ASU Scholarship Showcase

The electronic structure of eight zinc-centered porphyrin macrocyclic molecules are investigated using density functional theory for ground-state properties, time-dependent density functional theory (TDDFT) for excited states, and Franck-Condon (FC) analysis for further characterization of the UV-vis spectrum. Symmetry breaking was utilized to find the lowest energy of the excited states for many states in the spectra. To confirm the theoretical modeling, the spectroscopic result from zinc phthalocyanine (ZnPc) is used to compare to the TDDFT and FC result. After confirmation of the modeling, five more planar molecules are investigated: zinc tetrabenzoporphyrin (ZnTBP), zinc tetrabenzomonoazaporphyrin (ZnTBMAP), zinc tetrabenzocisdiazaporphyrin (ZnTBcisDAP), zinc tetrabenzotransdiazaporphyrin (ZnTBtransDAP), and zinc tetrabenzotriazaporphyrin (ZnTBTrAP). The two latter molecules are then compared to their phenylated sister molecules: zinc monophenyltetrabenzotriazaporphyrin (ZnMPTBTrAP) and zinc diphenyltetrabenzotransdiazaporphyrin (ZnDPTBtransDAP). The spectroscopic results from the synthesis of ZnMPTBTrAP and ZnDPTBtransDAP are then compared to their theoretical models and non-phenylated pairs. While the Franck-Condon results were not as illuminating for every B-band, the Q-band results were successful in all eight molecules, with a considerable amount of spectral analysis in the range of interest between 300 and 750 nm. The π-π^* transitions are evident in the results for all of the Q bands, while satellite vibrations are also visible in the spectra. In particular, this investigation finds that, while ZnPc has a D_4h symmetry at ground state, a C_4v symmetry is predicted in the excited-state Q band region. The theoretical results for ZnPc found an excitation energy at the Q-band 0-0 transition of 1.88 eV in vacuum, which is in remarkable agreement with published gas-phase spectroscopy, as well as our own results of ZnPc in solution with Tetrahydrofuran that are provided in this paper.

The number and variety of connectivity estimation methods is likely to continue to grow over the coming decade. Comparisons between methods are necessary to prune this growth to only the most accurate and robust methods. However, the nature of connectivity is elusive with different methods potentially attempting to identify different aspects of connectivity. Commonalities of connectivity definitions across methods upon which base direct comparisons can be difficult to derive. Here, we explicitly define “effective connectivity” using a common set of observation and state equations that are appropriate for three connectivity methods: dynamic causal modeling (DCM), multivariate autoregressive modeling (MAR), and switching linear dynamic systems for fMRI (sLDSf). In addition while deriving this set, we show how many other popular functional and effective connectivity methods are actually simplifications of these equations. We discuss implications of these connections for the practice of using one method to simulate data for another method. After mathematically connecting the three effective connectivity methods, simulated fMRI data with varying numbers of regions and task conditions is generated from the common equation. This simulated data explicitly contains the type of the connectivity that the three models were intended to identify. Each method is applied to the simulated data sets and the accuracy of parameter identification is analyzed. All methods perform above chance levels at identifying correct connectivity parameters. The sLDSf method was superior in parameter estimation accuracy to both DCM and MAR for all types of comparisons.

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.

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.

Background: Carriers of the APOE ε4 allele are at increased risk of developing Alzheimer’s disease (AD), and have been shown to have reduced cerebral metabolic rate of glucose (CMRgl) in the same brain areas frequently affected in AD. These individuals also exhibit reduced plasma levels of apolipoprotein E (apoE) attributed to a specific decrease in the apoE4 isoform as determined by quantification of individual apoE isoforms in APOE ε4 heterozygotes. Whether low plasma apoE levels are associated with structural and functional brain measurements and cognitive performance remains to be investigated.

Methods: Using quantitative mass spectrometry we quantified the plasma levels of total apoE and the individual apoE3 and apoE4 isoforms in 128 cognitively normal APOE ε3/ε4 individuals included in the Arizona APOE cohort. All included individuals had undergone extensive neuropsychological testing and 25 had in addition undergone FDG-PET and MRI to determine CMRgl and regional gray matter volume (GMV).

