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Mechanical Properties and Characterization of Nanocrystalline Ni and Ni Solid Solutions
Get PDFIn this work we investigate the mechanical properties of nanocrystalline Ni and Ni solid solutions made by both traditional fabrication methods (through a literature review) and by a newly developed chemical-derivation method (through experimental characterization and nanoindentaiton testing). Chapter 1 consists of a review of the current literature on nanocrystalline Ni. It focuses specifically on
how the grain size of these materials is related to hardness through the Hall-Petch relationship and at grain sizes past the Hall-Petch breakdown. Given the number of apparent deviations from the Hall-Petch relationship found in the literature, in Chapter 2 we consider factors other than grain size which can impact hardness, including additives, annealing, and texture. Chapter 3 provides a description of
our own experimental methods and results, including sample fabrication, grain size measurement, and nanoindentation. The hardness and reduced modulus of our nanocrystalline Ni samples are calculated to be 56 MPa and 1.76 GPa, respectively. These values are very low compared to what is described in the literature. Chapter 4 presents models for the hardness and Young’s modulus of nanocrystalline materials as functions of porosity, impurity content, and other factors which might cause anomalously low values. However, we find that these models are unable to account for the values we have observed. Chapter 5 includes a discussion of future work which should be done in order to better understand the deformation occurring in chemically-derived nanocrystalline Ni and how it differs from what is described in the literature
What Criteria Should be Used to Determine Whether an Automated Decision Procedure is Fair?
No full text[Introduction] As automated decision procedures become an increasing part of our lives, the question of how to ensure that they are fair is more relevant than ever. The freedoms, careers, and financial statuses of everyone whose lives depend on these decisions often hinge on whether the algorithms behind them are fair or not, so it is critical that algorithmic fairness is understood in a precise and rigorous manner
Mechanical Properties of Small-Scale Sputtered Metallic Glasses
Get PDFSputtered metallic glasses (MGs) represent a unique class of materials because their nonperiodic arrangements are far from equilibrium. This microstructure gives rise to their exceptional mechanical properties; for example, experiments and simulations on the deformation of small-scale sputtered Zr-based MGs demonstrate their exceptional compressive and tensile strengths in excess of 1 GPa and exceptional tensile ductility of ~150%.
We report a new property that emerges in sputtered MGs: age-induced strengthening. We measured the compressive strengths of cylindrical pillars with diameters between 300 nm to 1.1 μm, which were carved from a 5 μm-thick sputtered Zr–Ni–Al thin film that was aged in a nitrogen environment for three years. Nanomechanical experiments revealed that the aged samples had a stiffness of 91 ± 4 GPa and a yield strength of 2.7 ± 0.2 GPa for all cylinder sizes, which represents a nearly 43% increase in yield strength and a 31% increase in the elastic modulus compared to equivalently sized as-sputtered samples. We also observed nano-sized induced failure suppression: samples with diameters below 600 nm deformed smoothly and noncatastrophically. Those with larger diameters deformed via a series of observable and detectable shear bands that propagated to the surfaces. Molecular dynamics (MD) simulations of uniaxial compression of chemically equivalent Zr–Ni–Al MG nanowires revealed that the underlying physics of enhanced strengths involves the evolution of local disorder that can be quantified in the number of fivefold atomic bonds. The average amount of fivefold bonding increased systematically with energetic relaxation and the maximum compressive stress. Dynamic mechanical analysis (DMA) revealed the presence of hydrides within the MG. Hydrogen diffusion into the host matrix resulted in an increase in the local volume such that more–mobile atoms (i.e., Ni and Al) can redistribute and relax into a more–energetically favorable configuration.
Experiments and simulations in this work demonstrate that sputtered MGs strength by 43% when solely aged for three years, i.e., without any accompanying annealing or mechanical treatment, which originates from atomic-level microstructural relaxation in these materials. This provides a useful foundation for simple design of advanced materials whose mechanical properties can be predicted and prescribed a priori using physical principles of atomic-level relaxation.</p
High-Cycle Dynamic Cell Fatigue with Applications on Oncotripsy
Get PDFThe method of oncotripsy (from Greek, onco- meaning "tumor" and –tripsy "to break") exploits aberrations in the material properties and morphology of cancerous cells to target them selectively using tuned low-intensity pulsed ultrasound. Compared to other noninvasive ultrasound treatments that ablate malignant tissue, oncotripsy has the capability of targeting unhealthy tissue with minimal damage to healthy cells in the ablation process.
