Nonlinear responses in the dynamics of climate system could be triggered by small change of forcing. Interactions between different components of Earth’s climate system are believed to cause abrupt and catastrophic transitions, of which anthropogenic forcing is a major and the most irreversible driver. Meantime, in the face of global climate change, extreme climatic events, such as extreme precipitations, heatwaves, droughts, etc., are projected to be more frequent, more intense, and longer in duration. These nonlinear responses in climate dynamics from tipping points to extreme events pose serious threats to human society on a large scale. Understanding the physical mechanisms behind them has potential to reduce related risks through different ways. The overarching objective of this dissertation is to quantify complex interactions, detect tipping points, and explore propagations of extreme events in the hydroclimate system from a new structure-based perspective, by integrating climate dynamics, causal inference, network theory, spectral analysis, and machine learning. More specifically, a network-based framework is developed to find responses of hydroclimate system to potential critical transitions in climate. Results show that system-based early warning signals towards tipping points can be located successfully, demonstrated by enhanced connections in the network topology. To further evaluate the long-term nonlinear interactions among the U.S. climate regions, causality inference is introduced and directed complex networks are constructed from climatology records over one century. Causality networks reveal that the Ohio valley region acts as a regional gateway and mediator to the moisture transport and thermal transfer in the U.S. Furthermore, it is found that cross-regional causality variability manifests intrinsic frequency ranging from interannual to interdecadal scales, and those frequencies are associated with the physics of climate oscillations. Besides the long-term climatology, this dissertation also aims to explore extreme events from the system-dynamic perspective, especially the contributions of human-induced activities to propagation of extreme heatwaves in the U.S. cities. Results suggest that there are long-range teleconnections among the U.S. cities and supernodes in heatwave spreading. Findings also confirm that anthropogenic activities contribute to extreme heatwaves by the fact that causality during heatwaves is positively associated with population in megacities.

Predicting nonlinear dynamical systems has been a long-standing challenge in science. This field is currently witnessing a revolution with the advent of machine learning methods. Concurrently, the analysis of dynamics in various nonlinear complex systems continues to be crucial. Guided by these directions, I conduct the following studies. Predicting critical transitions and transient states in nonlinear dynamics is a complex problem. I developed a solution called parameter-aware reservoir computing, which uses machine learning to track how system dynamics change with a driving parameter. I show that the transition point can be accurately predicted while trained in a sustained functioning regime before the transition. Notably, it can also predict if the system will enter a transient state, the distribution of transient lifetimes, and their average before a final collapse, which are crucial for management. I introduce a machine-learning-based digital twin for monitoring and predicting the evolution of externally driven nonlinear dynamical systems, where reservoir computing is exploited. Extensive tests on various models, encompassing optics, ecology, and climate, verify the approach’s effectiveness. The digital twins can extrapolate unknown system dynamics, continually forecast and monitor under non-stationary external driving, infer hidden variables, adapt to different driving waveforms, and extrapolate bifurcation behaviors across varying system sizes. Integrating engineered gene circuits into host cells poses a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback. I conducted systematic studies on hundreds of circuit structures exhibiting various functionalities, and identified a comprehensive categorization of growth-induced failures. I discerned three dynamical mechanisms behind these circuit failures. Moreover, my comprehensive computations reveal a scaling law between the circuit robustness and the intensity of growth feedback. A class of circuits with optimal robustness is also identified. Chimera states, a phenomenon of symmetry-breaking in oscillator networks, traditionally have transient lifetimes that grow exponentially with system size. However, my research on high-dimensional oscillators leads to the discovery of ’short-lived’ chimera states. Their lifetime increases logarithmically with system size and decreases logarithmically with random perturbations, indicating a unique fragility. To understand these states, I use a transverse stability analysis supported by simulations.

A remarkable phenomenon in contemporary physics is quantum scarring in classically chaoticsystems, where the wave functions tend to concentrate on classical periodic orbits. Quantum scarring has been studied for more than four decades, but the problem of efficiently detecting quantum scars has remained to be challenging, relying mostly on human visualization of wave function patterns. This paper develops a machine learning approach to detecting quantum scars in an automated and highly efficient manner. In particular, this paper exploits Meta learning. The first step is to construct a few-shot classification algorithm, under the requirement that the one-shot classification accuracy be larger than 90%. Then propose a scheme based on a combination of neural networks to improve the accuracy. This paper shows that the machine learning scheme can find the correct quantum scars from thousands images of wave functions, without any human intervention, regardless of the symmetry of the underlying classical system. This will be the first application of Meta learning to quantum systems. Interacting spin networks are fundamental to quantum computing. Data-based tomography oftime-independent spin networks has been achieved, but an open challenge is to ascertain the structures of time-dependent spin networks using time series measurements taken locally from a small subset of the spins. Physically, the dynamical evolution of a spin network under time-dependent driving or perturbation is described by the Heisenberg equation of motion. Motivated by this basic fact, this paper articulates a physics-enhanced machine learning framework whose core is Heisenberg neural networks. This paper demonstrates that, from local measurements, not only the local Hamiltonian can be recovered but the Hamiltonian reflecting the interacting structure of the whole system can also be faithfully reconstructed. Using Heisenberg neural machine on spin networks of a variety of structures. In the extreme case where measurements are taken from only one spin, the achieved tomography fidelity values can reach about 90%. The developed machine learning framework is applicable to any time-dependent systems whose quantum dynamical evolution is governed by the Heisenberg equation of motion.

