Mesh effects on the computation of non-linear gravity waves of arbitrary discharge

Numerical computations of non-linear gravity waves are presented and the effects of mesh variations on the results are discussed. Waves are regarded as two-parameter families (λ,A)_Q of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm. Mesh effects are to a large extent dependent on the particular wave region under consideration. Three such regions are identified and typical examples are computed and discussed.     

Some asymptotic results for a class of stochastic systems with parametric excitations

Systems of stochastic ordinary differential equations dependent on a small parameter are studied. The equations are assumed to depend on two time scales: they are stochastic in a fast time t and they are deterministic in a slow time t. The method of analysis is based on a generalization of the Method of Averaging. Mathematical results are given valid for all t for sufficiently small. The mathematical results are applied to several examples of parametrically excited dynamical systems.     

Elastic properties of Al<Subscript>2</Subscript>O<Subscript>3</Subscript>–NiAl: a modified version of Hashin–Shtrikman bounds

The modified nonlinear relations for the estimation of elastic constants of Al₂O₃–NiAl composite material are developed. The concept of microstructure and interconnectivity of phases at the interface is used. Hashin–Shtrikman relations are described in their actual form and modified version of Hashin–Shtrikman relations for bulk and shear moduli are discussed. These relations for elastic and mechanical properties are applied mainly for Al₂O₃–NiAl composite material. Theoretical predictions using modified relations are compared with Hashin–Shtrikman bounds and experimental results of elastic properties for Al₂O₃–NiAl matrix-inclusion-based composite. It is found that the predicted values of elastic and mechanical properties using modified relations are quite close to the experimental results.     

Convection in electrochemical systems

Some theoretical and experimental results for the concentration and velocity fields that appear during unsteady electrolysis in small electrochemical cells are given. Two systems are considered: ¦Cu¦CuSO ₄(aq)¦Cu¦ and ¦PbO ₂,PbSO ₄¦H ₂ SO ₄(aq)¦Pb,PbSO ₄¦. For the former system, in which the electrodes are solid, both linear and nonlinear electrode kinetics are considered. For the more complicated latter system, where the electrodes are porous, attention is restricted to linear kinetics. Theoretical results are obtained by using both perturbation methods and numerical analysis. Experimental results are obtained by Laser Doppler Velocimetry and Image Laser Holography. It is shown that the evolution of the concentration and velocity fields is controlled by stratification of the electrolyte. The boundary layer structure is similar to that appearing during nonlinear spin up of a homogeneous fluid. Theoretical and experimental results are in good agreement.     

The two-dimensional electroelasticity problems for multiconnected bodies situated under electric potential difference action

Solutions of the two-dimensional electroelasticity problems for infinitely long piezoelectric cylinders with cavities and cracks under electrical potential difference action are obtained using the Lekhnitskii’s generalized complex potentials. Herewith, piezoelectric bodies under consideration are free from mechanical loads, some (or all) openings and maybe the exterior boundary of the cylinders are fully covered by thin electrodes. Voltage differences are supplied on the electroded surfaces, the rest boundary surfaces are charge-free. In this case, the complex potentials are investigated. Boundary conditions are satisfied by the least-squares method. There are carried out numerical investigations of behaviour of some basic electroelastic characteristics in a circular hollow cylinder and in an infinite body with two longitudinal cavities and a charge-free plane crack. New electromechanical regularities of influence of material properties, geometrical characteristics of considered regions on values of electroelastic state characteristics and the stress, electric displacements and tensions intensity factor $k_1$ are determined.     

Analysis of periodic-quasiperiodic nonlinear systems via Lyapunov-Floquet transformation and normal forms

In this paper a general technique for the analysis of nonlinear dynamical systems with periodic-quasiperiodic coefficients is developed. For such systems the coefficients of the linear terms are periodic with frequency ω while the coefficients of the nonlinear terms contain frequencies that are incommensurate with ω. No restrictions are placed on the size of the periodic terms appearing in the linear part of system equation. Application of Lyapunov-Floquet transformation produces a dynamically equivalent system in which the linear part is time-invariant and the time varying coefficients of the nonlinear terms are quasiperiodic. Then a series of quasiperiodic near-identity transformations are applied to reduce the system equation to a normal form. In the process a quasiperiodic homological equation and the corresponding ‘solvability condition’ are obtained. Various resonance conditions are discussed and examples are included to show practical significance of the method. Results obtained from the quasiperiodic time-dependent normal form theory are compared with the numerical solutions. A close agreement is found.     

