Understanding Micro- and Macro-Mechanics of Soil Liquefaction: A Necessary Step for Field-Scale Assessment

Liquefaction is a devastating instability associated with saturated, loose, and cohesionless soils. It poses a significant risk to distributed infrastructure systems that are vital for the security, economy, safety, health, and welfare of societies. In order to make our cities resilient to the effects of liquefaction, it is important to be able to identify areas that are most susceptible. Some of the prevalent methodologies employed to identify susceptible areas include conventional slope stability analysis and the use of so-called liquefaction charts. However, these methodologies have some limitations, which motivate our research objectives. In this dissertation, we investigate the mechanics of origin of liquefaction in a laboratory test using grain-scale simulations, which helps (i) understand why certain soils liquefy under certain conditions, and (ii) identify a necessary precursor for onset of flow liquefaction. Furthermore, we investigate the mechanics of liquefaction charts using a continuum plasticity model; this can help in modeling the surface hazards of liquefaction following an earthquake. Finally, we also investigate the microscopic definition of soil shear wave velocity, a soil property that is used as an index to quantify liquefaction resistance of soil. We show that anisotropy in fabric, or grain arrangement can be correlated with anisotropy in shear wave velocity. This has the potential to quantify the effects of sample disturbance when a soil specimen is extracted from the field. In conclusion, by developing a more fundamental understanding of soil liquefaction, this dissertation takes necessary steps for a more physical assessment of liquefaction susceptibility at the field-scale.

Part I. On the breaking of nonlinear dispersive waves. Part II. Variational principles in continuum mechanics

A model equation for water waves has been suggested by Whitham to study, qualitatively at least, the different kinds of breaking. This is an integro-differential equation which combines a typical nonlinear convection term with an integral for the dispersive effects and is of independent mathematical interest. For an approximate kernel of the form e^(-b|x|) it is shown first that solitary waves have a maximum height with sharp crests and secondly that waves which are sufficiently asymmetric break into "bores." The second part applies to a wide class of bounded kernels, but the kernel giving the correct dispersion effects of water waves has a square root singularity and the present argument does not go through. Nevertheless the possibility of the two kinds of breaking in such integro-differential equations is demonstrated.

Difficulties arise in finding variational principles for continuum mechanics problems in the Eulerian (field) description. The reason is found to be that continuum equations in the original field variables lack a mathematical "self-adjointness" property which is necessary for Euler equations. This is a feature of the Eulerian description and occurs in non-dissipative problems which have variational principles for their Lagrangian description. To overcome this difficulty a "potential representation" approach is used which consists of transforming to new (Eulerian) variables whose equations are self-adjoint. The transformations to the velocity potential or stream function in fluids or the scaler and vector potentials in electromagnetism often lead to variational principles in this way. As yet no general procedure is available for finding suitable transformations. Existing variational principles for the inviscid fluid equations in the Eulerian description are reviewed and some ideas on the form of the appropriate transformations and Lagrangians for fluid problems are obtained. These ideas are developed in a series of examples which include finding variational principles for Rossby waves and for the internal waves of a stratified fluid.

Proton transfers at the air-water interface

Proton transfer reactions at the interface of water with hydrophobic media, such as air or lipids, are ubiquitous on our planet. These reactions orchestrate a host of vital phenomena in the environment including, for example, acidification of clouds, enzymatic catalysis, chemistries of aerosol and atmospheric gases, and bioenergetic transduction. Despite their importance, however, quantitative details underlying these interactions have remained unclear. Deeper insight into these interfacial reactions is also required in addressing challenges in green chemistry, improved water quality, self-assembly of materials, the next generation of micro-nanofluidics, adhesives, coatings, catalysts, and electrodes. This thesis describes experimental and theoretical investigation of proton transfer reactions at the air-water interface as a function of hydration gradients, electrochemical potential, and electrostatics. Since emerging insights hold at the lipid-water interface as well, this work is also expected to aid understanding of complex biological phenomena associated with proton migration across membranes.