We propose a model of oncotripsy that follows as an application of cell dynamics, statistical mechanical theory of network elasticity and 'birth-death' kinetics to describe processes of damage and repair of the cytoskeleton. We also develop a reduced dynamical model that approximates the three-dimensional dynamics of the cell and facilitates parameter studies, including sensitivity analysis and process optimization.
The dynamical system encompasses the relative motion of the nucleus to the cell membrane and a state variable measuring the extent of damage to the cytoskeleton. The dynamical system evolves in time as a result of structural dynamics and kinetics of cytoskeletal damage and repair. The resulting dynamics are complex and exhibits behavior on multiple time scales, including the period of vibration and attenuation, the characteristic time of cytoskeletal healing, the pulsing period and the time of exposure to the ultrasound. Damage on the cells develops in the order of millions of ultrasound cycles, and the failure mechanism is explained as a fatigue process. We also account for cell variability and estimate the attendant variance of the time-to-death of a cell population. We show that the dynamical model predicts — and provides a conceptual basis for understanding — the oncotripsy effect and other trends observed in experiments.</p
Surface Reconstruction from Distributed Angle Measurements
Get PDFThis thesis presents an innovative solution to the shape measurement of large structures for space applications. The current state-of-the-art heavily relies on optical solutions such as cameras or lasers to recover the shape of a surface. Because of the impracticality of placing a system in front of a large structure flying in space, new solutions need to be developed. The proposed solution is to embed angular sensors (such as sun sensors) directly on the surface. The sensors provide a collection of distributed measurements that form a discrete map of the angular orientation of the structure. An integration scheme can then estimate the 3D shape of the surface.
A mathematical model to perform the integration from angle measurements to the shape of a 3D surface is presented first. This model is purely geometric and serves as a basis for similar concepts. The surface is known in a reference configuration and is assumed to have deformed inextensibly to its current shape. Inextensibility conditions are enforced through a discretization of the metric tensor generating a finite number of constraints. This model parameterizes the shape of the surface using a small number of unknowns, and thus requires a small number of sensors. We study the singularities of the equations and derive necessary conditions for the problem to be well-posed. The limitations of the algorithm are highlighted. Simulations are performed on developable surfaces to analyze the performance of the method and to show the influence of the parameters used in the algorithm. Optimal schemes which lower the RMS error between the reconstructed shape and the actual one are presented.
An experimental validation of the proposed solution and algorithm is performed on a 1.3 x 0.25 m structure with 14 embedded sun sensors. The sensors measure the two local angles of the surface from a light source placed in front of the surface. A small, lightweight and expandable design of the sensors is shown in this thesis. A calibration procedure accurately correlates the output of the sensor with a 0.5° precision. The procedure also highlights the limitations of the design. The structure was deformed in bending and torsion with amplitudes of a few centimeters, and its shape was reconstructed to an accuracy on the order of a millimeter.
The accuracy of the initial algorithm is found to be limited by local shape deformations caused by the mechanical response of the structure. A new algorithm, replacing the discrete inextensibility conditions with the equilibrium equations derived from a finite-element model, is shown. This new algorithm is tested on the experimental structure and the accuracy of the reconstruction is increased by a factor of 2. The RMS error is under a millimeter on average over the different applied shapes and goes as low as 0.3 mm.
