Grain growth in protoplanetary disks

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process.

As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

Wind-driven desertification: process modeling, remote monitoring, and forecasting

Arid and semiarid landscapes comprise nearly a third of the Earth's total land surface. These areas are coming under increasing land use pressures. Despite their low productivity these lands are not barren. Rather, they consist of fragile ecosystems vulnerable to anthropogenic disturbance.

The purpose of this thesis is threefold: (I) to develop and test a process model of wind-driven desertification, (II) to evaluate next-generation process-relevant remote monitoring strategies for use in arid and semiarid regions, and (III) to identify elements for effective management of the world's drylands.

In developing the process model of wind-driven desertification in arid and semiarid lands, field, remote sensing, and modeling observations from a degraded Mojave Desert shrubland are used. This model focuses on aeolian removal and transport of dust, sand, and litter as the primary mechanisms of degradation: killing plants by burial and abrasion, interrupting natural processes of nutrient accumulation, and allowing the loss of soil resources by abiotic transport. This model is tested in field sampling experiments at two sites and is extended by Fourier Transform and geostatistical analysis of high-resolution imagery from one site.

Next, the use of hyperspectral remote sensing data is evaluated as a substantive input to dryland remote monitoring strategies. In particular, the efficacy of spectral mixture analysis (SMA) in discriminating vegetation and soil types and detennining vegetation cover is investigated. The results indicate that hyperspectral data may be less useful than often thought in determining vegetation parameters. Its usefulness in determining soil parameters, however, may be leveraged by developing simple multispectral classification tools that can be used to monitor desertification.

Finally, the elements required for effective monitoring and management of arid and semiarid lands are discussed. Several large-scale multi-site field experiments are proposed to clarify the role of wind as a landscape and degradation process in dry lands. The role of remote sensing in monitoring the world's drylands is discussed in terms of optimal remote sensing platform characteristics and surface phenomena which may be monitored in order to identify areas at risk of desertification. A desertification indicator is proposed that unifies consideration of environmental and human variables.