Asymptotic analysis of thin plates under normal load and horizontal edge thrust

We consider the radially symmetric nonlinear von Kármán plate equations for circular or annular plates in the limit of small thickness. The loads on the plate consist of a radially symmetric pressure load and a uniform edge load. The dependence of the steady states on the edge load and thickness is studied using asymptotics as well as numerical calculations. The von Kármán plate equations are a singular perturbation of the Fӧppl membrane equation in the asymptotic limit of small thickness. We study the role of compressive membrane solutions in the small thickness asymptotic behavior of the plate solutions.

We give evidence for the existence of a singular compressive solution for the circular membrane and show by a singular perturbation expansion that the nonsingular compressive solution approach this singular solution as the radial stress at the center of the plate vanishes. In this limit, an infinite number of folds occur with respect to the edge load. Similar behavior is observed for the annular membrane with zero edge load at the inner radius in the limit as the circumferential stress vanishes.

We develop multiscale expansions, which are asymptotic to members of this family for plates with edges that are elastically supported against rotation. At some thicknesses this approximation breaks down and a boundary layer appears at the center of the plate. In the limit of small normal load, the points of breakdown approach the bifurcation points corresponding to buckling of the nondeflected state. A uniform asymptotic expansion for small thickness combining the boundary layer with a multiscale approximation of the outer solution is developed for this case. These approximations complement the well known boundary layer expansions based on tensile membrane solutions in describing the bending and stretching of thin plates. The approximation becomes inconsistent as the clamped state is approached by increasing the resistance against rotation at the edge. We prove that such an expansion for the clamped circular plate cannot exist unless the pressure load is self-equilibrating.

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

Part I.

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

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

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

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

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

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

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

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

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

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

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

Part II.

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

A dynamical systems analysis of vortex pinch-off

Vortex rings constitute the main structure in the wakes of a wide class of swimming and flying animals, as well as in cardiac flows and in the jets generated by some moss and fungi. However, there is a physical limit, determined by an energy maximization principle called the Kelvin-Benjamin principle, to the size that axisymmetric vortex rings can achieve. The existence of this limit is known to lead to the separation of a growing vortex ring from the shear layer feeding it, a process known as `vortex pinch-off', and characterized by the dimensionless vortex formation number. The goal of this thesis is to improve our understanding of vortex pinch-off as it relates to biological propulsion, and to provide future researchers with tools to assist in identifying and predicting pinch-off in biological flows.

To this end, we introduce a method for identifying pinch-off in starting jets using the Lagrangian coherent structures in the flow, and apply this criterion to an experimentally generated starting jet. Since most naturally occurring vortex rings are not circular, we extend the definition of the vortex formation number to include non-axisymmetric vortex rings, and find that the formation number for moderately non-axisymmetric vortices is similar to that of circular vortex rings. This suggests that naturally occurring vortex rings may be modeled as axisymmetric vortex rings. Therefore, we consider the perturbation response of the Norbury family of axisymmetric vortex rings. This family is chosen to model vortex rings of increasing thickness and circulation, and their response to prolate shape perturbations is simulated using contour dynamics. Finally, the response of more realistic models for vortex rings, constructed from experimental data using nested contours, to perturbations which resemble those encountered by forming vortices more closely, is simulated using contour dynamics. In both families of models, a change in response analogous to pinch-off is found as members of the family with progressively thicker cores are considered. We posit that this analogy may be exploited to understand and predict pinch-off in complex biological flows, where current methods are not applicable in practice, and criteria based on the properties of vortex rings alone are necessary.

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

The intergalactic and circumgalactic medium surrounding star-forming galaxies at redshifts 2 < z < 3

We present measurements of the spatial distribution, kinematics, and physical properties of gas in the circumgalactic medium (CGM) of 2.0<z<2.8 UV color-selected galaxies as well as within the 2<z<3 intergalactic medium (IGM). These measurements are derived from Voigt profile decomposition of the full Lyα and Lyβ forest in 15 high-resolution, high signal-to-noise ratio QSO spectra resulting in a catalog of ∼6000 HI absorbers.

