ASU Scholarship Showcase

It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field transverse to the symmetry axis of the system, turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed investigation of transitions in the flow structure, and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A finding is that, as the magnetic field is increased, onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence may be feasible by using ferrofluids. Our study of transition to and evolution of turbulence in the Taylor-Couette ferrofluidic flow system provides insights into the challenging problem of turbulence control.

A relatively unexplored issue in cybersecurity science and engineering is whether there exist intrinsic patterns of cyberattacks. Conventional wisdom favors absence of such patterns due to the overwhelming complexity of the modern cyberspace. Surprisingly, through a detailed analysis of an extensive data set that records the time-dependent frequencies of attacks over a relatively wide range of consecutive IP addresses, we successfully uncover intrinsic spatiotemporal patterns underlying cyberattacks, where the term “spatio” refers to the IP address space. In particular, we focus on analyzing macroscopic properties of the attack traffic flows and identify two main patterns with distinct spatiotemporal characteristics: deterministic and stochastic. Strikingly, there are very few sets of major attackers committing almost all the attacks, since their attack “fingerprints” and target selection scheme can be unequivocally identified according to the very limited number of unique spatiotemporal characteristics, each of which only exists on a consecutive IP region and differs significantly from the others. We utilize a number of quantitative measures, including the flux-fluctuation law, the Markov state transition probability matrix, and predictability measures, to characterize the attack patterns in a comprehensive manner. A general finding is that the attack patterns possess high degrees of predictability, potentially paving the way to anticipating and, consequently, mitigating or even preventing large-scale cyberattacks using macroscopic approaches.

Supply-demand processes take place on a large variety of real-world networked systems ranging from power grids and the internet to social networking and urban systems. In a modern infrastructure, supply-demand systems are constantly expanding, leading to constant increase in load requirement for resources and consequently, to problems such as low efficiency, resource scarcity, and partial system failures. Under certain conditions global catastrophe on the scale of the whole system can occur through the dynamical process of cascading failures. We investigate optimization and resilience of time-varying supply-demand systems by constructing network models of such systems, where resources are transported from the supplier sites to users through various links. Here by optimization we mean minimization of the maximum load on links, and system resilience can be characterized using the cascading failure size of users who fail to connect with suppliers.

We consider two representative classes of supply schemes: load driven supply and fix fraction supply. Our findings are: (1) optimized systems are more robust since relatively smaller cascading failures occur when triggered by external perturbation to the links; (2) a large fraction of links can be free of load if resources are directed to transport through the shortest paths; (3) redundant links in the performance of the system can help to reroute the traffic but may undesirably transmit and enlarge the failure size of the system; (4) the patterns of cascading failures depend strongly upon the capacity of links; (5) the specific location of the trigger determines the specific route of cascading failure, but has little effect on the final cascading size; (6) system expansion typically reduces the efficiency; and (7) when the locations of the suppliers are optimized over a long expanding period, fewer suppliers are required. These results hold for heterogeneous networks in general, providing insights into designing optimal and resilient complex supply-demand systems that expand constantly in time.

Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems.

The phenomenon of Fano resonance is ubiquitous in a large variety of wave scattering systems, where the resonance profile is typically asymmetric. Whether the parameter characterizing the asymmetry should be complex or real is an issue of great experimental interest. Using coherent quantum transport as a paradigm and taking into account of the collective contribution from all available scattering channels, we derive a universal formula for the Fano-resonance profile. We show that our formula bridges naturally the traditional Fano formulas with complex and real asymmetry parameters, indicating that the two types of formulas are fundamentally equivalent (except for an offset). The connection also reveals a clear footprint for the conductance resonance during a dephasing process. Therefore, the emergence of complex asymmetric parameter when fitting with experimental data needs to be properly interpreted. Furthermore, we have provided a theory for the width of the resonance, which relates explicitly the width to the degree of localization of the close-by eigenstates and the corresponding coupling matrices or the self-energies caused by the leads. Our work not only resolves the issue about the nature of the asymmetry parameter, but also provides deeper physical insights into the origin of Fano resonance. Since the only assumption in our treatment is that the transport can be described by the Green’s function formalism, our results are also valid for broad disciplines including scattering problems of electromagnetic waves, acoustics, and seismology.