Based on our current understanding, it is known that the physicochemical properties of the gas-phase water are drastically different from those of bulk water. For example, the gas-phase hydronium ion, H₃O⁺(g), can protonate most (non-alkane) organic species, whereas H₃O⁺(aq) can neutralize only relatively strong bases. Thus, to be able to understand and engineer water-hydrophobe interfaces, it is imperative to investigate this fluctuating region of molecular thickness wherein the ‘function’ of chemical species transitions from one phase to another via steep gradients in hydration, dielectric constant, and density. Aqueous interfaces are difficult to approach by current experimental techniques because designing experiments to specifically sample interfacial layers (< 1 nm thick) is an arduous task. While recent advances in surface-specific spectroscopies have provided valuable information regarding the structure of aqueous interfaces, but structure alone is inadequate to decipher the function. By similar analogy, theoretical predictions based on classical molecular dynamics have remained limited in their scope.

Recently, we have adapted an analytical electrospray ionization mass spectrometer (ESIMS) for probing reactions at the gas-liquid interface in real time. This technique is direct, surface-specific,and provides unambiguous mass-to-charge ratios of interfacial species. With this innovation, we have been able to investigate the following:

1. How do anions mediate proton transfers at the air-water interface?

2. What is the basis for the negative surface potential at the air-water interface?

3. What is the mechanism for catalysis ‘on-water’?

In addition to our experiments with the ESIMS, we applied quantum mechanics and molecular dynamics to simulate our experiments toward gaining insight at the molecular scale. Our results unambiguously demonstrated the role of electrostatic-reorganization of interfacial water during proton transfer events. With our experimental and theoretical results on the ‘superacidity’ of the surface of mildly acidic water, we also explored implications on atmospheric chemistry and green chemistry. Our most recent results explained the basis for the negative charge of the air-water interface and showed that the water-hydrophobe interface could serve as a site for enhanced autodissociation of water compared to the condensed phase.

Topics in gravitational-wave science : macroscopic quantum mechanics and black hole physics

The theories of relativity and quantum mechanics, the two most important physics discoveries of the 20th century, not only revolutionized our understanding of the nature of space-time and the way matter exists and interacts, but also became the building blocks of what we currently know as modern physics. My thesis studies both subjects in great depths --- this intersection takes place in gravitational-wave physics.

Gravitational waves are "ripples of space-time", long predicted by general relativity. Although indirect evidence of gravitational waves has been discovered from observations of binary pulsars, direct detection of these waves is still actively being pursued. An international array of laser interferometer gravitational-wave detectors has been constructed in the past decade, and a first generation of these detectors has taken several years of data without a discovery. At this moment, these detectors are being upgraded into second-generation configurations, which will have ten times better sensitivity. Kilogram-scale test masses of these detectors, highly isolated from the environment, are probed continuously by photons. The sensitivity of such a quantum measurement can often be limited by the Heisenberg Uncertainty Principle, and during such a measurement, the test masses can be viewed as evolving through a sequence of nearly pure quantum states.

The first part of this thesis (Chapter 2) concerns how to minimize the adverse effect of thermal fluctuations on the sensitivity of advanced gravitational detectors, thereby making them closer to being quantum-limited. My colleagues and I present a detailed analysis of coating thermal noise in advanced gravitational-wave detectors, which is the dominant noise source of Advanced LIGO in the middle of the detection frequency band. We identified the two elastic loss angles, clarified the different components of the coating Brownian noise, and obtained their cross spectral densities.

The second part of this thesis (Chapters 3-7) concerns formulating experimental concepts and analyzing experimental results that demonstrate the quantum mechanical behavior of macroscopic objects - as well as developing theoretical tools for analyzing quantum measurement processes. In Chapter 3, we study the open quantum dynamics of optomechanical experiments in which a single photon strongly influences the quantum state of a mechanical object. We also explain how to engineer the mechanical oscillator's quantum state by modifying the single photon's wave function.

In Chapters 4-5, we build theoretical tools for analyzing the so-called "non-Markovian" quantum measurement processes. Chapter 4 establishes a mathematical formalism that describes the evolution of a quantum system (the plant), which is coupled to a non-Markovian bath (i.e., one with a memory) while at the same time being under continuous quantum measurement (by the probe field). This aims at providing a general framework for analyzing a large class of non-Markovian measurement processes. Chapter 5 develops a way of characterizing the non-Markovianity of a bath (i.e.,whether and to what extent the bath remembers information about the plant) by perturbing the plant and watching for changes in the its subsequent evolution. Chapter 6 re-analyzes a recent measurement of a mechanical oscillator's zero-point fluctuations, revealing nontrivial correlation between the measurement device's sensing noise and the quantum rack-action noise.