Chapter 2 of this thesis focuses on HI surrounding high-z star-forming galaxies drawn from the Keck Baryonic Structure Survey (KBSS). The KBSS is a unique spectroscopic survey of the distant universe designed to explore the details of the connection between galaxies and intergalactic baryons within the same survey volumes. The KBSS combines high-quality background QSO spectroscopy with large densely-sampled galaxy redshift surveys to probe the CGM at scales of ∼50 kpc to a few Mpc. Based on these data, Chapter 2 presents the first quantitative measurements of the distribution, column density, kinematics, and absorber line widths of neutral hydrogen surrounding high-z star-forming galaxies.

Chapter 3 focuses on the thermal properties of the diffuse IGM. This analysis relies on measurements of the ∼6000 absorber line widths to constrain the thermal and turbulent velocities of absorbing "clouds." A positive correlation between the column density of HI and the minimum line width is recovered and implies a temperature-density relation within the low-density IGM for which higher-density regions are hotter, as is predicted by simple theoretical arguments.

Chapter 4 presents new measurements of the opacity of the IGM and CGM to hydrogen-ionizing photons. The chapter begins with a revised measurement of the HI column density distribution based on this new absorption line catalog that, due to the inclusion of high-order Lyman lines, provides the first statistically robust measurement of the frequency of absorbers with HI column densities 14 ≲ log(N_HI/cm^-2) ≲ 17.2. Also presented are the first measurements of the column density distribution of HI within the CGM (50 <d < 300 pkpc) of high-z galaxies. These distributions are used to calculate the total opacity of the IGM and IGM+CGM and to revise previous measurements of the mean free path of hydrogen-ionizing photons within the IGM. This chapter also considers the effect of the surrounding CGM on the transmission of ionizing photons out of the sites of active star-formation and into the IGM.

This thesis concludes with a brief discussion of work in progress focused on understanding the distribution of metals within the CGM of KBSS galaxies. Appendix B discusses my contributions to the MOSFIRE instrumentation project.

Diffraction-limited imaging on the 200-inch telescope

We have used the technique of non-redundant masking at the Palomar 200-inch telescope and radio VLBI imaging software to make optical aperture synthesis maps of two binary stars, β Corona Borealis and σ Herculis. The dynamic range of the map of β CrB, a binary star with a separation of 230 milliarcseconds is 50:1. For σ Her, we find a separation of 70 milliarcseconds and the dynamic range of our image is 30:1. These demonstrate the potential of the non-redundant masking technique for diffraction-limited imaging of astronomical objects with high dynamic range.

We find that the optimal integration time for measuring the closure phase is longer than that for measuring the fringe amplitude. There is not a close relationship between amplitude errors and phase errors, as is found in radio interferometry. Amplitude self calibration is less effective at optical wavelengths than at radio wavelengths. Primary beam sensitivity correction made in radio aperture synthesis is not necessary in optical aperture synthesis.

The effects of atmospheric disturbances on optical aperture synthesis have been studied by Monte Carlo simulations based on the Kolmogorov theory of refractive-index fluctuations. For the non-redundant masking with τ_c-sized apertures, the simulated fringe amplitude gives an upper bound of the observed fringe amplitude. A smooth transition is seen from the non-redundant masking regime to the speckle regime with increasing aperture size. The fractional reduction of the fringe amplitude according to the bandwidth is nearly independent of the aperture size. The limiting magnitude of optical aperture synthesis with τ_c-sized apertures and that with apertures larger than τ_c are derived.

Monte Carlo simulations are also made to study the sensitivity and resolution of the bispectral analysis of speckle interferometry. We present the bispectral modulation transfer function and its signal-to-noise ratio at high light levels. The results confirm the validity of the heuristic interferometric view of image-forming process in the mid-spatial-frequency range. The signal-to- noise ratio of the bispectrum at arbitrary light levels is derived in the mid-spatial-frequency range.

The non-redundant masking technique is suitable for imaging bright objects with high resolution and high dynamic range, while the faintest limit will be better pursued by speckle imaging.

