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In this paper, a discrete Markov chain model is developed to describe the inventory at a bike share station. The uniqueness of solutions is first studied. Then the model calibration is considered by investigating a constrained optimization problem. Numerical simulations involving real data are conducted to demonstrate the model effectiveness as well. 

Strain-sensitive Ba x Sr 1− x TiO 3 perovskite systems are widely used because of their superior nonlinear dielectric behaviors. In this research, new heterostructures including paraelectric Ba 0.5 Sr 0.5 TiO 3 (BSTO) and ferroelectric BaTiO 3 (BTO) materials were epitaxially fabricated on flexible muscovite substrate. Through simple bending, the application of mechanical force can regulate the dielectric constant of BSTO from −77 to 36% and the channel current of BTO-based ferroelectric field effect transistor by two orders. The detailed mechanism was studied through the exploration of phase transition and determination of band structure. In addition, the phase-field simulations were implemented to provide theoretical support. This research opens a new avenue for mechanically controllable components based on high-quality oxide heteroepitaxy. 

The Pliocene Epoch (∼5.3–2.6 million years ago, Ma) was characterized by a warmer than present climate with smaller Northern Hemisphere ice sheets, and offers an example of a climate system in long‐term equilibrium with current or predicted near‐future atmospheric CO₂concentrations (pCO₂). A long‐term trend of ice‐sheet expansion led to more pronounced glacial (cold) stages by the end of the Pliocene (∼2.6 Ma), known as the “intensification of Northern Hemisphere Glaciation” (iNHG). We assessed the spatial and temporal variability of ocean temperatures and ice‐volume indicators through the late Pliocene and early Pleistocene (from 3.3 to 2.4 Ma) to determine the character of this climate transition. We identified asynchronous shifts in long‐term means and the pacing and amplitude of shorter‐term climate variability, between regions and between climate proxies. Early changes in Antarctic glaciation and Southern Hemisphere ocean properties occurred even during the mid‐Piacenzian warm period (∼3.264–3.025 Ma) which has been used as an analog for future warming. Increased climate variability subsequently developed alongside signatures of larger Northern Hemisphere ice sheets (iNHG). Yet, some regions of the ocean felt no impact of iNHG, particularly in lower latitudes. Our analysis has demonstrated the complex, non‐uniform and globally asynchronous nature of climate changes associated with the iNHG. Shifting ocean gateways and ocean circulation changes may have pre‐conditioned the later evolution of ice sheets with falling atmosphericpCO₂. Further development of high‐resolution, multi‐proxy reconstructions of climate is required so that the full potential of the rich and detailed geological records can be realized.

 

ABSTRACT We present a detection of the splashback feature around galaxy clusters selected using the Sunyaev–Zel’dovich (SZ) signal. Recent measurements of the splashback feature around optically selected galaxy clusters have found that the splashback radius, rsp, is smaller than predicted by N-body simulations. A possible explanation for this discrepancy is that rsp inferred from the observed radial distribution of galaxies is affected by selection effects related to the optical cluster-finding algorithms. We test this possibility by measuring the splashback feature in clusters selected via the SZ effect in data from the South Pole Telescope SZ survey and the Atacama Cosmology Telescope Polarimeter survey. The measurement is accomplished by correlating these cluster samples with galaxies detected in the Dark Energy Survey Year 3 data. The SZ observable used to select clusters in this analysis is expected to have a tighter correlation with halo mass and to be more immune to projection effects and aperture-induced biases, potentially ameliorating causes of systematic error for optically selected clusters. We find that the measured rsp for SZ-selected clusters is consistent with the expectations from simulations, although the small number of SZ-selected clusters makes a precise comparison difficult. In agreement with previous work, when using optically selected redMaPPer clusters with similar mass and redshift distributions, rsp is ∼2σ smaller than in the simulations. These results motivate detailed investigations of selection biases in optically selected cluster catalogues and exploration of the splashback feature around larger samples of SZ-selected clusters. Additionally, we investigate trends in the galaxy profile and splashback feature as a function of galaxy colour, finding that blue galaxies have profiles close to a power law with no discernible splashback feature, which is consistent with them being on their first infall into the cluster.