The Probability Density Functions of Velocity Fluctuations Inside Steady Pressure-Driven Three-Dimensional Turbulent Boundary Layers

One-point time-averaged velocity correlations and joint probability density functions (p.d.f.s) are analyzed with a multi-step method for steady three-dimensional turbulent boundary layers (3DTBLs). The data are derived from a time series of velocity fluctuations measured along the measurement axes ( ₁, ₂, ₃). The method includes a Monte Carlo (MC) technique in which, firstly, the 3×3 Reynolds stress tensors are diagonalized locally in order to obtain the experimental eigenvalues or principal values and the experimental eigenvectors or principal axes ( ₁, ₂, ₃). Secondly, trial independent p.d.f.s are MC-generated along these are projected from system into and the built-in hypotheses are tested for validity, using stringent self-consistency tests. All p.d.f. investigations are made with “perturbed centered-Gaussians” hypotheses, in which the “centered-Gaussians” are experimentally defined and the “perturbations” are trial drift velocities. Our MC-analysis method [1-3] is applied to the first [4] and second [5] generation “S-duct” experiments performed at the école Polytechnique Fédérale de Lausanne (EPFL). Additionally, two complementary algebraic self-consistency tests are developed for the double and the triple correlations separately. New results in the p.d.f. properties of 3DTBLs are presented, using Kinetic Theory as background. Received 6 November 2001 and accepted 27 August 2002 Published online 28 February 2003 Communicated by J.R. Blake     

The pressure melting of ice around a horizontal elliptical cylinder

The pressure melting processes of a block of ice around a moving, horizontal, elliptical cylinder are investigated. The film thickness of liquid and the relation between the force exerted on the elliptical cylinder and the melting velocity are obtained analytically. The results include those of pressure melting around a horizontal cylinder, and are discussed and compared with that of ΔT-driven melting around an elliptical cylinder. The basic differences between Δp-driven and ΔT-driven melting are obtained. Some important conclusions are drawn.     

Numerical solution of singular integral equations in stress concentration problems under longitudinal shear loading

Summary The paper deals with numerical solutions of singular integral equations in stress concentration problems for longitudinal shear loading. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy-type singularities, where unknown functions are densities of body forces distributed in the longitudinal direction of an infinite body. First, four kinds of fundamental density functions are introduced to satisfy completely the boundary conditions for an elliptical boundary in the range 0≤φ _k ≤2π. To explain the idea of the fundamental densities, four kinds of equivalent auxiliary body force densities are defined in the range 0≤φ _k ≤π/2, and necessary conditions that the densities must satisfy are described. Then, four kinds of fundamental density functions are explained as sample functions to satisfy the necessary conditions. Next, the unknown functions of the body force densities are approximated by a linear combination of the fundamental density functions and weight functions, which are unknown. Calculations are carried out for several arrangements of elliptical holes. It is found that the present method yields rapidly converging numerical results. The body force densities and stress distributions along the boundaries are shown in figures to demonstrate the accuracy of the present solutions. Received 26 May 1998; accepted for publication 27 November 1998     

Unsteady natural convection in an enclosure with vertical wavy walls

In this paper, unsteady heat transfer and fluid flow characteristics in an enclosure are investigated. The enclosure consists of two vertical wavy and two horizontal straight walls. The top and the bottom walls are considered adiabatic. Two wavy walls are kept isothermal and their boundaries are approximated by a cosine function. Governing equations including continuity, momentum and energy were discretized using the finite-volume method and solved by SIMPLE method in curvilinear coordinate. Simulation was carried out for a range of Grashof number Gr = 10³–10⁶, Prandtl number Pr = 0.5–4.0, wave ratio A (defined by amplitude/wavelength) 0.0–0.35 and aspect ratio W (defined by average width/wavelength) 0.5–1.0. Streamlines and isothermal lines are presented to corresponding flow and thermal fields. Local and average Nusselt number distributions are presented. The obtained results are in good agreement with available numerical and experimental data.     

Evaluation of constitutive models for voided solids

In this work four constitutive models for voided solids are reviewed and evaluated; namely, Gurson's, Green's, Liao's et al. and Shima-Oyane's models. Two modified forms of Gurson's model and a non-quadratic form of Green's model are developed for normal anisotropy prevailing in the analysis of sheet metal forming. A simplified version — more amenable to analytical derivations — of Gurson's yield function and its modified forms are proposed for plane stress conditions. The associated flow rules are presented and the laws governing void growth with accumulated strain are derived using the above models. Their predictions are compared with experiments. As an application, the flow curves of voided materials of known initial porosities are predicted and compared with experiments.     

Domain decomposition method with hybrid approximations applied to solve problems of elasticity

To solve two-dimensional boundary-value problems of elasticity, two iteration algorithms of the domain decomposition method are proposed: parallel Neumann–Neumann and sequential Dirichlet–Neumann. They are based on the hybrid boundary–finite-element approximations. The algorithms are proved to converge. The optimal parameters are selected using the minimum-residual and steepest-descent methods. Some plane problems of elasticity are solved as examples, and stationary and nonstationary iteration algorithms in these examples are analyzed for efficiency Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 18–29, November 2008.     