A Study on iron-based amorphous alloys : alloy development, thermodynamics and soft magnetism

Metallic glass has since its debut been of great research interest due to its profound scientific significance. Magnetic metallic glasses are of special interest because of their promising technological applications. In this thesis, we introduced a novel series of Fe-based alloys and offer a holistic review of the physics and properties of these alloys. A systematic alloy development and optimization method was introduced, with experimental implementation on transition metal based alloying system. A deep understanding on the influencing factors of glass forming ability was brought up and discussed, based on classical nucleation theory. Experimental data of the new Fe-based amorphous alloys were interpreted to further analyze those influencing factors, including reduced glass transition temperature, fragility, and liquid-crystal interface free energy. Various treatments (fluxing, overheating, etc.) were discussed for their impacts on the alloying systems' thermodynamics and glass forming ability. Multiple experimental characterization methods were discussed to measure the alloys' soft magnetic properties. In addition to theoretical and experimental investigation, we also gave a detailed numerical analysis on the rapid-discharge-heating-and-forming platform. It is a novel experimental system which offers extremely fast heating rate for calorimetric characterization and alloy deformation.

Investigations of group IVA transition metal mediated carbon-carbon bond forming reactions

Zirconocene aldehyde and ketone complexes were synthesized in high yield by treatment of zirconocene acyl complexes with trimethylaluminum or diisobutylaluminum hydride. These complexes, which are activated by dialkylaluminum chloride ligands, inserted unsaturated substrates such as alkynes, allenes, ethylene, nitriles, ketenes, aldehydes, ketones, lactones, and acid chlorides with moderate to high conversion. Insertion of aldehyde substrates yielded zirconocene diolate complexes with up to 20:1 (anti:syn) diastereoselectivity. The zirconocene diolates were hydrolyzed to afford unsymmetrical 1,2-diols in 40-80% isolated yield. Unsymmetrical ketones gave similar insertion yields with little or no diastereoselectivity. A high yielding one-pot method was developed that coupled carbonyl substrates with zirconocene aldehyde complexes that were derived from olefins by hydrozirconation and carbonylation. The zirconocene aldehyde complexes also inserted carbon monoxide and gave acyloins in 50% yield after hydrolysis.

The insertion reaction of aryl epoxides with the trimethylphoshine adduct of titanocene methylidene was examined. The resulting oxytitanacyclopentanes were carbonylated and oxidatively cleaved with dioxygen to afford y-lactones in moderate yields. Due to the instability and difficult isolation of titanocene methylidene trimethylphoshine adducts, a one-pot method involving the addition of catalytic amounts of trimethylphosphine to β,β-dimethyltitanacyclobutane was developed. A series of disubstituted aryl epoxides were examined which gave mixtures of diastereomeric insertion products. Based on these results, as well as earlier Hammett studies and labeling experiments, a biradical transition state intermediate is proposed. The method is limited to aryl substituted epoxide substrates with aliphatic examples showing no insertion reactivity.

The third study involved the use of magnesium chloride supported titanium catalysts for the Lewis acid catalyzed silyl group transfer condensation of enol silanes with aldehydes. The reaction resulted in silylated aldol products with as many as 140 catalytic turnovers before catalyst inactivation. Low diastereoselectivities favoring the anti-isomer were consistent with an open transition state involving a titanium atom bound to the catalyst surface. The catalysts were also used for the aldol group transfer polymerization of t-butyldimethylsilyloxy-1-ethene resulting in polymers with molecular weights of 5000-31,000 and molar mass dispersities of 1.5-2.8. Attempts to polymerize methylmethacrylate using GTP proved unsuccessful with these catalysts.

Instrumentation for Kinetic-Inductance-Detector-Based Submillimeter Radio Astronomy

A substantial amount of important scientific information is contained within astronomical data at the submillimeter and far-infrared (FIR) wavelengths, including information regarding dusty galaxies, galaxy clusters, and star-forming regions; however, these wavelengths are among the least-explored fields in astronomy because of the technological difficulties involved in such research. Over the past 20 years, considerable efforts have been devoted to developing submillimeter- and millimeter-wavelength astronomical instruments and telescopes.

The number of detectors is an important property of such instruments and is the subject of the current study. Future telescopes will require as many as hundreds of thousands of detectors to meet the necessary requirements in terms of the field of view, scan speed, and resolution. A large pixel count is one benefit of the development of multiplexable detectors that use kinetic inductance detector (KID) technology.

This dissertation presents the development of a KID-based instrument including a portion of the millimeter-wave bandpass filters and all aspects of the readout electronics, which together enabled one of the largest detector counts achieved to date in submillimeter-/millimeter-wavelength imaging arrays: a total of 2304 detectors. The work presented in this dissertation has been implemented in the MUltiwavelength Submillimeter Inductance Camera (MUSIC), a new instrument for the Caltech Submillimeter Observatory (CSO).