Chapter 7 describes a model in which gravity is classical and matter motions are quantized, elaborating how the quantum motions of matter are affected by the fact that gravity is classical. It offers an experimentally plausible way to test this model (hence the nature of gravity) by measuring the center-of-mass motion of a macroscopic object.

The most promising gravitational waves for direct detection are those emitted from highly energetic astrophysical processes, sometimes involving black holes - a type of object predicted by general relativity whose properties depend highly on the strong-field regime of the theory. Although black holes have been inferred to exist at centers of galaxies and in certain so-called X-ray binary objects, detecting gravitational waves emitted by systems containing black holes will offer a much more direct way of observing black holes, providing unprecedented details of space-time geometry in the black-holes' strong-field region.

The third part of this thesis (Chapters 8-11) studies black-hole physics in connection with gravitational-wave detection.

Chapter 8 applies black hole perturbation theory to model the dynamics of a light compact object orbiting around a massive central Schwarzschild black hole. In this chapter, we present a Hamiltonian formalism in which the low-mass object and the metric perturbations of the background spacetime are jointly evolved. Chapter 9 uses WKB techniques to analyze oscillation modes (quasi-normal modes or QNMs) of spinning black holes. We obtain analytical approximations to the spectrum of the weakly-damped QNMs, with relative error O(1/L^2), and connect these frequencies to geometrical features of spherical photon orbits in Kerr spacetime. Chapter 11 focuses mainly on near-extremal Kerr black holes, we discuss a bifurcation in their QNM spectra for certain ranges of (l,m) (the angular quantum numbers) as a/M → 1. With tools prepared in Chapter 9 and 10, in Chapter 11 we obtain an analytical approximate for the scalar Green function in Kerr spacetime.

Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.

Chemical and mineralogical characterization of micro-inclusions in diamonds

Secondary-ion mass spectrometry (SIMS), electron probe analysis (EPMA), analytical scanning electron microscopy (SEM) and infrared (IR) spectroscopy were used to determine the chemical composition and the mineralogy of sub-micrometer inclusions in cubic diamonds and in overgrowths (coats) on octahedral diamonds from Zaire, Botswana, and some unknown localities.

The inclusions are sub-micrometer in size. The typical diameter encountered during transmission electron microscope (TEM) examination was 0.1-0.5 µm. The micro-inclusions are sub-rounded and their shape is crystallographically controlled by the diamond. Normally they are not associated with cracks or dislocations and appear to be well isolated within the diamond matrix. The number density of inclusions is highly variable on any scale and may reach 10^(11) inclusions/cm^3 in the most densely populated zones. The total concentration of metal oxides in the diamonds varies between 20 and 1270 ppm (by weight).

SIMS analysis yields the average composition of about 100 inclusions contained in the sputtered volume. Comparison of analyses of different volumes of an individual diamond show roughly uniform composition (typically ±10% relative). The variation among the average compositions of different diamonds is somewhat greater (typically ±30%). Nevertheless, all diamonds exhibit similar characteristics, being rich in water, carbonate, SiO_2, and K_2O, and depleted in MgO. The composition of micro-inclusions in most diamonds vary within the following ranges: SiO_2, 30-53%; K_2O, 12-30%; CaO, 8-19%; FeO, 6-11%; Al_2O_3, 3-6%; MgO, 2-6%; TiO_2, 2-4%; Na_2O, 1-5%; P_2O_5, 1-4%; and Cl, 1-3%. In addition, BaO, 1-4%; SrO, 0.7-1.5%; La_2O_3, 0.1-0.3%; Ce_2O_3, 0.3-0.5%; smaller amounts of other rare-earth elements (REE), as well as Mn, Th, and U were also detected by instrumental neutron activation analysis (INAA). Mg/(Fe+Mg), 0.40-0.62 is low compared with other mantle derived phases; K/ AI ratios of 2-7 are very high, and the chondrite-normalized Ce/Eu ratios of 10-21 are also high, indicating extremely fractionated REE patterns.

