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- Language: English
- Creators: Ira A. Fulton Schools of Engineering
technological systems that affect society, such as communication infrastructures. Data
assimilation addresses the challenge of state specification by incorporating system
observations into the model estimates. In this research, a particular data
assimilation technique called the Local Ensemble Transform Kalman Filter (LETKF) is
applied to the ionosphere, which is a domain of practical interest due to its effects
on infrastructures that depend on satellite communication and remote sensing. This
dissertation consists of three main studies that propose strategies to improve space-
weather specification during ionospheric extreme events, but are generally applicable
to Earth-system models:
Topic I applies the LETKF to estimate ion density with an idealized model of
the ionosphere, given noisy synthetic observations of varying sparsity. Results show
that the LETKF yields accurate estimates of the ion density field and unobserved
components of neutral winds even when the observation density is spatially sparse
(2% of grid points) and there is large levels (40%) of Gaussian observation noise.
Topic II proposes a targeted observing strategy for data assimilation, which uses
the influence matrix diagnostic to target errors in chosen state variables. This
strategy is applied in observing system experiments, in which synthetic electron density
observations are assimilated with the LETKF into the Thermosphere-Ionosphere-
Electrodynamics Global Circulation Model (TIEGCM) during a geomagnetic storm.
Results show that assimilating targeted electron density observations yields on
average about 60%–80% reduction in electron density error within a 600 km radius of
the observed location, compared to 15% reduction obtained with randomly placed
vertical profiles.
Topic III proposes a methodology to account for systematic model bias arising
ifrom errors in parametrized solar and magnetospheric inputs. This strategy is ap-
plied with the TIEGCM during a geomagnetic storm, and is used to estimate the
spatiotemporal variations of bias in electron density predictions during the
transitionary phases of the geomagnetic storm. Results show that this strategy reduces
error in 1-hour predictions of electron density by about 35% and 30% in polar regions
during the main and relaxation phases of the geomagnetic storm, respectively.
Lagrangian measures, identified with finite-time Lyapunov exponents, are first used to characterize transport patterns of inertial pollutant particles. Motivated by actual events the focus is on flows in realistic urban geometry. Both deterministic and stochastic transport patterns are identified, as inertial Lagrangian coherent structures. For the deterministic case, the organizing structures are well defined and are extracted at different hours of a day to reveal the variability of coherent patterns. For the stochastic case, a random displacement model for fluid particles is formulated, and used to derive the governing equations for inertial particles to examine the change in organizing structures due to ``zeroth-order'' random noise. It is found that, (1) the Langevin equation for inertial particles can be reduced to a random displacement model; (2) using random noise based on inhomogeneous turbulence, whose diffusivity is derived from $k$-$\epsilon$ models, major coherent structures survive to organize local flow patterns and weaker structures are smoothed out due to random motion.
A study of three-dimensional Lagrangian coherent structures (LCS) near HKIA is then presented and related to previous developments of two-dimensional (2D) LCS analyses in detecting windshear experienced by landing aircraft. The LCS are contrasted among three independent models and against 2D coherent Doppler light detection and ranging (LIDAR) data. Addition of the velocity information perpendicular to the lidar scanning cone helps solidify flow structures inferred from previous studies; contrast among models reveals the intramodel variability; and comparison with flight data evaluates the performance among models in terms of Lagrangian analyses. It is found that, while the three models and the LIDAR do recover similar features of the windshear experienced by a landing aircraft (along the landing trajectory), their Lagrangian signatures over the entire domain are quite different - a portion of each numerical model captures certain features resembling those LCS extracted from independent 2D LIDAR analyses based on observations. Overall, it was found that the Weather Research and Forecast (WRF) model provides the best agreement with the LIDAR data.
Finally, the three-dimensional variational (3DVAR) data assimilation scheme in WRF is used to incorporate the LIDAR line of sight velocity observations into the WRF model forecast at HKIA. Using two different days as test cases, it is found that the LIDAR data can be successfully and consistently assimilated into WRF. Using the updated model forecast LCS are extracted along the LIDAR scanning cone and compare to onboard flight data. It is found that the LCS generated from the updated WRF forecasts are generally better correlated with the windshear experienced by landing aircraft as compared to the LIDAR extracted LCS alone, which suggests that such a data assimilation scheme could be used for the prediction of windshear events.
A detailed evaluation of the environmental forecast is conducted by investigating the Surface Energy Balance (SEB) obtained from observations made with an eddy-covariance flux tower compared with SEB from simulations using several physical parameterizations of urban effects and planetary boundary layer schemes. Diurnal variation in SEB constituent fluxes are examined in relation to surface layer stability and modeled diagnostic variables. Improvement is found when adapting parameterizations for Phoenix with reduced errors in the SEB components. Finer model resolution (to 333 m) is seen to have insignificant ($<1\sigma$) influence on mean absolute percent difference of 30-minute diurnal mean SEB terms. A new method of representing inhomogeneous urban development density derived from observations of impervious surfaces with sub-grid scale resolution is then proposed for mesoscale applications. This method was implemented and evaluated within the environmental modeling framework. Finally, a new semi-implicit scheme based on Leapfrog and a fourth-order implicit time-filter is developed.
