Battery-Powered RF Pre-Ionization System for the Caltech Magnetohydrodynamically-Driven Jet Experiment: RF Discharge Properties and MHD-Driven Jet Dynamics

This thesis describes investigations of two classes of laboratory plasmas with rather different properties: partially ionized low pressure radiofrequency (RF) discharges, and fully ionized high density magnetohydrodynamically (MHD)-driven jets. An RF pre-ionization system was developed to enable neutral gas breakdown at lower pressures and create hotter, faster jets in the Caltech MHD-Driven Jet Experiment. The RF plasma source used a custom pulsed 3 kW 13.56 MHz RF power amplifier that was powered by AA batteries, allowing it to safely float at 4-6 kV with the cathode of the jet experiment. The argon RF discharge equilibrium and transport properties were analyzed, and novel jet dynamics were observed.

Although the RF plasma source was conceived as a wave-heated helicon source, scaling measurements and numerical modeling showed that inductive coupling was the dominant energy input mechanism. A one-dimensional time-dependent fluid model was developed to quantitatively explain the expansion of the pre-ionized plasma into the jet experiment chamber. The plasma transitioned from an ionizing phase with depressed neutral emission to a recombining phase with enhanced emission during the course of the experiment, causing fast camera images to be a poor indicator of the density distribution. Under certain conditions, the total visible and infrared brightness and the downstream ion density both increased after the RF power was turned off. The time-dependent emission patterns were used for an indirect measurement of the neutral gas pressure.

The low-mass jets formed with the aid of the pre-ionization system were extremely narrow and collimated near the electrodes, with peak density exceeding that of jets created without pre-ionization. The initial neutral gas distribution prior to plasma breakdown was found to be critical in determining the ultimate jet structure. The visible radius of the dense central jet column was several times narrower than the axial current channel radius, suggesting that the outer portion of the jet must have been force free, with the current parallel to the magnetic field. The studies of non-equilibrium flows and plasma self-organization being carried out at Caltech are relevant to astrophysical jets and fusion energy research.

Movement of a Spherical Brownian Particle Between Infinite Parallel Plates: Hindered Dispersion and Sedimentation

The dispersion of an isolated, spherical, Brownian particle immersed in a Newtonian fluid between infinite parallel plates is investigated. Expressions are developed for both a 'molecular' contribution to dispersion, which arises from random thermal fluctuations, and a 'convective' contribution, arising when a shear flow is applied between the plates. These expressions are evaluated numerically for all sizes of the particle relative to the bounding plates, and the method of matched asymptotic expansions is used to develop analytical expressions for the dispersion coefficients as a function of particle size to plate spacing ratio for small values of this parameter.

It is shown that both the molecular and convective dispersion coefficients decrease as the size of the particle relative to the bounding plates increase. When the particle is small compared to the plate spacing, the coefficients decrease roughly proportional to the particle size to plate spacing ratio. When the particle closely fills the space between the plates, the molecular dispersion coefficient approaches zero slowly as an inverse logarithmic function of the particle size to plate spacing ratio, and the convective dispersion coefficent approaches zero approximately proportional to the width of the gap between the edges of the sphere and the bounding plates.

Estimation and inference for grasping and manipulation tasks using vision and kinesthetic sensors

This thesis presents a novel framework for state estimation in the context of robotic grasping and manipulation. The overall estimation approach is based on fusing various visual cues for manipulator tracking, namely appearance and feature-based, shape-based, and silhouette-based visual cues. Similarly, a framework is developed to fuse the above visual cues, but also kinesthetic cues such as force-torque and tactile measurements, for in-hand object pose estimation. The cues are extracted from multiple sensor modalities and are fused in a variety of Kalman filters.

A hybrid estimator is developed to estimate both a continuous state (robot and object states) and discrete states, called contact modes, which specify how each finger contacts a particular object surface. A static multiple model estimator is used to compute and maintain this mode probability. The thesis also develops an estimation framework for estimating model parameters associated with object grasping. Dual and joint state-parameter estimation is explored for parameter estimation of a grasped object's mass and center of mass. Experimental results demonstrate simultaneous object localization and center of mass estimation.

Dual-arm estimation is developed for two arm robotic manipulation tasks. Two types of filters are explored; the first is an augmented filter that contains both arms in the state vector while the second runs two filters in parallel, one for each arm. These two frameworks and their performance is compared in a dual-arm task of removing a wheel from a hub.