SEM analyses indicate that individual inclusions within a single diamond are roughly of similar composition. The average composition of individual inclusions as measured with the SEM is similar to that measured by SIMS. Compositional variations revealed by the SEM are larger than those detected by SIMS and indicate a small variability in the composition of individual inclusions. No compositions of individual inclusions were determined that might correspond to mono-mineralic inclusions.

IR spectra of inclusion- bearing zones exhibit characteristic absorption due to: (1) pure diamonds, (2) nitrogen and hydrogen in the diamond matrix; and (3) mineral phases in the micro-inclusions. Nitrogen concentrations of 500-1100 ppm, typical of the micro-inclusion-bearing zones, are higher than the average nitrogen content of diamonds. Only type IaA centers were detected by IR. A yellow coloration may indicate small concentration of type IB centers.

The absorption due to the micro-inclusions in all diamonds produces similar spectra and indicates the presence of hydrated sheet silicates (most likely, Fe-rich clay minerals), carbonates (most likely calcite), and apatite. Small quantities of molecular CO_2 are also present in most diamonds. Water is probably associated with the silicates but the possibility of its presence as a fluid phase cannot be excluded. Characteristic lines of olivine, pyroxene and garnet were not detected and these phases cannot be significant components of the inclusions. Preliminary quantification of the IR data suggests that water and carbonate account for, on average, 20-40 wt% of the micro-inclusions.

The composition and mineralogy of the micro-inclusions are completely different from those of the more common, larger inclusions of the peridotitic or eclogitic assemblages. Their bulk composition resembles that of potassic magmas, such as kimberlites and lamproites, but is enriched in H_2O, CO_3, K_2O, and incompatible elements, and depleted in MgO.

It is suggested that the composition of the micro-inclusions represents a volatile-rich fluid or a melt trapped by the diamond during its growth. The high content of K, Na, P, and incompatible elements suggests that the trapped material found in the micro-inclusions may represent an effective metasomatizing agent. It may also be possible that fluids of similar composition are responsible for the extreme enrichment of incompatible elements documented in garnet and pyroxene inclusions in diamonds.

The origin of the fluid trapped in the micro-inclusions is still uncertain. It may have been formed by incipient melting of a highly metasomatized mantle rocks. More likely, it is the result of fractional crystallization of a potassic parental magma at depth. In either case, the micro-inclusions document the presence of highly potassic fluids or melts at depths corresponding to the diamond stability field in the upper mantle. The phases presently identified in the inclusions are believed to be the result of closed system reactions at lower pressures.

Experimental Investigation of Thrust Fault Rupture Mechanics

Thrust fault earthquakes are investigated in the laboratory by generating dynamic shear ruptures along pre-existing frictional faults in rectangular plates. A considerable body of evidence suggests that dip-slip earthquakes exhibit enhanced ground motions in the acute hanging wall wedge as an outcome of broken symmetry between hanging and foot wall plates with respect to the earth surface. To understand the physical behavior of thrust fault earthquakes, particularly ground motions near the earth surface, ruptures are nucleated in analog laboratory experiments and guided up-dip towards the simulated earth surface. The transient slip event and emitted radiation mimic a natural thrust earthquake. High-speed photography and laser velocimeters capture the rupture evolution, outputting a full-field view of photo-elastic fringe contours proportional to maximum shearing stresses as well as continuous ground motion velocity records at discrete points on the specimen. Earth surface-normal measurements validate selective enhancement of hanging wall ground motions for both sub-Rayleigh and super-shear rupture speeds. The earth surface breaks upon rupture tip arrival to the fault trace, generating prominent Rayleigh surface waves. A rupture wave is sensed in the hanging wall but is, however, absent from the foot wall plate: a direct consequence of proximity from fault to seismometer. Signatures in earth surface-normal records attenuate with distance from the fault trace. Super-shear earthquakes feature greater amplitudes of ground shaking profiles, as expected from the increased tectonic pressures required to induce super-shear transition. Paired stations measure fault parallel and fault normal ground motions at various depths, which yield slip and opening rates through direct subtraction of like components. Peak fault slip and opening rates associated with the rupture tip increase with proximity to the fault trace, a result of selective ground motion amplification in the hanging wall. Fault opening rates indicate that the hanging and foot walls detach near the earth surface, a phenomenon promoted by a decrease in magnitude of far-field tectonic loads. Subsequent shutting of the fault sends an opening pulse back down-dip. In case of a sub-Rayleigh earthquake, feedback from the reflected S wave re-ruptures the locked fault at super-shear speeds, providing another mechanism of super-shear transition.

