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.

Explosive extrusion of cold material from the interior of icy bodies, or cryovolcanism, has been observed on Enceladus and, perhaps, Europa, Triton, and Ceres. It may explain the observed evidence for a young surface on Charon (Pluto’s surface is masked by frosts). Here, we evaluate prerequisites for cryovolcanism on dwarf planet-class Kuiper belt objects (KBOs). We first review the likely spatial and temporal extent of subsurface liquid, proposed mechanisms to overcome the negative buoyancy of liquid water in ice, and the volatile inventory of KBOs. We then present a new geochemical equilibrium model for volatile exsolution and its ability to drive upward crack propagation. This novel approach bridges geophysics and geochemistry, and extends geochemical modeling to the seldom-explored realm of liquid water at subzero temperatures. We show that carbon monoxide (CO) is a key volatile for gas-driven fluid ascent; whereas CO₂ and sulfur gases only play a minor role. N₂, CH₄, and H₂ exsolution may also drive explosive cryovolcanism if hydrothermal activity produces these species in large amounts (a few percent with respect to water). Another important control on crack propagation is the internal structure: a hydrated core makes explosive cryovolcanism easier, but an undifferentiated crust does not. We briefly discuss other controls on ascent such as fluid freezing on crack walls, and outline theoretical advances necessary to better understand cryovolcanic processes. Finally, we make testable predictions for the 2015 New Horizons flyby of the Pluto-Charon system.

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.

Uncovering the chemical and physical links between natural environments and microbial communities is becoming increasingly amenable owing to geochemical observations and metagenomic sequencing. At the hot spring known as Bison Pool in Yellowstone National Park, the cooling of the water in the outflow channel is associated with an increase in oxidation potential estimated from multiple field-based measurements. Representative groups of proteins whose sequences were derived from metagenomic data also exhibit an increase in average oxidation state of carbon in the protein molecules with distance from the hot-spring source. The energetic requirements of reactions to form selected proteins used in the model were computed using amino-acid group additivity for the standard molal thermodynamic properties of the proteins, and the relative chemical stabilities of the proteins were investigated by varying temperature, pH and oxidation state, expressed as activity of dissolved hydrogen. The relative stabilities of the proteins were found to track the locations of the sampling sites when the calculations included a function for hydrogen activity that increases with temperature and is higher, or more reducing, than values consistent with measurements of dissolved oxygen, sulfide and oxidation-reduction potential in the field. These findings imply that spatial patterns in the amino acid compositions of proteins can be linked, through energetics of overall chemical reactions representing the formation of the proteins, to the environmental conditions at this hot spring, even if microbial cells maintain considerably different internal conditions. Further applications of the thermodynamic calculations are possible for other natural microbial ecosystems.

We have constructed a conceptual model of biogeochemical cycles and metabolic and microbial community shifts within a hot spring ecosystem via coordinated analysis of the “Bison Pool” (BP) Environmental Genome and a complementary contextual geochemical dataset of ∼75 geochemical parameters. 2,321 16S rRNA clones and 470 megabases of environmental sequence data were produced from biofilms at five sites along the outflow of BP, an alkaline hot spring in Sentinel Meadow (Lower Geyser Basin) of Yellowstone National Park. This channel acts as a >22 m gradient of decreasing temperature, increasing dissolved oxygen, and changing availability of biologically important chemical species, such as those containing nitrogen and sulfur. Microbial life at BP transitions from a 92°C chemotrophic streamer biofilm community in the BP source pool to a 56°C phototrophic mat community. We improved automated annotation of the BP environmental genomes using BLAST-based Markov clustering. We have also assigned environmental genome sequences to individual microbial community members by complementing traditional homology-based assignment with nucleotide word-usage algorithms, allowing more than 70% of all reads to be assigned to source organisms. This assignment yields high genome coverage in dominant community members, facilitating reconstruction of nearly complete metabolic profiles and in-depth analysis of the relation between geochemical and metabolic changes along the outflow. We show that changes in environmental conditions and energy availability are associated with dramatic shifts in microbial communities and metabolic function. We have also identified an organism constituting a novel phylum in a metabolic “transition” community, located physically between the chemotroph- and phototroph-dominated sites. The complementary analysis of biogeochemical and environmental genomic data from BP has allowed us to build ecosystem-based conceptual models for this hot spring, reconstructing whole metabolic networks in order to illuminate community roles in shaping and responding to geochemical variability.

Over 100 hot spring sediment samples were collected from 28 sites in 12 areas/regions, while recording as many coincident geochemical properties as feasible (>60 analytes). PCR was used to screen samples for Korarchaeota 16S rRNA genes. Over 500 Korarchaeota 16S rRNA genes were screened by RFLP analysis and 90 were sequenced, resulting in identification of novel Korarchaeota phylotypes and exclusive geographical variants. Korarchaeota diversity was low, as in other terrestrial geothermal systems, suggesting a marine origin for Korarchaeota with subsequent niche-invasion into terrestrial systems. Korarchaeota endemism is consistent with endemism of other terrestrial thermophiles and supports the existence of dispersal barriers. Korarchaeota were found predominantly in >55°C springs at pH 4.7–8.5 at concentrations up to 6.6×10⁶ 16S rRNA gene copies g^-1 wet sediment. In Yellowstone National Park (YNP), Korarchaeota were most abundant in springs with a pH range of 5.7 to 7.0. High sulfate concentrations suggest these fluids are influenced by contributions from hydrothermal vapors that may be neutralized to some extent by mixing with water from deep geothermal sources or meteoric water. In the Great Basin (GB), Korarchaeota were most abundant at spring sources of pH<7.2 with high particulate C content and high alkalinity, which are likely to be buffered by the carbonic acid system. It is therefore likely that at least two different geological mechanisms in YNP and GB springs create the neutral to mildly acidic pH that is optimal for Korarchaeota. A classification support vector machine (C-SVM) trained on single analytes, two analyte combinations, or vectors from non-metric multidimensional scaling models was able to predict springs as Korarchaeota-optimal or sub-optimal habitats with accuracies up to 95%. To our knowledge, this is the most extensive analysis of the geochemical habitat of any high-level microbial taxon and the first application of a C-SVM to microbial ecology.