I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Sensor networks for geospatial event detection - theory and applications

This thesis presents theories, analyses, and algorithms for detecting and estimating parameters of geospatial events with today's large, noisy sensor networks. A geospatial event is initiated by a significant change in the state of points in a region in a 3-D space over an interval of time. After the event is initiated it may change the state of points over larger regions and longer periods of time. Networked sensing is a typical approach for geospatial event detection. In contrast to traditional sensor networks comprised of a small number of high quality (and expensive) sensors, trends in personal computing devices and consumer electronics have made it possible to build large, dense networks at a low cost. The changes in sensor capability, network composition, and system constraints call for new models and algorithms suited to the opportunities and challenges of the new generation of sensor networks. This thesis offers a single unifying model and a Bayesian framework for analyzing different types of geospatial events in such noisy sensor networks. It presents algorithms and theories for estimating the speed and accuracy of detecting geospatial events as a function of parameters from both the underlying geospatial system and the sensor network. Furthermore, the thesis addresses network scalability issues by presenting rigorous scalable algorithms for data aggregation for detection. These studies provide insights to the design of networked sensing systems for detecting geospatial events. In addition to providing an overarching framework, this thesis presents theories and experimental results for two very different geospatial problems: detecting earthquakes and hazardous radiation. The general framework is applied to these specific problems, and predictions based on the theories are validated against measurements of systems in the laboratory and in the field.

Social saliency : visual psychophysics and single-neuron recordings in humans

My thesis studies how people pay attention to other people and the environment. How does the brain figure out what is important and what are the neural mechanisms underlying attention? What is special about salient social cues compared to salient non-social cues? In Chapter I, I review social cues that attract attention, with an emphasis on the neurobiology of these social cues. I also review neurological and psychiatric links: the relationship between saliency, the amygdala and autism. The first empirical chapter then begins by noting that people constantly move in the environment. In Chapter II, I study the spatial cues that attract attention during locomotion using a cued speeded discrimination task. I found that when the motion was expansive, attention was attracted towards the singular point of the optic flow (the focus of expansion, FOE) in a sustained fashion. The more ecologically valid the motion features became (e.g., temporal expansion of each object, spatial depth structure implied by distribution of the size of the objects), the stronger the attentional effects. However, compared to inanimate objects and cues, people preferentially attend to animals and faces, a process in which the amygdala is thought to play an important role. To directly compare social cues and non-social cues in the same experiment and investigate the neural structures processing social cues, in Chapter III, I employ a change detection task and test four rare patients with bilateral amygdala lesions. All four amygdala patients showed a normal pattern of reliably faster and more accurate detection of animate stimuli, suggesting that advantageous processing of social cues can be preserved even without the amygdala, a key structure of the “social brain”. People not only attend to faces, but also pay attention to others’ facial emotions and analyze faces in great detail. Humans have a dedicated system for processing faces and the amygdala has long been associated with a key role in recognizing facial emotions. In Chapter IV, I study the neural mechanisms of emotion perception and find that single neurons in the human amygdala are selective for subjective judgment of others’ emotions. Lastly, people typically pay special attention to faces and people, but people with autism spectrum disorders (ASD) might not. To further study social attention and explore possible deficits of social attention in autism, in Chapter V, I employ a visual search task and show that people with ASD have reduced attention, especially social attention, to target-congruent objects in the search array. This deficit cannot be explained by low-level visual properties of the stimuli and is independent of the amygdala, but it is dependent on task demands. Overall, through visual psychophysics with concurrent eye-tracking, my thesis found and analyzed socially salient cues and compared social vs. non-social cues and healthy vs. clinical populations. Neural mechanisms underlying social saliency were elucidated through electrophysiology and lesion studies. I finally propose further research questions based on the findings in my thesis and introduce my follow-up studies and preliminary results beyond the scope of this thesis in the very last section, Future Directions.

Development of protein-catalyzed capture (PCC) agents with application to the specific targeting of the E17K Point mutation of Akt1

This thesis describes the expansion and improvement of the iterative in situ click chemistry OBOC peptide library screening technology. Previous work provided a proof-of-concept demonstration that this technique was advantageous for the production of protein-catalyzed capture (PCC) agents that could be used as drop-in replacements for antibodies in a variety of applications. Chapter 2 describes the technology development that was undertaken to optimize this screening process and make it readily available for a wide variety of targets. This optimization is what has allowed for the explosive growth of the PCC agent project over the past few years.

