Optimized Group Velocity Control Scheme and DNS of Decaying Compressible Turbulence of Relative High Turbulent Mach Number

To overcome the difficulty in the DNS of compressible turbulence at high turbulent Mach number, a new difference scheme called GVC8 is developed. We have succeeded in the direct numerical simulation of decaying compressible turbulence up to turbulent Mach number 0.95. The statistical quantities thus obtained at lower turbulent Mach number agree well with those from previous authors with the same initial conditions, but they are limited to simulate at lower turbulent Mach numbers due to the so-called start-up problem. The energy spectrum and coherent structure of compressible turbulent flow are analysed. The scaling law of compressible turbulence is studied. The computed results indicate that the extended self-similarity holds in decaying compressible turbulence despite the occurrence of shocklets, and compressibility has little effects on relative scaling exponents when turbulent Mach number is not very high.

Vibration of an Adhered Microbeam Under a Periodically Shaking Electrical Force

The vibration analysis of an adhered S-shaped microbeam under alternating sinusoidal voltage is presented. The shaking force is the electrical force due to the sinusoidal voltage. During vibration, both the microbeam deflection and the adhesion length keep changing. The microbeam deflection and adhesion length are numerically determined by the iteration method. As the adhesion length keeps changing, the domain of the equation of motion for the microbeam (unadhered part) changes correspondingly, which results in changes of the structure natural frequencies. For this reason, the system can never reach a steady state. The transient behaviors of the microbeam under different shaking frequencies are compared. We deliberately choose the initial conditions to compare our dynamic results with the existing static theory. The paper also analyzes the changing behavior of adhesion length during vibration and an asymmetric pattern of adhesion length change is revealed, which may be used to guide the dynamic de-adhering process. The abnormal behavior of the adhered microbeam vibrating at almost the same frequency under two quite different shaking frequencies is also shown. The Galerkin method is used to discretize the equation of motion and its convergence study is also presented. The model is only applicable in the case that the peel number is equal to 1. Some other model limitations are also discussed.

Behaviour analysis of numerical solutions and simulation of coherent structures in compressible mixing layers

For understanding the correctness of simulations the behaviour of numerical solutions is analysed, Tn order to improve the accuracy of solutions three methods are presented. The method with GVC (group velocity control) is used to simulate coherent structures in compressible mixing layers. The effect of initial conditions for the mixing layer with convective Mach number 0.8 on coherent structures is discussed. For the given initial conditions two types of coherent structures in the mixing layer are obtained.

First-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems

An n degree-of-freedom Hamiltonian system with r (1¡r¡n) independent 0rst integrals which are in involution is calledpartially integrable Hamiltonian system. A partially integrable Hamiltonian system subject to light dampings andweak stochastic excitations is called quasi-partially integrable Hamiltonian system. In the present paper, the procedures for studying the 0rst-passage failure and its feedback minimization of quasi-partially integrable Hamiltonian systems are proposed. First, the stochastic averaging methodfor quasi-partially integrable Hamiltonian systems is brie4y reviewed. Then, basedon the averagedIt ˆo equations, a backwardKolmogorov equation governing the conditional reliability function, a set of generalized Pontryagin equations governing the conditional moments of 0rst-passage time and their boundary and initial conditions are established. After that, the dynamical programming equations and their associated boundary and 0nal time conditions for the control problems of maximization of reliability andof maximization of mean 0rst-passage time are formulated. The relationship between the backwardKolmogorov equation andthe dynamical programming equation for reliability maximization, andthat between the Pontryagin equation andthe dynamical programming equation for maximization of mean 0rst-passage time are discussed. Finally, an example is worked out to illustrate the proposed procedures and the e9ectiveness of feedback control in reducing 0rst-passage failure.

Thermocapillary Migration Of Nondeformable Drops

In this paper, we present a numerical study on the thermocapillary migration of drops. The Navier-Stokes equations coupled with the energy conservation equation are solved by the finite-difference front-tracking scheme. The axisymmetric model is adopted in Our simulations, and the drops are assumed to be perfectly spherical and nondeformable. The benchmark simulation starts from the classical initial condition with a uniform temperature gradient. The detailed discussions and physical explanations of migration phenomena are presented for the different values of (1) the Marangoni numbers and Reynolds numbers of continuous phases and drops and (2) the ratios of drop densities and specific heats to those of continuous phases. It is found that fairly large Marangoni numbers may lead to fluctuations in drop velocities at the beginning part of simulations. Finally, we also discuss the influence of initial conditions on the thermocapillary migrations. (C) 2008 American Institute of Physics.

Synchronization of modified Chua's circuit with x vertical bar x vertical bar function

This paper considers the chaos synchronization of the modified Chua's circuit with x vertical bar x vertical bar function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be synchronized using active control when the values of parameters both in drive system and response system are known aforehand. Furthermore, based on Lyapunov stability theory we propose an adaptive active control approach to make the states of two identical Chua systems with unknown constant parameters asymptotically synchronized. Moreover the designed controller is independent of those unknown parameters. Numerical simulations are given to validate the proposed synchronization approach.

Nonlinear dynamics of atomic force microscopy with intermittent contact

When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown. (c) 2006 Published by Elsevier Ltd.

