Faculty and Staff

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.

Sensory systems encode both the static quality of a stimulus (e.g., color or shape) and its kinetics (e.g., speed and direction). The limits with which stimulus kinetics can be resolved are well understood in vision, audition, and somatosensation. However, the maximum temporal resolution of olfactory systems has not been accurately determined. Here, we probe the limits of temporal resolution in insect olfaction by delivering high frequency odor pulses and measuring sensory responses in the antennae. We show that transduction times and pulse tracking capabilities of olfactory receptor neurons are faster than previously reported. Once an odorant arrives at the boundary layer of the antenna, odor transduction can occur within less than 2 ms and fluctuating odor stimuli can be resolved at frequencies more than 100 Hz. Thus, insect olfactory receptor neurons can track stimuli of very short duration, as occur when their antennae encounter narrow filaments in an odor plume. These results provide a new upper bound to the kinetics of odor tracking in insect olfactory receptor neurons and to the latency of initial transduction events in olfaction.

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.

Studies on urban heat island (UHI) have been more than a century after the phenomenon was first discovered in the early 1800s. UHI emerges as the source of many urban environmental problems and exacerbates the living environment in cities. Under the challenges of increasing urbanization and future climate changes, there is a pressing need for sustainable adaptation/mitigation strategies for UHI effects, one popular option being the use of reflective materials. While it is introduced as an effective method to reduce temperature and energy consumption in cities, its impacts on environmental sustainability and large-scale non-local effect are inadequately explored. This paper provides a synthetic overview of potential environmental impacts of reflective materials at a variety of scales, ranging from energy load on a single building to regional hydroclimate. The review shows that mitigation potential of reflective materials depends on a set of factors, including building characteristics, urban environment, meteorological and geographical conditions, to name a few. Precaution needs to be exercised by city planners and policy makers for large-scale deployment of reflective materials before their environmental impacts, especially on regional hydroclimates, are better understood. In general, it is recommended that optimal strategy for UHI needs to be determined on a city-by-city basis, rather than adopting a “one-solution-fits-all” strategy.

Land surface energy balance in a built environment is widely modelled using urban canopy models with representation of building arrays as big street canyons. Modification of this simplified geometric representation, however, leads to challenging numerical difficulties in improving physical parameterization schemes that are deterministic in nature. In this paper, we develop a stochastic algorithm to estimate view factors between canyon facets in the presence of shade trees based on Monte Carlo simulation, where an analytical formulation is inhibited by the complex geometry. The model is validated against analytical solutions of benchmark radiative problems as well as field measurements in real street canyons. In conjunction with the matrix method resolving infinite number of reflections, the proposed model is capable of predicting the radiative exchange inside the street canyon with good accuracy. Modeling of transient evolution of thermal filed inside the street canyon using the proposed method demonstrate the potential of shade trees in mitigating canyon surface temperatures as well as saving of building energy use. This new numerical framework also deepens our insight into the fundamental physics of radiative heat transfer and surface energy balance for urban climate modeling.

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.

We know very little about how soil-borne pollutants such as selenium (Se) can impact pollinators, even though Se has contaminated soils and plants in areas where insect pollination can be critical to the functioning of both agricultural and natural ecosystems. Se can be biotransferred throughout the food web, but few studies have examined its effects on the insects that feed on Se-accumulating plants, particularly pollinators. In laboratory bioassays, we used proboscis extension reflex (PER) and taste perception to determine if the presence of Se affected the gustatory response of honey bee (Apis mellifera L., Hymenoptera: Apidae) foragers. Antennae and proboscises were stimulated with both organic (selenomethionine) and inorganic (selenate) forms of Se that commonly occur in Se-accumulating plants. Methionine was also tested. Each compound was dissolved in 1 M sucrose at 5 concentrations, with sucrose alone as a control. Antennal stimulation with selenomethionine and methionine reduced PER at higher concentrations. Selenate did not reduce gustatory behaviors. Two hours after being fed the treatments, bees were tested for sucrose response threshold. Bees fed selenate responded less to sucrose stimulation. Mortality was higher in bees chronically dosed with selenate compared with a single dose. Selenomethionine did not increase mortality except at the highest concentration. Methionine did not significantly impact survival. Our study has shown that bees fed selenate were less responsive to sucrose, which may lead to a reduction in incoming floral resources needed to support coworkers and larvae in the field. If honey bees forage on nectar containing Se (particularly selenate), reductions in population numbers may occur due to direct toxicity. Given that honey bees are willing to consume food resources containing Se and may not avoid Se compounds in the plant tissues on which they are foraging, they may suffer similar adverse effects as seen in other insect guilds.