To understand how this solution can apply to large space structures, simulations are performed on a model of a large planar spacecraft. A 25 x 25 m structure representing the current concept for the Caltech Space Solar Power Project satellite is used as an example. Sensors with similar noise properties as the ones built for the experiment are placed on the spacecraft. A finite-element model combining the vibration of the spacecraft with large rigid body rotations is presented. This model is used in a Kalman filter that estimates the shape of the structure by iterative prediction from the dynamic finite-element model and correction from the angle measurements. Simulations are performed around the thruster actuation applied at the corner of the structure to follow a specific guidance scheme that is optimal for space solar power satellites. The actuation creates both vibrations of the structure with amplitudes of few centimeters and large rotations of the spacecraft. The designed Kalman filter can accurately estimate both effects and it is shown that millimeter accuracy is achievable. The relationship between the number of sensors, the reconstructed shape error, as well as potential stiffness deviations in the FE model is studied. The results provide first order estimates of the performance of this measurement system, in order to enable the design of future space missions.</p
Quantum Correlations, Certifying Quantum Devices, and the Quest for Infinite Entanglement
Get PDFQuantum information has the potential to disrupt the present computational landscape. Much of this potential rests on the existence of efficient quantum algorithms for classically intractable problems and of quantum cryptographic protocols for tasks that are provably impossible to realize classically. At the heart of many quantum advantages is one of the most counterintuitive features of quantum mechanics, known as entanglement. The central motivating question of this thesis is the following: if quantum devices will perform tasks that are beyond the reach of classical devices, can we hope to certify that they are performing these tasks correctly? Bell's theorem, a landmark result in physics, provides a partial answer to this question: it asserts that measurements on spatially isolated, but entangled, particles can result in outcomes that are correlated in a way that cannot be explained by any local hidden variable theory (such as Newtonian physics). A direct operational consequence of this theorem is that one can devise a statistical test to certify the presence of entanglement (and hence of genuine quantumness). Remarkably, nature allows us to take this certification one step further: in some cases, the correlation of measurement outcomes is sufficient to single out a unique quantum setup compatible with this correlation. This phenomenon is often referred to as self-testing, and is the central topic of this thesis.
In the first part of this thesis, we review the basic terminology and results in the theory of self-testing. We then explore a concrete application to the problem of verifiably delegating a quantum computation. Our main technical contribution is a test that robustly certifies products of single-qubit Clifford measurements on many EPR pairs. We employ this test to obtain a protocol which allows a classical user to verifiably delegate her quantum computation to two spatially isolated quantum servers. The overall complexity of our protocol is near-optimal, requiring resources that scale almost linearly in the size of the circuit being delegated.
In the second part of this thesis, the driving question is the following: what is the class of quantum states and measurements that can be certified through self-testing? Does self-testing only apply to a few special cases, like EPR pairs or copies of EPR pairs, or are these instances of a more general phenomenon? One of the main results of this thesis is that we settle this question for the case of bipartite states. We show the existence of a self-testing correlation for any pure bipartite entangled state of any finite local dimension. We then move on to explore the multipartite case, and we show that a significantly larger class of states can be self-tested than was previously known. This includes all multipartite partially entangled GHZ states, and more generally all multipartite qudit states which admit a Schmidt decomposition.
In the final part of this thesis, we explore connections of the theory of self-testing to basic questions about entanglement and quantum correlation sets. In particular, we set out to understand the expressive power of infinite-dimensional quantum systems. We consider two questions: can spatially isolated quantum systems of infinite dimension produce correlations that are unattainable by finite-dimensional systems? Does there exist a correlation that cannot be attained exactly by spatially isolated quantum systems (not even infinite-dimensional ones), but can be approximated arbitrarily well by a sequence of finite or infinite-dimensional systems? The first question was posed by Tsirelson in 1993, and its answer has been elusive. One of the main results of this thesis is a resolution of this question. The second question is better known as the "non-closure of the set of quantum correlations", and was answered affirmatively in a breakthrough of Slofstra. We give a new elementary proof of this result which leverages one of our self-testing results and a phenomenon known as embezzlement.</p
L-Band Multi-Polarization Radar Scatterometry over Global Forests: Modelling, Analysis, and Applications
Get PDFSpaceborne L-band radars have the ability to penetrate vegetation canopies over forested areas, suggesting a potential for regular and frequent global monitoring of both the vegetation state and the subcanopy soil moisture. However, L-band radar’s sensitivity to both vegetation and ground also complicates the relationship between the radar observations and the ecological and geophysical parameters. Accurate yet parsimonious forward models of the radar backscatter are valuable to building an understanding of these relationships. In the first part of this thesis, a model of L-band multi-polarization radar backscatter from forests, intended for use at regional to global spatial scales, is presented. Novel developments in the model include the consideration of multiple scattering within the dense vegetation canopy, and the application of a general model of plant allometry to mitigate the need for much intensive field data for training or over-tuning towards specific sites and tree species.