Suspension mechanics: I. Inertial and non-Newtonian migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows; II. The effect of viscoelasticity on the creeping motion of a train of neutrally buoyant Newtonian drops through a circular tube

The lateral migration of neutrally buoyant rigid spheres in two-dimensional unidirectional flows was studied theoretically. The cases of both inertia-induced migration in a Newtonian fluid and normal stress-induced migration in a second-order fluid were considered. Analytical results for the lateral velocities were obtained, and the equilibrium positions and trajectories of the spheres compared favorably with the experimental data available in the literature. The effective viscosity was obtained for a dilute suspension of spheres which were simultaneously undergoing inertia-induced migration and translational Brownian motion in a plane Poiseuille flow. The migration of spheres suspended in a second-order fluid inside a screw extruder was also considered.

The creeping motion of neutrally buoyant concentrically located Newtonian drops through a circular tube was studied experimentally for drops which have an undeformed radius comparable to that of the tube. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop due to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow were obtained for various viscosity ratios, total flow rates, and drop sizes. The results were compared with existing theoretical and experimental data.

Rate and Microstructure Effects on the Dynamics of Carbon Nanotube Foams

Soft hierarchical materials often present unique functional properties that are sensitive to the geometry and organization of their micro- and nano-structural features across different lengthscales. Carbon Nanotube (CNT) foams are hierarchical materials with fibrous morphology that are known for their remarkable physical, chemical and electrical properties. Their complex microstructure has led them to exhibit intriguing mechanical responses at different length-scales and in different loading regimes. Even though these materials have been studied for mechanical behavior over the past few years, their response at high-rate finite deformations and the influence of their microstructure on bulk mechanical behavior and energy dissipative characteristics remain elusive.

In this dissertation, we study the response of aligned CNT foams at the high strain-rate regime of 10² - 10⁴ s^-1. We investigate their bulk dynamic response and the fundamental deformation mechanisms at different lengthscales, and correlate them to the microstructural characteristics of the foams. We develop an experimental platform, with which to study the mechanics of CNT foams in high-rate deformations, that includes direct measurements of the strain and transmitted forces, and allows for a full field visualization of the sample’s deformation through high-speed microscopy.

We synthesize various CNT foams (e.g., vertically aligned CNT (VACNT) foams, helical CNT foams, micro-architectured VACNT foams and VACNT foams with microscale heterogeneities) and show that the bulk functional properties of these materials are highly tunable either by tailoring their microstructure during synthesis or by designing micro-architectures that exploit the principles of structural mechanics. We also develop numerical models to describe the bulk dynamic response using multiscale mass-spring models and identify the mechanical properties at length scales that are smaller than the sample height.

The ability to control the geometry of microstructural features, and their local interactions, allows the creation of novel hierarchical materials with desired functional properties. The fundamental understanding provided by this work on the key structure-function relations that govern the bulk response of CNT foams can be extended to other fibrous, soft and hierarchical materials. The findings can be used to design materials with tailored properties for different engineering applications, like vibration damping, impact mitigation and packaging.

Fiber-optic integration and efficient detection schemes for optomechanical resonators

With the advent of the laser in the year 1960, the field of optics experienced a renaissance from what was considered to be a dull, solved subject to an active area of development, with applications and discoveries which are yet to be exhausted 55 years later. Light is now nearly ubiquitous not only in cutting-edge research in physics, chemistry, and biology, but also in modern technology and infrastructure. One quality of light, that of the imparted radiation pressure force upon reflection from an object, has attracted intense interest from researchers seeking to precisely monitor and control the motional degrees of freedom of an object using light. These optomechanical interactions have inspired myriad proposals, ranging from quantum memories and transducers in quantum information networks to precision metrology of classical forces. Alongside advances in micro- and nano-fabrication, the burgeoning field of optomechanics has yielded a class of highly engineered systems designed to produce strong interactions between light and motion.

