Some approximate solutions of dynamic problems in the linear theory of thin elastic shells

Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

Wave propagation in an inhomogeneous medium

This paper is in two parts. In the first part we give a qualitative study of wave propagation in an inhomogeneous medium principally by geometrical optics and ray theory. The inhomogeneity is represented by a sound-speed profile which is dependent upon one coordinate, namely the depth; and we discuss the general characteristics of wave propagation which result from a source placed on the sound channel axis. We show that our mathematical model of the sound- speed in the ocean actually predicts some of the behavior of the observed physical phenomena in the underwater sound channel. Using ray theoretic techniques we investigate the implications of our profile on the following characteristics of SOFAR propagation: (i) the sound energy traveling further away from the axis takes less time to travel from source to receiver than sound energy traveling closer to the axis, (ii) the focusing of sound energy in the sound channel at certain ranges, (iii) the overall ray picture in the sound channel.

In the second part a more penetrating quantitative study is done by means of analytical techniques on the governing equations. We study the transient problem for the Epstein profile by employing a double transform to formally derive an integral representation for the acoustic pressure amplitude, and from this representation we obtain several alternative representations. We study the case where both source and receiver are on the channel axis and greatly separated. In particular we verify some of the earlier results derived by ray theory and obtain asymptotic results for the acoustic pressure in the far-field.

The biological sense of smell: olfactory search behavior and a metabolic view for olfactory perception

Part I of the thesis describes the olfactory searching and scanning behaviors of rats in a wind tunnel, and a detailed movement analysis of terrestrial arthropod olfactory scanning behavior. Olfactory scanning behaviors in rats may be a behavioral correlate to hippocampal place cell activity.

Part II focuses on the organization of olfactory perception, what it suggests about a natural order for chemicals in the environment, and what this in tum suggests about the organization of the olfactory system. A model of odor quality space (analogous to the "color wheel") is presented. This model defines relationships between odor qualities perceived by human subjects based on a quantitative similarity measure. Compounds containing Carbon, Nitrogen, or Sulfur elicit odors that are contiguous in this odor representation, which thus allows one to predict the broad class of odor qualities a compound is likely to elicit. Based on these findings, a natural organization for olfactory stimuli is hypothesized: the order provided by the metabolic process. This hypothesis is tested by comparing compounds that are structurally similar, perceptually similar, and metabolically similar in a psychophysical cross-adaptation paradigm. Metabolically similar compounds consistently evoked shifts in odor quality and intensity under cross-adaptation, while compounds that were structurally similar or perceptually similar did not. This suggests that the olfactory system may process metabolically similar compounds using the same neural pathways, and that metabolic similarity may be the fundamental metric about which olfactory processing is organized. In other words, the olfactory system may be organized around a biological basis.

The idea of a biological basis for olfactory perception represents a shift in how olfaction is understood. The biological view has predictive power while the current chemical view does not, and the biological view provides explanations for some of the most basic questions in olfaction, that are unanswered in the chemical view. Existing data do not disprove a biological view, and are consistent with basic hypotheses that arise from this viewpoint.

The strategic behavior of rational novices

There is a growing amount of experimental evidence that suggests people often deviate from the predictions of game theory. Some scholars attempt to explain the observations by introducing errors into behavioral models. However, most of these modifications are situation dependent and do not generalize. A new theory, called the rational novice model, is introduced as an attempt to provide a general theory that takes account of erroneous behavior. The rational novice model is based on two central principals. The first is that people systematically make inaccurate guesses when they are evaluating their options in a game-like situation. The second is that people treat their decisions similar to a portfolio problem. As a result, non optimal actions in a game theoretic sense may be included in the rational novice strategy profile with positive weights.

