The influence of cell geometry on the Godunov scheme applied to the linear wave equation

By studying the structure of the discrete kernel of the linear acoustic operator discretized with a Godunov scheme, we clearly explain why the behaviour of the Godunov scheme applied to the linear wave equation deeply depends on the space dimension and, especially, on the type of mesh. This approach allows us to explain why, in the periodic case, the Godunov scheme applied to the resolution of the compressible Euler or Navier–Stokes system is accurate at low Mach number when the mesh is triangular or tetrahedral and is not accurate when the mesh is a 2D (or 3D) cartesian mesh. This approach confirms also the fact that a Godunov scheme remains accurate when it is modified by simply centering the discretization of the pressure gradient.     

Synthesis surface effects on the stress and deformation of film/substrate system

The closed-form solutions of bending curvature and stress distribution in film/substrate system with the synthesis surface effect are proposed by minimizing the total potential energy. Effects of the roughness and the residual surface stress on stress in film are addressed. Results reveal that, at a given thickness of the substrate, effects of roughness and residual surface stress on the bending curvature become significant with decreasing the film thickness. The roughing surface will enlarge the magnitudes of bending curvature and film stress. The direction change of residual surface stresses can lead to a reversed bending of film/substrate system.     

Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller

This Letter investigates chaos synchronization of chaotic and hyperchaotic systems. Based on finite-time stability theory, a simple adaptive control method for realizing chaos synchronization in a finite time is proposed. In comparison with previous methods, the present method is not only simple, but could also be easily utilized in application. Numerical simulations are given to illustrate the effectiveness and validity of the proposed approach.     

The N-soliton solution of a two-component modified nonlinear Schrödinger equation

The N-soliton solution is presented for a two-component modified nonlinear Schrödinger equation which describes the propagation of short pulses in birefringent optical fibers. The solution is found to be expressed in terms of determinants. The proof of the solution is carried out by means of an elementary theory of determinants. The generalization of the 2-component system to the multi-component system is discussed as well as a (2+1)-dimensional nonlocal equation arising from its continuum limit.     

Oscillatory expression and variability in p53 regulatory network

The effect of delay, nonlinearity and noise on oscillatory motion is of permanent interest for theoretical and experimental research. Here we explore a negative feedback loop between p53 and Mdm2 with a time delay, which is a key circuit in the response of cells to damage. This circuit shows noisy sustained oscillations in individual human cells following DNA damage, and damped oscillations at the cell population level. We demonstrate the effect of delay on the oscillation, and the correlation in time course. In a multi-species system, the events at different time points which span a time delay are coupled even when the delay is large compared with the other characteristic times of the system. We also clarify that the dynamics at the single-cell level appears to be coherent resonance, and the origin of the damped oscillation at the macroscopic level out of the sustained ones at the single-cell level can be ascribed to the dephasing process which is induced by the interplay between nonlinearity and noise. The findings are consistent with experimental observations and advance our understanding of the dynamics of the p53 network.     

Adaptive control of chaotic systems based on a single layer neural network

This Letter presents an adaptive neural network control method for the chaos control problem. Based on a single layer neural network, the dynamic about the unstable fixed period point of the chaotic system can be adaptively identified without detailed information about the chaotic system. And the controlled chaotic system can be stabilized on the unstable fixed period orbit. Simulation results of Henon map and Lorenz system verify the effectiveness of the proposed control method.     

Extended Fan's Algebraic Method and Its Application to KdV and Variant Boussinesq Equations

An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinear partial differential equations. The key idea of this method is to introduce an auxiliary ordinary differential equation which is regarded as an extended elliptic equation and whose degree r is expanded to the case of r>4. The efficiency of the method is demonstrated by the KdV equation and the variant Boussinesq equations. The results indicate that the method not only offers all solutions obtained by using Fu's and Fan's methods, but also some new solutions.     

A New Statistical Aspect of the Cluster Variation Method for Lattice Systems

This paper presents an alternative statistical way to derive the cluster variation method (CVM) for lattice systems. The formulation is developed for a series of different clusters, each of which is the largest overlap cluster between two clusters of the next larger type. We arrive at the CVM expression of the lattice configuration factor by deriving the number of different ways of distributing clusters of a selected type in the lattice so that they overlap each other at the largest overlap clusters in a physically correct manner. The essential assumption employed is that individual overlapping events are statistically independent of each other. This reveals a new statistical aspect of the CVM: The CVM is based on a Bethe tree of clusters of the selected type.