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.

Introduction: Urbanization can considerably impact animal ecology, evolution, and behavior. Among the new conditions that animals experience in cities is anthropogenic noise, which can limit the sound space available for animals to communicate using acoustic signals. Some urban bird species increase their song frequencies so that they can be heard above low-frequency background city noise. However, the ability to make such song modifications may be constrained by several morphological factors, including bill gape, size, and shape, thereby limiting the degree to which certain species can vocally adapt to urban settings. We examined the relationship between song characteristics and bill morphology in a species (the house finch, Haemorhous mexicanus) where both vocal performance and bill size are known to differ between city and rural animals.

Results: We found that bills were longer and narrower in more disturbed, urban areas. We observed an increase in minimum song frequency of urban birds, and we also found that the upper frequency limit of songs decreased in direct relation to bill morphology.

Conclusions: These findings are consistent with the hypothesis that birds with longer beaks and therefore longer vocal tracts sing songs with lower maximum frequencies because longer tubes have lower-frequency resonances. Thus, for the first time, we reveal dual constraints (one biotic, one abiotic) on the song frequency range of urban animals. Urban foraging pressures may additionally interact with the acoustic environment to shape bill traits and vocal performance.

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.

Vertebrates cannot synthesize carotenoid pigments de novo, so to produce carotenoid-based coloration they must ingest carotenoids. Most songbirds that deposit red carotenoids in feathers, bills, eyes, or skin ingest only yellow or orange dietary pigments, which they oxidize to red pigments via a ketolation reaction. It has been hypothesized that carotenoid ketolation occurs in the liver of vertebrates, but this hypothesis remains to be confirmed. To better understand the role of hepatocytes in the production of ketolated carotenoids in songbirds, we measured the carotenoid content of subcellular components of hepatocytes from wild male house finches (Haemorhous mexicanus) that were molting red, ketocarotenoid-containing feathers (e.g., 3-hydroxy-echinenone). We homogenized freshly collected livers of house finches and isolated subcellular fractions, including mitochondria. We found the highest concentration of ketocarotenoids in the mitochondrial fraction. These observations are consistent with the hypothesis that carotenoid pigments are oxidized on or within hepatic mitochondria, esterified, and then transported to the Golgi apparatus for secretory processing.

Background: The coevolution of male traits and female mate preferences has led to the elaboration and diversification of sexually selected traits; however the mechanisms that mediate trait-preference coevolution are largely unknown. Carotenoid acquisition and accumulation are key determinants of the expression of male sexually selected carotenoid-based coloration and a primary mechanism maintaining the honest information content of these signals. Carotenoids also influence female health and reproduction in ways that may alter the costs and benefits of mate choice behaviors and thus provide a potential biochemical link between the expression of male traits and female preferences. To test this hypothesis, we manipulated the dietary carotenoid levels of captive female house finches (Carpodacus mexicanus) and assessed their mate choice behavior in response to color-manipulated male finches.

Results: Females preferred to associate with red males, but carotenoid supplementation did not influence the direction or strength of this preference. Females receiving a low-carotenoid diet were less responsive to males in general, and discrimination among the colorful males was positively linked to female plasma carotenoid levels at the beginning of the study when the diet of all birds was carotenoid-limited.

Conclusions: Although female preference for red males was not influenced by carotenoid intake, changes in mating responsiveness and discrimination linked to female carotenoid status may alter how this preference is translated into choice. The reddest males, with the most carotenoid rich plumage, tend to pair early in the breeding season. If carotenoid-related variations in female choice behavior shift the timing of pairing, then they have the potential to promote assortative mating by carotenoid status and drive the evolution of carotenoid-based male plumage coloration.

Background: Diet-derived carotenoid pigments are concentrated in the retinas of birds and serve a variety of functions, including photoprotection. In domesticated bird species (e.g., chickens and quail), retinal carotenoid pigmentation has been shown to respond to large manipulations in light exposure and provide protection against photodamage. However, it is not known if or how wild birds respond to ecologically relevant variation in sun exposure.

Methods: We manipulated the duration of natural sunlight exposure and dietary carotenoid levels in wild-caught captive House Finches (Haemorhous mexicanus), then measured carotenoid accumulation and oxidative stress in the retina.

Results: We found no significant effects of sun exposure on retinal levels of carotenoids or lipid peroxidation, in replicate experiments, in winter (Jan–Mar) and spring/summer (May–June). Dietary carotenoid supplementation in the spring/summer experiment led to significantly higher retinal carotenoid levels, but did not affect lipid peroxidation. Carotenoid levels differed significantly between the winter and spring/summer experiments, with higher retinal and lower plasma carotenoid levels in birds from the later experiment.

Conclusion: Our results suggest that variation in the duration of exposure to direct sunlight have limited influence on intraspecific variation in retinal carotenoid accumulation, but that accumulation may track other seasonal–environmental cues and physiological processes.