The rational novice model can be divided into two parts: the behavioral model and the equilibrium concept. In a theoretical chapter, the mathematics of the behavioral model and the equilibrium concept are introduced. The existence of the equilibrium is established. In addition, the Nash equilibrium is shown to be a special case of the rational novice equilibrium. In another chapter, the rational novice model is applied to a voluntary contribution game. Numerical methods were used to obtain the solution. The model is estimated with data obtained from the Palfrey and Prisbrey experimental study of the voluntary contribution game. It is found that the rational novice model explains the data better than the Nash model. Although a formal statistical test was not used, pseudo R^2 analysis indicates that the rational novice model is better than a Probit model similar to the one used in the Palfrey and Prisbrey study.

The rational novice model is also applied to a first price sealed bid auction. Again, computing techniques were used to obtain a numerical solution. The data obtained from the Chen and Plott study were used to estimate the model. The rational novice model outperforms the CRRAM, the primary Nash model studied in the Chen and Plott study. However, the rational novice model is not the best amongst all models. A sophisticated rule-of-thumb, called the SOPAM, offers the best explanation of the data.

Seismic structure above and below the core-mantle boundary

Seismic structure above and below the core-mantle boundary (CMB) has been studied through use of travel time and waveform analyses of several different seismic wave groups. Anomalous systematic trends in observables document mantle heterogeneity on both large and small scales. Analog and digital data has been utilized, and in many cases the analog data has been optically scanned and digitized prior to analysis.

Differential travel times of S - SKS are shown to be an excellent diagnostic of anomalous lower mantle shear velocity (V s) structure. Wavepath geometries beneath the central Pacific exhibit large S- SKS travel time residuals (up to 10 sec), and are consistent with a large scale 0(1000 km) slower than average V_s region (≥3%). S - SKS times for paths traversing this region exhibit smaller scale patterns and trends 0(100 km) indicating V_s perturbations on many scale lengths. These times are compared to predictions of three tomographically derived aspherical models: MDLSH of Tanimoto [1990], model SH12_WM13 of Suet al. [1992], and model SH.10c.17 of Masters et al. [1992]. Qualitative agreement between the tomographic model predictions and observations is encouraging, varying from fair to good. However, inconsistencies are present and suggest anomalies in the lower mantle of scale length smaller than the present 2000+ km scale resolution of tomographic models. 2-D wave propagation experiments show the importance of inhomogeneous raypaths when considering lateral heterogeneities in the lowermost mantle.

A dataset of waveforms and differential travel times of S, ScS, and the arrival from the D" layer, Scd, provides evidence for a laterally varying V_s velocity discontinuity at the base of the mantle. Two different localized D" regions beneath the central Pacific have been investigated. Predictions from a model having a V_s discontinuity 180 km above the CMB agree well with observations for an eastern mid-Pacific CMB region. This thickness differs from V_s discontinuity thicknesses found in other regions, such as a localized region beneath the western Pacific, which average near 280 km. The "sharpness" of the V_s jump at the top of D", i.e., the depth range over which the V_s increase occurs, is not resolved by our data, and our data can in fact may be modeled equally well by a lower mantle with the increase in V_s at the top of D" occurring over a 100 krn depth range. It is difficult at present to correlate D" thicknesses from this study to overall lower mantle heterogeneity, due to uncertainties in the 3-D models, as well as poor coverage in maps of D" discontinuity thicknesses.

P-wave velocity structure (V_p) at the base of the mantle is explored using the seismic phases SKS and SPdKS. SPdKS is formed when SKS waves at distances around 107° are incident upon the CMB with a slowness that allows for coupling with diffracted P-waves at the base of the mantle. The P-wave diffraction occurs at both the SKS entrance and exit locations of the outer core. SP_dKS arrives slightly later in time than SKS, having a wave path through the mantle and core very close to SKS. The difference time between SKS and SP_dKS strongly depends on V_p at the base of the mantle near SK Score entrance and exit points. Observations from deep focus Fiji-Tonga events recorded by North American stations, and South American events recorded by European and Eurasian stations exhibit anomalously large SP_dKS - SKS difference times. SKS and the later arriving SP_dKS phase are separated by several seconds more than predictions made by 1-D reference models, such as the global average PREM [Dziewonski and Anderson, 1981] model. Models having a pronounced low-velocity zone (5%) in V_p in the bottom 50-100 km of the mantle predict the size of the observed SP_dK S-SKS anomalies. Raypath perturbations from lower mantle V_s structure may also be contributing to the observed anomalies.

