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We consider inverse problems for the first- and half-order time-fractional equation. We establish the stability estimates of Lipschitz type in inverse source and inverse coefficient problems by means of the Carleman estimates. [ABSTRACT FROM AUTHOR]

Locomotive soft robots (SoRos) have gained prominence due to their adaptability. Traditional locomotive SoRo design is based on limb structures inspired by biological organisms and requires human intervention. Evolutionary robotics, designed using evolutionary algorithms (EAs), have shown potential for automatic design. However, EA-based methods face the challenge of high computational cost when considering multiphysics in locomotion, including materials, actuations, and interactions with environments. Here, we present a design approach for pneumatic SoRos that integrates gradient-based topology optimization with multiphysics material point method (MPM) simulations. This approach starts with a simple initial shape (a cube with a central cavity). The topology optimization with MPM then automatically and iteratively designs the SoRo shape. We design two SoRos, one for walking and one for climbing. These SoRos are 3D printed and exhibit the same locomotion features as in the simulations. This study presents an efficient strategy for designing SoRos, demonstrating that a purely mathematical process can produce limb-like structures seen in biological organisms. [ABSTRACT FROM AUTHOR]

The organic conductor κ-(BEDT-TTF)2Cu[N(CN)2]Cl has been studied for the examination of the conducting mechanism of the semiconducting behavior at high temperatures by 13C-NMR spectroscopy. We found that the temperature dependence of the linewidths and the spin-spin relaxation rate T2-1 showed a peak structure characterized by the hyperfine coupling constant in this region, suggesting a connection between ethylene motion and conducting electrons similar to that observed in κ-(BEDT-TTF)2Cu(NCS)2. Although all κ-(BEDT-TTF)2Cu[N(CN)2]Cl salt was thought to be an insulator at high temperature, our findings suggest that all κ-type salts at high temperatures could be in the same phase where the scattering caused by ethylene motion is added to bad metal. [ABSTRACT FROM AUTHOR]

We have performed ¹H NMR and 13C NMR measurements to investigate the coupling between molecular dynamics and the electronic state of β'-(BEDT-TTF)2ICl2. From the 1HNMR measurements, we observed a frequency-dependent anomaly in the nuclear spin-lattice relaxation rate ¹T-11 that originates from the slowing down of the ethylene motion. In the 13C NMR measurements, we found an anomaly in the linewidth of the NMR spectra at around 150 K, which is attributed to a nuclear spin-spin relaxation rate (13T2) anomaly. The magnitudes of the anomalies in the linewidth and in 13T-12 are related to the hyperfine coupling constant. These results suggest that the ethylene motion modulates the molecular orbital of the BEDT-TTF molecules and gives rise to a difference in the orbital energy between the "staggered" and "eclipsed" conformations. We propose that significant coupling exists between the ethylene motion and the electronic state of the molecular dimer and that the ethylene dynamics can trigger the emergence of charge degrees of freedom inside the dimers and cause the dielectric anomaly in β'-(BEDT-TTF)2ICl2. [ABSTRACT FROM AUTHOR]