism of complexes of sheaves on the étale site, along with a technical twist that one needs to replace the Deligne-Beilinson cohomology by the analytic Deligne cohomology inspired by the work of Kerr, Lewis, and Müller-Stach. A vanishing statement of infinite divisible torsions under Φ^r,n_et is established for r > 2n + 1.