Outer core structure is investigated using the family of SmKS (m=2,3,4) seismic waves. SmKS are waves that travel as S-waves in the mantle, P-waves in the core, and reflect (m-1) times on the underside of the CMB, and are well-suited for constraining outermost core V_p structure. This is due to closeness of the mantle paths and also the shallow depth range these waves travel in the outermost core. S3KS - S2KS and S4KS - S3KS differential travel times were measured using the cross-correlation method and compared to those from reflectivity synthetics created from core models of past studies. High quality recordings from a deep focus Java Sea event which sample the outer core beneath the northern Pacific, the Arctic, and northwestern North America (spanning 1/8th of the core's surface area), have SmKS wavepaths that traverse regions where lower mantle heterogeneity is pre- dieted small, and are well-modeled by the PREM core model, with possibly a small V_p decrease (1.5%) in the outermost 50 km of the core. Such a reduction implies chemical stratification in this 50 km zone, though this model feature is not uniquely resolved. Data having wave paths through areas of known D" heterogeneity (±2% and greater), such as the source-side of SmKS lower mantle paths from Fiji-Tonga to Eurasia and Africa, exhibit systematic SmKS differential time anomalies of up to several seconds. 2-D wave propagation experiments demonstrate how large scale lower mantle velocity perturbations can explain long wavelength behavior of such anomalous SmKS times. When improperly accounted for, lower mantle heterogeneity maps directly into core structure. Raypaths departing from homogeneity play an important role in producing SmKS anomalies. The existence of outermost core heterogeneity is difficult to resolve at present due to uncertainties in global lower mantle structure. Resolving a one-dimensional chemically stratified outermost core also remains difficult due to the same uncertainties. Restricting study to higher multiples of SmKS (m=2,3,4) can help reduce the affect of mantle heterogeneity due to the closeness of the mantle legs of the wavepaths. SmKS waves are ideal in providing additional information on the details of lower mantle heterogeneity.

Phase behavior of complex superprotonic solid acids

Superprotonic phase transitions and thermal behaviors of three complex solid acid systems are presented, namely Rb3H(SO4)2-RbHSO4 system, Rb3H(SeO4)2-Cs3H(SeO4)2 solid solution system, and Cs6(H2SO4)3(H1.5PO4)4. These material systems present a rich set of phase transition characteristics that set them apart from other, simpler solid acids. A.C. impedance spectroscopy, high-temperature X-ray powder diffraction, and thermal analysis, as well as other characterization techniques, were employed to investigate the phase behavior of these systems.

Rb3H(SO4)2 is an atypical member of the M3H(XO4)2 class of compounds (M = alkali metal or NH4+ and X = S or Se) in that a transition to a high-conductivity state involves disproportionation into two phases rather than a simple polymorphic transition [1]. In the present work, investigations of the Rb3H(SO4)2-RbHSO4 system have revealed the disproportionation products to be Rb2SO4 and the previously unknown compound Rb5H3(SO4)4. The new compound becomes stable at a temperature between 25 and 140 °C and is isostructural to a recently reported trigonal phase with space group P3̅m of Cs5H3(SO4)4 [2]. At 185 °C the compound undergoes an apparently polymorphic transformation with a heat of transition of 23.8 kJ/mol and a slight additional increase in conductivity.

The compounds Rb3H(SeO4)2 and Cs3H(SeO4)2, though not isomorphous at ambient temperatures, are quintessential examples of superprotonic materials. Both adopt monoclinic structures at ambient temperatures and ultimately transform to a trigonal (R3̅m) superprotonic structure at slightly elevated temperatures, 178 and 183 °C, respectively. The compounds are completely miscible above the superprotonic transition and show extensive solubility below it. Beyond a careful determination of the phase boundaries, we find a remarkable 40-fold increase in the superprotonic conductivity in intermediate compositions rich in Rb as compared to either end-member.