Results: Our results demonstrated higher apoE4 levels in females versus males and an age-dependent increase in the apoE3 isoform levels in females only. Importantly, a higher relative ratio of apoE4 over apoE3 was associated with GMV loss in the right posterior cingulate and with reduced CMRgl bilaterally in the anterior cingulate and in the right hippocampal area. Additional exploratory analysis revealed several negative associations between total plasma apoE, individual apoE isoform levels, GMV and CMRgl predominantly in the frontal, occipital and temporal areas. Finally, our results indicated only weak associations between apoE plasma levels and cognitive performance which further appear to be affected by sex.

Conclusions: Our study proposes a sex-dependent and age-dependent variation in plasma apoE isoform levels and concludes that peripheral apoE levels are associated with GMV, CMRgl and possibly cognitive performance in cognitively healthy individuals with a genetic predisposition to AD.

Most previous works on complete synchronization of chaotic oscillators focused on the one-channel interaction scheme where the oscillators are coupled through only one variable or a symmetric set of variables. Using the standard framework of master-stability function (MSF), we investigate the emergence of complex synchronization behaviors under all possible configurations of two-channel coupling, which include, for example, all possible cross coupling schemes among the dynamical variables. Utilizing the classic Rössler and Lorenz oscillators, we find a rich variety of synchronization phenomena not present in any previously extensively studied, single-channel coupling configurations. For example, in many cases two coupling channels can enhance or even generate synchronization where there is only weak or no synchronization under only one coupling channel, which has been verified in a coupled neuron system. There are also cases where the oscillators are originally synchronized under one coupling channel, but an additional synchronizable coupling channel can, however, destroy synchronization. Direct numerical simulations of actual synchronization dynamics verify the MSF-based predictions. Our extensive computation and heuristic analysis provide an atlas for synchronization of chaotic oscillators coupled through two channels, which can be used as a systematic reference to facilitate further research in this area.

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking "clustering" phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the "mixed" role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

Background: We introduced a hypometabolic convergence index (HCI) to characterize in a single measurement the extent to which a person’s fluorodeoxyglucose positron emission tomogram (FDG PET) corresponds to that in Alzheimer’s disease (AD). Apolipoprotein E ε4 (APOE ε4) gene dose is associated with three levels of risk for late-onset AD. We explored the association between gene dose and HCI in cognitively normal ε4 homozygotes, heterozygotes, and non-carriers.

Methods: An algorithm was used to characterize and compare AD-related HCIs in cognitively normal individuals, including 36 ε4 homozygotes, 46 heterozygotes, and 78 non-carriers.

Results: These three groups differed significantly in their HCIs (ANOVA, p = 0.004), and there was a significant association between HCIs and gene dose (linear trend, p = 0.001).

Conclusions: The HCI is associated with three levels of genetic risk for late-onset AD. This supports the possibility of using a single FDG PET measurement to help in the preclinical detection and tracking of AD.

Unidirectional glass fiber reinforced polymer (GFRP) is tested at four initial strain rates (25, 50, 100 and 200 s^-1) and six temperatures (−25, 0, 25, 50, 75 and 100 °C) on a servo-hydraulic high-rate testing system to investigate any possible effects on their mechanical properties and failure patterns. Meanwhile, for the sake of illuminating strain rate and temperature effect mechanisms, glass yarn samples were complementally tested at four different strain rates (40, 80, 120 and 160 s^-1) and varying temperatures (25, 50, 75 and 100 °C) utilizing an Instron drop-weight impact system. In addition, quasi-static properties of GFRP and glass yarn are supplemented as references. The stress–strain responses at varying strain rates and elevated temperatures are discussed. A Weibull statistics model is used to quantify the degree of variability in tensile strength and to obtain Weibull parameters for engineering applications.

The Quadrangles Av-11 and Av-12 on Vesta are located at the northern rim of the giant Rheasilvia south polar impact basin. The primary geologic units in Av-11 and Av-12 include material from the Rheasilvia impact basin formation, smooth material and different types of impact crater structures (such as bimodal craters, dark and bright crater ray material and dark ejecta material). Av-11 and Av-12 exhibit almost the full range of mass wasting features observed on Vesta, such as slump blocks, spur-and-gully morphologies and landslides within craters. Processes of collapse, slope instability and seismically triggered events force material to slump down crater walls or scarps and produce landslides or rotational slump blocks. The spur-and-gully morphology that is known to form on Mars is also observed on Vesta; however, on Vesta this morphology formed under dry conditions.