ASU Scholarship Showcase

Two classes of scaling behaviours, namely the super-linear scaling of links or activities, and the sub-linear scaling of area, diversity, or time elapsed with respect to size have been found to prevail in the growth of complex networked systems. Despite some pioneering modelling approaches proposed for specific systems, whether there exists some general mechanisms that account for the origins of such scaling behaviours in different contexts, especially in socioeconomic systems, remains an open question. We address this problem by introducing a geometric network model without free parameter, finding that both super-linear and sub-linear scaling behaviours can be simultaneously reproduced and that the scaling exponents are exclusively determined by the dimension of the Euclidean space in which the network is embedded. We implement some realistic extensions to the basic model to offer more accurate predictions for cities of various scaling behaviours and the Zipf distribution reported in the literature and observed in our empirical studies. All of the empirical results can be precisely recovered by our model with analytical predictions of all major properties. By virtue of these general findings concerning scaling behaviour, our models with simple mechanisms gain new insights into the evolution and development of complex networked systems.

The compositional dependence of the lowest direct and indirect band gaps in Ge_1-ySn_y alloys has been determined from room-temperature photoluminescence measurements. This technique is particularly attractive for a comparison of the two transitions because distinct features in the spectra can be associated with the direct and indirect gaps. However, detailed modeling of these room temperature spectra is required to extract the band gap values with the high accuracy required to determine the Sn concentration y_c at which the alloy becomes a direct gap semiconductor. For the direct gap, this is accomplished using a microscopic model that allows the determination of direct gap energies with meV accuracy. For the indirect gap, it is shown that current theoretical models are inadequate to describe the emission properties of systems with close indirect and direct transitions. Accordingly, an ad hoc procedure is used to extract the indirect gap energies from the data. For y < 0.1 the resulting direct gap compositional dependence is given by ΔE₀ = −(3.57 ± 0.06)y (in eV). For the indirect gap, the corresponding expression is ΔE_ind = −(1.64 ± 0.10)y (in eV). If a quadratic function of composition is used to express the two transition energies over the entire compositional range 0 ≤ y ≤ 1, the quadratic (bowing) coefficients are found to be b₀ = 2.46 ± 0.06 eV (for E0) and b_ind = 1.03 ± 0.11 eV (for E_ind). These results imply a crossover concentration y_c = $0.073 [+0.007 over -0.006], much lower than early theoretical predictions based on the virtual crystal approximation, but in better agreement with predictions based on large atomic supercells.

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.

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.

Earth-abundant sustainable inorganic thin-film solar cells, independent of precious elements, pivot on a marginal material phase space targeting specific compounds. Advanced materials characterization efforts are necessary to expose the roles of microstructure, chemistry, and interfaces. Herein, the earth-abundant solar cell device, Cu₂ZnSnS_(4-x)Se_x, is reported, which shows a high abundance of secondary phases compared to similarly grown Cu₂ZnSnSe₄.

A challenging problem in network science is to control complex networks. In existing frameworks of structural or exact controllability, the ability to steer a complex network toward any desired state is measured by the minimum number of required driver nodes. However, if we implement actual control by imposing input signals on the minimum set of driver nodes, an unexpected phenomenon arises: due to computational or experimental error there is a great probability that convergence to the final state cannot be achieved. In fact, the associated control cost can become unbearably large, effectively preventing actual control from being realized physically. The difficulty is particularly severe when the network is deemed controllable with a small number of drivers. Here we develop a physical controllability framework based on the probability of achieving actual control. Using a recently identified fundamental chain structure underlying the control energy, we offer strategies to turn physically uncontrollable networks into physically controllable ones by imposing slightly augmented set of input signals on properly chosen nodes. Our findings indicate that, although full control can be theoretically guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control cost to achieve physical control.