The compound Cs6(H2SO4)3(H1.5PO4)4 is unusual amongst solid acid compounds in that it has a complex cubic structure at ambient temperature and apparently transforms to a simpler cubic structure of the CsCl-type (isostructural with CsH2PO4) at its transition temperature of 100-120 °C [3]. Here it is found that, depending on the level of humidification, the superprotonic transition of this material is superimposed with a decomposition reaction, which involves both exsolution of (liquid) acid and loss of H2O. This reaction can be suppressed by application of sufficiently high humidity, in which case Cs6(H2SO4)3(H1.5PO4)4 undergoes a true superprotonic transition. It is proposed that, under conditions of low humidity, the decomposition/dehydration reaction transforms the compound to Cs6(H2-0.5xSO4)3(H1.5PO4)4-x, also of the CsCl structure type at the temperatures of interest, but with a smaller unit cell. With increasing temperature, the decomposition/dehydration proceeds to greater and greater extent and unit cell of the solid phase decreases. This is identified to be the source of the apparent negative thermal expansion behavior.

References

[1] L.A. Cowan, R.M. Morcos, N. Hatada, A. Navrotsky, S.M. Haile, Solid State Ionics 179 (2008) (9-10) 305.

[2] M. Sakashita, H. Fujihisa, K.I. Suzuki, S. Hayashi, K. Honda, Solid State Ionics 178 (2007) (21-22) 1262.

[3] C.R.I. Chisholm, Superprotonic Phase Transitions in Solid Acids: Parameters affecting the presence and stability of superprotonic transitions in the MHnXO4 family of compounds (X=S, Se, P, As; M=Li, Na, K, NH4, Rb, Cs), Materials Science, California Institute of Technology, Pasadena, California (2003).

Using space geodesy to constrain variations in seismogenic behavior on subduction megathrusts

The concept of seismogenic asperities and aseismic barriers has become a useful paradigm within which to understand the seismogenic behavior of major faults. Since asperities and barriers can be thought of as defining the potential rupture area of large megathrust earthquakes, it is thus important to identify their respective spatial extents, constrain their temporal longevity, and to develop a physical understanding for their behavior. Space geodesy is making critical contributions to the identification of slip asperities and barriers but progress in many geographical regions depends on improving the accuracy and precision of the basic measurements. This thesis begins with technical developments aimed at improving satellite radar interferometric measurements of ground deformation whereby we introduce an empirical correction algorithm for unwanted effects due to interferometric path delays that are due to spatially and temporally variable radar wave propagation speeds in the atmosphere. In chapter 2, I combine geodetic datasets with complementary spatio-temporal resolutions to improve our understanding of the spatial distribution of crustal deformation sources and their associated temporal evolution – here we use observations from Long Valley Caldera (California) as our test bed. In the third chapter I apply the tools developed in the first two chapters to analyze postseismic deformation associated with the 2010 Mw=8.8 Maule (Chile) earthquake. The result delimits patches where afterslip occurs, explores their relationship to coseismic rupture, quantifies frictional properties associated with inferred patches of afterslip, and discusses the relationship of asperities and barriers to long-term topography. The final chapter investigates interseismic deformation of the eastern Makran subduction zone by using satellite radar interferometry only, and demonstrates that with state-of-art techniques it is possible to quantify tectonic signals with small amplitude and long wavelength. Portions of the eastern Makran for which we estimate low fault coupling correspond to areas where bathymetric features on the downgoing plate are presently subducting, whereas the region of the 1945 M=8.1 earthquake appears to be more highly coupled.