Suppressing chaos and transient in parameter perturbed systems

The systems with some system parameters perturbed are investigated. These systems might exist in nature or be obtained by perturbation or truncation theory. Chaos might be suppressed or induced. Some of these dynamical systems exhibit extraordinary long transients, which makes the temporal structure seem sensitively dependent on initial conditions in finite observation time interval.

Numerical study of bifurcation solutions of spherical Taylor-Couette flow

The steady bifurcation flows in a spherical gap (gap ratio sigma=0.18) with rotating inner and stationary outer spheres are simulated numerically for Re(c1)less than or equal to Re less than or equal to 1 500 by solving steady axisymmetric incompressible Navier-Stokes equations using a finite difference method. The simulation shows that there exist two steady stable flows with 1 or 2 vortices per hemisphere for 775 less than or equal to Re less than or equal to 1 220 and three steady stable flows with 0, 1, or 2 vortices for 1 220initial conditions which on be generated by different accelerations of the inner sphere. Generation of zero-or two-vortex flow depends mainly on the acceleratio n, but that of one-vortex flow also depends on the perturbation breaking the equatorial symmetry. The mechanism of development of a saddle point in the meridional plane at higher Re number and its role in the formation of two-vortex flow are analyzed.

The strange attractor of a kind of 2-dimensional map and dynamical properties on it

On the basis of previous works, the strange attractor in real physical systems is discussed. Louwerier attractor is used as an example to illustrate the geometric structure and dynamical properties of strange attractor. Then the strange attractor of a kind of two-dimensional map is analysed. Based on some conditions, it is proved that the closure of the unstable manifolds of hyberbolic fixed point of map is a strange attractor in real physical systems.

The geometric structure and dynamic properties of lauwerier attractor

 Introduction The strange chaotic attractor (ACS) is an important subject in the nonlinear field. On the basis of the theory of transversal heteroclinic cycles, it is suggested that the strange attractor is the closure of the unstable manifolds of countable infinite hyperbolic periodic points. From this point of view some nonlinear phenomena are explained reasonably. 更多还原

Two-time scales inner solutions and motion of a geostrophic vortex

Based on the authors' previous work, in this paper the systematical analyses on the motion and the inner solutions of a geostrophic vortex have been presented by means of thematched asymptotic expansion method with multiple time scales (S/gh001/2 and α S/gh001/2) and space scales. It has been shown that the leading inner solutions to the core structure in two-time scales analyses are identified with the results in normal one-time scale analyses. The time averages of the first-order solutions on short time variable τ are the same as the first-order solutions obtained in one normal time scale analyses. The geostrophic vortex induces an oscillatory motion in addition to moving with the background flow. The period, amplitude andthe deviation from the mean trajectory depend on the core structure and the initial conditions. The velocity of the motion of vortex center varies periodically and the time average of the velocity on short time variable τ is equal to the value of the local mean velocity.

Influence of Rayleigh-Taylor Instability on Liquid Propellant Reorientation in a Low-Gravity Environment

A computational simulation is conducted to investigate the influence of Rayleigh-Taylor instability on liquid propellant reorientation flow dynamics for the tank of CZ-3A launch vehicle series fuel tanks in a low-gravity environment. The volume-of-fluid (VOF) method is used to simulate the free surface flow of gas-liquid. The process of the liquid propellant reorientation started from initially flat and curved interfaces are numerically studied. These two different initial conditions of the gas-liquid interface result in two modes of liquid flow. It is found that the Rayleigh-Taylor instability can be reduced evidently at the initial gas-liquid interface with a high curve during the process of liquid reorientation in a low-gravity environment.

Further acceleration of MeV electrons by a relativistic laser pulse

With the development of photocathode rf electron gun, electrons with high-brightness and mono-energy can be obtained easily. By numerically solving the relativistic equations of motion of an electron generated from this facility in laser fields modelled by a circular polarized Gaussian laser pulse, we find the electron can obtain high energy gain from the laser pulse. The corresponding acceleration distance for this electron driven by the ascending part of the laser pulse is much longer than the Rayleigh length, and the light amplitude experienced on the electron is very weak when the laser pulse overtakes the electron. The electron is accelerated effectively and the deceleration can be neglected. For intensities around 10(19) W(.)mu m(2)/cm(2), an electron's energy gain near 0.1 GeV can be realized when its initial energy is 4.5 MeV, and the final velocity of the energetic electron is parallel with the propagation axis. The energy gain can be up to 1 GeV if the intensity is about 10(21) W(.)mu m(2)/cm(2). The final energy gain of the electron as a function of its initial conditions and the parameters of the laser beam has also been discussed.

The electron trajectory in a relativistic femtosecond laser pulse

In this report, we start from Lagrange equation and analyze theoretically the electron dynamics in electromagnetic field. By solving the relativistic government equations of electron, the trajectories of an electron in plane laser pulse, focused laser pulse have been given for different initial conditions. The electron trajectory is determined by its initial momentum, the amplitude, spot size and polarization of the laser pulse. The optimum initial momentum of the electron for LSS (laser synchrotron source) is obtained. Linear polarized laser is more advantaged than circular polarized laser for generating harmonic radiation.