Optomechanical crystals are one such system in which the patterning of periodic holes in thin dielectric films traps both light and sound waves to a micro-scale volume. These devices feature strong radiation pressure coupling between high-quality optical cavity modes and internal nanomechanical resonances. Whether for applications in the quantum or classical domain, the utility of optomechanical crystals hinges on the degree to which light radiating from the device, having interacted with mechanical motion, can be collected and detected in an experimental apparatus consisting of conventional optical components such as lenses and optical fibers. While several efficient methods of optical coupling exist to meet this task, most are unsuitable for the cryogenic or vacuum integration required for many applications. The first portion of this dissertation will detail the development of robust and efficient methods of optically coupling optomechanical resonators to optical fibers, with an emphasis on fabrication processes and optical characterization.

I will then proceed to describe a few experiments enabled by the fiber couplers. The first studies the performance of an optomechanical resonator as a precise sensor for continuous position measurement. The sensitivity of the measurement, limited by the detection efficiency of intracavity photons, is compared to the standard quantum limit imposed by the quantum properties of the laser probe light. The added noise of the measurement is seen to fall within a factor of 3 of the standard quantum limit, representing an order of magnitude improvement over previous experiments utilizing optomechanical crystals, and matching the performance of similar measurements in the microwave domain.

The next experiment uses single photon counting to detect individual phonon emission and absorption events within the nanomechanical oscillator. The scattering of laser light from mechanical motion produces correlated photon-phonon pairs, and detection of the emitted photon corresponds to an effective phonon counting scheme. In the process of scattering, the coherence properties of the mechanical oscillation are mapped onto the reflected light. Intensity interferometry of the reflected light then allows measurement of the temporal coherence of the acoustic field. These correlations are measured for a range of experimental conditions, including the optomechanical amplification of the mechanics to a self-oscillation regime, and comparisons are drawn to a laser system for phonons. Finally, prospects for using phonon counting and intensity interferometry to produce non-classical mechanical states are detailed following recent proposals in literature.

Quantum Mechanics Studies of Fuel Cell Catalysts and Proton Conducting Ceramics with Validation by Experiment

We carried out quantum mechanics (QM) studies aimed at improving the performance of hydrogen fuel cells. This led to predictions of improved materials, some of which were subsequently validated with experiments by our collaborators.

In part I, the challenge was to find a replacement for the Pt cathode that would lead to improved performance for the Oxygen Reduction Reaction (ORR) while remaining stable under operational conditions and decreasing cost. Our design strategy was to find an alloy with composition Pt3M that would lead to surface segregation such that the top layer would be pure Pt, with the second and subsequent layers richer in M. Under operating conditions we expect the surface to have significant O and/or OH chemisorbed on the surface, and hence we searched for M that would remain segregated under these conditions. Using QM we examined surface segregation for 28 Pt₃M alloys, where M is a transition metal. We found that only Pt₃Os and Pt₃Ir showed significant surface segregation when O and OH are chemisorbed on the catalyst surfaces. This result indicates that Pt₃Os and Pt3Ir favor formation of a Pt-skin surface layer structure that would resist the acidic electrolyte corrosion during fuel cell operation environments. We chose to focus on Os because the phase diagram for Pt-Ir indicated that Pt-Ir could not form a homogeneous alloy at lower temperature. To determine the performance for ORR, we used QM to examine all intermediates, reaction pathways, and reaction barriers involved in the processes for which protons from the anode reactions react with O₂ to form H₂O. These QM calculations used our Poisson-Boltzmann implicit solvation model include the effects of the solvent (water with dielectric constant 78 with pH 7 at 298K). We found that the rate determination step (RDS) was the O_ad hydration reaction (O_ad + H₂O_ad -> OH_ad + OH_ad) in both cases, but that the barrier for pure Pt of 0.50 eV is reduced to 0.48 eV for Pt₃Os, which at 80 degrees C would increase the rate by 218%. We collaborated with the Pu-Wei Wu’s group to carry out experiments, where we found that the dealloying process-treated Pt2Os catalyst showed two-fold higher activity at 25 degrees C than pure Pt and that the alloy had 272% improved stability, validating our theoretical predictions.

