ASU Scholarship Showcase

We develop a general framework to analyze the controllability of multiplex networks using multiple-relation networks and multiple-layer networks with interlayer couplings as two classes of prototypical systems. In the former, networks associated with different physical variables share the same set of nodes and in the latter, diffusion processes take place. We find that, for a multiple-relation network, a layer exists that dominantly determines the controllability of the whole network and, for a multiple-layer network, a small fraction of the interconnections can enhance the controllability remarkably. Our theory is generally applicable to other types of multiplex networks as well, leading to significant insights into the control of complex network systems with diverse structures and interacting patterns.

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.

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.

Dynamical processes occurring on the edges in complex networks are relevant to a variety of real-world situations. Despite recent advances, a framework for edge controllability is still required for complex networks of arbitrary structure and interaction strength. Generalizing a previously introduced class of processes for edge dynamics, the switchboard dynamics, and exploit- ing the exact controllability theory, we develop a universal framework in which the controllability of any node is exclusively determined by its local weighted structure. This framework enables us to identify a unique set of critical nodes for control, to derive analytic formulas and articulate efficient algorithms to determine the exact upper and lower controllability bounds, and to evaluate strongly structural controllability of any given network. Applying our framework to a large number of model and real-world networks, we find that the interaction strength plays a more significant role in edge controllability than the network structure does, due to a vast range between the bounds determined mainly by the interaction strength. Moreover, transcriptional regulatory networks and electronic circuits are much more strongly structurally controllable (SSC) than other types of real-world networks, directed networks are more SSC than undirected networks, and sparse networks are typically more SSC than dense networks.

Recent works revealed that the energy required to control a complex network depends on the number of driving signals and the energy distribution follows an algebraic scaling law. If one implements control using a small number of drivers, e.g. as determined by the structural controllability theory, there is a high probability that the energy will diverge. We develop a physical theory to explain the scaling behaviour through identification of the fundamental structural elements, the longest control chains (LCCs), that dominate the control energy. Based on the LCCs, we articulate a strategy to drastically reduce the control energy (e.g. in a large number of real-world networks). Owing to their structural nature, the LCCs may shed light on energy issues associated with control of nonlinear dynamical networks.

Given a complex geospatial network with nodes distributed in a two-dimensional region of physical space, can the locations of the nodes be determined and their connection patterns be uncovered based solely on data? We consider the realistic situation where time series/signals can be collected from a single location. A key challenge is that the signals collected are necessarily time delayed, due to the varying physical distances from the nodes to the data collection centre. To meet this challenge, we develop a compressive-sensing-based approach enabling reconstruction of the full topology of the underlying geospatial network and more importantly, accurate estimate of the time delays. A standard triangularization algorithm can then be employed to find the physical locations of the nodes in the network. We further demonstrate successful detection of a hidden node (or a hidden source or threat), from which no signal can be obtained, through accurate detection of all its neighbouring nodes. As a geospatial network has the feature that a node tends to connect with geophysically nearby nodes, the localized region that contains the hidden node can be identified.

Locating sources of diffusion and spreading from minimum data is a significant problem in network science with great applied values to the society. However, a general theoretical framework dealing with optimal source localization is lacking. Combining the controllability theory for complex networks and compressive sensing, we develop a framework with high efficiency and robustness for optimal source localization in arbitrary weighted networks with arbitrary distribution of sources. We offer a minimum output analysis to quantify the source locatability through a minimal number of messenger nodes that produce sufficient measurement for fully locating the sources. When the minimum messenger nodes are discerned, the problem of optimal source localization becomes one of sparse signal reconstruction, which can be solved using compressive sensing. Application of our framework to model and empirical networks demonstrates that sources in homogeneous and denser networks are more readily to be located. A surprising finding is that, for a connected undirected network with random link weights and weak noise, a single messenger node is sufficient for locating any number of sources. The framework deepens our understanding of the network source localization problem and offers efficient tools with broad applications.

In this paper, we study oscillating solutions of the 1D-quintic nonlinear Schrödinger equation with the help of Wigner's quasiprobability distribution in quantum phase space. An "absolute squeezing property," namely a periodic in time total localization of wave packets at some finite spatial points without violation of the Heisenberg uncertainty principle, is analyzed in this nonlinear model.

Explicit solutions of the inhomogeneous paraxial wave equation in a linear and quadratic approximation are applied to wave fields with invariant features, such as oscillating laser beams in a parabolic waveguide and spiral light beams in varying media. A similar effect of superfocusing of particle beams in a thin monocrystal film, harmonic oscillations of cold trapped atoms, and motion in magnetic field are also mentioned.