Synchronization criteria for multiple memristor-based neural networks with time delay and inertial term

This present work uses different methods to synchronize the inertial memristor systems with linear coupling. Firstly, the mathematical model of inertial memristor-based neural networks(IMNNs) with time delay is proposed, where the coupling matrix satisfies the diffusion condition, which can be symmetric or asymmetric. Secondly, by using differential inclusion method and Halanay inequality, some algebraic self-synchronization criteria are obtained. Then, via constructing effective Lyapunov functional, designing discontinuous control algorithms, some new sufficient conditions are gained to achieve synchronization of networks. Finally, two illustrative simulations are provided to show the validity of the obtained results, which cannot be contained by each other.

Pointwise Estimate of Cahn-Hilliard Equation with Inertial Term in R^(3)

Cauchy problem of Cahn-Hilliard equation with inertial term in three-dimensional space is considered.Using delicate analysis of its Green function and its convolution with nonlinear term,pointwise decay rate is obtained.

Energy Spectrum of Turbulent Velocity Pulsations at Arbitrary Values of Fluid Viscosity

The problem of calculating the energy spectrum of turbulent velocity pulsations in the case of homogeneous isotropic and stationary turbulence is considered. The domain of turbulent energy production is treated as “a black box” on which boundary the spectral energy flux is given. It is assumed that the spectrum is formatted due to intermodal interactions being local in the wave-number space that leads to a cascade mechanism of energy transfer along the wave-number spectrum and the possibility of using the renormalization-group method related to the Markovian features of the process under consideration. The obtained formula for energy spectrum is valid in a wide wave-number range and at arbitrary values of fluid viscosity. It is shown that in functional formulation of the statistical theory of turbulence, the procedure of separating local intermodal interactions, which govern energy transfer (straining effect), and filtering out nonlocal interactions, which have no influence on energy transfer (sweeping effect), is directly described without providing additional arguments or conjectures commonly used in the renormalization-group analysis of turbulent spectra.

Numerical study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets

A study on the resistance of rigid projectiles penetrating into semi-infinite concrete targets is performed in this paper.Experimental data are analyzed to examine the penetration resistance during various stages of the penetration process.A numerical tool using AUTODYN hydrocode is applied in the study.The numerical results on both deceleration-time history and depth of penetration of projectiles are in good agreement with experimental data,which demonstrate the feasibility of the numerical model in these conditions.Based on the numerical model with a two-staged pre-drilled hole,the rigid projectile penetration in tunneling stage is studied for concrete targets with different strengths in a wide range of impact velocities.The results show that the penetration in tunnel stage can be divided into two different cases in terms of initial impact velocity.In the first case,when the impact velocity is approximately less than 600 m/s,the deceleration depends on initial impact velocity.In the second case,when the impact velocity is greater than 600 m/s,the effect of target inertia becomes apparent,which agrees with commonly used concrete penetration resistance equations based on cavity expansion model.