Method of homogenization applied to dispersion in porous media

The theory of homogenization which is a rigorous method of averaging by multiple scale expansions, is applied here to the transport of a solute in a porous medium. The main assumption is that the matrix has a periodic pore structure on the local scale. Starting from the pores with the Navier-Stokes equations for the fluid motion and the usual convective-diffusion equation for the solute, we give an alternative derivation of the three-dimensional macroscale dispersion tensor for solute concentration. The original result was first found by Brenner by extending Brownian motion theory. The method of homogenization is an expedient approach based on conventional continuum equations and the technique of multiple-scale expansions, and can be extended to more complex media involving three or more contrasting scales with periodicity in every but the largest scale.     

Direct modeling of flow of FENE fluids

Direct simulations of macromolecular fluids are carried out for flows between parallel plates and in expanding and contracting channels. The macromolecules are modeled as FENE dumbbells with soft disks or Lennard-Jones dumbbell-dumbbell interactions. The results are presented in terms of profiles and contour plots of velocity, pressure, temperature, density, and flow fields. In addition the data for potential energy, shear stress, and the normal components of the stress tensor are collected. In general, an excellent agreement is found between the simulated profiles and the well-known flow structures, such as flow separation and formation of viscous eddies, indicating that micro-hydrodynamics is a viable tool in linking macroscopic phenomena with the underlying physical mechanisms. The simulations are performed in the Newtonian regime, for medium-size systems comprising up to 3888 dumbbells. This number is sufficiently large to control boundary and particle number effects. The flow is induced by gravity. The traditional stochastic (thermal) and periodic boundary conditions are employed. Also, diffusive boundary conditions, which could include a stagnant fluid layer and repulsive potential walls, are developed. The scaling problems, which are related to the application of a large external force in a microscopic system (of the size of the order 100 Å), result in extreme pressure and temperature gradients. In addition, the viscosity and thermal conductivity coefficients obtained from velocity and temperature profiles of the channel flow are presented. These results are confirmed independently from modeling of Couette flow by the SLLOD equations of motion and from the Evans algorithm for thermal conductivity.     

Limit states of elastic–viscoplastic plate deformations caused by repeated shock wave-loadings. Part 1: Experimental observation

In the present work, the evolution of the inelastic centre deflections of shock wave-loaded circular metal plates due to repeated loadings is studied experimentally and numerically. These displacements are compared to those of quasi-statically deformed plates loaded by a pressure equal to the peak pressure of the impulsive loading. Thereby three types of permanent centre deflections are observed: (1) The quasi-statically obtained deflection is exceeded by the middle point displacement of a dynamically loaded structure already after the first impulse and tends towards a limit state after repeated shock wave-loadings. (2) The centre deflection of the impulsively loaded plate exceeds also the quasi-statically caused deflection and does not increase after repeated impulsive loadings any more. (3) The permanent middle point displacement of a dynamically loaded plate is smaller than the deflection of a quasi-statically loaded one and tends towards the middle point displacement of the quasi-static counterpart after repeated shock wave loadings. This phenomenon is known in the literature as ‘Pseudo-shakedown’.

In Part 1 of this study the experimental observation is described, followed by a theoretical study in Part 2.     

On a Discrete Fourier Series Solution to Static Problem for Conical Shells of Circumferentially Varying Thickness

An approach is developed to solve the two-dimensional boundary-value problems of the stress-strain state of conical shells with circumferentially varying thickness. The approach employs discrete Fourier series to separate variables and make the problem one-dimensional. The one-dimensional boundary-value problem is solved by the stable discrete-orthogonalization method. The results obtained are presented as plots and tables __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 26–37, September 2005.     

Propogation of waves in a linear elastic fluid

The non-classical symmetry method is used to determine particular forms of the arbitrary velocity and forcing terms in a linear wave equation used to model the propogation of waves in a linear elastic fluid. The behaviour of solutions derived using the non-classical symmetry method are discussed. Solutions satisfy a given initial profile and wave velocity. For some solutions the arbitrary forcing terms and wave velocity can be written in terms of the initial wave profile. Relationships between the arbitrary forcing, arbitrary velocity and the solution are derived.     

A field method for solving the equations of motion of nonholonomic systems

In this paper, the field method^[1] for solving the equations of motion of holonomic nonconservative systems is extended to nonholonomic systems with constant mass and with variable mass. Two examples are given to illustrate its application. The project supported by the National Natural Science Foundation of China.     

One-dimensional unsteady inertial flow in phreatic aquifers induced by a sudden change of the boundary head

We are examining the classical problem of unsteady flow in a phreatic semi-infinite aquifer, induced by sudden rise or drawdown of the boundary head, by taking into account the influence of the inertial effects. We demonstrate that for short times the inertial effects are dominant and the equation system describing the flow behavior can be reduced to a single ordinary differential equation. This equation is solved both numerically by the Runge-Kutta method and analytically by the Adomian’s decomposition approach and an adequate polynomial-exponential approximation as well. The influence of the viscous term, occurring for longer times, is also taken into account by solving the full Forchheimer equation by a finite difference approach. It is also demonstrated that as for the Darcian flow, for the case of small fluctuations of the water table, the computation procedure can be simplified by using a linearized form of the mass balance equation. Compact analytical expressions for the computation of the water stored or extracted from an aquifer, including viscous corrections are also developed.     

Uniform asymptotics for the linearized Boltzmann equation describing sound wave propagation

The multiple-scale expansionmethod is used for constructing a uniformly applicable asymptotic approximation of the solution of the linearized Boltzmann equation for small Knudsen numbers. The asymptotic expansion is constructed for the particular example of a sound wave generated by a plane oscillation source and dissipating in a half-space. The simplicity of the problem makes it possible clearly to demonstrate the appearance of secular terms in the expansion and the introduction of multiple scales opens the way to eliminating them.     

Precise control for vibration of rigid–flexible mechanical arm

In the present paper, based on the nonlinear dynamic equation of spacial flexible mechanical arm with dual-link bar, the method of linear quadratic control is used to eliminate the remain vibration of mechanical arm. In the process of computation, the traditional differential algorithm is replaced by the time integration method. Because of taking the more precise time-intervals in the given time-interval and avoiding a lot of computational difficulties, the method of this paper has the characteristics of high precision and unconditional stable. For a typical structure, the precise control law is obtained and the advantages of the algorithm in this paper are shown.     

非线性特征方程的重根特征灵敏度

在大型结构工程的控制工程中，对非线性特征方程的需求将愈来愈多，在以非线性特征方程分析结构或控制系统的动态特性，进而指导系统的动态设计时，其特征灵敏度是不可缺少的信息。为此，本文针对具有生根的非线性特征方程的特征导数计算提出了一种较为实用的方法。