Initial boundary value problem for a class of strongly damped semilinear wave equations with logarithmic nonlinearity

This paper deals with the initial boundary value problem for strongly damped semilinear wave equations with logarithmic nonlinearity $u_{tt}-\Delta u-\Delta u_t={\phi }_p\left(u\right)log\left|u\right|$ in a bounded domain $\Omega \subset {\mathbb{R}}^n$. We discuss the existence, uniqueness and polynomial or exponential energy decay estimates of global weak solutions under some appropriate conditions. Moreover, we derive the finite time blow up results of weak solutions, and give the lower and upper bounds for blow-up time by the combination of the concavity method, perturbation energy method and differential–integral inequality technique.     

On the Motion of Substance in a Channel of a Network: Extended Model and New Classes of Probability Distributions

We discuss the motion of substance in a channel containing nodes of a network. Each node of the channel can exchange substance with: (i) neighboring nodes of the channel, (ii) network nodes which do not belong to the channel, and (iii) environment of the network. The new point in this study is that we assume possibility for exchange of substance among flows of substance between nodes of the channel and: (i) nodes that belong to the network but do not belong to the channel and (ii) environment of the network. This leads to an extension of the model of motion of substance and the extended model contains previous models as particular cases. We use a discrete-time model of motion of substance and consider a stationary regime of motion of substance in a channel containing a finite number of nodes. As results of the study, we obtain a class of probability distributions connected to the amount of substance in nodes of the channel. We prove that the obtained class of distributions contains all truncated discrete probability distributions of discrete random variable ω which can take values 0,1,⋯,N. Theory for the case of a channel containing infinite number of nodes is presented in Appendix A. The continuous version of the discussed discrete probability distributions is described in Appendix B. The discussed extended model and obtained results can be used for the study of phenomena that can be modeled by flows in networks: motion of resources, traffic flows, motion of migrants, etc.     

Nowcasting Avalanches as Earthquakes and the Predictability of Strong Avalanches in the Olami-Feder-Christensen Model

Nowcasting earthquakes, suggested recently as a method to estimate the state of a fault and hence the seismic risk, is based on the concept of natural time. Here, we generalize nowcasting to a prediction method the merits of which are evaluated by means of the receiver operating characteristics. This new prediction method is applied to a simple (toy) model for the waiting (natural) time of the stronger earthquakes, real seismicity, and the Olami-Feder-Christensen earthquake model with interesting results revealing acceptable to excellent or even outstanding performance.     

小孔流速实验中的排水时间和流量系数的研究

本文以水作为理想流体,考虑到水头损失和孔口缩流效应,对小孔流速实验涉及的容器排水问题进行了系统的理论和实验研究.从理论上推导得出了圆柱形容器排水时间的解析解,分析了排水时间和自由液面速度、流量系数之间的规律,提出了排水时间的等效性.实验上,加工了底部开有不同小孔的大型圆柱形容器,测量了容器排水时间随液面高度的变化关系,借助实验结果计算了流量系数值,验证了容器排水时间的等效性关系,实验结果与理论计算符合较好.     

Investigation of electrochemical performance of MgNiO2 prepared by sol-gel synthesis route for aqueous-based supercapacitor application

In this work, we have successfully synthesized MgNiO₂ using a sol-gel wet chemical synthesis technique named MNO - 3. Electrochemical measurements in the presence of aqueous 1 M Li₂SO₄ electrolyte indicate that MNO - 3 samples exhibit a capacitance value of about 30 F/g and an energy density of about 20 Wh/kg. Subsequently, in the experiment involving aqueous 0.5 M Na₂SO₄ electrolyte system, it has been found that the capacitance for MNO - 3 sample is about 34 F/g and the energy density is about 23 Wh/kg for MNO - 3 sample. Finally, in the presence of aqueous-based 1 M Mg(ClO₄)₂ electrolyte, MNO - 3 sample is found to exhibit a capacitance of about 26 F/g and an energy density of about 17 Wh/kg, respectively. In all three electrolyte systems, the MNO -3 sample exhibit a long cycle capacitance retention of greater than 85% for 1000 charge-discharge cycles.     

1,2‐Dimethoxyethane Degradation Thermodynamics in Li−O2 Redox Environments

The reaction thermodynamics of the 1,2‐dimethoxyethane (DME), a model solvent molecule commonly used in electrolytes for Li?O₂ rechargeable batteries, has been studied by first‐principles methods to predict its degradation processes in highly oxidizing environments. In particular, the reactivity of DME towards the superoxide anion O₂^? in oxygen‐poor or oxygen‐rich environments is studied by density functional calculations. Solvation effects are considered by employing a self‐consistent reaction field in a continuum solvation model. The degradation of DME occurs through competitive thermodynamically driven reaction paths that end with the formation of partially oxidized final products such as formaldehyde and methoxyethene in oxygen‐poor environments and methyl oxalate, methyl formate, 1‐formate methyl acetate, methoxy ethanoic methanoic anhydride, and ethylene glycol diformate in oxygen‐rich environments. This chemical reactivity indirectly behaves as an electroactive parasitic process and therefore wastes part of the charge exchanged in Li?O₂ cells upon discharge. This study is the first complete rationale to be reported about the degradation chemistry of DME due to direct interaction with O₂^?/O₂ molecules. These findings pave the way for a rational development of new solvent molecules for Li?O₂ electrolytes.