Quantifying Earthquake Collapse Risk of Tall Steel Moment Frame Buildings Using Rupture-to-Rafters Simulations

There is a sparse number of credible source models available from large-magnitude past earthquakes. A stochastic source model generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes. We present an algorithm that combines the physics of fault ruptures as imaged in laboratory earthquakes with stress estimates on the fault constrained by field observations to generate stochastic source models for large-magnitude (Mw 6.0-8.0) strike-slip earthquakes. The algorithm is validated through a statistical comparison of synthetic ground motion histories from a stochastically generated source model for a magnitude 7.90 earthquake and a kinematic finite-source inversion of an equivalent magnitude past earthquake on a geometrically similar fault. The synthetic dataset comprises of three-component ground motion waveforms, computed at 636 sites in southern California, for ten hypothetical rupture scenarios (five hypocenters, each with two rupture directions) on the southern San Andreas fault. A similar validation exercise is conducted for a magnitude 6.0 earthquake, the lower magnitude limit for the algorithm. Additionally, ground motions from the Mw7.9 earthquake simulations are compared against predictions by the Campbell-Bozorgnia NGA relation as well as the ShakeOut scenario earthquake. The algorithm is then applied to generate fifty source models for a hypothetical magnitude 7.9 earthquake originating at Parkfield, with rupture propagating from north to south (towards Wrightwood), similar to the 1857 Fort Tejon earthquake. Using the spectral element method, three-component ground motion waveforms are computed in the Los Angeles basin for each scenario earthquake and the sensitivity of ground shaking intensity to seismic source parameters (such as the percentage of asperity area relative to the fault area, rupture speed, and risetime) is studied.

Under plausible San Andreas fault earthquakes in the next 30 years, modeled using the stochastic source algorithm, the performance of two 18-story steel moment frame buildings (UBC 1982 and 1997 designs) in southern California is quantified. The approach integrates rupture-to-rafters simulations into the PEER performance based earthquake engineering (PBEE) framework. Using stochastic sources and computational seismic wave propagation, three-component ground motion histories at 636 sites in southern California are generated for sixty scenario earthquakes on the San Andreas fault. The ruptures, with moment magnitudes in the range of 6.0-8.0, are assumed to occur at five locations on the southern section of the fault. Two unilateral rupture propagation directions are considered. The 30-year probabilities of all plausible ruptures in this magnitude range and in that section of the fault, as forecast by the United States Geological Survey, are distributed among these 60 earthquakes based on proximity and moment release. The response of the two 18-story buildings hypothetically located at each of the 636 sites under 3-component shaking from all 60 events is computed using 3-D nonlinear time-history analysis. Using these results, the probability of the structural response exceeding Immediate Occupancy (IO), Life-Safety (LS), and Collapse Prevention (CP) performance levels under San Andreas fault earthquakes over the next thirty years is evaluated.

Furthermore, the conditional and marginal probability distributions of peak ground velocity (PGV) and displacement (PGD) in Los Angeles and surrounding basins due to earthquakes occurring primarily on the mid-section of southern San Andreas fault are determined using Bayesian model class identification. Simulated ground motions at sites within 55-75km from the source from a suite of 60 earthquakes (Mw 6.0 − 8.0) primarily rupturing mid-section of San Andreas fault are considered for PGV and PGD data.

A fully-nonlocal energy-based formulation and high-performance realization of the quasicontinuum method

The quasicontinuum (QC) method was introduced to coarse-grain crystalline atomic ensembles in order to bridge the scales from individual atoms to the micro- and mesoscales. Though many QC formulations have been proposed with varying characteristics and capabilities, a crucial cornerstone of all QC techniques is the concept of summation rules, which attempt to efficiently approximate the total Hamiltonian of a crystalline atomic ensemble by a weighted sum over a small subset of atoms. In this work we propose a novel, fully-nonlocal, energy-based formulation of the QC method with support for legacy and new summation rules through a general energy-sampling scheme. Our formulation does not conceptually differentiate between atomistic and coarse-grained regions and thus allows for seamless bridging without domain-coupling interfaces. Within this structure, we introduce a new class of summation rules which leverage the affine kinematics of this QC formulation to most accurately integrate thermodynamic quantities of interest. By comparing this new class of summation rules to commonly-employed rules through analysis of energy and spurious force errors, we find that the new rules produce no residual or spurious force artifacts in the large-element limit under arbitrary affine deformation, while allowing us to seamlessly bridge to full atomistics. We verify that the new summation rules exhibit significantly smaller force artifacts and energy approximation errors than all comparable previous summation rules through a comprehensive suite of examples with spatially non-uniform QC discretizations in two and three dimensions. Due to the unique structure of these summation rules, we also use the new formulation to study scenarios with large regions of free surface, a class of problems previously out of reach of the QC method. Lastly, we present the key components of a high-performance, distributed-memory realization of the new method, including a novel algorithm for supporting unparalleled levels of deformation. Overall, this new formulation and implementation allows us to efficiently perform simulations containing an unprecedented number of degrees of freedom with low approximation error.