Aided by our model, in the remainder and majority of the thesis, a detailed analysis and interpretation of L-band backscatter over global forests is performed, using data from the Aquarius and SMAP missions. Quantitative differences in backscatter predicted by our model due to freeze/thaw states, branch orientation, and flooding are partially verified against the data, and fitted values of aboveground-biomass and microwave vegetation optical depths are comparable to independent estimates in the literature. Polarization information is used to help distinguish vegetation and ground effects on spatial and temporal variations. We show that neither vegetation nor ground effects alone can explain spatial variations within the same land cover class. For temporal variations during unfrozen periods, soil moisture is found to often be an important factor at timescales of a week to several months, although vegetation changes remain a non-negligible factor. We report the observation of significant differences in backscatter depending on beam azimuthal angle, possibly due to plant phototropism.
We also investigated diurnal variations, which have the potential to reveal signals related to plant transpiration. SMAP data from May-July 2015 showed that globally, co-polarized backscatter was generally higher at 6PM compared to 6AM over boreal forests, which is not what one might expect based on previous studies. Based on our modelling, increased canopy extinction at 6AM is a possible cause, but this is unproven and its true underlying physical cause undetermined.
Finally, by making simplifying approximations on our forward model, we propose and explore algorithms for soil moisture retrieval under forest canopies using L-band scatterometry, with preliminary evaluations suggesting improved performance over existing algorithms.</p
Integrating Quantum Optical and Superconducting Circuits with Quantum Acoustics for Scalable Quantum Network and Computation
Get PDFDue to its high coherence in transmission over a large distance in the ambient environment, the quantum optical system has been a prevailing platform for long-distance quantum communication, which was recently realized over a continental distance with a low earth orbit satellite and ground stations [102, 70]. However, the pure quantum optical system has so far shown weak interactions between photon and matter, which makes it inefficient in carrying out deterministic quantum gates for quantum repeater based scalable quantum network and quantum computing. On the other hand, superconducting quantum systems operating in the microwave domain with Josephson junction transmon qubits have proven to be capable of efficient deterministic quantum operations on quantum states [86, 87, 66]. Nevertheless, such architecture is prone to errors and decoherence due to cross-talk between microwave elements in a large-scale superconducting quantum circuit. Furthermore, superconducting systems, in general, also have large footprint (100s um) elements (resonators and superconducting quantum bits) [92, 60] that limit the ability to scale up a superconducting quantum system. Moreover, microwave quantum circuits require cooling to around 10 mK, making it unsuitable for communicating quantum information outside a dilution refrigerator (DF). Micro- and nano- acoustic elements have been extensively used in conventional integrated information processing systems due to their compactness and high coherence [97]. Acoustic systems in quantum engineering also have the advantage of being a platform for universal couplings between various quantum systems including spins, optical photons, and superconducting circuits. As it will be discussed in this thesis, elements critical to scalable optical quantum network and superconducting quantum circuit can be constructed relying on the cavity optomechanics and piezoelectric interactions.
Optomechanical interaction is concerned with the light pressure coupling of cavity mechanical deformation to a strong optical field. This interaction has allowed the close to mechanical ground state cooling of mechanical resonators using laser and the ultra-sensitive displacement measurement that led to the detection of gravitational waves in the LIGO collaboration [125, 25]. Optomechanical crystals (OMCs) are lithographically patterned devices which contain a periodic structure that host bandgaps for both optical band electromagnetic waves and microwave band acoustic waves. A properly engineered defect in the crystal can confine and localize acoustic and electromagnetic modes of similar wavelengths into a small mode volume [17, 20, 21]. A strong optomechanical coupling, which can be achieved between such strongly confined co-localized optical and acoustic modes, can be used in engineering the quantum state of mechanical motion to realize useful quantum devices such as a high-coherence quantum memory [74] and an optomechanical high efficiency optical isolator for unidirectionally connecting distant optical cavities via an acoustic bus [37].
