Convergence to diffusion waves for solutions of Euler equations with time-depending damping on quadrant

This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad \partial_t u + \partial_x p(v) =\displaystyle -\frac{\alpha}{(1+t)^\lambda} u, \end{equation} with null-Dirichlet boundary condition or null-Neumann boundary condition on $u$. We show that the corresponding initial-boundary value problem admits a unique global smooth solution which tends time-asymptotically to the nonlinear diffusion wave. Compared with the previous work about Euler equations with constant coefficient damping, studied by Nishihara and Yang (1999, J. Differential Equations, 156, 439-458), and Jiang and Zhu (2009, Discrete Contin. Dyn. Syst., 23, 887-918), we obtain a general result when the initial perturbation belongs to the same space. In addition, our main novelty lies in the facts that the cut-off points of the convergence rates are different from our previous result about the Cauchy problem. Our proof is based on the classical energy method and the analyses of the nonlinear diffusion wave

Mechanism of the slow-moving landslides in Jurassic red-strata in the Three Gorges Reservoir, China

Landslides in Jurassic red-strata make up a great part of geohazards in the Three Gorges Reservoir (TGR) in China. Most of them begin to move slowly with the accumulated displacement increasing stepwise, which corresponds to seasonal rainfall and 30 m of reservoir water level fluctuation (145 m to 175 m on elevation). We analyzed the movement of 21 slow moving landslides in the Jurassic red-strata in TGR, and found that all these landslides involved two differing processes; one is the sliding process with different shear speeds of soils within the sliding zone (landslide activity), and the other one is in steady state with different durations (dormant state). This means that the soil within the sliding surface may experience shearing at different shear rates and recovery in shear strength during the dormant period. To clarify the mechanism of this kind of movement, we took soil samples from the sliding surface of Xiangshanlu landslide, which occurred on August 30, 2008 in the Jurassic red-strata in TGR, and examined the shear rate dependency and recovery of shear resistance by means of ring shear tests. The results of tests at different shear rates show that the shear strength is positively dependent on the shear rate, and can be recovered within a short consolidation duration after the shearing ceased. By increasing the pore-water pressure (PWP) from the upper layer of the sample, we also examined the initiation of shearing which can simulate the restart of landsliding due to the fluctuation of groundwater level caused by rainfall or changes in reservoir water level. The monitored PWP near the sliding surface revealed that there was a delayed response of PWP near the sliding surface to the applied one. This kind of delayed response in pore-water pressure may provide help for the prediction of landslide occurrence due to rainfall or fluctuation of reservoir water level

Distilling Knowledge from Resource Management Algorithms to Neural Networks: A Unified Training Assistance Approach

As a fundamental problem, numerous methods are dedicated to the optimization of signal-to-interference-plus-noise ratio (SINR), in a multi-user setting. Although traditional model-based optimization methods achieve strong performance, the high complexity raises the research of neural network (NN) based approaches to trade-off the performance and complexity. To fully leverage the high performance of traditional model-based methods and the low complexity of the NN-based method, a knowledge distillation (KD) based algorithm distillation (AD) method is proposed in this paper to improve the performance and convergence speed of the NN-based method, where traditional SINR optimization methods are employed as ``teachers" to assist the training of NNs, which are ``students", thus enhancing the performance of unsupervised and reinforcement learning techniques. This approach aims to alleviate common issues encountered in each of these training paradigms, including the infeasibility of obtaining optimal solutions as labels and overfitting in supervised learning, ensuring higher convergence performance in unsupervised learning, and improving training efficiency in reinforcement learning. Simulation results demonstrate the enhanced performance of the proposed AD-based methods compared to traditional learning methods. Remarkably, this research paves the way for the integration of traditional optimization insights and emerging NN techniques in wireless communication system optimization

Theoretical investigation of bridge seismic responses with pounding under near-fault vertical ground motions

Vertical earthquake loading is normally regarded not as important as its horizontal components and are not explicitly considered in many seismic design codes. However, some previous severe near-fault earthquakes reveal that the vertical ground motion component can be much larger than the horizontal components and may cause serious damage to the bridge structures. This paper theoretically investigates the vertical pounding responses of a two-span continuous bridge subjected to the severe near-fault vertical ground motions. The bridge is simplified as a continuous beam-spring-rod model. The structural wave effect and the vertical pounding between the bridge girder and the supporting bearing are considered, and the theoretical solutions of bridge seismic responses are derived from the expansion of transient wave functions as a series of eigenfunctions. The effects of vertical earthquake and vertical pounding on the bridge bearing, girder and pier are investigated. The numerical results show that the severe vertical earthquake loading may cause the bridge girder to separate from the supporting bearing and hence result in vertical poundings between them when they are in contact again. These vertical poundings can significantly alter the seismic responses of the bridge structure and may cause severe damage to the bridge components such as bridge girder, supporting bearing and bridge pier. Neglecting the influence of vertical earthquake loading may lead to inaccurate estimation of seismic responses of bridge structures, especially when they are subjected to near-fault earthquake with relatively large vertical motion

A Review of Surface Treatments for Sliding Bearings Used at Different Temperature

The boundary lubrication and dry friction of plain bearings at different work temperature are unable to be avoided under the start and stop condition. The poor lubrication is one reason of bearing broken. In order to improve the tribological properties and select the best treatment for different bearings used at different temperature, the studies of different treatment technologies are reviewed in this paper. The review shows that the shortages of bonding fiber woven materials, inlaying solid lubricating materials, electro plating and magnetron sputtering are poor temperature resistance, low load capacity, environment pollution and low production efficiencies respectively. Based on the analyses and summaries, the liquid dope spraying and thermal powder spraying are suggested to deposit coating on the surface of bearing which working temperature is lower than 200 and above 800°C respectively. However, the technology processes, the mechanisms of spraying and self-lubrication materials should be studied further and deeply

SIRT2, ERK and Nrf2 Mediate NAD+ Treatment-Induced Increase in the Antioxidant Capacity of PC12 Cells Under Basal Conditions

NAD+ (oxidized form of nicotinamide adenine dinucleotide) administration is highly beneficial in numerous models of diseases and aging. It is becoming increasingly important to determine if NAD+ treatment may directly increase the antioxidant capacity of cells under basal conditions. In the current study, we tested our hypothesis that NAD+ can directly enhance the antioxidant capacity of cells under basal conditions by using PC12 cells as a cellular model. We found that NAD+ treatment can increase the GSH/GSSG ratios in the cells under basal conditions. NAD+ can also increase both the mRNA and protein level of γ-glutamylcysteine ligase (γ-GCL)—a key enzyme for glutathione synthesis, which appears to be mediated by the NAD+-induced increase in Nrf2 activity. These NAD+-induced changes can be prevented by both SIRT2 siRNA and the SIRT2 inhibitor AGK2. The NAD+-induced changes can also be blocked by the ERK signaling inhibitor U0126. Moreover, the NAD+-induced ERK activation can be blocked by both SIRT2 siRNA and AGK2. Collectively, our study has provided the first evidence that NAD+ can enhance directly the antioxidant capacity of the cells under basal conditions, which is mediated by SIRT2, ERK, and Nrf2. These findings have suggested not only the great nutritional potential of NAD+, but also a novel mechanism underlying the protective effects of the NAD+ administration in the disease models: the NAD+ administration can enhance the resistance of the normal cells to oxidative insults by increasing the antioxidant capacity of the cells