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Organic trisradicals featuring three-fold symmetry have attracted significant interest because of their unique magnetic properties associated with spin frustration. Herein, we describe the synthesis and characterization of a triangular prism-shaped organic cage for which we have coined the name PrismCage6+ and its trisradical trication—TR3(•+). PrismCage6+ is composed of three 4,4'-bipyridinium dications and two 1,3,5-phenylene units bridged by six methylene groups. In the solid state, PrismCage6+ adopts a highly twisted conformation with close to C3 symmetry as a result of encapsulating one PF6− anion as a guest. PrismCage6+ undergoes stepwise reduction to its mono-, di- and trisradical cations in MeCN on account of strong electronic communication between its 4,4'-bipyridinium units. TR3(•+), which is obtained by reduction of PrismCage6+ employing CoCp2, adopts a triangular prism-shaped conformation with close to C2v symmetry in the solid state. Temperature-dependent continuous-wave and nutation frequency-selective EPR spectra of TR3(•+) in frozen N,N-dimethylformamide indicate its doublet ground state. The doublet-quartet energy gap of TR3(•+) is estimated to be −0.06 kcal mol−1 and the critical temperature of spin-state conversion is found to be ca. 50 K, suggesting that it displays pronounced spin-frustration at the molecular level. To the best of our knowledge, this example is the first organic radicalmore »cage to exhibit spin frustration. The trisradical trication of PrismCage6+ opens up new possibilities for fundamental investigations and potential applications in the fields of both organic cages and spin chemistry.« less

Background The distribution of resources can affect animal range sizes, which in turn may alter infectious disease dynamics in heterogenous environments. The risk of pathogen exposure or the spatial extent of outbreaks may vary with host range size. This study examined the range sizes of herbivorous anthrax host species in two ecosystems and relationships between spatial behavior and patterns of disease outbreaks for a multi-host environmentally transmitted pathogen. Methods We examined range sizes for seven host species and the spatial extent of anthrax outbreaks in Etosha National Park, Namibia and Kruger National Park, South Africa, where the main host species and numbers of cases differ. We evaluated host range sizes using the local convex hull method at different temporal scales, within-individual temporal range overlap, and relationships between ranging behavior and species contributions to anthrax cases in each park. We estimated the spatial extent of annual anthrax mortalities and evaluated whether the extent was correlated with case numbers of a given host species. Results Range size differences among species were not linearly related to anthrax case numbers. In Kruger the main host species had small range sizes and high range overlap, which may heighten exposure when outbreaks occur within their ranges.more »However, different patterns were observed in Etosha, where the main host species had large range sizes and relatively little overlap. The spatial extent of anthrax mortalities was similar between parks but less variable in Etosha than Kruger. In Kruger outbreaks varied from small local clusters to large areas and the spatial extent correlated with case numbers and species affected. Case numbers of secondary host species with larger range sizes were positively correlated with the spatial extent of outbreaks in both parks. Conclusions Our results provide new information on the spatiotemporal structuring of ranging movements of anthrax host species in two ecosystems. The results linking anthrax dynamics to host space use are correlative, yet suggest that, though partial and proximate, host range size and overlap may be contributing factors in outbreak characteristics for environmentally transmitted pathogens.« less

We consider the problems of asymptotic stability and robustness in large-scale second-order consensus networks and vehicle platoons in the discrete-time domain. First, we develop a graph-theoretic methodology to design the state feedback law for the second-order consensus networks and vehicle platoons in a discrete-time framework. We analyze the stability of such networks based on algebraic properties of the Laplacian matrices of underlying graphs and each vehicle’s update cycle (also known as the time step). We further provide a necessary and sufficient condition of stability of a linear second-order consensus network in the discrete-time domain. Moreover, we evaluate the robustness of the consensus networks by employing the expected value of the steady-state dispersion of the state of the entire network, also known as squared H2-norm, as a performance measure. We show the connection between performance measures with respect to network size, connectivity, and the update cycle. The main contribution of this work is that we provide a formal framework to quantify the relation between scaling performance measures and restrictions of the vehicles’ update cycles. Specifically, we show that denser networks (i.e., networks with more communications/edges) require faster agents (i.e., smaller update cycles) to outperform or achieve the same level of robustnessmore »as sparse networks (i.e., networks with fewer communications/edges).« less