Development of a Cationic Mucic Acid Polymer-Based Nanoparticle siRNA Delivery System

Cancer chemotherapy has advanced from highly toxic drugs to more targeted treatments in the last 70 years. Chapter 1 opens with an introduction to targeted therapy for cancer. The benefits of using a nanoparticle to deliver therapeutics are discussed. We move on to siRNA in particular, and why it would be advantageous as a therapy. Specific to siRNA delivery are some challenges, such as nuclease degradation, quick clearance from circulation, needing to enter cells, and getting to the cytosol. We propose the development of a nanoparticle delivery system to tackle these challenges so that siRNA can be effective.

Chapter 2 of this thesis discusses the synthesis and analysis of a cationic mucic acid polymer (cMAP) which condenses siRNA to form a nanoparticle. Various methods to add polyethylene glycol (PEG) for stabilizing the nanoparticle in physiologic solutions, including using a boronic acid binding to diols on mucic acid, forming a copolymer of cMAP with PEG, and creating a triblock with mPEG on both ends of cMAP. The goal of these various pegylation strategies was to increase the circulation time of the siRNA nanoparticle in the bloodstream to allow more of the nanoparticle to reach tumor tissue by the enhanced permeation and retention effect. We found that the triblock mPEG-cMAP-PEGm polymer condensed siRNA to form very stable 30-40 nm particles that circulated for the longest time – almost 10% of the formulation remained in the bloodstream of mice 1 h after intravenous injection.

Chapter 3 explores the use of an antibody as a targeting agent for nanoparticles. Some antibodies of the IgG1 subtype are able to recruit natural killer cells that effect antibody dependent cellular cytotoxicity (ADCC) to kill the targeted cell to which the antibody is bound. There is evidence that the ADCC effect remains in antibody-drug conjugates, so we wanted to know whether the ADCC effect is preserved when the antibody is bound to a nanoparticle, which is a much larger and complex entity. We utilized antibodies against epidermal growth factor receptor with similar binding and pharmacokinetics, cetuximab and panitumumab, which differ in that cetuximab is an IgG1 and panitumumab is an IgG2 (which does not cause ADCC). Although a natural killer cell culture model showed that gold nanoparticles with a full antibody targeting agent can elicit target cell lysis, we found that this effect was not preserved in vivo. Whether this is due to the antibody not being accessible to immune cells or whether the natural killer cells are inactivated in a tumor xenograft remains unknown. It is possible that using a full antibody still has value if there are immune functions which are altered in a complex in vivo environment that are intact in an in vitro system, so the value of using a full antibody as a targeting agent versus using an antibody fragment or a protein such as transferrin is still open to further exploration.

In chapter 4, nanoparticle targeting and endosomal escape are further discussed with respect to the cMAP nanoparticle system. A diboronic acid entity, which gives an order of magnitude greater binding (than boronic acid) to cMAP due to the vicinal diols in mucic acid, was synthesized, attached to 5kD or 10kD PEG, and conjugated to either transferrin or cetuximab. A histidine was incorporated into the triblock polymer between cMAP and the PEG blocks to allow for siRNA endosomal escape. Nanoparticle size remained 30-40 nm with a slightly negative ca. -3 mV zeta potential with the triblock polymer containing histidine and when targeting agents were added. Greater mRNA knockdown was seen with the endosomal escape mechanism than without. The nanoparticle formulations were able to knock down the targeted mRNA in vitro. Mixed effects suggesting function were seen in vivo.

Chapter 5 summarizes the project and provides an outlook on siRNA delivery as well as targeted combination therapies for the future of personalized medicine in cancer treatment.