Wave dynamic processes in cellular detonation reflection from wedges

When the cell width of the incident detonation wave （IDW） is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H2/O2 diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes.

Stochastic Differential Games with Reflection and Related Obstacle Problems for Isaacs Equations

In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations （RBSDEs）. We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bettman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of E1 Karoui, Kapoudjian, Pardoux, Peng and Quenez （1997）, which turns out to be very useful because it allows us to estimate the LP-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.

Performance evaluation of DHRR-RIS based HP design using machine learning algorithms

Reconfigurable Intelligent Surfaces(RIS)have emerged as a promising technology for improving the reliability of massive MIMO communication networks.However,conventional RIS suffer from poor Spectral Efficiency(SE)and high energy consumption,leading to complex Hybrid Precoding(HP)designs.To address these issues,we propose a new low-complexity HP model,named Dynamic Hybrid Relay Reflecting RIS based Hybrid Precoding(DHRR-RIS-HP).Our approach combines active and passive elements to cancel out the downsides of both conventional designs.We first design a DHRR-RIS and optimize the pilot and Channel State Information(CSI)estimation using an adaptive threshold method and Adaptive Back Propagation Neural Network(ABPNN)algorithm,respectively,to reduce the Bit Error Rate(BER)and energy consumption.To optimize the data stream,we cluster them into private and public streams using Enhanced Fuzzy C-Means(EFCM)algorithm,and schedule them based on priority and emergency level.To maximize the sum rate and SE,we perform digital precoder optimization at the Base Station(BS)side using Deep Deterministic Policy Gradient(DDPG)algorithm and analog precoder optimization at the DHRR-RIS using Fire Hawk Optimization(FHO)algorithm.We implement our proposed work using MATLAB R2020a and compare it with existing works using several validation metrics.Our results show that our proposed work outperforms existing works in terms of SE,Weighted Sum Rate(WSR),and BER.