Atomistic investigation of the effects of temperature and surface roughness on diffusion bonding between Cu and Al

Molecular dynamics (MD) simulations are carried out to analyze the diffusion bonding at Cu/Al interfaces. The results indicate that the thickness of the interfacial layer is temperature-dependent, with higher temperatures yielding larger thicknesses. At temperatures below 750 K, the interface thickness is found to increase in a stepwise manner as a function of time. At temperatures above 750 K, the thickness increases rapidly and smoothly. When surface roughness is present, the bonding process consists of three stages. In the first stage, surfaces deform under stress, resulting in increased contact areas. The second stage involves significant plastic deformation at the interface as temperature increases, resulting in the disappearance of interstices and full contact of the surface pair. The last stage entails the diffusion of atoms under constant temperature. The bonded specimens show tensile strengths reaching 88% of the ideal Cu/Al contact strength. (c) 2007 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Rigorous finite-time guarantees for optimization on continuous domains by simulated annealing

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Effect of nonlinear wave-current interaction on flow fields and hydrodynamic forces

A fifth-order theory for solving the problem of interaction between Stokes waves and exponential profile currents is proposed. The calculated flow fields are compared with measurements. Then the errors caused by the linear superposition method and approximate theory are discussed. It is found that the total wave-current field consists of pure wave, pure current and interaction components. The shear current not only directly changes the flow field, but also indirectly does sx, by changing the wave parameters due to wave-current interaction. The present theory can predict the wave kinematics on shear currents satisfactorily. The linear superposition method may give rise to more than 40% loading error in extreme conditions. When the apparent wave period is used and the Wheeler stretching method is adopted to extrapolate the current, application of the approximate theory is the best.

A new dynamic model for study of dislocation pattern formation

Based on the principle given in nonlinear diffusion-reaction dynamics, a new dynamic model for dislocation patterning is proposed by introducing a relaxation time to the relation between dislocation density and dislocation flux. The so-called chemical potential like quantities, which appear in the model can be derived from variation principle for free energy functional of dislocated media, where the free energy density function is expressed in terms of not only the dislocation density itself but also their spatial gradients. The Linear stability analysis on the governing equations of a simple dislocation density shows that there exists an intrinsic wave number leading to bifurcation of space structure of dislocation density. At the same time, the numerical results also demonstrate the coexistence and transition between different dislocation patterns.

A BIEM optimization method for fracture dynamics inverse problem

In the present paper, based on the theory of dynamic boundary integral equation, an optimization method for crack identification is set up in the Laplace frequency space, where the direct problem is solved by the author's new type boundary integral equations and a method for choosing the high sensitive frequency region is proposed. The results show that the method proposed is successful in using the information of boundary elastic wave and overcoming the ill-posed difficulties on solution, and helpful to improve the identification precision.

3-dimensional transient wave response in a cracked elastic solid

The three-dimensional transient wave response problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. Tractions are applied suddenly to the crack, which simulates the case of impact loading. The integral transforms are utilized to reduce the problem to a standard Fredholm integral equation in the Laplace transform variable and sequentially invert the Laplace transforms of the stress components by numerical inversion method. The dynamic mode I stress intensity factors at the crack tip are obtained and some numerical results are presented in graphical form.

A perturbational h4 exponential finite-difference scheme for the convective diffusion equation

A perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order are exerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transformation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one- to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes, the h4 accuracy of the perturbational scheme is verified using double precision arithmetic.

Standing wave of finite-amplitude in an circular basin with uneven bottom

The effect of the particle cover over the density interface between two layers of fluids and of the suspended solid particles in the upper turbulcnt layer on the turbulent entrainment has been studied experimentally. The entrainment distance D is a function of the time of power: D=kt, where =0.200-0.130p. For suspended particles in the upper layer and pure 2-layer fluid is equal to 0.200, but the value of k for the suspended particles is smaller than that for the pure 2-layer fluid. The non-dimensional entrainment velocity is E=KRiln, where n=1.50+0.93 p. It is shown that the particle cover over the interface changes the power of Ril in the entrainment and hinders the turbulent entrainment. The variation rule of E for the suspended particles is the same as that for the pure 2-layer fluid, but the K value of the former is smaller than that of the latter. The turbulent mixing mechanism has been discussed.

The wave model of mesothermal plasma near wakes and Korteweg-de Vries equation

The stationary two-dimensional (x, z) near wakes behind a flat-based projectile which moves at a constant mesothermal speed (V∞) along a z-axis in a rarefied, fully ionized, plasma is studied using the wave model previously proposed by one of the authors (VCL). One-fluid theory is used to depict the free expansion of ambient plasma into the vacuum produced behind a fast-moving projectile. This nonstationary, one-dimensional (x, t) flow which is approximated by the K-dV equation can be transformed, through substitution, t=z/V∞, into a stationary two-dimensional (x, z) near wake flow seen by an observer moving with the body velocity (V∞). The initial value problem of the K-dV equation in (x, t) variables is solved by a specially devised numerical method. Comparisons of the present numerical solution for the asymptotically small and large times with available analytical solutions are made and found in satisfactory agreements.

