Modelling the nano-scale phenomena in condensed matter physics via computer-based numerical simulations

A review of the atomistic modelling of the behaviour of nano-scale structures and processes via molecular dynamics (MD) simulation method of a canonical ensemble is presented. Three areas of application in condensed matter physics are considered. We focus on the adhesive and indentation properties of the solid surfaces in nano-contacts, the nucleation and growth of nano-phase metallic and semi-conducting atomic and molecular films on supporting substrates, and the nano- and multi-scale crack propagation properties of metallic lattices. A set of simulations selected from these fields are discussed, together with a brief introduction to the methodology of the MD simulation. The pertinent inter-atomic potentials that model the energetics of the metallic and semi-conducting systems are also given.

Macro-segregation of multi-component alloys in shape casting simulation

The objective of this work is to present a new scheme for temperature-solute coupling in a solidification model, where the temperature and concentration fields simultaneously satisfy the macro-scale transport equations and, in the mushy region, meet the constraints imposed by the thermodynamics and the local scale processes. A step-by-step explanation of the macrosegregation algorithm, implemented in the finite volume unstructured mesh multi-physics modelling code PHYSICA, is initially presented and then the proposed scheme is validated against experimental results obtained by Krane for binary and a ternary alloys.

Modelling technologies and applications

Numerical modelling technology and software is now being used to underwrite the design of many microelectronic and microsystems components. The demands for greater capability of these analysis tools are increasing dramatically, as the user community is faced with the challenge of producing reliable products in ever shorter lead times. This leads to the requirement for analysis tools to represent the interactions amongst the distinct phenomena and physics at multiple length and timescales. Multi-physics and Multi-scale technology is now becoming a reality with many code vendors. This chapter discusses the current status of modelling tools that assess the impact of nano-technology on the fabrication/packaging and testing of microsystems. The chapter is broken down into three sections: Modelling Technologies, Modelling Application to Fabrication, and Modelling Application to Assembly/Packing and Modelling Applied for Test and Metrology.

A coarse grid extraction of sound signals for computational aeroacoustics

Sound waves are propagating pressure fluctuations, which are typically several orders of magnitude smaller than the pressure variations in the flow field that account for flow acceleration. On the other hand, these fluctuations travel at the speed of sound in the medium, not as a transported fluid quantity. Due to the above two properties, the Reynolds averaged Navier–Stokes equations do not resolve the acoustic fluctuations. This paper discusses a defect correction method for this type of multi-scale problems in aeroacoustics. Numerical examples in one dimensional and two dimensional are used to illustrate the concept. Copyright (C) 2002 John Wiley & Sons, Ltd.

Dynamic solid mechanics using finite volume methods

A procedure for evaluating the dynamic structural response of elastic solid domains is presented. A prerequisite for the analysis of dynamic fluid–structure interaction is the use of a consistent set of finite volume (FV) methods on a single unstructured mesh. This paper describes a three-dimensional (3D) FV, vertex-based method for dynamic solid mechanics. A novel Newmark predictor–corrector implicit scheme was developed to provide time accurate solutions and the scheme was evaluated on a 3D cantilever problem. By employing a small amount of viscous damping, very accurate predictions of the fundamental natural frequency were obtained with respect to both the amplitude and period of oscillation. This scheme has been implemented into the multi-physics modelling software framework, PHYSICA, for later application to full dynamic fluid structure interaction.

Modelling of industrial multi-physics processes—a key role for computational mechanics.

In the analysis of industrial processes, there is an increasing emphasis on systems governed by interacting continuum phenomena. Mathematical models of such multi-physics processes can only be achieved for practical simulations through computational solution procedures—computational mechanics. Examples of such multi-physics systems in the context of metals processing are used to explore some of the key issues. Finite-volume methods on unstructured meshes are proposed as a means to achieve efficient rapid solutions to such systems. Issues associated with the software design, the exploitation of high performance computers, and the concept of the virtual computational-mechanics modelling laboratory are also addressed in this context.

The numerical modelling of multi-physics phenomena: The shape casting process

In this paper a computer simulation tool capable of modelling multi-physics processes in complex geometry has been developed and applied to the casting process. The quest for high-quality complex casting components demanded by the aerospace and automobile industries, requires more precise numerical modelling techniques and one that need to be generic and modular in its approach to modelling multi-processes problems. For such a computer model to be successful in shape casting, the complete casting process needs to be addressed, the major events being:-• Filling of hot liquid metal into a cavity mould • Solidification and latent heat evolution of liquid metal • Convection currents generated in liquid metal by thermal gradients • Deformation of cast and stress development in solidified metal • Macroscopic porosity formation The above phenomena combines the analysis of fluid flow, heat transfer, change of phase and thermal stress development. None of these events can be treated in isolation as they inexorably interact with each other in a complex way. Also conditions such as design of running system, location of feeders and chills, moulding materials and types of boundary conditions can all affect on the final cast quality and must be appropriately represented in the model.