The short-timescale behavior of glacial ice

Glaciers are often assumed to deform only at slow (i.e., glacial) rates. However, with the advent of high rate geodetic observations of ice motion, many of the intricacies of glacial deformation on hourly and daily timescales have been observed and quantified. This thesis explores two such short timescale processes: the tidal perturbation of ice stream motion and the catastrophic drainage of supraglacial meltwater lakes. Our investigation into the transmission length-scale of a tidal load represents the first study to explore the daily tidal influence on ice stream motion using three-dimensional models. Our results demonstrate both that the implicit assumptions made in the standard two-dimensional flow-line models are inherently incorrect for many ice streams, and that the anomalously large spatial extent of the tidal influence seen on the motion of some glaciers cannot be explained, as previously thought, through the elastic or viscoelastic transmission of tidal loads through the bulk of the ice stream. We then discuss how the phase delay between a tidal forcing and the ice stream’s displacement response can be used to constrain in situ viscoelastic properties of glacial ice. Lastly, for the problem of supraglacial lake drainage, we present a methodology for implementing linear viscoelasticity into an existing model for lake drainage. Our work finds that viscoelasticity is a second-order effect when trying to model the deformation of ice in response to a meltwater lake draining to a glacier’s bed. The research in this thesis demonstrates that the first-order understanding of the short-timescale behavior of naturally occurring ice is incomplete, and works towards improving our fundamental understanding of ice behavior over the range of hours to days.

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.

Characterization of diverse megathrust fault behavior related to seismic supercycles, Mentawai Islands, Sumatra

Long paleoseismic histories are necessary for understanding the full range of behavior of faults, as the most destructive events often have recurrence intervals longer than local recorded history. The Sunda megathrust, the interface along which the Australian plate subducts beneath Southeast Asia, provides an ideal natural laboratory for determining a detailed paleoseismic history over many seismic cycles. The outer-arc islands above the seismogenic portion of the megathrust cyclically rise and subside in response to processes on the underlying megathrust, providing uncommonly good illumination of megathrust behavior. Furthermore, the growth histories of coral microatolls, which record tectonic uplift and subsidence via relative sea level, can be used to investigate the detailed coseismic and interseismic deformation patterns. One particularly interesting area is the Mentawai segment of the megathrust, which has been shown to characteristically fail in a series of ruptures over decades, rather than a single end-to-end rupture. This behavior has been termed a seismic “supercycle.” Prior to the current rupture sequence, which began in 2007, the segment previously ruptured during the 14th century, the late 16th to late 17th century, and most recently during historical earthquakes in 1797 and 1833. In this study, we examine each of these previous supercycles in turn.

First, we expand upon previous analysis of the 1797–1833 rupture sequence with a comprehensive review of previously published coral microatoll data and the addition of a significant amount of new data. We present detailed maps of coseismic uplift during the two great earthquakes and of interseismic deformation during the periods 1755–1833 and 1950–1997 and models of the corresponding slip and coupling on the underlying megathrust. We derive magnitudes of Mw 8.7–9.0 for the two historical earthquakes, and determine that the 1797 earthquake fundamentally changed the state of coupling on the fault for decades afterward. We conclude that while major earthquakes generally do not involve rupture of the entire Mentawai segment, they undoubtedly influence the progression of subsequent ruptures, even beyond their own rupture area. This concept is of vital importance for monitoring and forecasting the progression of the modern rupture sequence.

Turning our attention to the 14th century, we present evidence of a shallow slip event in approximately A.D. 1314, which preceded the “conventional” megathrust rupture sequence. We calculate a suite of slip models, slightly deeper and/or larger than the 2010 Pagai Islands earthquake, that are consistent with the large amount of subsidence recorded at our study site. Sea-level records from older coral microatolls suggest that these events occur at least once every millennium, but likely far less frequently than their great downdip neighbors. The revelation that shallow slip events are important contributors to the seismic cycle of the Mentawai segment further complicates our understanding of this subduction megathrust and our assessment of the region’s exposure to seismic and tsunami hazards.