Network reconstruction is a fundamental problem for understanding many complex systems with unknown interaction structures. In many complex systems, there are indirect interactions between two individuals without immediate connection but with common neighbors. Despite recent advances in network reconstruction, we continue to lack an approach for reconstructing complex networks with indirect interactions. Here we introduce a two-step strategy to resolve the reconstruction problem, where in the first step, we recover both direct and indirect interactions by employing the Lasso to solve a sparse signal reconstruction problem, and in the second step, we use matrix transformation and optimization to distinguish between direct and indirect interactions. The network structure corresponding to direct interactions can be fully uncovered. We exploit the public goods game occurring on complex networks as a paradigm for characterizing indirect interactions and test our reconstruction approach. We find that high reconstruction accuracy can be achieved for both homogeneous and heterogeneous networks, and a number of empirical networks in spite of insufficient data measurement contaminated by noise. Although a general framework for reconstructing complex networks with arbitrary types of indirect interactions is yet lacking, our approach opens new routes to separate direct and indirect interactions in a representative complex system.

We present two-dimensional Mg(OH)₂ sheets and their vertical heterojunctions with CVD-MoS₂ for the first time as flexible 2D insulators with anomalous lattice vibration and chemical and physical properties. New hydrothermal crystal growth technique enabled isolation of environmentally stable monolayer Mg(OH)₂ sheets. Raman spectroscopy and vibrational calculations reveal that the lattice vibrations of Mg(OH)₂ have fundamentally different signature peaks and dimensionality effects compared to other 2D material systems known to date. Sub-wavelength electron energy-loss spectroscopy measurements and theoretical calculations show that Mg(OH)₂ is a 6 eV direct-gap insulator in 2D, and its optical band gap displays strong band renormalization effects from monolayer to bulk, marking the first experimental confirmation of confinement effects in 2D insulators. Interestingly, 2D-Mg(OH)₂ sheets possess rather strong surface polarization (charge) effects which is in contrast to electrically neutral h-BN materials. Using 2D-Mg(OH)₂ sheets together with CVD-MoS₂ in the vertical stacking shows that a strong change transfer occurs from n-doped CVD-MoS₂ sheets to Mg(OH)₂, naturally depleting the semiconductor, pushing towards intrinsic doping limit and enhancing overall optical performance of 2D semiconductors. Results not only establish unusual confinement effects in 2D-Mg(OH)₂, but also offer novel 2D-insulating material with unique physical, vibrational, and chemical properties for potential applications in flexible optoelectronics.

Transition metal trichalcogenides form a class of layered materials with strong in-plane anisotropy. For example, titanium trisulfide (TiS₃) whiskers are made out of weakly interacting TiS₃ layers, where each layer is made of weakly interacting quasi-one-dimensional chains extending along the b axis. Here we establish the unusual vibrational properties of TiS₃ both experimentally and theoretically. Unlike other two-dimensional systems, the Raman active peaks of TiS₃ have only out-of-plane vibrational modes, and interestingly some of these vibrations involve unique rigid-chain vibrations and S–S molecular oscillations. High-pressure Raman studies further reveal that the A_g^S-S S-S molecular mode has an unconventional negative pressure dependence, whereas other peaks stiffen as anticipated. Various vibrational modes are doubly degenerate at ambient pressure, but the degeneracy is lifted at high pressures. These results establish the unusual vibrational properties of TiS₃ with strong in-plane anisotropy, and may have relevance to understanding of vibrational properties in other anisotropic two-dimensional material systems.

Controlling complex networks has become a forefront research area in network science and engineering. Recent efforts have led to theoretical frameworks of controllability to fully control a network through steering a minimum set of driver nodes. However, in realistic situations not every node is accessible or can be externally driven, raising the fundamental issue of control efficacy: if driving signals are applied to an arbitrary subset of nodes, how many other nodes can be controlled? We develop a framework to determine the control efficacy for undirected networks of arbitrary topology. Mathematically, based on non-singular transformation, we prove a theorem to determine rigorously the control efficacy of the network and to identify the nodes that can be controlled for any given driver nodes. Physically, we develop the picture of diffusion that views the control process as a signal diffused from input signals to the set of controllable nodes. The combination of mathematical theory and physical reasoning allows us not only to determine the control efficacy for model complex networks and a large number of empirical networks, but also to uncover phenomena in network control, e.g., hub nodes in general possess lower control centrality than an average node in undirected networks.