For autonomous systems, invariant manifold theory can be used to separate the system into dynamically distinct regions. Despite there being no equivalent method for nonautonomous systems, a similar analysis can be done. Systems with general time dependencies must resort to using finite-time transport barriers for partitioning; these barriers are the edges of Lagrangian coherent structures (LCS), the analog to the stable and unstable manifolds of invariant manifold theory. Using the coherent structures of a flow to analyze the statistics of trapping, flight, and residence times, the signature of anomalous diffusion are obtained.
This research also investigates the use of linear models for approximating the elements of the covariance matrix of nonlinear flows, and then applying the covariance matrix approximation over coherent regions. The first and second-order moments can be used to fully describe an ensemble evolution in linear systems, however there is no direct method for nonlinear systems. The problem is only compounded by the fact that the moments for nonlinear flows typically don't have analytic representations, therefore direct numerical simulations would be needed to obtain the moments throughout the domain. To circumvent these many computations, the nonlinear system is approximated as many linear systems for which analytic expressions for the moments exist. The parameters introduced in the linear models are obtained locally from the nonlinear deformation tensor.
prostate cancer is most commonly treated with hormonal therapy. The idea behind
hormonal therapy is to reduce androgen production, which prostate cancer cells
require for growth. Recently, the exploration of the synergistic effects of the drugs
used in hormonal therapy has begun. The aim was to build off of these recent
advancements and further refine the synergistic drug model. The advancements I
implement come by addressing biological shortcomings and improving the model’s
internal mechanistic structure. The drug families being modeled, anti-androgens,
and gonadotropin-releasing hormone analogs, interact with androgen production in a
way that is not completely understood in the scientific community. Thus the models
representing the drugs show progress through their ability to capture their effect
on serum androgen. Prostate-specific antigen is the primary biomarker for prostate
cancer and is generally how population models on the subject are validated. Fitting
the model to clinical data and comparing it to other clinical models through the
ability to fit and forecast prostate-specific antigen and serum androgen is how this
improved model achieves validation. The improved model results further suggest that
the drugs’ dynamics should be considered in adaptive therapy for prostate cancer.
In this paper, we present a Bayesian analysis for the Weibull proportional hazard (PH) model used in step-stress accelerated life testings. The key mathematical and graphical difference between the Weibull cumulative exposure (CE) model and the PH model is illustrated. Compared with the CE model, the PH model provides more flexibility in fitting step-stress testing data and has the attractive mathematical properties of being desirable in the Bayesian framework. A Markov chain Monte Carlo algorithm with adaptive rejection sampling technique is used for posterior inference. We demonstrate the performance of this method on both simulated and real datasets.
We describe mechanical metamaterials created by folding flat sheets in the tradition of origami, the art of paper folding, and study them in terms of their basic geometric and stiffness properties, as well as load bearing capability. A periodic Miura-ori pattern and a non-periodic Ron Resch pattern were studied. Unexceptional coexistence of positive and negative Poisson's ratio was reported for Miura-ori pattern, which are consistent with the interesting shear behavior and infinity bulk modulus of the same pattern. Unusually strong load bearing capability of the Ron Resch pattern was found and attributed to the unique way of folding. This work paves the way to the study of intriguing properties of origami structures as mechanical metamaterials.
Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.
We develop a completely data-driven approach to reconstructing coupled neuronal networks that contain a small subset of chaotic neurons. Such chaotic elements can be the result of parameter shift in their individual dynamical systems and may lead to abnormal functions of the network. To accurately identify the chaotic neurons may thus be necessary and important, for example, applying appropriate controls to bring the network to a normal state. However, due to couplings among the nodes, the measured time series, even from non-chaotic neurons, would appear random, rendering inapplicable traditional nonlinear time-series analysis, such as the delay-coordinate embedding method, which yields information about the global dynamics of the entire network. Our method is based on compressive sensing. In particular, we demonstrate that identifying chaotic elements can be formulated as a general problem of reconstructing the nodal dynamical systems, network connections and all coupling functions, as well as their weights. The working and efficiency of the method are illustrated by using networks of non-identical FitzHugh–Nagumo neurons with randomly-distributed coupling weights.
X-ray tomography has provided a non-destructive means for microstructure characterization in three and four dimensions. A stochastic procedure to accurately reconstruct material microstructure from limited-angle X-ray tomographic projections is presented and its utility is demonstrated by reconstructing a variety of distinct heterogeneous materials and elucidating the information content of different projection data sets. A small number of projections (e.g. 20–40) are necessary for accurate reconstructions via the stochastic procedure, indicating its high efficiency in using limited structural information.