Moment decay rates of solutions of stochastic differential equations

The objective of this paper is to investigate the p-ίh moment asymptotic stability decay rates for certain finite-dimensional Itό stochastic differential equations. Motivated by some practical examples, the point of our analysis is a special consideration of general decay speeds, which contain as a special case the usual exponential or polynomial type one, to meet various situations. Sufficient conditions for stochastic differential equations (with variable delays or not) are obtained to ensure their asymptotic properties. Several examples are studied to illustrate our theory.

A computational model of coupled heat and moisture transfer with phase change in granular sugar during varying environmental conditions

As part of a comprehensive effort to predict the development of caking in granular materials, a mathematical model is introduced to model simultaneous heat and moisture transfer with phase change in porous media when undergoing temperature oscillations/cycling. The resulting model partial differential equations were solved using finite-volume procedures in the context of the PHYSICA framework and then applied to the analysis of sugar in storage. The influence of temperature on absorption/desorption and diffusion coefficients is coupled into the transport equations. The temperature profile, the depth of penetration of the temperature oscillation into the bulk solid, and the solids moisture content distribution were first calculated, and these proved to be in good agreement with experimental data. Then, the influence of temperature oscillation on absolute humidity, moisture concentration, and moisture migration for different parameters and boundary conditions was examined. As expected, the results show that moisture near boundary regions responds faster than farther away from them with surface temperature changes. The moisture absorption and desorption in materials occurs mainly near boundary regions (where interactions with the environment are more pronounced). Small amounts of solids moisture content, driven by both temperature and vapour concentration gradients, migrate between boundary and center with oscillating temperature.

Multi-physics modelling for microelectronics and microsystems - current capabilities and future challenges

At present the vast majority of Computer-Aided- Engineering (CAE) analysis calculations for microelectronic and microsystems technologies are undertaken using software tools that focus on single aspects of the physics taking place. For example, the design engineer may use one code to predict the airflow and thermal behavior of an electronic package, then another code to predict the stress in solder joints, and then yet another code to predict electromagnetic radiation throughout the system. The reason for this focus of mesh-based codes on separate parts of the governing physics is essentially due to the numerical technologies used to solve the partial differential equations, combined with the subsequent heritage structure in the software codes. Using different software tools, that each requires model build and meshing, leads to a large investment in time, and hence cost, to undertake each of the simulations. During the last ten years there has been significant developments in the modelling community around multi- physics analysis. These developments are being followed by many of the code vendors who are now providing multi-physics capabilities in their software tools. This paper illustrates current capabilities of multi-physics technology and highlights some of the future challenges

Application of modelling for predicting the behaviour of polymers and adhesives in microelectronic and photonic devices

With the growth in computing power, and advances in numerical methods for the solution of partial differential equations, modeling technologies based around computational fluid dynamics, finite element analysis and optimisation are now being widely used by researchers and industry. Polymer and adhesive materials are now being widely used in electronic and photonic devices. This paper will illustrate the use of modeling tools to predict the behaviour of these materials from product assembly to its performance and reliability.

Conservative semi-Lagrangian finite volume schemes

Semi-Lagrangian finite volume schemes for the numerical approximation of linear advection equations are presented. These schemes are constructed so that the conservation properties are preserved by the numerical approximation. This is achieved using an interpolation procedure based on area-weighting. Numerical results are presented illustrating some of the features of these schemes.

On the coupling of Navier–Stokes and linearised Euler equations for aeroacoustic simulation

Aerodynamic generation of sound is governed by the Navier–Stokes equations while acoustic propagation in a non-uniform medium is effectively described by the linearised Euler equations. Different numerical schemes are required for the efficient solution of these two sets of equations, and therefore, coupling techniques become an essential issue. Two types of one-way coupling between the flow solver and the acoustic solver are discussed: (a) for aerodynamic sound generated at solid surfaces, and (b) in the free stream. Test results indicate how the coupling achieves the necessary accuracy so that Computational Fluid Dynamics codes can be used in aeroacoustic simulations.

Concise introduction to image processing using C++

A Concise Intro to Image Processing using C++ presents state-of-the-art image processing methodology, including current industrial practices for image compression, image de-noising methods based on partial differential equations, and new image compression methods such as fractal image compression and wavelet compression. It includes elementary concepts of image processing and related fundamental tools with coding examples as well as exercises. With a particular emphasis on illustrating fractal and wavelet compression algorithms, the text covers image segmentation, object recognition, and morphology. An accompanying CD-ROM contains code for all algorithms.