A notable challenge when assembling synthetic gene circuits is that modularity often fails to function as intended. A crucial underlying reason for this modularity failure is the existence of competition for shared and limited gene expression resources. By designing a synthetic cascading bistable switches (Syn-CBS) circuit in a single strain with two coupled self-activation modules to achieve successive cell fate transitions, nonlinear resource competition within synthetic gene circuits is unveiled. However, in vivo it can be seen that the transition path was redirected with the activation of one switch always prevailing over that of the other, contradictory to coactivation theoretically expected. This behavior is a result of resource competition between genes and follows a ‘winner-takes-all’ rule, where the winner is determined by the relative connection strength between the two modules. Despite investigation demonstrating that resource competition between gene modules can significantly alter circuit deterministic behaviors, how resource competition contributes to gene expression noise and how this noise can be controlled is still an open issue of fundamental importance in systems biology and biological physics. By utilizing a two-gene circuit, the effects of resource competition on protein expression noise levels can be closely studied. A surprising double-edged role is discovered: the competition for these resources decreases noise while the constraint on resource availability adds its own term of noise into the system, denoted “resource competitive” noise. Noise reduction effects are then studied using orthogonal resources. Results indicate that orthogonal resources are a good strategy for eliminating the contribution of resource competition to gene expression noise. Noise propagation through a cascading circuit has been considered without resource competition. It has been noted that the noise from upstream genes can be transmitted downstream. However, resource competition’s effects on this cascading noise have yet to be studied. When studied, it is found that resource competition can induce stochastic state switching and perturb noise propagation. Orthogonal resources can remove some of the resource competitive behavior and allow for a system with less noise.

Few-layer black phosphorous (FLBP) is one of the most important two-dimensional (2D) materials due to its strongly layer-dependent quantized bandstructure, which leads to wavelength-tunable optical and electrical properties. This thesis focuses on the preparation of stable, high-quality FLBP, the characterization of its optical properties, and device applications.Part I presents an approach to preparing high-quality, stable FLBP samples by combining O2 plasma etching, boron nitride (BN) sandwiching, and subsequent rapid thermal annealing (RTA). Such a strategy has successfully produced FLBP samples with a record-long lifetime, with 80% of photoluminescence (PL) intensity remaining after 7 months. The improved material quality of FLBP allows the establishment of a more definitive relationship between the layer number and PL energies. Part II presents the study of oxygen incorporation in FLBP. The natural oxidation formed in the air environment is dominated by the formation of interstitial oxygen and dangling oxygen. By the real-time PL and Raman spectroscopy, it is found that continuous laser excitation breaks the bonds of interstitial oxygen, and free oxygen atoms can diffuse around or form dangling oxygen under low heat. RTA at 450 °C can turn the interstitial oxygen into dangling oxygen more thoroughly. Such oxygen-containing samples show similar optical properties to the pristine BP samples. The bandgap of such FLBP samples increases with the concentration of the incorporated oxygen. Part III deals with the investigation of emission natures of the prepared samples. The power- and temperature-dependent measurements demonstrate that PL emissions are dominated by excitons and trions, with a combined percentage larger than 80% at room temperature. Such measurements allow the determination of trion and exciton binding energies of 2-, 3-, and 4-layer BP, with values around 33, 23, 15 meV for trions and 297, 276, 179 meV for excitons at 77K, respectively. Part IV presents the initial exploration of device applications of such FLBP samples. The coupling between photonic crystal cavity (PCC) modes and FLBP's emission is realized by integrating the prepared sandwich structure onto 2D PCC. Electroluminescence has also been achieved by integrating such materials onto interdigital electrodes driven by alternating electric fields.

This dissertation aims to study the electron and spin transport, scattering in two dimensional pseudospin-1 lattice systems, hybrid systems of topological insulator and magnetic insulators, and molecule chain systems. For pseudospin-1 systems, the energy band consists of a pair of Dirac cones and a flat band through the connecting point of the cones. First, contrary to the conditional wisdom that flatband can localize electrons, I find that in a non-equilibrium situation where a constant electric field is suddenly switched on, the flat band can enhance the resulting current in both the linear and nonlinear response regimes compared to spin-1/2 system. Second, in the setup of massive pseudospin-1 electron scattering over a gate potential scatterer, I discover the large resonant skew scattering called super skew scattering, which does not arise in the corresponding spin-1/2 system and massless pseudospin-1 system. Third, by applying an appropriate gate voltage to generate a cavity in an alpha-T3 lattice, I find the exponential decay of the quasiparticles from a chaotic cavity, with a one-to-one correspondence between the exponential decay rate and the Berry phase for the entire family of alpha-T3 materials. Based on the hybrid system of a ferromagnetic insulator on top of a topological insulator, I first investigate the magnetization dynamics of a pair of ferromagnetic insulators deposited on the surface of a topological insulator. The spin polarized current on the surface of topological insulator can affect the magnetization of the two ferromagnetic insulators through proximity effect, which in turn modulates the electron transport, giving rise to the robust phase locking between the two magnetization dynamics. Second, by putting a skyrmion structure on top of a topological insulator, I find robust electron skew scattering against skyrmion structure even with deformation, due to the emergence of resonant modes. The chirality of molecule can lead to spin polarized transport due to the spin orbit interaction. I investigate spin transport through a chiral polyacetylene molecule and uncover the emergence of spin Fano resonances as a manifestation of the chiral induced spin selectivity effect.

