Stability Criterion for Mass Oscillation in the Surge Tank of a Hydropower Station Considering Velocity Head and Throttle Loss

Surge tanks (STs) are important facilities for ensuring the safety of hydropower stations. Reducing the ST size under the premise of ensuring stable mass oscillations within the ST is the main issue. First, according to the basic equations of the mass oscillation for a hydropower station with an ST, a novel expression of the critical stability section of an ST is deduced considering the velocity head and throttle loss. Then, the sensitivity of each influencing factor of the proposed stability criterion is analyzed. Ultimately, through the simulation of small oscillation transients in two case studies, the water level oscillations (WLOs) in an ST based on three stability criteria are compared. The results show that a 20% smaller ST in a hydropower station may result in 10.4% larger oscillations and a 60% smaller ST in a pumped storage power station may result in 14.3% larger oscillations. Compared with the Thoma criterion and the Chinese specification criterion, the stability criterion proposed in this paper can safely reduce the size of the ST since it considers the influence of the velocity head and throttle loss. The proposed stability criterion can provide an important reference for the optimal design of the STs.

Understanding of spatiotemporal congestion patterns: A lattice model with predictive effect and density integral

To further enhance the adaptability of traffic model in actual traffic flow, this paper puts forward a lattice model with considering both the predictive effect and the continuous density of historical information. The critical stability condition is derived from linear stability analysis, and the phase diagram clearly shows that considering the predictive effect and the continuous historical density information is beneficial to reduce traffic congestion. Then, a mKdV equation is obtained by nonlinear analysis, which enable to depict the development process of blocked flow. Finally, the numerical simulation results are confirmed that the predictive effects and continuous historical density information have the ability to suppress traffic congestion.

Laboratory Study on the Stability of Large-Size Graded Crushed Stone under Cyclic Rotating Axial Compression

In this paper, the stability of large-size graded crushed stone used for road base or cushioning under repeated load is investigated. Using an in-house developed device, large-size crushed stone mix was compacted and molded by the vibration and rotary compaction method. Cyclic rotating axial compression was applied, and the shakedown theory was used to study the cumulative deformation of the large-size crushed stone specimens. The effects of gradation parameters on the cumulative strain and stability behavior were analyzed, and the critical stability and failure loads were determined according to the shakedown theory. The test results indicate that there are three obvious instability behavior stages of large-size graded crushed stone under cyclic rotating axial compression: elastic stability, plastic creep, and incremental plastic failure. Large-size graded crushed stone has a higher critical stability load stiffness than conventional-size graded crushed stone. The critical shakedown load of the specimen is mainly affected by the skeleton structure performance, and the critical failure load by the properties of the crushed stone material. Increasing the content and compactness of large-size crushed stone in the specimen can improve the stiffness and stability performance, and to achieve improvements, the content of large-size crushed stone should be controlled between 22% and 26%. The critical shakedown load increases with the increase in the California bearing ratio (CBR) value, while, on the other hand, the CBR value has little relationship with the critical failure load.

Bathymetry and Shallow Seismic Imaging of the 2018 Flank Collapse of Anak Krakatau

The flank failure and collapse of Anak Krakatau on December 22nd, 2018 triggered a destructive tsunami. Whether the prior activity of the volcano led to this collapse, or it was triggered by another means, remains a challenge to understand. This study seeks to investigate the recent volcano submarine mass-landslide deposit and emplacement processes, including the seafloor morphology of the flank collapse and the landslide deposit extent. Bathymetry and sparker seismic data were used during this study. Bathymetry data collected in August, 2019 shows the run-out area and the seafloor landslide deposit morphology. Bathymetry data acquired in May, 2017, is used as the base limit of the collapse to estimate the volume of the flank collapse. Comparisons between seismic data acquired in 2017 and 2019 provide an insight into the landslide emplacement processes, the deposit sequence, and structure below the seafloor. From these results we highlight two areas of the submarine-mass landslide deposit, one proximal to Anak Krakatau island (∼1.6 km) and one distal (∼1.4 km). The resulting analysis suggests that the submarine-mass landslide deposit might be produced by a frontally compressional, faulted, landslide, triggered by the critical stability slope, and due to the recent volcanic activity. Blocky seabed features clearly lie to the southwest of Anak Krakatau, and may represent the collapse blocks of the landslide. The seismic analysis of the data acquired in August, 2019 reveals that the blocky facies extends to ∼1.62 km in the width around Anak Krakatau, and the block thicknesses vary up to 70.4 m. The marine data provides a new insight into the landslide run out and extent, together with the landslide deposit morphology and structure that are not available from satellite imagery or subaerial surveys. We conclude that the landslide run out area southwest of the recent collapse, is ∼7.02 ± 0.21 km2.

Reduction principle at work

The purpose of this informal paper is three-fold: First, filling a gap in the literature, we provide a (necessary and sufficient) principle of linearized stability for nonautonomous difference equations in Banach spaces based on the dichotomy spectrum. Second, complementing the above, we survey and exemplify an ambient nonautonomous and infinite-dimensional center manifold reduction, that is Pliss’s reduction principle suitable for critical stability situations. Third, these results are applied to integrodifference equations of Hammerstein- and Urysohn-type both in C- and Lp -spaces. Specific features of the nonautonomous case are underlined. Yet, for the simpler situation of periodic time-dependence even explicit computations are feasible.