This thesis also presents a new method for action selection involving touch. This next best touch method selects an available action for interacting with an object that will gain the most information. The algorithm employs information theory to compute an information gain metric that is based on a probabilistic belief suitable for the task. An estimation framework is used to maintain this belief over time. Kinesthetic measurements such as contact and tactile measurements are used to update the state belief after every interactive action. Simulation and experimental results are demonstrated using next best touch for object localization, specifically a door handle on a door. The next best touch theory is extended for model parameter determination. Since many objects within a particular object category share the same rough shape, principle component analysis may be used to parametrize the object mesh models. These parameters can be estimated using the action selection technique that selects the touching action which best both localizes and estimates these parameters. Simulation results are then presented involving localizing and determining a parameter of a screwdriver.

Lastly, the next best touch theory is further extended to model classes. Instead of estimating parameters, object class determination is incorporated into the information gain metric calculation. The best touching action is selected in order to best discern between the possible model classes. Simulation results are presented to validate the theory.

Analog VLSI-based, neuromorphic sensorimotor systems: modeling the primate oculomotor system

Using neuromorphic analog VLSI techniques for modeling large neural systems has several advantages over software techniques. By designing massively-parallel analog circuit arrays which are ubiquitous in neural systems, analog VLSI models are extremely fast, particularly when local interactions are important in the computation. While analog VLSI circuits are not as flexible as software methods, the constraints posed by this approach are often very similar to the constraints faced by biological systems. As a result, these constraints can offer many insights into the solutions found by evolution. This dissertation describes a hardware modeling effort to mimic the primate oculomotor system which requires both fast sensory processing and fast motor control. A one-dimensional hardware model of the primate eye has been built which simulates the physical dynamics of the biological system. It is driven by analog VLSI circuits mimicking brainstem and cortical circuits that control eye movements. In this framework, a visually-triggered saccadic system is demonstrated which generates averaging saccades. In addition, an auditory localization system, based on the neural circuits of the barn owl, is used to trigger saccades to acoustic targets in parallel with visual targets. Two different types of learning are also demonstrated on the saccadic system using floating-gate technology allowing the non-volatile storage of analog parameters directly on the chip. Finally, a model of visual attention is used to select and track moving targets against textured backgrounds, driving both saccadic and smooth pursuit eye movements to maintain the image of the target in the center of the field of view. This system represents one of the few efforts in this field to integrate both neuromorphic sensory processing and motor control in a closed-loop fashion.

Nuclear Hartree-Fock calculations on parallel computers

Hartree-Fock (HF) calculations have had remarkable success in describing large nuclei at high spin, temperature and deformation. To allow full range of possible deformations, the Skyrme HF equations can be discretized on a three-dimensional mesh. However, such calculations are currently limited by the computational resources provided by traditional supercomputers. To take advantage of recent developments in massively parallel computing technology, we have implemented the LLNL Skyrme-force static and rotational HF codes on Intel's DELTA and GAMMA systems at Caltech.

We decomposed the HF code by assigning a portion of the mesh to each node, with nearest neighbor meshes assigned to nodes connected by communication· channels. This kind of decomposition is well-suited for the DELTA and the GAMMA architecture because the only non-local operations are wave function orthogonalization and the boundary conditions of the Poisson equation for the Coulomb field.

Our first application of the HF code on parallel computers has been the study of identical superdeformed (SD) rotational bands in the Hg region. In the last ten years, many SD rotational bands have been found experimentally. One very surprising feature found in these SD rotational bands is that many pairs of bands in nuclei that differ by one or two mass units have nearly identical deexcitation gamma-ray energies. Our calculations of the five rotational bands in ^(192)Hg and ^(194)Pb show that the filling of specific orbitals can lead to bands with deexcitation gamma-ray energies differing by at most 2 keV in nuclei differing by two mass units and over a range of angular momenta comparable to that observed experimentally. Our calculations of SD rotational bands in the Dy region also show that twinning can be achieved by filling or emptying some specific orbitals.

The interpretation of future precise experiments on atomic parity nonconservation (PNC) in terms of parameters of the Standard Model could be hampered by uncertainties in the atomic and nuclear structure. As a further application of the massively parallel HF calculations, we calculated the proton and neutron densities of the Cesium isotopes from A = 125 to A = 139. Based on our good agreement with experimental charge radii, binding energies, and ground state spins, we conclude that the uncertainties in the ratios of weak charges are less than 10^(-3), comfortably smaller than the anticipated experimental error.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

Geological evolution of two crustal scale shear zones. Part I. The Rand thrust complex, northwestern Mojave Desert, California. Part II. The Magdalena metamorphic core complex, north central Sonora, Mexico

The geology and structure of two crustal scale shear zones were studied to understand the partitioning of strain within intracontinental orogenic belts. Movement histories and regional tectonic implications are deduced from observational data. The two widely separated study areas bear the imprint of intense Late Mesozoic through Middle Cenozoic tectonic activity. A regional transition from Late Cretaceous-Early Tertiary plutonism, metamorphism, and shortening strain to Middle Tertiary extension and magmatism is preserved in each area, with contrasting environments and mechanisms. Compressional phases of this tectonic history are better displayed in the Rand Mountains, whereas younger extensional structures dominate rock fabrics in the Magdalena area.

