Boundary Control of Coupled Wave Systems with Spatially-Varying Coefficients

This paper considers the stabilization of the coupled wave systems with spatially-varying coefficients.The authors design a state feedback controller by backstepping method.In contrast to the previous work in the literature,the kernel equations become more complicated and the main difficulty lies in proving the existence and uniqueness of the solution to the kernel equations.Firstly,using the backstepping approach,the authors verify the kernel equations,which is a system of coupled hyperbolic equations with spatially-varying coefficients.Then,the existence and uniqueness of the kernel matrices is obtained.Finally,the authors use a Lyapunov function to get the exponential stabilization of the closed-loop system.A numerical example is presented to illustrate the effectiveness of the proposed controller.

Rogue Waves in Nonintegrable KdV-Type Systems

It is proved that rogue waves can be found in Korteweg de-Vries（KdV） systems if real nonintegrable effects, higher order nonlinearity and nonlinear diffusion are considered. Rogue waves can also be formed without modulation instability which is considered as the main formation mechanism of the rogue waves.

THE INTERACTIONS OF SHOCK WAVES OF NONSTRICTLY HYPERBOLIC SYSTEMS

The interaction of shock waves is investigated for the following nonstrictly hyperbolic system: [GRAPHICS] The interaction of shock waves is complicated, with new types of shock waves, and new singula rities in the dependence of interaction on the relative positions of the three states separated by shock waves. Several ideas are introduced to helo organize and clarify the new phenomena.

LoS sensing-based superimposed CSI feedback for UAV-assisted mmWave systems

In Unmanned Aerial Vehicle(UAV)-assisted millimeter Wave(mmWave)systems,Channel State Information(CSI)feedback is critical for the selection of modulation schemes,resource management,beamforming,etc.However,traditional CSI feedback methods lead to significant feedback overhead and energy consumption of the UAV transmitter,therefore shortening the system operation time.To tackle these issues,inspired by superimposed feedback and Integrated Sensing and Communications(ISAC),a Line of Sight(LoS)sensing-based superimposed CSI feedback scheme is proposed.Specifically,on the UAV transmitter side,the Ground-to-UAV(G2U)CSI is superimposed on the UAV-to-Ground(U2G)data to feed back to the ground Base Station(gBS).At the gBS,the dedicated LoS Sensing Network(LoS-SenNet)is designed to sense the U2G CSI in LoS and NLoS scenarios.With the sensed result of LoS-SenNet,the determined G2U CSI from the initial feature extraction will work as the priori information to guide the subsequent operation.Specifically,for the G2U CSI in NLoS,a CSI Recovery Network(CSI-RecNet)and superimposed interference cancellation are developed to recover the G2U CSI and U2G data.As for the LoS scenario,a dedicated LoS Aid Network(LoS-Aid Net)is embedded before the CSI-RecNet and the block of superimposed interference cancellation to highlight the feature of the G2U CSI.Compared with other methods of superimposed CSI feedback,simulation results demonstrate that the proposed feedback scheme effectively improves the recovery accuracy of the G2U CSI and U2G data.Besides,against parameter variations,the proposed feedback scheme presents its robustness.

δ-WAVE FOR 1-D AND 2-D HYPERBOLIC SYSTEMS

Here a new kind of nonlinear wave, which is called δ-wave, is described by some high resolution difference solutions for Riemann problems of one-dimensional (1-D) and two-dimensional (2-D) nonlinear hyperbolic systems in conservation laws. Some phenomena are numerically shown for the solutions of Riemann problems for 2-D gas dynamics systems

Shock fragmentation model for gravitational collapse

A cloud of gas collapsing under gravity will fragment. We present a new theory for this process, in which layers of shocked gas fragment due to their gravitational instability. Our model explains why angular momentum does not inhibit the collapse process. The theory predicts that the fragmentation process produces objects which are significantly smaller than most stars, implying that accretion onto the fragments plays an essential role in determining the initial masses of stars. This prediction is also consistent with the hypothesis that planets can be produced by gravitational collapse.

Global solutions and blow-up for a class of strongly damped wave equations systems

The initial-boundary value problem for semilinear wave equation systems with a strong dissipative term in bounded domain is studied.The existence of global solutions for this problem is proved by using potential well method,and the exponential decay of global solutions is given through introducing an appropriate Lyapunov function.Meanwhile,blow-up of solutions in the unstable set is also obtained.

Laminated Wave Turbulence: Generic Algorithms Ⅱ

The model of laminated wave turbulence puts forth a novel computational problem–construction of fast algorithms for finding exact solutions of Diophantine equations in integers of order 10^(12) and more.The equations to be solved in integers are resonant conditions for nonlinearly interacting waves and their form is defined by the wave dispersion.It is established that for the most common dispersion as an arbitrary function of a wave-vector length two different generic algorithms are necessary:(1)one-class-case algorithm for waves interacting through scales,and(2)two-class-case algorithm for waves interacting through phases.In our previous paper we described the one-class-case generic algorithm and in our present paper we present the two-classcase generic algorithm.

Energy-efficiency based downlink multi-user hybrid beamforming for millimeter wave massive MIMO system

The fifth generation mobile communication（5G） systems can provide Gbit/s data rates from massive multiple-input multiple-output（MIMO） combined with the emerging use of millimeter wavelengths in small heterogeneous cells. This paper develops an energy-efficiency based multi-user hybrid beamforming for downlink millimeter wave（mm Wave） massive MIMO systems. To make better use of directivity gains of the analog beamforming and flexible baseband processing of the digital beamforming, this paper proposes the analog beamforming to select the optimal beam which can maximize the power of the objective user and minimize the interference to all other users. In addition, the digital beamforming maximizes the energy efficiency of the objective user with zero-gradient-based approach. Simulation results show the proposed algorithm provide better bit error rate（BER） performance compared with the traditional hybrid beamforming and obviously improved the sum rate with the increase in the number of users. It is proved that multi-user MIMO（MU-MIMO） can be a perfect candidate for mm Wave massive MIMO communication system. Furthermore, the analog beamforming can mitigate the inter-user interference more effectively with the selection of the optimal beam and the digital beamforming can greatly improve the system performance through flexible baseband processing.

Sufficiency of Kalman's Rank Condition for the Approximate Boundary Controllability on an Annular Domain

In this paper the author establishes the sufficiency of Kalman’s rank condition on the approximate boundary controllability at a finite time for diagonalizable systems on an annular domain in higher dimensional case.