Practical applications of the likelihood, time transcendence and metadata in virtual models of heritage elements

Contributed to: III Bienal de Restauración Monumental: "Sobre la des-restauración" (Sevilla, Spain, Nov 23-25, 2006)

The Effects of Backfill Soil Properties on Wave-induced Pore Pressures around a Trenched Pipeline

Offshore pipelines are always trenched into seabed to reduce wave-induced forces and thereby to enhance their stability. The trenches are generally backfilled either by in-site sediments or by depositing selected backfill materials over the pipeline from bottom-dump barge. The actual waves in shallow water zone are always characterized as nonlinear. The proper evaluation of the wave-induced pressures upon pipeline is important for coastal geotechnical engineers. However, most previous investigations of the wave–seabed–pipe interaction problem have been concerned only with a single sediment layer and linear wave loading. In this paper, based on Biot’s consolidation theory, a two-dimensional finite element model is developed to investigate non-linear wave induced pore pressures around trenched pipeline. The influences of the permeability of backfill soil and the geometry profiles of trenches upon soil responses around pipeline are studied respectively.

A Multiscale-Domain Decomposition Method for High Reynolds Number Flows

The high Reynolds number flow contains a wide range of length and time scales, and the flow domain can be divided into several sub-domains with different characteristic scales. In some sub-domains, the viscosity dissipation scale can only be considered in a certain direction; in some sub-domains, the viscosity dissipation scales need to be considered in all directions; in some sub-domains, the viscosity dissipation scales are unnecessary to be considered at all. For laminar boundary layer region, the characteristic length scales in the streamwise and normal directions are L and L Re-1/ 2 , respectively. The characteristic length scale and the velocity scale in the outer region of the boundary layer are L and U, respectively. In the neighborhood region of the separated point, the length scale l<

Experimental Study and Numerical Simulation of Cellular Structures and Mach Reflection of Gaseous Detonation Wave

In this paper the Deflagration to Detonation Transition (DDT) process of gaseous H-2-O-2 mixture and Mach reflection of gaseous detonation wave on a wedge have been conducted experimentally. The cellular pattern of DDT process and Mach reflection were obtained from experiments with wedge angle theta = 10(0) similar to 40(0) and initial pressure of gaseous mixture 16kPa similar to 26.7kPa. The 2-D numerical simulations of DDT process and Mach reflection of detonation wave were performed by using the simplified ZND model and improved space-time conservation element and solution element (CE/SE) method. The numerical cellular structures were compared with the cellular patterns of soot track. Compared results were shown that it is satisfactory. The characteristic comparisons on Mach reflection of air shock wave and detonation wave were carried also out and their differences were given.

“Deborah Numbers”, Coupling Multiple Space and Time Scales and Governing Damage Evolution to Failure

Two different spatial levels are involved concerning damage accumulation to eventual failure. nucleation and growth rates of microdamage nN* and V*. It is found that the trans-scale length ratio c*/L does not directly affect the process. Instead, two independent dimensionless numbers: the trans-scale one * * ( V*)including the * **5 * N c V including mesoscopic parameters only, play the key role in the process of damage accumulation to failure. The above implies that there are three time scales involved in the process: the macroscopic imposed time scale tim = /a and two meso-scopic time scales, nucleation and growth of damage, (* *4) N N t =1 n c and tV=c*/V*. Clearly, the dimensionless number De*=tV/tim refers to the ratio of microdamage growth time scale over the macroscopically imposed time scale. So, analogous to the definition of Deborah number as the ratio of relaxation time over external one in rheology. Let De be the imposed Deborah number while De represents the competition and coupling between the microdamage growth and the macroscopically imposed wave loading. In stress-wave induced tensile failure (spallation) De* < 1, this means that microdamage has enough time to grow during the macroscopic wave loading. Thus, the microdamage growth appears to be the predominate mechanism governing the failure. Moreover, the dimensionless number D* = tV/tN characterizes the ratio of two intrinsic mesoscopic time scales: growth over nucleation. Similarly let D be the “intrinsic Deborah number”. Both time scales are relevant to intrinsic relaxation rather than imposed one. Furthermore, the intrinsic Deborah number D* implies a certain characteristic damage. In particular, it is derived that D* is a proper indicator of macroscopic critical damage to damage localization, like D* ∼ (10–3~10–2) in spallation. More importantly, we found that this small intrinsic Deborah number D* indicates the energy partition of microdamage dissipation over bulk plastic work. This explains why spallation can not be formulated by macroscopic energy criterion and must be treated by multi-scale analysis.

The induced flow field by internal solitary wave and its action on cylindrical piles in the stratified ocean

The induced flow fields by internal solitary waves and its actions on cylindrical piles in density stratified ocean with a basic density profile and a basic velocity profile are investigated. Some results, such as the time evolution of flow fields and hydrodynamic forces on the piles are yielded both by theoretical analysis and numerical calculation for general and specific cases. Several kinds of ambient sea conditions of the South China Sea are specified for numerical simulation. Moreover, the effects of relative density difference, depth ratio and wave steepness on maximal total force and total torque are analyzed.