In this study, an AR-based mobile learning application is proposed to assist online civil engineering course learning during the COVID-19 pandemic. A quasi-experiment has been conducted, and feedback from both the teacher and students has been analysed to examine the effectiveness of the proposed approach in terms of learning achievements. The subjects were 46 sophomores who majored in civil engineering in one class taught by one instructor in a southern U.S. state university. The quasi-experimental results showed that the proposed approach could not significantly improve the students’ online learning achievements. However, the feedbacks brought some explanation to this non-significant result. They indicated that students found this mobile AR app to be an interesting, helpful, practical, and effective approach in their online learning that helped them gain more in-depth knowledge than traditional teacher-centred classroom instruction.

Dynamic and steady-state aspects of wave propagation are deeply connected in lossless open systems ‎in which the scattering matrix is unitary. There is then an equivalence among the energy excited within ‎the medium through all channels, the Wigner time delay, which is the sum of dwell times in all ‎channels coupled to the medium, and the density of states. But these equivalences fall away in the ‎presence of material loss or gain. In this paper, we use microwave measurements, numerical ‎simulations, and theoretical analysis to discover the changing relationships among fundamental wave ‎properties with loss and gain, and their dependence upon dimensionality and spectral overlap. We ‎begin with the demonstrations that the transmission time in random 1D media is equal to the density ‎of states even in the presence of ultrastrong absorption and that its ensemble average is independent ‎of the strengths of scattering and absorption. In contrast, the Wigner time becomes imaginary in the ‎presence of loss, with real and imaginary parts that fall with absorption. In multichannel media, the ‎transmission time remains equal to the density of states and is independent of the scattering strength ‎in unitary systems but falls with absorption to a degree that increases withmore »the strengths of absorption ‎and scattering, and the number of channels coupled to the medium. We show that the relationships ‎between key propagation variables in non-Hermitian systems can be understood in terms of the ‎singularities of the phase of the determinant of the transmission matrix. The poles of the transmission ‎matrix are the same as those of the scattering matrix, but the transmission zeros are fundamentally ‎different. Whereas the zeros of the scattering matrix are the complex conjugates of the poles, the ‎transmission zeros are topological: in unitary systems they occur only singly on the real axis or as ‎conjugate pairs. We follow the evolution and statistics of zeros in the complex plane as random ‎samples are deformed. The sensitivity of the spacing of zeros in the complex plane with deformation ‎of the sample has a square-root singularity at a zero point at which two single zeros and a complex ‎pair interconvert. The transmission time is a sum of Lorentzian functions associated with poles and ‎zeros. The sum over poles is the density of states with an average that is independent of scattering ‎and dissipation. But the sum over zeros changes with loss, gain, scattering strength and the number of ‎channels in ways that make it possible to control ultranarrow spectral features in transmission and ‎transmission time. We show that the field, including the contribution of the still coherent incident ‎wave, is a sum over modal partial fractions with amplitudes that are independent of loss and gain. The ‎energy excited may be expressed in terms of the resonances of the medium and is equal to the dwell ‎time even in the presence of loss or gain.‎« less

We combine state-of-the-art oxide epitaxial growth by hybrid molecular beam epitaxy with transport, x-ray photoemission, and surface diffraction, along with classical and first-principles quantum mechanical modeling to investigate the nuances of insulating layer formation in otherwise high-mobility homoepitaxial n-SrTiO 3 (001) films. Our analysis points to charge immobilization at the buried n-SrTiO 3 /undoped SrTiO 3 (001) interface as well as within the surface contamination layer resulting from air exposure as the drivers of electronic dead-layer formation. As Fermi level equilibration occurs at the surface and the buried interface, charge trapping reduces the sheet carrier density ( n 2 D ) and renders the n-STO film insulating if n 2 D falls below the critical value for the metal-to-insulator transition.