Finally, we present an outline of the complex intervening rupture sequence that took place in the 16th and 17th centuries, which involved at least five distinct uplift events. We conclude that each of the supercycles had unique features, and all of the types of fault behavior we observe are consistent with highly heterogeneous frictional properties of the megathrust beneath the south-central Mentawai Islands. We conclude that the heterogeneous distribution of asperities produces terminations and overlap zones between fault ruptures, resulting in the seismic “supercycle” phenomenon.

Multiplexed DNA-mediated electrochemistry

The aromatic core of double helical DNA possesses the unique and remarkable ability to form a conduit for electrons to travel over exceptionally long molecular distances. This core of π-stacked nucleobases creates an efficient pathway for charge transfer to proceed that is exquisitely sensitive to even subtle perturbations. Ground state electrochemistry of DNA-modified electrodes has been one of the major techniques used both to investigate and to harness the property of DNA-mediated charge transfer. DNA-modified electrodes have been an essential tool for both gaining insights into the fundamental properties of DNA and, due to the exquisite specificity of DNA-mediated charge transfer for the integrity of the π-stack, for use in next generation diagnostic sensing. Here, multiplexed DNA-modified electrodes are used to (i) gain new insights on the electrochemical coupling of metalloproteins to the DNA π-stack with relevance to the fundaments of in vivo DNA-mediated charge transfer and (ii) enhance the overall sensitivity of DNA-mediated reduction for use in the detection of low abundance diagnostic targets.

First, Methylene Blue (MB′) was covalently attached to DNA through a flexible C12 alkyl linker to yield a new redox reporter for DNA electrochemistry measurements with enhanced sensitivity. Tethered, intercalated MB′ was reduced through DNA-mediated charge transport. The redox signal intensity for MB′-dT-C12-DNA was found to be at least 3 fold larger than that of previously used Nile Blue (NB)-dT-DNA, which is coupled to the base stack via direct conjugation. The signal attenuation, due to an intervening mismatch, and therefore the degree of DNA-mediated reduction, does, however, depend on the DNA film morphology and the backfilling agent used to passivate the surface. These results highlight two possible mechanisms for the reduction of MB′ on the DNA-modified electrode that are distinguishable by their kinetics: reduction mediated by the DNA base pair stack and direct surface reduction of MB′ at the electrode. The extent of direct reduction at the surface can be minimized by overall DNA assembly conditions.

Next, a series of intercalation-based DNA-mediated electrochemical reporters were developed, using a flexible alkane linkage to validate and explore their DNA-mediated reduction. The general mechanism for the reduction of distally bound redox active species, covalently tethered to DNA through flexible alkyl linkages, was established to be an intraduplex DNA-mediated pathway. MB, NB, and anthraquinone were covalently tethered to DNA with three different covalent linkages. The extent of electronic coupling of the reporter was shown to correlate with the DNA binding affinity of the redox active species, supporting an intercalative mechanism. These electrochemical signals were shown to be exceptionally sensitive to a single intervening π-stack perturbation, an AC mismatch, in a densely packed DNA monolayer, which further supports that the reduction is DNA-mediated. Finally, this DNA-mediated reduction of MB occurs primarily via intra- rather than inter duplex intercalation, as probed through varying the proximity and integrity of the neighboring duplex DNA. Further gains to electrochemical sensitivity of our DNA-modified devices were then achieved through the application of electrocatalytic signal amplification using these solvent accessible intercalative reporters, MB-dT-C8, and hemoglobin as a novel electron sink. Electrocatalysis offers an excellent means of electrochemical signal amplification, yet in DNA based sensors, its application has been limited due to strict assembly conditions. We describe the use of hemoglobin as a robust and effective electron sink for electrocatalysis in DNA sensing on low density DNA films. Protein shielding of the heme redox center minimizes direct reduction at the electrode surface and permits assays on low density DNA films. Electrocatalysis of MB that is covalently tethered to the DNA by a flexible alkyl linkage allows for efficient interactions with both the base stack and hemoglobin. Consistent suppression of the redox signal upon incorporation of single CA mismatch in the DNA oligomer demonstrates that both the unamplified and the electrocatalytically amplified redox signals are generated through DNA-mediated charge transport. Electrocatalysis with hemoglobin is robust: it is stable to pH and temperature variations. The utility and applicability of electrocatalysis with hemoglobin is demonstrated through restriction enzyme detection, and an enhancement in sensitivity permits femtomole DNA sampling.