PHYSICA - A software environment for the modelling of multi-physics phenomena

A brief description of a software environment in FORTRAN77 for the modelling of multi-physics phenomena is given. The numerical approach is based on finite volume methods but extended to unstructured meshes (ie. FV-UM). A range of interacting solution procedures for turbulent fluid flow, heat transfer with solidification/melting and elasto-visco-plastic solid mechanics are implemented in the first version of PHYSICA, which will be released in source code form to the academic community in late 1995.

Computational modelling of multi-physics processes on high performance parallel computer systems

The demands of the process of engineering design, particularly for structural integrity, have exploited computational modelling techniques and software tools for decades. Frequently, the shape of structural components or assemblies is determined to optimise the flow distribution or heat transfer characteristics, and to ensure that the structural performance in service is adequate. From the perspective of computational modelling these activities are typically separated into: • fluid flow and the associated heat transfer analysis (possibly with chemical reactions), based upon Computational Fluid Dynamics (CFD) technology • structural analysis again possibly with heat transfer, based upon finite element analysis (FEA) techniques.

Modelling meso-scale diffusion processes in stochastic fluid bio-membranes

The space–time dynamics of rigid inhomogeneities (inclusions) free to move in a randomly fluctuating fluid bio-membrane is derived and numerically simulated as a function of the membrane shape changes. Both vertically placed (embedded) inclusions and horizontally placed (surface) inclusions are considered. The energetics of the membrane, as a two-dimensional (2D) meso-scale continuum sheet, is described by the Canham–Helfrich Hamiltonian, with the membrane height function treated as a stochastic process. The diffusion parameter of this process acts as the link coupling the membrane shape fluctuations to the kinematics of the inclusions. The latter is described via Ito stochastic differential equation. In addition to stochastic forces, the inclusions also experience membrane-induced deterministic forces. Our aim is to simulate the diffusion-driven aggregation of inclusions and show how the external inclusions arrive at the sites of the embedded inclusions. The model has potential use in such emerging fields as designing a targeted drug delivery system.

Utilising computational fluid dynamics (CFD) for the modelling of granular material in large-scale engineering processes

In this paper, the framework is described for the modelling of granular material by employing Computational Fluid Dynamics (CFD). This is achieved through the use and implementation in the continuum theory of constitutive relations, which are derived in a granular dynamics framework and parametrise particle interactions that occur at the micro-scale level. The simulation of a process often met in bulk solids handling industrial plants involving granular matter, (i.e. filling of a flat-bottomed bin with a binary material mixture through pneumatic conveying-emptying of the bin in core flow mode-pneumatic conveying of the material coming out of a the bin) is presented. The results of the presented simulation demonstrate the capability of the numerical model to represent successfully key granular processes (i.e. segregation/degradation), the prediction of which is of great importance in the process engineering industry.

Macro-Micro Modelling Analysis for High Density Packaged Flip Chips

A wide range of flip chip technologies with solder or adhesives have become dominant solutions for high density packaging applications due to the excellent electrical performance, high I/O density and good thermal performance. This paper discusses the use of modeling technique to predict the reliability of high density packaged flip chips in the humid environment. Reliability assessment is discussed for flip chip package at ultra-fine pitch with anisotropic conductive film (ACF). The purpose of this modeling work is to understand the role that moisture plays in the failure of ACF flip chips. A macro-micro 3D finite element modeling technique was used in order to make the multi-length-scale modeling of the ACF flip chip possible. Modeling results are consistent with the findings in the experimental work

Modelling continuum mechanics phenomena using three dimensional unstructured meshes on massively parallel processors

The difficulties encountered in implementing large scale CM codes on multiprocessor systems are now fairly well understood. Despite the claims of shared memory architecture manufacturers to provide effective parallelizing compilers, these have not proved to be adequate for large or complex programs. Significant programmer effort is usually required to achieve reasonable parallel efficiencies on significant numbers of processors. The paradigm of Single Program Multi Data (SPMD) domain decomposition with message passing, where each processor runs the same code on a subdomain of the problem, communicating through exchange of messages, has for some time been demonstrated to provide the required level of efficiency, scalability, and portability across both shared and distributed memory systems, without the need to re-author the code into a new language or even to support differing message passing implementations. Extension of the methods into three dimensions has been enabled through the engineering of PHYSICA, a framework for supporting 3D, unstructured mesh and continuum mechanics modeling. In PHYSICA, six inspectors are used. Part of the challenge for automation of parallelization is being able to prove the equivalence of inspectors so that they can be merged into as few as possible.

Molecular dynamics simulation of observed c(4x4) and c(4x3) C60 alignments on the Si(100) reconstructed surface.

We have implemented a large-scale classical molecular dynamics simulation at constant temperature to provide a theoretical insight into the results of a recently performed experiment on the monolayer and multi-layer formations of molecular films on the Si(100) reconstructed dimerized surface. Our simulation has successfully reproduced all of the morphologies observed on the monolayer film by this experiment. We have obtained the formation of both c(4 4) and c(4 3) structures of the molecules and have also obtained phase transitions of the former into the latter.