We also carried out similar QM studies followed by experimental validation for the Os/Pt core-shell catalyst fabricated by the underpotential deposition (UPD) method. The QM results indicated that the RDS for ORR is a compromise between the OOH formation step (0.37 eV for Pt, 0.23 eV for Pt_2ML/Os core-shell) and H₂O formation steps (0.32 eV for Pt, 0.22 eV for Pt_2ML/Os core-shell). We found that Pt_2ML/Os has the highest activity (compared to pure Pt and to the Pt₃Os alloy) because the 0.37 eV barrier decreases to 0.23 eV. To understand what aspects of the core shell structure lead to this improved performance, we considered the effect on ORR of compressing the alloy slab to the dimensions of pure Pt. However this had little effect, with the same RDS barrier 0.37 eV. This shows that the ligand effect (the electronic structure modification resulting from the Os substrate) plays a more important role than the strain effect, and is responsible for the improved activity of the core- shell catalyst. Experimental materials characterization proves the core-shell feature of our catalyst. The electrochemical experiment for Pt_2ML/Os/C showed 3.5 to 5 times better ORR activity at 0.9V (vs. NHE) in 0.1M HClO₄ solution at 25 degrees C as compared to those of commercially available Pt/C. The excellent correlation between experimental half potential and the OH binding energies and RDS barriers validate the feasibility of predicting catalyst activity using QM calculation and a simple Langmuir–Hinshelwood model.

In part II, we used QM calculations to study methane stream reforming on a Ni-alloy catalyst surfaces for solid oxide fuel cell (SOFC) application. SOFC has wide fuel adaptability but the coking and sulfur poisoning will reduce its stability. Experimental results suggested that the Ni4Fe alloy improves both its activity and stability compared to pure Ni. To understand the atomistic origin of this, we carried out QM calculations on surface segregation and found that the most stable configuration for Ni₄Fe has a Fe atom distribution of (0%, 50%, 25%, 25%, 0%) starting at the bottom layer. We calculated that the binding of C atoms on the Ni4Fe surface is 142.9 Kcal/mol, which is about 10 Kcal/mol weaker compared to the pure Ni surface. This weaker C binding energy is expected to make coke formation less favorable, explaining why Ni₄Fe has better coking resistance. This result confirms the experimental observation. The reaction energy barriers for CHx decomposition and C binding on various alloy surface, Ni₄X (X=Fe, Co, Mn, and Mo), showed Ni₄Fe, Ni₄Co, and Fe₄Mn all have better coking resistance than pure Ni, but that only Ni₄Fe and Fe₄Mn have (slightly) improved activity compared to pure Ni.

In part III, we used QM to examine the proton transport in doped perovskite-ceramics. Here we used a 2x2x2 supercell of perovskite with composition Ba₈X₇M₁(OH)₁O₂₃ where X=Ce or Zr and M=Y, Gd, or Dy. Thus in each case a 4⁺ X is replace by a 3⁺ M plus a proton on one O. Here we predicted the barriers for proton diffusion allowing both includes intra-octahedron and inter-octahedra proton transfer. Without any restriction, we only observed the inter-octahedra proton transfer with similar energy barrier as previous computational work but 0.2 eV higher than experimental result for Y doped zirconate. For one restriction in our calculations is that the O_donor-O_acceptor atoms were kept at fixed distances, we found that the barrier difference between cerates/zirconates with various dopants are only 0.02~0.03 eV. To fully address performance one would need to examine proton transfer at grain boundaries, which will require larger scale ReaxFF reactive dynamics for systems with millions of atoms. The QM calculations used here will be used to train the ReaxFF force field.

Mechanics of landslides

The purpose of this investigation was to determine whether landslides could be predicted for hill slopes of known inclinations from data secured by laboratory tests performed on samples of the ground under consideration. Specifically, the investigation was to show whether a correlation existed between experimentally determined values for friction and cohesion of ground and calculated values based upon the configuration of earth masses that had slid. The ability to determine the stability of slopes from experimental data is of obvious significance.