These technology improvements were applied to the discovery of PCC agents specific for single amino acid point mutations in proteins, which have many applications in cancer detection and treatment. Chapter 3 describes the use of a general all-chemical epitope-targeting strategy that can focus PCC agent development directly to a site of interest on a protein surface. This technique utilizes a chemically-synthesized chunk of the protein, called an epitope, substituted with a click handle in combination with the OBOC in situ click chemistry libraries in order to focus ligand development at a site of interest. Specifically, Chapter 3 discusses the use of this technique in developing a PCC agent specific for the E17K mutation of Akt1. Chapter 4 details the expansion of this ligand into a mutation-specific inhibitor, with applications in therapeutics.

Two roads to planet detection

One of the most exciting discoveries in astrophysics of the last last decade is of the sheer diversity of planetary systems. These include "hot Jupiters", giant planets so close to their host stars that they orbit once every few days; "Super-Earths", planets with sizes intermediate to those of Earth and Neptune, of which no analogs exist in our own solar system; multi-planet systems with planets smaller than Mars to larger than Jupiter; planets orbiting binary stars; free-floating planets flying through the emptiness of space without any star; even planets orbiting pulsars. Despite these remarkable discoveries, the field is still young, and there are many areas about which precious little is known. In particular, we don't know the planets orbiting Sun-like stars nearest to our own solar system, and we know very little about the compositions of extrasolar planets. This thesis provides developments in those directions, through two instrumentation projects.

The first chapter of this thesis concerns detecting planets in the Solar neighborhood using precision stellar radial velocities, also known as the Doppler technique. We present an analysis determining the most efficient way to detect planets considering factors such as spectral type, wavelengths of observation, spectrograph resolution, observing time, and instrumental sensitivity. We show that G and K dwarfs observed at 400-600 nm are the best targets for surveys complete down to a given planet mass and out to a specified orbital period. Overall we find that M dwarfs observed at 700-800 nm are the best targets for habitable-zone planets, particularly when including the effects of systematic noise floors caused by instrumental imperfections. Somewhat surprisingly, we demonstrate that a modestly sized observatory, with a dedicated observing program, is up to the task of discovering such planets.

We present just such an observatory in the second chapter, called the "MINiature Exoplanet Radial Velocity Array," or MINERVA. We describe the design, which uses a novel multi-aperture approach to increase stability and performance through lower system etendue, as well as keeping costs and time to deployment down. We present calculations of the expected planet yield, and data showing the system performance from our testing and development of the system at Caltech's campus. We also present the motivation, design, and performance of a fiber coupling system for the array, critical for efficiently and reliably bringing light from the telescopes to the spectrograph. We finish by presenting the current status of MINERVA, operational at Mt. Hopkins observatory in Arizona.

The second part of this thesis concerns a very different method of planet detection, direct imaging, which involves discovery and characterization of planets by collecting and analyzing their light. Directly analyzing planetary light is the most promising way to study their atmospheres, formation histories, and compositions. Direct imaging is extremely challenging, as it requires a high performance adaptive optics system to unblur the point-spread function of the parent star through the atmosphere, a coronagraph to suppress stellar diffraction, and image post-processing to remove non-common path "speckle" aberrations that can overwhelm any planetary companions.

To this end, we present the "Stellar Double Coronagraph," or SDC, a flexible coronagraphic platform for use with the 200" Hale telescope. It has two focal and pupil planes, allowing for a number of different observing modes, including multiple vortex phase masks in series for improved contrast and inner working angle behind the obscured aperture of the telescope. We present the motivation, design, performance, and data reduction pipeline of the instrument. In the following chapter, we present some early science results, including the first image of a companion to the star delta Andromeda, which had been previously hypothesized but never seen.

A further chapter presents a wavefront control code developed for the instrument, using the technique of "speckle nulling," which can remove optical aberrations from the system using the deformable mirror of the adaptive optics system. This code allows for improved contrast and inner working angles, and was written in a modular style so as to be portable to other high contrast imaging platforms. We present its performance on optical, near-infrared, and thermal infrared instruments on the Palomar and Keck telescopes, showing how it can improve contrasts by a factor of a few in less than ten iterations.

One of the large challenges in direct imaging is sensing and correcting the electric field in the focal plane to remove scattered light that can be much brighter than any planets. In the last chapter, we present a new method of focal-plane wavefront sensing, combining a coronagraph with a simple phase-shifting interferometer. We present its design and implementation on the Stellar Double Coronagraph, demonstrating its ability to create regions of high contrast by measuring and correcting for optical aberrations in the focal plane. Finally, we derive how it is possible to use the same hardware to distinguish companions from speckle errors using the principles of optical coherence. We present results observing the brown dwarf HD 49197b, demonstrating the ability to detect it despite it being buried in the speckle noise floor. We believe this is the first detection of a substellar companion using the coherence properties of light.