Finally, we expanded the application of our multiplexed DNA-modified electrodes to the electrochemical characterization of DNA-bound proteins containing [4Fe-4S] clusters. DNA-modified electrodes have become an essential tool for the characterization of the redox chemistry of DNA repair proteins that contain redox cofactors. Multiplexed analysis of EndonucleaseIII (EndoIII), a DNA repair protein containing a [4Fe-4S] cluster known to be accessible via DNA-mediated charge transport, elucidated subtle differences in the electrochemical behavior as a function of DNA morphology. DNA-bound EndoIII is seen to have two different electron transfer pathways for reduction, either through the DNA base stack or through direct surface reduction. Closely packed DNA films, where the protein has limited surface accessibility, produce electrochemical signals reflecting electron transfer that is DNA-mediated. The electrochemical comparison of EndoIII mutants, including a new family of mutations altering the electrostatics surrounding the [4Fe-4S] cluster, was able to be quantitatively performed. While little change in the midpoint potential was found for this family of mutants, significant variations in the efficiency of DNA-mediated electron transfer were apparent. Based on the stability of these proteins, examined by circular dichroism, we propose that the electron transfer pathway can be perturbed not only by the removal of aromatic residues, but also through changes in solvation near the cluster.

Travel time tomographic studies of seismic structures around subducted lithospheric slabs

The nature of the subducted lithospheric slab is investigated seismologically by tomographic inversions of ISC residual travel times. The slab, in which nearly all deep earthquakes occur, is fast in the seismic images because it is much cooler than the ambient mantle. High resolution three-dimensional P and S wave models in the NW Pacific are obtained using regional data, while inversion for the SW Pacific slabs includes teleseismic arrivals. Resolution and noise estimations show the models are generally well-resolved.

The slab anomalies in these models, as inferred from the seismicity, are generally coherent in the upper mantle and become contorted and decrease in amplitude with depth. Fast slabs are surrounded by slow regions shallower than 350 km depth. Slab fingering, including segmentation and spreading, is indicated near the bottom of the upper mantle. The fast anomalies associated with the Japan, Izu-Bonin, Mariana and Kermadec subduction zones tend to flatten to sub-horizontal at depth, while downward spreading may occur under parts of the Mariana and Kuril arcs. The Tonga slab appears to end around 550 km depth, but is underlain by a fast band at 750-1000 km depths.

The NW Pacific model combined with the Clayton-Comer mantle model predicts many observed residual sphere patterns. The predictions indicate that the near-source anomalies affect the residual spheres less than the teleseismic contributions. The teleseismic contributions may be removed either by using a mantle model, or using teleseismic station averages of residuals from only regional events. The slab-like fast bands in the corrected residual spheres are are consistent with seismicity trends under the Mariana Tzu-Bonin and Japan trenches, but are inconsistent for the Kuril events.

The comparison of the tomographic models with earthquake focal mechanisms shows that deep compression axes and fast velocity slab anomalies are in consistent alignment, even when the slab is contorted or flattened. Abnormal stress patterns are seen at major junctions of the arcs. The depth boundary between tension and compression in the central parts of these arcs appears to depend on the dip and topology of the slab.