We investigate high-dimensional nonlinear dynamical systems exhibiting multiple resonances under adiabatic parameter variations. Our motivations come from experimental considerations where time-dependent sweeping of parameters is a practical approach to probing and characterizing the bifurcations of the system. The question is whether bifurcations so detected are faithful representations of the bifurcations intrinsic to the original stationary system. Utilizing a harmonically forced, closed fluid flow system that possesses multiple resonances and solving the Navier-Stokes equation under proper boundary conditions, we uncover the phenomenon of the early effect. Specifically, as a control parameter, e.g., the driving frequency, is adiabatically increased from an initial value, resonances emerge at frequency values that are lower than those in the corresponding stationary system. The phenomenon is established by numerical characterization of physical quantities through the resonances, which include the kinetic energy and the vorticity field, and a heuristic analysis based on the concept of instantaneous frequency. A simple formula is obtained which relates the resonance points in the time-dependent and time-independent systems. Our findings suggest that, in general, any true bifurcation of a nonlinear dynamical system can be unequivocally uncovered through adiabatic parameter sweeping, in spite of a shift in the bifurcation point, which is of value to experimental studies of nonlinear dynamical systems.

Most previous works on complete synchronization of chaotic oscillators focused on the one-channel interaction scheme where the oscillators are coupled through only one variable or a symmetric set of variables. Using the standard framework of master-stability function (MSF), we investigate the emergence of complex synchronization behaviors under all possible configurations of two-channel coupling, which include, for example, all possible cross coupling schemes among the dynamical variables. Utilizing the classic Rössler and Lorenz oscillators, we find a rich variety of synchronization phenomena not present in any previously extensively studied, single-channel coupling configurations. For example, in many cases two coupling channels can enhance or even generate synchronization where there is only weak or no synchronization under only one coupling channel, which has been verified in a coupled neuron system. There are also cases where the oscillators are originally synchronized under one coupling channel, but an additional synchronizable coupling channel can, however, destroy synchronization. Direct numerical simulations of actual synchronization dynamics verify the MSF-based predictions. Our extensive computation and heuristic analysis provide an atlas for synchronization of chaotic oscillators coupled through two channels, which can be used as a systematic reference to facilitate further research in this area.

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking "clustering" phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the "mixed" role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

The urban heat island (UHI) phenomenon is a significant worldwide problem caused by rapid population growth and associated urbanization. The UHI effect exacerbates heat waves during the summer, increases energy and water consumption, and causes the high risk of heat-related morbidity and mortality. UHI mitigation efforts have increasingly relied on wisely designing the urban residential environment such as using high albedo rooftops, green rooftops, and planting trees and shrubs to provide canopy coverage and shading. Thus, strategically designed residential rooftops and their surrounding landscaping have the potential to translate into significant energy, long-term cost savings, and health benefits. Rooftop albedo, material, color, area, slope, height, aspect and nearby landscaping are factors that potentially contribute. To extract, derive, and analyze these rooftop parameters and outdoor landscaping information, high resolution optical satellite imagery, LIDAR (light detection and ranging) point clouds and thermal imagery are necessary. Using data from the City of Tempe AZ (a 2010 population of 160,000 people), we extracted residential rooftop footprints and rooftop configuration parameters from airborne LIDAR point clouds and QuickBird satellite imagery (2.4 m spatial resolution imagery). Those parameters were analyzed against surface temperature data from the MODIS/ASTER airborne simulator (MASTER). MASTER images provided fine resolution (7 m) surface temperature data for residential areas during daytime and night time. Utilizing these data, ordinary least squares (OLS) regression was used to evaluate the relationships between residential building rooftops and their surface temperature in urban environment. The results showed that daytime rooftop temperature was closely related to rooftop spectral attributes, aspect, slope, and surrounding trees. Night time temperature was only influenced by rooftop spectral attributes and slope.

This study examines the spatial and temporal patterns of the surface urban heat island (SUHI) intensity in the Phoenix metropolitan area and the relationship with land use land cover (LULC) change between 2000 and 2014. The objective is to identify specific regions in Phoenix that have been increasingly heated and cooled to further understand how LULC change influences the SUHI intensity. The data employed include MODerate-resolution Imaging Spectroradiometer (MODIS) land surface temperature (LST) 8-day composite June imagery, and classified LULC maps generated using 2000 and 2014 Landsat imagery. Results show that the regions that experienced the most significant LST changes during the study period are primarily on the outskirts of the Phoenix metropolitan area for both daytime and nighttime. The conversion to urban, residential, and impervious surfaces from all other LULC types has been identified as the primary cause of the UHI effect in Phoenix. Vegetation cover has been shown to significantly lower LST for both daytime and nighttime due to its strong cooling effect by producing more latent heat flux and less sensible heat flux. We suggest that urban planners, decision-makers, and city managers formulate new policies and regulations that encourage residential, commercial, and industrial developers to include more vegetation when planning new construction.