ASU Scholarship Showcase

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.

The interplay between individual behaviors and epidemic dynamics in complex networks is a topic of recent interest. In particular, individuals can obtain different types of information about the disease and respond by altering their behaviors, and this can affect the spreading dynamics, possibly in a significant way. We propose a model where individuals' behavioral response is based on a generic type of local information, i.e., the number of neighbors that has been infected with the disease. Mathematically, the response can be characterized by a reduction in the transmission rate by a factor that depends on the number of infected neighbors. Utilizing the standard susceptible-infected-susceptible and susceptible-infected-recovery dynamical models for epidemic spreading, we derive a theoretical formula for the epidemic threshold and provide numerical verification. Our analysis lays on a solid quantitative footing the intuition that individual behavioral response can in general suppress epidemic spreading. Furthermore, we find that the hub nodes play the role of “double-edged sword” in that they can either suppress or promote outbreak, depending on their responses to the epidemic, providing additional support for the idea that these nodes are key to controlling epidemic spreading in complex networks.

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.

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.

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.

Widespread contamination of groundwater by chlorinated ethenes and their biological dechlorination products necessitates the reliable monitoring of liquid matrices; current methods approved by the U.S. Environmental Protection Agency (EPA) require a minimum of 5 mL of sample volume and cannot simultaneously detect all transformative products. This paper reports on the simultaneous detection of six chlorinated ethenes and ethene itself, using a liquid sample volume of 1 mL by concentrating the compounds onto an 85-µm carboxen-polydimenthylsiloxane solid-phase microextraction fiber in 5 min and subsequent chromatographic analysis in 9.15 min. Linear increases in signal response were obtained over three orders of magnitude (∼0.05 to ∼50 µM) for simultaneous analysis with coefficient of determination (R²) values of ≥ 0.99. The detection limits of the method (1.3–6 µg/L) were at or below the maximum contaminant levels specified by the EPA. Matrix spike studies with groundwater and mineral medium showed recovery rates between 79–108%. The utility of the method was demonstrated in lab-scale sediment flow-through columns assessing the bioremediation potential of chlorinated ethene-contaminated groundwater. Owing to its low sample volume requirements, good sensitivity and broad target analyte range, the method is suitable for routine compliance monitoring and is particularly attractive for interpreting the bench-scale feasibility studies that are commonly performed during the remedial design stage of groundwater cleanup projects.

Dehalococcoides mccartyi strains are of particular importance for bioremediation due to their unique capability of transforming perchloroethene (PCE) and trichloroethene (TCE) to non-toxic ethene, through the intermediates cis-dichloroethene (cis-DCE) and vinyl chloride (VC). Despite the widespread environmental distribution of Dehalococcoides, biostimulation sometimes fails to promote dechlorination beyond cis-DCE. In our study, microcosms established with garden soil and mangrove sediment also stalled at cis-DCE, albeit Dehalococcoides mccartyi containing the reductive dehalogenase genes tceA, vcrA and bvcA were detected in the soil/sediment inocula. Reductive dechlorination was not promoted beyond cis-DCE, even after multiple biostimulation events with fermentable substrates and a lengthy incubation.

However, transfers from microcosms stalled at cis-DCE yielded dechlorination to ethene with subsequent enrichment cultures containing up to 10⁹ Dehalococcoides mccartyi cells mL^-1. Proteobacterial classes which dominated the soil/sediment communities became undetectable in the enrichments, and methanogenic activity drastically decreased after the transfers. We hypothesized that biostimulation of Dehalococcoides in the cis-DCE-stalled microcosms was impeded by other microbes present at higher abundances than Dehalococcoides and utilizing terminal electron acceptors from the soil/sediment, hence, outcompeting Dehalococcoides for H₂. In support of this hypothesis, we show that garden soil and mangrove sediment microcosms bioaugmented with their respective cultures containing Dehalococcoides in high abundance were able to compete for H² for reductive dechlorination from one biostimulation event and produced ethene with no obvious stall. Overall, our results provide an alternate explanation to consolidate conflicting observations on the ubiquity of Dehalococcoides mccartyi and occasional stalling of dechlorination at cis-DCE; thus, bringing a new perspective to better assess biological potential of different environments and to understand microbial interactions governing bioremediation.

Resource allocation takes place in various types of real-world complex systems such as urban traffic, social services institutions, economical and ecosystems. Mathematically, the dynamical process of resource allocation can be modeled as minority games. Spontaneous evolution of the resource allocation dynamics, however, often leads to a harmful herding behavior accompanied by strong fluctuations in which a large majority of agents crowd temporarily for a few resources, leaving many others unused. Developing effective control methods to suppress and eliminate herding is an important but open problem. Here we develop a pinning control method, that the fluctuations of the system consist of intrinsic and systematic components allows us to design a control scheme with separated control variables. A striking finding is the universal existence of an optimal pinning fraction to minimize the variance of the system, regardless of the pinning patterns and the network topology. We carry out a generally applicable theory to explain the emergence of optimal pinning and to predict the dependence of the optimal pinning fraction on the network topology. Our work represents a general framework to deal with the broader problem of controlling collective dynamics in complex systems with potential applications in social, economical and political systems.

Background: Buffering to achieve pH control is crucial for successful trichloroethene (TCE) anaerobic bioremediation. Bicarbonate (HCO3−) is the natural buffer in groundwater and the buffer of choice in the laboratory and at contaminated sites undergoing biological treatment with organohalide respiring microorganisms. However, HCO3− also serves as the electron acceptor for hydrogenotrophic methanogens and hydrogenotrophic homoacetogens, two microbial groups competing with organohalide respirers for hydrogen (H2). We studied the effect of HCO3− as a buffering agent and the effect of HCO3−-consuming reactions in a range of concentrations (2.5-30 mM) with an initial pH of 7.5 in H2-fed TCE reductively dechlorinating communities containing Dehalococcoides, hydrogenotrophic methanogens, and hydrogenotrophic homoacetogens.

Results: Rate differences in TCE dechlorination were observed as a result of added varying HCO3− concentrations due to H2-fed electrons channeled towards methanogenesis and homoacetogenesis and pH increases (up to 8.7) from biological HCO3− consumption. Significantly faster dechlorination rates were noted at all HCO3− concentrations tested when the pH buffering was improved by providing 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) as an additional buffer. Electron balances and quantitative PCR revealed that methanogenesis was the main electron sink when the initial HCO3− concentrations were 2.5 and 5 mM, while homoacetogenesis was the dominant process and sink when 10 and 30 mM HCO3− were provided initially.

Conclusions: Our study reveals that HCO3− is an important variable for bioremediation of chloroethenes as it has a prominent role as an electron acceptor for methanogenesis and homoacetogenesis. It also illustrates the changes in rates and extent of reductive dechlorination resulting from the combined effect of electron donor competition stimulated by HCO3− and the changes in pH exerted by methanogens and homoacetogens.