Complex behavior and perception in Drosophila emerges from iterative feedback-regulated reflexes

For a hungry fruit fly, locating and landing on a fermenting fruit where it can feed, find mates, and lay eggs, is an essential and difficult task requiring the integration of both olfactory and visual cues. Understanding how flies accomplish this will help provide a comprehensive ethological context for the expanding knowledge of their neural circuits involved in processing olfaction and vision, as well as inspire novel engineering solutions for control and estimation in computationally limited robotic applications. In this thesis, I use novel high throughput methods to develop a detailed overview of how flies track odor plumes, land, and regulate flight speed. Finally, I provide an example of how these insights can be applied to robotic applications to simplify complicated estimation problems. To localize an odor source, flies exhibit three iterative, reflex-driven behaviors. Upon encountering an attractive plume, flies increase their flight speed and turn upwind using visual cues. After losing the plume, flies begin zigzagging crosswind, again using visual cues to control their heading. After sensing an attractive odor, flies become more attracted to small visual features, which increases their chances of finding the plume source. Their changes in heading are largely controlled by open-loop maneuvers called saccades, which they direct towards and away from visual features. If a fly decides to land on an object, it begins to decelerate so as to maintain a stereotypical ratio of expansion to retinal size. Once they reach a stereotypical distance from the target, flies extend their legs in preparation for touchdown. Although it is unclear what cues they use to trigger this behavior, previous studies have indicated that it is likely under visual control. In Chapter 3, I use a nonlinear control theoretic analysis and robotic testbed to propose a novel and putative mechanism for how a fly might visually estimate distance by actively decelerating according to a visual control law. Throughout these behaviors, a common theme is the visual control of flight speed. Using genetic tools I show that the neuromodulator octopamine plays an important role in regulating flight speed, and propose a neural circuit for how this controller might be implemented in the flies brain. Two general biological and engineering principles are evident across my experiments: (1) complex behaviors, such as foraging, can emerge from the interactions of simple independent sensory-motor modules; (2) flies control their behavior in such a way that simplifies complex estimation problems.

Modeling and analysis of hysteretic structural behavior

For damaging response, the force-displacement relationship of a structure is highly nonlinear and history-dependent. For satisfactory analysis of such behavior, it is important to be able to characterize and to model the phenomenon of hysteresis accurately. A number of models have been proposed for response studies of hysteretic structures, some of which are examined in detail in this thesis. There are two popular classes of models used in the analysis of curvilinear hysteretic systems. The first is of the distributed element or assemblage type, which models the physical behavior of the system by using well-known building blocks. The second class of models is of the differential equation type, which is based on the introduction of an extra variable to describe the history dependence of the system.

Owing to their mathematical simplicity, the latter models have been used extensively for various applications in structural dynamics, most notably in the estimation of the response statistics of hysteretic systems subjected to stochastic excitation. But the fundamental characteristics of these models are still not clearly understood. A response analysis of systems using both the Distributed Element model and the differential equation model when subjected to a variety of quasi-static and dynamic loading conditions leads to the following conclusion: Caution must be exercised when employing the models belonging to the second class in structural response studies as they can produce misleading results.

The Massing's hypothesis, originally proposed for steady-state loading, can be extended to general transient loading as well, leading to considerable simplification in the analysis of the Distributed Element models. A simple, nonparametric identification technique is also outlined, by means of which an optimal model representation involving one additional state variable is determined for hysteretic systems.

On the behavior of pliable plate dynamics in wind : application to vertical axis wind turbines

Numerous studies have shown that flexible materials improve resilience and durability of a structure. Several studies have investigated the behavior of elastic plates under the influence of a free stream, such as studies of the fluttering flag and others of shape reconfiguration, due to a free stream.

The principle engineering contribution of this thesis is the design and development of a vertical axis wind turbine that features pliable blades which undergo various modes of behavior, ultimately leading to rotational propulsion of the turbine. The wind turbine design was tested in a wind tunnel and at the Caltech Laboratory for Optimized Wind Energy. Ultimately, the flexible blade vertical axis wind turbine proved to be an effective way of harnessing the power of the wind.

In addition, this body of work builds on the current knowledge of elastic cantilever plates in a free stream flow by investigating the inverted flag. While previous studies have focused on the fluid structure interaction of a free stream on elastic cantilever plates, none had studied the plate configuration where the trailing edge was clamped, leaving the leading edge free to move. Furthermore, the studies presented in this thesis establish the geometric boundaries of where the large-amplitude flapping occurs.