In the northwestern Mojave desert, the Rand Thrust Complex reveals a stack of four distinctive tectonic plates offset along the Garlock Fault. The lowermost plate, Rand Schist, is composed of greenschist facies metagraywacke, metachert, and metabasalt. Rand Schist is structurally overlain by Johannesburg Gneiss (= garnet-amphibolite grade orthogneisses, marbles and quartzites), which in turn is overlain by a Late Cretaceous hornblende-biotite granodiorite. Biotite granite forms the fourth and highest plate. Initial assembly of the tectonic stack involved a Late Cretaceous? south or southwest vergent overthrusting event in which Johannesburg Gneiss was imbricated and attenuated between Rand Schist and hornblende-biotite granodiorite. Thrusting postdated metamorphism and deformation of the lower two plates in separate environments. A post-kinematic stock, the Late Cretaceous Randsburg Granodiorite, intrudes deep levels of the complex and contains xenoliths of both Rand Schist and mylonitized Johannesburg? gneiss. Minimum shortening implied by the map patterns is 20 kilometers.

Some low angle faults of the Rand Thrust Complex formed or were reactivated between Late Cretaceous and Early Miocene time. South-southwest directed mylonites derived from Johannesburg Gneiss are commonly overprinted by less penetrative north-northeast vergent structures. Available kinematic information at shallower structural levels indicates that late disturbance(s) culminated in northward transport of the uppermost plate. Persistence of brittle fabrics along certain structural horizons suggests a possible association of late movement(s) with regionally known detachment faults. The four plates were juxtaposed and significant intraplate movements had ceased prior to Early Miocene emplacement of rhyolite porphyry dikes.

In the Magdalena region of north central Sonora, components of a pre-Middle Cretaceous stratigraphy are used as strain markers in tracking the evolution of a long lived orogenic belt. Important elements of the tectonic history include: (1) Compression during the Late Cretaceous and Early Tertiary, accompanied by plutonism, metamorphism, and ductile strain at depth, and thrust driven? syntectonic sedimentation at the surface. (2) Middle Tertiary transition to crustal extension, initially recorded by intrusion of leucogranites, inflation of the previously shortened middle and upper crustal section, and surface volcanism. (3) Gravity induced development of a normal sense ductile shear zone at mid crustal levels, with eventual detachment and southwestward displacement of the upper crustal stratigraphy by Early Miocene time.

Elucidation of the metamorphic core complex evolution just described was facilitated by fortuitous preservation of a unique assemblage of rocks and structures. The "type" stratigraphy utilized for regional correlation and strain analysis includes a Jurassic volcanic arc assemblage overlain by an Upper Jurassic-Lower Cretaceous quartz pebble conglomerate, in turn overlain by marine strata with fossiliferous Aptian-Albian limestones. The Jurassic strata, comprised of (a) rhyolite porphyries interstratified with quartz arenites, (b) rhyolite cobble conglomerate, and (c) intrusive granite porphyries, are known to rest on Precambrian basement north and east of the study area. The quartz pebble conglomerate is correlated with the Glance Conglomerate of southeastern Arizona and northeastern Sonora. The marine sequence represents part of an isolated arm? of the Bisbee Basin.

Crosscutting structural relationships between the pre-Middle Cretaceous supracrustal section, younger plutons, and deformational fabrics allow the tectonic sequence to be determined. Earliest phases of a Late Cretaceous-Early Tertiary orogeny are marked by emplacement of the 78 ± 3 Ma Guacomea Granodiorite (U/Pb zircon, Anderson et al., 1980) as a sill into deep levels of the layered Jurassic series. Subsequent regional metamorphism and ductile strain is recorded by a penetrative schistosity and lineation, and east-west trending folds. These fabrics are intruded by post-kinematic Early Tertiary? two mica granites. At shallower crustal levels, the orogeny is represented by north directed thrust faulting, formation of a large intermontane basin, and development of a pronounced unconformity. A second important phase of ductile strain followed Middle Tertiary? emplacement of leucogranites as sills and northwest trending dikes into intermediate levels of the deformed section (surficial volcanism was also active during this transitional period to regional extension). Gravitational instabilities resulting from crustal swelling via intrusion and thermal expansion led to development of a ductile shear zone within the stratigraphic horizon occupied by a laterally extensive leucogranite sill. With continued extension, upper crustal brittle normal faults (detachment faults) enhanced the uplift and tectonic denudation of this mylonite zone, ultimately resulting in southwestward displacement of the upper crustal stratigraphy.