Dynamic characterization of micro-particle systems

Ordered granular systems have been a subject of active research for decades. Due to their rich dynamic response and nonlinearity, ordered granular systems have been suggested for several applications, such as solitary wave focusing, acoustic signals manipulation, and vibration absorption. Most of the fundamental research performed on ordered granular systems has focused on macro-scale examples. However, most engineering applications require these systems to operate at much smaller scales. Very little is known about the response of micro-scale granular systems, primarily because of the difficulties in realizing reliable and quantitative experiments, which originate from the discrete nature of granular materials and their highly nonlinear inter-particle contact forces.

In this work, we investigate the physics of ordered micro-granular systems by designing an innovative experimental platform that allows us to assemble, excite, and characterize ordered micro-granular systems. This new experimental platform employs a laser system to deliver impulses with controlled momentum and incorporates non-contact measurement apparatuses to detect the particles’ displacement and velocity. We demonstrated the capability of the laser system to excite systems of dry (stainless steel particles of radius 150 micrometers) and wet (silica particles of radius 3.69 micrometers, immersed in fluid) micro-particles, after which we analyzed the stress propagation through these systems.

We derived the equations of motion governing the dynamic response of dry and wet particles on a substrate, which we then validated in experiments. We then measured the losses in these systems and characterized the collision and friction between two micro-particles. We studied wave propagation in one-dimensional dry chains of micro-particles as well as in two-dimensional colloidal systems immersed in fluid. We investigated the influence of defects to wave propagation in the one-dimensional systems. Finally, we characterized the wave-attenuation and its relation to the viscosity of the surrounding fluid and performed computer simulations to establish a model that captures the observed response.

The findings of the study offer the first systematic experimental and numerical analysis of wave propagation through ordered systems of micro-particles. The experimental system designed in this work provides the necessary tools for further fundamental studies of wave propagation in both granular and colloidal systems.

Mechanics of sediment transport and bedrock erosion in steep landscapes

Erosion is concentrated in steep landscapes such that, despite accounting for only a small fraction of Earth’s total surface area, these areas regulate the flux of sediment to downstream basins, and their rugged morphology records transient changes (or lack thereof) in geologic and climatic forcing. Steep landscapes are geomorphically active; large sediment fluxes and rapid landscape evolution rates can create or destroy habitat for humans and wildlife alike, and landslides, debris flows, and floods common in mountainous areas represent a persistent natural and structural hazard. Despite the central role that steep landscapes play in the geosciences and in landscape management, the processes controlling their evolution have been poorly studied compared to lower-gradient areas. This thesis focuses on the basic mechanics of sediment transport and bedrock incision in steep landscapes, as these are the fundamental processes which set the pace and style of landscape evolution. Chapter 1 examines the spatial distribution of slow-moving landslides; these landslides can dominate sediment fluxes to river networks, but the controls on their occurrence are poorly understood. Using a case-study along the San Andreas Fault, California, I show that slow-moving landslides preferentially occur near the fault, suggesting a rock-strength control on landslide distribution. Chapter 2 provides the first field-measurements of incipient sediment motion in streams steeper than 14% and shows a large influence of slope-dependent flow hydraulics and grain-scale roughness on particle motion. Chapter 3 presents experimental evidence for bedrock erosion by suspended sediment, suggesting that, in contrast to prevailing theoretical predictions, suspension-regime transport in steep streams can be the dominant erosion agent. Steep streams are often characterized by the presence of waterfalls and bedrock steps which can have locally high rates of erosion; Chapters 4 and 5 present newly developed, experimentally validated theory on sediment transport through and bedrock erosion in waterfall plunge pools. Finally, Chapter 6 explores the formation of a bedrock slot canyon where interactions between sediment transport and bedrock incision lead to the formation of upstream-propagating bedrock step-pools and waterfalls.

Particle fluid mechanics in shear flows, acoustic waves, and shock waves

Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, non-reacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).

Part I

A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluid-particle mixture by assuming W = W_p. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_v, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.

Part II

The “inviscid” equation for a gas-particle mixture is linearized to describe the flow over a wavy wall. Corresponding to the Prandtl-Glauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_v and λ_T approach zero and frozen flows in which λ_v and λ_T become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_v and λ_T, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_D is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.

Part III

Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_D. Thus, it seems advantageous in the general study of two-dimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_D within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.

Part IV

The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gas-vapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_D.

For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.

The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particle-gas mixture interaction.

Part V

For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.