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.

Background: Foam rolling has been shown to acutely increase range of motion (ROM) during knee flexion and hip flexion with the experimenter applying an external force, yet no study to date has measured hip extensibility as a result of foam rolling with controlled knee flexion and hip extension moments. The purpose of this study was to investigate the acute effects of foam rolling on hip extension, knee flexion, and rectus femoris length during the modified Thomas test.

Methods: Twenty-three healthy participants (male = 7; female = 16; age = 22 ± 3.3 years; height = 170 ± 9.18 cm; mass = 67.7 ± 14.9 kg) performed two, one-minute bouts of foam rolling applied to the anterior thigh. Hip extension and knee flexion were measured via motion capture before and after the foam rolling intervention, from which rectus femoris length was calculated.

Results: Although the increase in hip extension (change = +1.86° (+0.11, +3.61); z(22) = 2.08; p = 0.0372; Pearson’s r = 0.43 (0.02, 0.72)) was not due to chance alone, it cannot be said that the observed changes in knee flexion (change = −1.39° (−5.53, +2.75); t(22) = −0.70; p = 0.4933; Cohen’s d = − 0.15 (−0.58, 0.29)) or rectus femoris length (change = −0.005 (−0.013, +0.003); t(22) = −1.30; p = 0.2070; Cohen’s d = − 0.27 (−0.70, 0.16)) were not due to chance alone.

Conclusions: Although a small change in hip extension was observed, no changes in knee flexion or rectus femoris length were observed. From these data, it appears unlikely that foam rolling applied to the anterior thigh will improve passive hip extension and knee flexion ROM, especially if performed in combination with a dynamic stretching protocol.

Muscle hypertrophy and atrophy occur frequently as a result of mechanical loading or unloading, with implications for clinical, general, and athletic populations. The effects of muscle hypertrophy and atrophy on force production and joint moments have been previously described. However, there is a paucity of research showing how hypertrophy and atrophy may affect moment arm (MA) lengths. The purpose of this model was to describe the mathematical relationship between the anatomical cross-sectional area (ACSA) of a muscle and its MA length. In the model, the ACSAs of the biceps brachii and brachialis were altered to hypertrophy up to twice their original size and to atrophy to one-half of their original size. The change in MA length was found to be proportional to the arcsine of the square root of the change in ACSA. This change in MA length may be a small but important contributor to strength, especially in sports that require large joint moments at slow joint angular velocities, such as powerlifting. The paradoxical implications of the increase in MA are discussed, as physiological factors influencing muscle contraction velocity appear to favor a smaller MA length for high velocity movements but a larger muscle MA length for low velocity, high force movements.

Background: The purpose of this study was to compare the peak electromyography (EMG) of the most commonly-used position in the literature, the prone bent-leg (90°) hip extension against manual resistance applied to the distal thigh (PRONE), to a novel position, the standing glute squeeze (SQUEEZE).

Methods: Surface EMG electrodes were placed on the upper and lower gluteus maximus of thirteen recreationally active females (age = 28.9 years; height = 164 cm; body mass = 58.2 kg), before three maximum voluntary isometric contraction (MVIC) trials for each position were obtained in a randomized, counterbalanced fashion.

Results: No statistically significant (p < 0.05) differences were observed between PRONE (upper: 91.94%; lower: 94.52%) and SQUEEZE (upper: 92.04%; lower: 85.12%) for both the upper and lower gluteus maximus. Neither the PRONE nor SQUEEZE was more effective between all subjects.

Conclusions: In agreement with other studies, no single testing position is ideal for every participant. Therefore, it is recommended that investigators employ multiple MVIC positions, when possible, to ensure accuracy. Future research should investigate a variety of gluteus maximus MVIC positions in heterogeneous samples.

The modified Thomas test was developed to assess the presence of hip flexion contracture and to measure hip extensibility. Despite its widespread use, to the authors’ knowledge, its criterion reference validity has not yet been investigated. The purpose of this study was to assess the criterion reference validity of the modified Thomas test for measuring peak hip extension angle and hip extension deficits, as defined by the hip not being able to extend to 0º, or neutral. Twenty-nine healthy college students (age = 22.00 ± 3.80 years; height = 1.71 ± 0.09 m; body mass = 70.00 ± 15.60 kg) were recruited for this study. Bland–Altman plots revealed poor validity for the modified Thomas test’s ability to measure hip extension, which could not be explained by differences in hip flexion ability alone. The modified Thomas test displayed a sensitivity of 31.82% (95% CI [13.86–54.87]) and a specificity of 57.14% (95% CI [18.41–90.10]) for testing hip extension deficits. It appears, however, that by controlling pelvic tilt, much of this variance can be accounted for (r = 0.98). When pelvic tilt is not controlled, the modified Thomas test displays poor criterion reference validity and, as per previous studies, poor reliability. However, when pelvic tilt is controlled, the modified Thomas test appears to be a valid test for evaluating peak hip extension angle.