Strains associated with the two ductile deformation events have been successfully partitioned through a multifaceted analysis. R_f/Ø measurements on various markers from the "type" stratigraphy allow a gradient representing cumulative strain since Middle Cretaceous time to be determined. From this gradient, noncoaxial strains accrued since emplacement of the leucogranites may be removed. Irrotational components of the postleucogranite strain are measured from quartz grain shapes in deformed granites; rotational components (shear strains) are determined from S-C fabrics and from restoration of rotated dike and vein networks. Structural observations and strain data are compatable with a deformation path of: (1) coaxial strain (pure shear?), followed by (2) injection of leucogranites as dikes (perpendicular to the minimum principle stress) and sills (parallel to the minimum principle stress), then (3) southwest directed simple shear. Modeling the late strain gradient as a simple shear zone permits a minimum displacement of 10 kilometers on the Magdalena mylonite zone/detachment fault system. Removal of the Middle Tertiary noncoaxial strains yields a residual (or pre-existing) strain gradient representative of the Late Cretaceous-Early Tertiary deformation. Several partially destrained cross sections, restored to the time of leucogranite emplacement, illustrate the idea that the upper plate of the core complex bas been detached from a region of significant topographic relief. 50% to 100% bulk extension across a 50 kilometer wide corridor is demonstrated.

Late Cenozoic tectonics of the Magdalena region are dominated by Basin and Range style faulting. Northeast and north-northwest trending high angle normal faults have interacted to extend the crust in an east-west direction. Net extension for this period is minor (10% to 15%) in comparison to the Middle Tertiary detachment related extensional episode.

Wind-driven desertification: process modeling, remote monitoring, and forecasting

Arid and semiarid landscapes comprise nearly a third of the Earth's total land surface. These areas are coming under increasing land use pressures. Despite their low productivity these lands are not barren. Rather, they consist of fragile ecosystems vulnerable to anthropogenic disturbance.

The purpose of this thesis is threefold: (I) to develop and test a process model of wind-driven desertification, (II) to evaluate next-generation process-relevant remote monitoring strategies for use in arid and semiarid regions, and (III) to identify elements for effective management of the world's drylands.

In developing the process model of wind-driven desertification in arid and semiarid lands, field, remote sensing, and modeling observations from a degraded Mojave Desert shrubland are used. This model focuses on aeolian removal and transport of dust, sand, and litter as the primary mechanisms of degradation: killing plants by burial and abrasion, interrupting natural processes of nutrient accumulation, and allowing the loss of soil resources by abiotic transport. This model is tested in field sampling experiments at two sites and is extended by Fourier Transform and geostatistical analysis of high-resolution imagery from one site.

Next, the use of hyperspectral remote sensing data is evaluated as a substantive input to dryland remote monitoring strategies. In particular, the efficacy of spectral mixture analysis (SMA) in discriminating vegetation and soil types and detennining vegetation cover is investigated. The results indicate that hyperspectral data may be less useful than often thought in determining vegetation parameters. Its usefulness in determining soil parameters, however, may be leveraged by developing simple multispectral classification tools that can be used to monitor desertification.

Finally, the elements required for effective monitoring and management of arid and semiarid lands are discussed. Several large-scale multi-site field experiments are proposed to clarify the role of wind as a landscape and degradation process in dry lands. The role of remote sensing in monitoring the world's drylands is discussed in terms of optimal remote sensing platform characteristics and surface phenomena which may be monitored in order to identify areas at risk of desertification. A desertification indicator is proposed that unifies consideration of environmental and human variables.

Experimental, Numerical and Analytical Studies of the MHD-driven plasma jet, instabilities and waves

This thesis describes a series of experimental, numerical, and analytical studies involving the Caltech magnetohydrodynamically (MHD)-driven plasma jet experiment. The plasma jet is created via a capacitor discharge that powers a magnetized coaxial planar electrodes system. The jet is collimated and accelerated by the MHD forces.

We present three-dimensional ideal MHD finite-volume simulations of the plasma jet experiment using an astrophysical magnetic tower as the baseline model. A compact magnetic energy/helicity injection is exploited in the simulation analogous to both the experiment and to astrophysical situations. Detailed analysis provides a comprehensive description of the interplay of magnetic force, pressure, and flow effects. We delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms.

When the experimental jet is sufficiently long, it undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability caused by lateral acceleration of the kink instability. We present an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface.