To strongly couple the mechanical degree of freedom with a superconducting quantum circuit, various methods can be used, ranging from electromechanic coupling (electric coupling to a mechanically compliant capacitor), magnetomechanical coupling (magnetic coupling to a vibrating SQUID loop), and piezoelectric coupling. The recent advent of quantum acoustics [23, 8, 9] was realized with the strong piezoelectric coupling between a superconducting transmon qubit and a high-coherence mechanical resonator. The engineered strong piezoacoustic coupling provides the possibility to carry out deterministic ultra-high fidelity two-qubit quantum gates on non-classical mechanical quantum states [52]. This ability together with the recent demonstration of ultra-long phonon lifetime mechanical resonators show the possibility of integrating the ultra-high quality mechanical resonator as a compact quantum memory element and even a new ultra-compact (10s um) quantum bit architecture for scalable superconducting quantum circuits. Furthermore, the strong piezoelectric coupling that can transduce quantum state in a superconducting circuit into mechanical wave also makes it possible to efficiently transduce a quantum state between a superconducting quantum circuit and a telecommunication band optical channel via a mechanical waveguide connected to an optomechanical crystal cavity.</p
Latent-Variable Modeling: Algorithms, Inference, and Applications
Get PDFMany driving factors of physical systems are often latent or unobserved. Thus, understanding such systems crucially relies on accounting for the influence of the latent structure. This thesis makes advances in three aspects of latent-variable modeling: inference, algorithms, and applications. Specifically, we develop and explore latent-variable techniques that a) ensure interpretable and statistically significant models, b) can be efficiently optimized to identify best fit to data, and c) provide useful insights in real-world applications. The specific contributions of this thesis are:
1. We employ a latent-variable graphical modeling technique to develop the first state-wide statistical model of the California reservoir network. With this model, we precisely characterize the system-wide behavior of the network to hypothetical drought conditions, and proposed guidelines for more sustainable reservoir management.
2. Motivated by the previous application, we provide a geometric framework to assess the extent to which our latent variable model has learned true or false discoveries about the relevant physical phenomena. Our approach generalizes the classical notions of true and false discoveries in mathematical statistics that rely on the discrete structure of the decision space to settings where the decision space is continuous and more complicated. We highlight the utility of this viewpoint in problems involving subspace selection and low-rank estimation.
3. We propose a convex optimization procedure to fit a latent-variable graphical model for generalized linear models. This framework provides a flexible approach to model non-Gaussian variables including Poisson, Bernoulli, and exponential variables. A particularly novel aspect of our formulation is that it incorporates regularizers that are tailored to the type of latent variables.
4. We describe a computationally efficient framework to learn a latent-variable model with high-dimensional and non-iid data. This framework is based on factoriable precision operators that decouple the component associated with the observational dependencies and the component associated to interdependencies among the variables.
5. We propose a convex optimization technique to provide semantics to latent variables of a factor model. This approach is based on linking auxiliary variables -- chosen based on domain expertise -- to these latent variables.</p
Variational and Multiscale Modeling of Amorphous Silica Glass
Get PDFWe develop a critical-state model of fused silica plasticity on the basis of data mined from molecular dynamics (MD) calculations. The MD data is suggestive of an irreversible densification transition in volumetric compression resulting in permanent, or plastic, densification upon unloading. Moreover, this data exhibits dependence on temperature and the rate of deformation. We show that these characteristic behaviors are well-captured by a critical state model of plasticity, where the densification law for glass takes the place of the classical consolidation law of granular media and the locus of constant volume states denotes the critical-state line. A salient feature of the critical-state line of fused silica, as identified from the MD data, that renders its yield behavior anomalous is that it is strongly non-convex, owing to the existence of two well-differentiated phases at low and high pressures. We argue that this strong non-convexity of yield explains the patterning that is observed in molecular dynamics calculations of amorphous solids deforming in shear. We employ an explicit and exact rank-2 envelope construction to upscale the microscopic critical-state model to the macroscale. Remarkably, owing to the equilibrium constraint the resulting effective macroscopic behavior is still characterized by a non-convex critical-state line. Despite this lack of convexity, the effective macroscopic model is stable against microstructure formation and defines well-posed boundary-value problems. We present examples of ballistic impact of silica glass rods by way of the optimal transport meshfree method. We extend the study of the inelastic behavior of silica glass to include the effect of many different temperatures, pressures, and strain rates using MD and maximum entropy atomistics (MXE) calculations. Owing to the temperature dependence of the model, the macroscopic model becomes unstable against adiabatic shear localization. Thus, the material adopts small inter-facial regions where the shear strain is extremely high. We characterize the shear band size, thereby predicting a yield knockdown factor at the macroscale, and compare the results to behavior reported in flyer plate impact experiments.</p