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.

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.

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.

Background: Physical activity (PA) interventions typically include components or doses that are static across participants. Adaptive interventions are dynamic; components or doses change in response to short-term variations in participant's performance. Emerging theory and technologies make adaptive goal setting and feedback interventions feasible.

Objective: To test an adaptive intervention for PA based on Operant and Behavior Economic principles and a percentile-based algorithm. The adaptive intervention was hypothesized to result in greater increases in steps per day than the static intervention.

Methods: Participants (N = 20) were randomized to one of two 6-month treatments: 1) static intervention (SI) or 2) adaptive intervention (AI). Inactive overweight adults (85% women, M = 36.9±9.2 years, 35% non-white) in both groups received a pedometer, email and text message communication, brief health information, and biweekly motivational prompts. The AI group received daily step goals that adjusted up and down based on the percentile-rank algorithm and micro-incentives for goal attainment. This algorithm adjusted goals based on a moving window; an approach that responded to each individual's performance and ensured goals were always challenging but within participants' abilities. The SI group received a static 10,000 steps/day goal with incentives linked to uploading the pedometer's data.

Results: A random-effects repeated-measures model accounted for 180 repeated measures and autocorrelation. After adjusting for covariates, the treatment phase showed greater steps/day relative to the baseline phase (p<.001) and a group by study phase interaction was observed (p = .017). The SI group increased by 1,598 steps/day on average between baseline and treatment while the AI group increased by 2,728 steps/day on average between baseline and treatment; a significant between-group difference of 1,130 steps/day (Cohen's d = .74).

Conclusions: The adaptive intervention outperformed the static intervention for increasing PA. The adaptive goal and feedback algorithm is a “behavior change technology” that could be incorporated into mHealth technologies and scaled to reach large populations.

Background: An evidence-based steps/day translation of U.S. federal guidelines for youth to engage in ≥60 minutes/day of moderate-to-vigorous physical activity (MVPA) would help health researchers, practitioners, and lay professionals charged with increasing youth’s physical activity (PA). The purpose of this study was to determine the number of free-living steps/day (both raw and adjusted to a pedometer scale) that correctly classified children (6–11 years) and adolescents (12–17 years) as meeting the 60-minute MVPA guideline using the 2005–2006 National Health and Nutrition Examination Survey (NHANES) accelerometer data, and to evaluate the 12,000 steps/day recommendation recently adopted by the President’s Challenge Physical Activity and Fitness Awards Program.

Methods: Analyses were conducted among children (n = 915) and adolescents (n = 1,302) in 2011 and 2012. Receiver Operating Characteristic (ROC) curve plots and classification statistics revealed candidate steps/day cut points that discriminated meeting/not meeting the MVPA threshold by age group, gender and different accelerometer activity cut points. The Evenson and two Freedson age-specific (3 and 4 METs) cut points were used to define minimum MVPA, and optimal steps/day were examined for raw steps and adjusted to a pedometer-scale to facilitate translation to lay populations.

Results: For boys and girls (6–11 years) with ≥ 60 minutes/day of MVPA, a range of 11,500–13,500 uncensored steps/day for children was the optimal range that balanced classification errors. For adolescent boys and girls (12–17) with ≥60 minutes/day of MVPA, 11,500–14,000 uncensored steps/day was optimal. Translation to a pedometer-scaling reduced these minimum values by 2,500 step/day to 9,000 steps/day. Area under the curve was ≥84% in all analyses.

Conclusions: No single study has definitively identified a precise and unyielding steps/day value for youth. Considering the other evidence to date, we propose a reasonable ‘rule of thumb’ value of ≥ 11,500 accelerometer-determined steps/day for both children and adolescents (and both genders), accepting that more is better. For practical applications, 9,000 steps/day appears to be a more pedometer-friendly value.

Background: Many studies used the older ActiGraph (7164) for physical activity measurement, but this model has been replaced with newer ones (e.g., GT3X+). The assumption that new generation models are more accurate has been questioned, especially for measuring lower intensity levels. The low-frequency extension (LFE) increases the low-intensity sensitivity of newer models, but its comparability with older models is unknown. This study compared step counts and physical activity collected with the 7164 and GT3X + using the Normal Filter and the LFE (GT3X+N and GT3X+LFE, respectively).

Findings: Twenty-five adults wore 2 accelerometer models simultaneously for 3Âdays and were instructed to engage in typical behaviors. Average daily step counts and minutes per day in nonwear, sedentary, light, moderate, and vigorous activity were calculated. Repeated measures ANOVAs with post-hoc pairwise comparisons were used to compare mean values. Means for the GT3X+N and 7164 were significantly different in 4 of the 6 categories (p < .05). The GT3X+N showed 2041 fewer steps per day and more sedentary, less light, and less moderate than the 7164 (+25.6, -31.2, -2.9 mins/day, respectively). The GT3X+LFE showed non-significant differences in 5 of 6 categories but recorded significantly more steps (+3597 steps/day; p < .001) than the 7164.

Conclusion: Studies using the newer ActiGraphs should employ the LFE for greater sensitivity to lower intensity activity and more comparable activity results with studies using the older models. Newer generation ActiGraphs do not produce comparable step counts to the older generation devices with the Normal filter or the LFE.

Background: Public parks can be an important setting for physical activity promotion, but to increase park use and the activity levels of park users, the crucial attributes related to active park use need to be defined. Not only user characteristics and structural park attributes, but also characteristics of the surrounding neighborhood are important to examine. Furthermore, internationally comparable studies are needed, to find out if similar intervention strategies might be effective worldwide. The main aim of this study was to examine whether the overall number of park visitors and their activity levels depend on study site, neighborhood walkability and neighborhood income.

Methods: Data were collected in 20 parks in Ghent, Belgium and San Diego, USA. Two trained observers systematically coded park characteristics using the Environmental Assessment of Public Recreation Spaces (EAPRS) tool, and park user characteristics using the System for Observing Play and recreation in Communities (SOPARC) tool. Multilevel multiple regression models were conducted in MLwiN 2.25.

Results: In San Diego parks, activity levels of park visitors and number of vigorously active visitors were higher than in Ghent, while the number of visitors walking and the overall number of park visitors were lower. Neighborhood walkability was positively associated with the overall number of visitors, the number of visitors walking, number of sedentary visitors and mean activity levels of visitors. Neighborhood income was positively associated with the overall number of visitors, but negatively with the number of visitors being vigorously active.

Conclusions: Neighborhood characteristics are important to explain park use. Neighborhood walkability-related attributes should be taken into account when promoting the use of existing parks or creating new parks. Because no strong differences were found between parks in high- and low-income neighborhoods, it seems that promoting park use might be a promising strategy to increase physical activity in low-income populations, known to be at higher risk for overweight and obesity.