Complex dynamical systems are the kind of systems with many interacting components that usually have nonlinear dynamics. Those systems exist in a wide range of disciplines, such as physical, biological, and social fields. Those systems, due to a large amount of interacting components, tend to possess very high dimensionality. Additionally, due to the intrinsic nonlinear dynamics, they have tremendous rich system behavior, such as bifurcation, synchronization, chaos, solitons. To develop methods to predict and control those systems has always been a challenge and an active research area.

My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.

Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.

Complex human controls is a topic of much interest in the fields of robotics, manufacturing, space exploration and many others. Even simple tasks that humans perform with ease can be extremely complicated when observed from a controls and complex systems perspective. One such simple task is that of a human carrying and moving a coffee cup. Though this may be a mundane task for humans, when this task is modelled and analyzed, the system may be quite chaotic in nature. Understanding such systems is key to the development robots and autonomous systems that can perform these tasks themselves.

The coffee cup system can be simplified and modeled by a cart-and-pendulum system. Bazzi et al. and Maurice et al. present two different cart-and-pendulum systems to represent the coffee cup system [1],[2]. The purpose of this project was to build upon these systems and to gain a better understanding of the coffee cup system and to determine where chaos existed within the system. The honors thesis team first worked with their senior design group to develop a mathematical model for the cart-and-pendulum system based on the Bazzi and Maurice papers [1],[2]. This system was analyzed and then built upon by the honors thesis team to build a cart-and-two-pendulum model to represent the coffee cup system more accurately.

Analysis of the single pendulum model showed that there exists a low frequency region where the pendulum and the cart remain in phase with each other and a high frequency region where the cart and pendulum have a π phase difference between them. The transition point of the low and high frequency region is determined by the resonant frequency of the pendulum. The analysis of the two-pendulum system also confirmed this result and revealed that differences in length between the pendulum cause the pendulums to transition to the high frequency regions at separate frequency. The pendulums have different resonance frequencies and transition into the high frequency region based on their own resonant frequency. This causes a range of frequencies where the pendulums are out of phase from each other. After both pendulums have transitioned, they remain in phase with each other and out of phase from the cart.

However, if the length of the pendulum is decreased too much, the system starts to exhibit chaotic behavior. The short pendulum starts to act in a chaotic manner and the phase relationship between the pendulums and the carts is no longer maintained. Since the pendulum length represents the distance between the particle of coffee and the top of the cup, this implies that coffee near the top of the cup would cause the system to act chaotically. Further analysis would be needed to determine the reason why the length affects the system in this way.

Resilience is emerging as the preferred way to improve the protection of infrastructure systems beyond established risk management practices. Massive damages experienced during tragedies like Hurricane Katrina showed that risk analysis is incapable to prevent unforeseen infrastructure failures and shifted expert focus towards resilience to absorb and recover from adverse events. Recent, exponential growth in research is now producing consensus on how to think about infrastructure resilience centered on definitions and models from influential organizations like the US National Academy of Sciences. Despite widespread efforts, massive infrastructure failures in 2017 demonstrate that resilience is still not working, raising the question: Are the ways people think about resilience producing resilient infrastructure systems?



This dissertation argues that established thinking harbors misconceptions about infrastructure systems that diminish attempts to improve their resilience. Widespread efforts based on the current canon focus on improving data analytics, establishing resilience goals, reducing failure probabilities, and measuring cascading losses. Unfortunately, none of these pursuits change the resilience of an infrastructure system, because none of them result in knowledge about how data is used, goals are set, or failures occur. Through the examination of each misconception, this dissertation results in practical, new approaches for infrastructure systems to respond to unforeseen failures via sensing, adapting, and anticipating processes. Specifically, infrastructure resilience is improved by sensing when data analytics include the modeler-in-the-loop, adapting to stress contexts by switching between multiple resilience strategies, and anticipating crisis coordination activities prior to experiencing a failure.

Overall, results demonstrate that current resilience thinking needs to change because it does not differentiate resilience from risk. The majority of research thinks resilience is a property that a system has, like a noun, when resilience is really an action a system does, like a verb. Treating resilience as a noun only strengthens commitment to risk-based practices that do not protect infrastructure from unknown events. Instead, switching to thinking about resilience as a verb overcomes prevalent misconceptions about data, goals, systems, and failures, and may bring a necessary, radical change to the way infrastructure is protected in the future.