In the experiment, this instability cascade from macro-scale to micro-scale eventually leads to the failure of MHD. When the Rayleigh-Taylor instability becomes nonlinear, it compresses and pinches the plasma jet to a scale smaller than the ion skin depth and triggers a fast magnetic reconnection. We built a specially designed high-speed 3D magnetic probe and successfully detected the high frequency magnetic fluctuations of broadband whistler waves associated with the fast reconnection. The magnetic fluctuations exhibit power-law spectra. The magnetic components of single-frequency whistler waves are found to be circularly polarized regardless of the angle between the wave propagation direction and the background magnetic field.

Firing Patterns of Cerebellar Purkinje Cells During Locomotion and Sleep

The cerebellum is a major supraspinal center involved in the coordination of movement. The principal neurons of the cerebellar cortex, Purkinje cells, receive excitatory synaptic input from two sources: the parallel and climbing fibers. These pathways have markedly different effects: the parallel fibers control the rate of simple sodium spikes, while the climbing fibers induce characteristic complex spike bursts, which are accompanied by dendritic calcium transients and play a key role in regulating synaptic plasticity. While many studies using a variety of species, behaviors, and cerebellar regions have documented modulation in Purkinje cell activity during movement, few have attempted to record from these neurons in unrestrained rodents. In this dissertation, we use chronic, multi-tetrode recording in freely-behaving rats to study simple and complex spike firing patterns during locomotion and sleep. Purkinje cells discharge rhythmically during stepping, but this activity is highly variable across steps. We show that behavioral variables systematically influence the step-locked firing rate in a step-phase-dependent way, revealing a functional clustering of Purkinje cells. Furthermore, we find a pronounced disassociation between patterns of variability driven by the parallel and climbing fibers, as well as functional differences between cerebellar lobules. These results suggest that Purkinje cell activity not only represents step phase within each cycle, but is also shaped by behavior across steps, facilitating control of movement under dynamic conditions. During sleep, we observe an attenuation of both simple and complex spiking, relative to awake behavior. Although firing rates during slow wave sleep (SWS) and rapid eye movement sleep (REM) are similar, simple spike activity is highly regular in SWS, while REM is characterized by phasic increases and pauses in simple spiking. This phasic activity in REM is associated with pontine waves, which propagate into the cerebellar cortex and modulate both simple and complex spiking. Such a temporal coincidence between parallel and climbing fiber activity is known to drive plasticity at parallel fiber synapses; consequently, pontocerebellar waves may provide a mechanism for tuning synaptic weights in the cerebellum during active sleep.

A hybrid-parallel framework for the nonlinear seismic analysis of very tall buildings

FRAME3D, a program for the nonlinear seismic analysis of steel structures, has previously been used to study the collapse mechanisms of steel buildings up to 20 stories tall. The present thesis is inspired by the need to conduct similar analysis for much taller structures. It improves FRAME3D in two primary ways.

First, FRAME3D is revised to address specific nonlinear situations involving large displacement/rotation increments, the backup-subdivide algorithm, element failure, and extremely narrow joint hysteresis. The revisions result in superior convergence capabilities when modeling earthquake-induced collapse. The material model of a steel fiber is also modified to allow for post-rupture compressive strength.

Second, a parallel FRAME3D (PFRAME3D) is developed. The serial code is optimized and then parallelized. A distributed-memory divide-and-conquer approach is used for both the global direct solver and element-state updates. The result is an implicit finite-element hybrid-parallel program that takes advantage of the narrow-band nature of very tall buildings and uses nearest-neighbor-only communication patterns.

Using three structures of varied sized, PFRAME3D is shown to compute reproducible results that agree with that of the optimized 1-core version (displacement time-history response root-mean-squared errors are ~〖10〗^(-5) m) with much less wall time (e.g., a dynamic time-history collapse simulation of a 60-story building is computed in 5.69 hrs with 128 cores—a speedup of 14.7 vs. the optimized 1-core version). The maximum speedups attained are shown to increase with building height (as the total number of cores used also increases), and the parallel framework can be expected to be suitable for buildings taller than the ones presented here.

PFRAME3D is used to analyze a hypothetical 60-story steel moment-frame tube building (fundamental period of 6.16 sec) designed according to the 1994 Uniform Building Code. Dynamic pushover and time-history analyses are conducted. Multi-story shear-band collapse mechanisms are observed around mid-height of the building. The use of closely-spaced columns and deep beams is found to contribute to the building's “somewhat brittle” behavior (ductility ratio ~2.0). Overall building strength is observed to be sensitive to whether a model is fracture-capable.