Faculty and Staff

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.

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.

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.

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.

Oppia Quadrangle Av-10 (288–360°E, ±22°) is a junction of key geologic features that preserve a rough history of Asteroid (4) Vesta and serves as a case study of using geologic mapping to define a relative geologic timescale. Clear filter images, stereo-derived topography, slope maps, and multispectral color-ratio images from the Framing Camera on NASA’s Dawn spacecraft served as basemaps to create a geologic map and investigate the spatial and temporal relationships of the local stratigraphy. Geologic mapping reveals the oldest map unit within Av-10 is the cratered highlands terrain which possibly represents original crustal material on Vesta that was then excavated by one or more impacts to form the basin Feralia Planitia. Saturnalia Fossae and Divalia Fossae ridge and trough terrains intersect the wall of Feralia Planitia indicating that this impact basin is older than both the Veneneia and Rheasilvia impact structures, representing Pre-Veneneian crustal material. Two of the youngest geologic features in Av-10 are Lepida (∼45 km diameter) and Oppia (∼40 km diameter) impact craters that formed on the northern and southern wall of Feralia Planitia and each cross-cuts a trough terrain. The ejecta blanket of Oppia is mapped as ‘dark mantle’ material because it appears dark orange in the Framing Camera ‘Clementine-type’ color-ratio image and has a diffuse, gradational contact distributed to the south across the rim of Rheasilvia. Mapping of surface material that appears light orange in color in the Framing Camera ‘Clementine-type’ color-ratio image as ‘light mantle material’ supports previous interpretations of an impact ejecta origin. Some light mantle deposits are easily traced to nearby source craters, but other deposits may represent distal ejecta deposits (emplaced >5 crater radii away) in a microgravity environment.

We produced two 1:250,000 scale geologic maps of the adjacent quadrangles Av-6 Gegania and Av-7 Lucaria, located in the equatorial region of (4) Vesta (0–144°E, 22°S to 22°N). The mapping is based on clear and color filter images of the Framing Camera (FC) onboard the Dawn spacecraft, which has captured the entire illuminated surface of Vesta with high spatial resolution (up to ∼20 m/pixel), and on a digital terrain model derived from FC imagery. Besides the geologic mapping itself, a secondary purpose of this work is to investigate one of the most prominent morphological features on Vesta, namely the aggregation of several giant equatorial troughs termed the Divalia Fossae, most probably formed during the Rheasilvia impact near Vesta’s south pole. The up to 465 km long and 22 km wide troughs show height differences of up to 5 km between adjacent troughs and ridges. Another imprint of the Rheasilvia impact is the >350 km long and ∼250 km wide swath of ejecta crossing quadrangle Av-6 Gegania. This lobe shows a distinct appearance in FC color ratios and a high albedo in FC images, indicating a mineralogical similarity to material typically found within the Rheasilvia basin, in particular composed of diogenite-rich howardites. Almost the entire northern half of the mapping area shows the oldest surface, being dominated by upper crustal basaltic material. To the south, increasingly younger formations related to the Rheasilvia impact occur, either indicated by the troughs formed by Rheasilvia or by the Rheasilvia ejecta itself. Only medium sized impact craters with diameters less than 22 km occur within the two mapped quadrangles. Some of the craters exhibit ejecta blankets and/or distinctly dark or bright ejecta material in ejecta rays outside and exposures within the crater, and mass-wasting deposits down crater slopes, forming the youngest surfaces.

We used Dawn spacecraft data to identify and delineate geological units and landforms in the Marcia quadrangle of Vesta as a means to assess the role of the large, relatively young impact craters Marcia (∼63 km diam.) and Calpurnia (∼53 km diam.) and their surrounding ejecta field on the local geology. We also investigated a local topographic high with a dark-rayed crater named Aricia Tholus, and the impact crater Octavia that is surrounded by a distinctive diffuse mantle. Crater counts and stratigraphic relations suggest that Marcia is the youngest large crater on Vesta, in which a putative impact melt on the crater floor ranges in age between ∼40 and 60 Ma (depending upon choice of chronology system), and Marcia’s ejecta blanket ranges in age between ∼120 and 390 Ma (depending upon choice of chronology system).

We interpret the geologic units in and around Marcia crater to mark a major vestan time-stratigraphic event, and that the Marcia Formation is one of the geologically youngest formations on Vesta. Marcia crater reveals pristine bright and dark material in its walls and smooth and pitted terrains on its floor. The smooth unit we interpret as evidence of flow of impact melts and (for the pitted terrain) release of volatiles during or after the impact process. The distinctive dark ejecta surrounding craters Marcia and Calpurnia is enriched in OH- or H-bearing phases and has a variable morphology, suggestive of a complex mixture of impact ejecta and impact melts including dark materials possibly derived from carbonaceous chondrite-rich material. Aricia Tholus, which was originally interpreted as a putative vestan volcanic edifice based on lower resolution observations, appears to be a fragment of an ancient impact basin rim topped by a dark-rayed impact crater. Octavia crater has a cratering model formation age of ∼280–990 Ma based on counts of its ejecta field (depending upon choice of chronology system), and its ejecta field is the second oldest unit in this quadrangle. The relatively young craters and their related ejecta materials in this quadrangle are in stark contrast to the surrounding heavily cratered units that are related to the billion years old or older Rheasilvia and Veneneia impact basins and Vesta’s ancient crust preserved on Vestalia Terra.

The purpose of this paper is to introduce the Geologic Mapping of Vesta Special Issue/Section of Icarus, which includes several papers containing geologic maps of the surface of Vesta made to support data analysis conducted by the Dawn Science Team during the Vesta Encounter (July 2011–September 2012). In this paper we briefly discuss pre-Dawn knowledge of Vesta, provide the goals of our geologic mapping campaign, discuss the methodologies and materials used for geologic mapping, review the global geologic context of Vesta, discuss the challenges of mapping the geology of Vesta as a small airless body, and describe the content of the papers in this Special Issue/Section. We conclude with a discussion of lessons learned from our quadrangle-based mapping effort and provide recommendations for conducting mapping campaigns as part of planetary spacecraft nominal missions.