ASU Scholarship Showcase

The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.

The effects of urbanization on ozone levels have been widely investigated over cities primarily located in temperate and/or humid regions. In this study, nested WRF-Chem simulations with a finest grid resolution of 1 km are conducted to investigate ozone concentrations O₃ due to urbanization within cities in arid/semi-arid environments. First, a method based on a shape preserving Monotonic Cubic Interpolation (MCI) is developed and used to downscale anthropogenic emissions from the 4 km resolution 2005 National Emissions Inventory (NEI05) to the finest model resolution of 1 km. Using the rapidly expanding Phoenix metropolitan region as the area of focus, we demonstrate the proposed MCI method achieves ozone simulation results with appreciably improved correspondence to observations relative to the default interpolation method of the WRF-Chem system. Next, two additional sets of experiments are conducted, with the recommended MCI approach, to examine impacts of urbanization on ozone production: (1) the urban land cover is included (i.e., urbanization experiments) and, (2) the urban land cover is replaced with the region's native shrubland. Impacts due to the presence of the built environment on O₃ are highly heterogeneous across the metropolitan area. Increased near surface O₃ due to urbanization of 10–20 ppb is predominantly a nighttime phenomenon while simulated impacts during daytime are negligible. Urbanization narrows the daily O₃ range (by virtue of increasing nighttime minima), an impact largely due to the region's urban heat island. Our results demonstrate the importance of the MCI method for accurate representation of the diurnal profile of ozone, and highlight its utility for high-resolution air quality simulations for urban areas.

An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit〈f〉and its fluctuation σ : σ ∼〈f⟩^β with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other.

Forecasts of noise pollution from a highway line segment noise source are obtained from a sound propagation model utilizing effective sound speed profiles derived from a Numerical Weather Prediction (NWP) limited area forecast with 1 km horizontal resolution and near-ground vertical resolution finer than 20 m. Methods for temporal along with horizontal and vertical spatial nesting are demonstrated within the NWP model for maintaining forecast feasibility. It is shown that vertical nesting can improve the prediction of finer structures in near-ground temperature and velocity profiles, such as morning temperature inversions and low level jet-like features. Accurate representation of these features is shown to be important for modeling sound refraction phenomena and for enabling accurate noise assessment. Comparisons are made using the parabolic equation model for predictions with profiles derived from NWP simulations and from field experiment observations during mornings on November 7 and 8, 2006 in Phoenix, Arizona. The challenges faced in simulating accurate meteorological profiles at high resolution for sound propagation applications are highlighted and areas for possible improvement are discussed.

Physical mechanisms of incongruency between observations and Weather Research and Forecasting (WRF) Model predictions are examined. Limitations of evaluation are constrained by (i) parameterizations of model physics, (ii) parameterizations of input data, (iii) model resolution, and (iv) flux observation resolution. Observations from a new 22.1-m flux tower situated within a residential neighborhood in Phoenix, Arizona, are utilized to evaluate the ability of the urbanized WRF to resolve finescale surface energy balance (SEB) when using the urban classes derived from the 30-m-resolution National Land Cover Database. Modeled SEB response to a large seasonal variation of net radiation forcing was tested during synoptically quiescent periods of high pressure in winter 2011 and premonsoon summer 2012. Results are presented from simulations employing five nested domains down to 333-m horizontal resolution. A comparative analysis of model cases testing parameterization of physical processes was done using four configurations of urban parameterization for the bulk urban scheme versus three representations with the Urban Canopy Model (UCM) scheme, and also for two types of planetary boundary layer parameterization: the local Mellor–Yamada–Janjić scheme and the nonlocal Yonsei University scheme. Diurnal variation in SEB constituent fluxes is examined in relation to surface-layer stability and modeled diagnostic variables. Improvement is found when adapting UCM for Phoenix with reduced errors in the SEB components. Finer model resolution is seen to have insignificant (<1 standard deviation) influence on mean absolute percent difference of 30-min diurnal mean SEB terms.

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.

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.

We develop a framework to uncover and analyse dynamical anomalies from massive, nonlinear and non-stationary time series data. The framework consists of three steps: preprocessing of massive datasets to eliminate erroneous data segments, application of the empirical mode decomposition and Hilbert transform paradigm to obtain the fundamental components embedded in the time series at distinct time scales, and statistical/scaling analysis of the components. As a case study, we apply our framework to detecting and characterizing high-frequency oscillations (HFOs) from a big database of rat electroencephalogram recordings. We find a striking phenomenon: HFOs exhibit on–off intermittency that can be quantified by algebraic scaling laws. Our framework can be generalized to big data-related problems in other fields such as large-scale sensor data and seismic data analysis.