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The magnitude‐frequency distribution (MFD) describes the relative proportion of earthquake magnitudes and provides vital information for seismic hazard assessment. Theb‐value, derived from the MFD, is commonly used to estimate the probability that a future earthquake will exceed a specified magnitude threshold. Improved MFD andb‐value estimates are of great importance in the central and eastern United States where high volumes of fluid injection have contributed to a significant rise in seismicity over the last decade. In this study, we recalculate the magnitudes of 8,775 events for the 2011 Prague, Oklahoma sequence using a relative magnitude approach that depends only on waveform data to calculate magnitudes. We also compare the distribution of successive magnitude differences to the MFD and show that a combination of the magnitude difference distribution (MDFD) and relative magnitudes yields a reliable estimate ofb‐value. Using the MDFD and relative magnitudes, we examine the temporal and spatial variations in theb‐value and show thatb‐value ranges between ∼0.6 and 0.85 during the aftershock sequence for at least 5 months after theM5.7 mainshock, though areas surrounding the northeast part of the sequence experience higherb‐values (0.7–0.85) than the southwestern part of the Meeker‐Prague fault whereb‐value is the lowest (0.6–0.7). We also identify a cluster of off‐fault events with the highestb‐values in the catalog (0.85). These new estimates of MFD andb‐value will contribute to understanding of the relations between induced and tectonic earthquake sequences and promote discussion regarding the use ofb‐value in induced seismic hazard estimation.

 

The past ∼200 million years of Earth's geomagnetic field behavior have been recorded within oceanic basalts, many of which are only accessible via scientific ocean drilling. Obtaining the best possible paleomagnetic measurements from such valuable samples requires an a priori understanding of their magnetic mineralogies when choosing the most appropriate protocol for stepwise demagnetization experiments (either alternating field or thermal). Here, we present a quick, and non‐destructive method that utilizes the amplitude‐dependence of magnetic susceptibility to screen submarine basalts prior to choosing a demagnetization protocol, whenever conducting a pilot study or other detailed rock‐magnetic characterization is not possible. We demonstrate this method using samples acquired during International Ocean Discovery Program Expedition 391. Our approach is rooted in the observation that amplitude‐dependent magnetic susceptibility is observed in basalt samples whose dominant magnetic carrier is multidomain titanomagnetite (∼TM_60–65, (Ti_0.60–0.65Fe_0.35–0.40)Fe₂O₄). Samples with low Ti contents within titanomagnetite or samples that have experienced a high degree of oxidative weathering do not display appreciable amplitude dependence. Due to their low Curie temperatures, basalts that possess amplitude‐dependence should ideally be demagnetized either using alternating fields or via finely‐spaced thermal demagnetization heating steps below 300°C. Our screening method can enhance the success rate of paleomagnetic studies of oceanic basalt samples.

 

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 radical 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. 

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 robustness as sparse networks (i.e., networks with fewer communications/edges). 

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. 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.