Block H-matrices and spectrum of block matrices

The block H-matrices are studied by the concept of G-functions, several concepts of block matrices are introduced. Equivalent characters of block H-matrices are obtained. Spectrum localizations characterized by G-functions for block matrices are got. Foundation item: Sichuan Youth Science & Technology Foundation of China (Jsa1081) Biography: HUANG Ting-zhu (1964-)     

Cubically Nonlinear Waves in a Piezoelastic Material

The paper proposes a new deformation model of piezomaterials that includes linear, quadratic, and cubic, and piezoeffect mechanisms. A nonlinear system of equations describing the propagation of plane waves is derived. Two new problems are solved analytically: generation of the third harmonic of an SH-wave and generation and interaction of new SH- and SV-waves after SH- and SV-waves are excited. All data needed for computer modeling are determined. The results of computer modeling are discussed     

Evolution of perturbations of a charged interface between immiscible inviscid fluids in the interelectrode gap

Perturbations of the interface between two immiscible ideal fluids of finite thickness (the lower and upper fluids are the conductor and the dielectric, respectively) located in the gap between two electrodes are considered. In the cases of the “shallow” and “deep” upper fluid the dispersion relations of linear waves and their longwave expansions are found. The methods of determining the space-time evolution of an initial surface perturbation are developed on the basis of the linear approximation. In the cases of the “shallow” and “deep” upper fluid examples of the development of an initial perturbation of the “step” type are given. The development of an initial perturbation of the “step” type are also considered in the near-critical electric fields and in the case of degeneration of cubic dispersion.     

Effects of channel dimension,heat flux,and mass flux on flow boiling regimes in microchannels

Experiments are conducted with a perfluorinated dielectric fluid, Fluorinert FC-77, to investigate the effects of channel size and mass flux (225–1420 kg/m²s) on microchannel flow boiling regimes by means of high-speed photography. Seven different silicon test pieces with parallel microchannels of widths ranging from 100 to 5850 μm, all with a depth of 400 μm, are considered. Flow visualizations are performed with a high-speed digital video camera while local measurements of the heat transfer coefficient are simultaneously obtained. The visualizations and the heat transfer data show that flow regimes in the microchannels of width 400 μm and larger are similar, with nucleate boiling being dominant in these channels over a wide range of heat flux. In contrast, flow regimes in the smaller microchannels are different and bubble nucleation at the walls is suppressed at a relatively low heat flux for these sizes. Two types of flow regime maps are developed and the effects of channel width on the flow regime transitions are discussed.     

Time-dependent natural convection in a square cavity: Application of a new finite volume method

A new finite volume (FV) approach with adaptive upwind convection is used to predict the two-dimensional unsteady flow in a square cavity. The fluid is air and natural convection is induced by differentially heated vertical walls. The formulation is made in terms of the vorticity and the integral velocity (induction) law. Biquadratic interpolation formulae are used to approximate the temperature and vorticity fields over the finite volumes, to which the conservation laws are applied in integral form. Image vorticity is used to enforce the zero-penetration condition at the cavity walls. Unsteady predictions are carried sufficiently forward in time to reach a steady state. Results are presented for a Prandtl number (Pr) of 0-71 and Rayleigh numbers equal to 10³, 10⁴ and 10⁵. Both 11 × 11 and 21 × 21 meshes are used. The steady state predictions are compared with published results obtained using a finite difference (FD) scheme for the same values of Pr and Ra and the same meshes, as well as a numerical bench-mark solution. For the most part the FV predictions are closer to the bench-mark solution than are the FD predictions.     

To derive Lagrange equations of nonholonomic systems without using the Chetaev conditions

The present paper derives the equation of motion for a class of nonholonomic dynamical systems from the d’Alembert–Lagrange equation. In this paper, the relation dδ = δd is assumed only for those generalized coordinates whose variations are independent. For the remaining coordinates, the transpositional relations are derived by means of mathematics method, which are different from the Chetaev condition. Several examples are given.     

Mixed Convection of Water at 4°C Along a Wedge with Variable Surface Flux in a Porous Medium

In this study, the mixed convection of water at 4°C along a wedge in a porous medium is investigated numerically using finite difference method. In order to explore the effect of mixed convection, both forced and free convection-dominated regimes are considered. Non-similarity solutions are obtained for the variable wall flux boundary condition. Velocity and temperature profiles as well as local dimensionless skin friction and Nusselt number are obtained and compared with the available numerical results for various values of different parameters. The wedge angle geometry parameter m and mixed convection parameter ξ are ranged from 0 to 1 in both regimes whereas different values of λ are considered for the purpose of comparison of heat transfer results.     

A group representation of canonical transformation

InclassicalmechanicsaphasespaceofZsdimensionsisdefinedasthatwhichisconstructedofsgeneralizedcoordinatesandsgeneralizedmomenta.IntheZs-dilllellsionsphasespace,whentileformofHamiltoniancanonicalequationsismy;lriable,HamiltonianfullctionH(q.,P.'t)ofasystemistransformedtoK(Q.'Pa't),wherethea=l,2....,s;theq.andQ.aregelleralizedcoordinates,thePaandPnaregeneralizedmomenta,tileItime.ThetransformedconditionisoneofthefourformsofLagendretransformationsasf'Ollows,whereFI,F2,F3andF4arecalledgenerat…