Ordering of Ge islands on Si(001) substrates patterned by nanoindentation

Spatial organization of Ge islands, grown by physical vapor deposition, on prepatterned Si(001) substrates has been investigated. The substrates were patterned prior to Ge deposition by nanoindentation. Characterization of Ge dots is performed by atomic force microscopy and scanning electron microscopy. The nanoindents act as trapping sites, allowing ripening of Ge islands at those locations during subsequent deposition and diffusion of Ge on the surface. The results show that island ordering is intrinsically linked to the nucleation and growth at indented sites and it strongly depends on pattern parameters.

Diffusion tensor of water in model articular cartilage

We used Monte Carlo simulations of Brownian dynamics of water to study anisotropic water diffusion in an idealised model of articular cartilage. The main aim was to use the simulations as a tool for translation of the fractional anisotropy of the water diffusion tensor in cartilage into quantitative characteristics of its collagen fibre network. The key finding was a linear empirical relationship between the collagen volume fraction and the fractional anisotropy of the diffusion tensor. Fractional anisotropy of the diffusion tensor is potentially a robust indicator of the microstructure of the tissue because, in the first approximation, it is invariant to the inclusion of proteoglycans or chemical exchange between free and collagen-bound water in the model. We discuss potential applications of Monte Carlo diffusion-tensor simulations for quantitative biophysical interpretation of MRI diffusion-tensor images of cartilage. Extension of the model to include collagen fibre disorder is also discussed.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Implementing a Pattern and Structure Mathematics Awareness Program (PASMAP) in kindergarten

This paper provides an interim report of a large empirical evaluation study in progress. An intervention was implemented to evaluate the effectiveness of the Pattern and Structure Mathematical Awareness Program (PASMAP) on Kindergarten students’ mathematical development. Four large schools (two from Sydney and two from Brisbane), 16 teachers and their 316 students participated in the first phase of a 2-year longitudinal study. Eight of 16 classes implemented the PASMAP program over three school terms. This paper provides an overview of key aspects of the intervention, and preliminary analysis of the impact of PASMAP on students’ representation, abstraction and generalisation of mathematical ideas.

Household type and structure, time-use pattern, and trip-chaining behavior

In order to examine time allocation patterns within household-level trip-chaining, simultaneous doubly-censored Tobit models are applied to model time-use behavior within the context of household activity participation. Using the entire sample and a sub-sample of worker households from Tucson's Household Travel Survey, two sets of models are developed to better understand the phenomena of trip-chaining behavior among five types of households: single non-worker households, single worker households, couple non-worker households, couple one-worker households, and couple two-worker households. Durations of out-of-home subsistence, maintenance, and discretionary activities within trip chains are examined. Factors found to be associated with trip-chaining behavior include intra-household interactions with the household types and their structure and household head attributes.

Nonlinear diffusion and exclusion processes with contact interactions

Exclusion processes on a regular lattice are used to model many biological and physical systems at a discrete level. The average properties of an exclusion process may be described by a continuum model given by a partial differential equation. We combine a general class of contact interactions with an exclusion process. We determine that many different types of contact interactions at the agent-level always give rise to a nonlinear diffusion equation, with a vast variety of diffusion functions D(C). We find that these functions may be dependent on the chosen lattice and the defined neighborhood of the contact interactions. Mild to moderate contact interaction strength generally results in good agreement between discrete and continuum models, while strong interactions often show discrepancies between the two, particularly when D(C) takes on negative values. We present a measure to predict the goodness of fit between the discrete and continuous model, and thus the validity of the continuum description of a motile, contact-interacting population of agents. This work has implications for modeling cell motility and interpreting cell motility assays, giving the ability to incorporate biologically realistic cell-cell interactions and develop global measures of discrete microscopic data.

Predictions of road traffic noise on residential balconies using a specular and diffusion model

A combined specular reflection and diffusion model using the radiosity technique was developed to calculate road traffic noise level on residential balconies. The model is capable of numerous geometrical configurations for a single balcony situated in the centre of a street canyon. The geometry of the balcony and the street can be altered with width,length and height. The model was used to calculate for three different geometrical and acoustic absorption characteristics for a balcony. The calculated results are presented in this paper.

Dynamics of pattern writing and erasure in photorefractive lithium niobate for data storage applications

The present rate of technological advance continues to place significant demands on data storage devices. The sheer amount of digital data being generated each year along with consumer expectations, fuels these demands. At present, most digital data is stored magnetically, in the form of hard disk drives or on magnetic tape. The increase in areal density (AD) of magnetic hard disk drives over the past 50 years has been of the order of 100 million times, and current devices are storing data at ADs of the order of hundreds of gigabits per square inch. However, it has been known for some time that the progress in this form of data storage is approaching fundamental limits. The main limitation relates to the lower size limit that an individual bit can have for stable storage. Various techniques for overcoming these fundamental limits are currently the focus of considerable research effort. Most attempt to improve current data storage methods, or modify these slightly for higher density storage. Alternatively, three dimensional optical data storage is a promising field for the information storage needs of the future, offering very high density, high speed memory. There are two ways in which data may be recorded in a three dimensional optical medium; either bit-by-bit (similar in principle to an optical disc medium such as CD or DVD) or by using pages of bit data. Bit-by-bit techniques for three dimensional storage offer high density but are inherently slow due to the serial nature of data access. Page-based techniques, where a two-dimensional page of data bits is written in one write operation, can offer significantly higher data rates, due to their parallel nature. Holographic Data Storage (HDS) is one such page-oriented optical memory technique. This field of research has been active for several decades, but with few commercial products presently available. Another page-oriented optical memory technique involves recording pages of data as phase masks in a photorefractive medium. A photorefractive material is one by which the refractive index can be modified by light of the appropriate wavelength and intensity, and this property can be used to store information in these materials. In phase mask storage, two dimensional pages of data are recorded into a photorefractive crystal, as refractive index changes in the medium. A low-intensity readout beam propagating through the medium will have its intensity profile modified by these refractive index changes and a CCD camera can be used to monitor the readout beam, and thus read the stored data. The main aim of this research was to investigate data storage using phase masks in the photorefractive crystal, lithium niobate (LiNbO3). Firstly the experimental methods for storing the two dimensional pages of data (a set of vertical stripes of varying lengths) in the medium are presented. The laser beam used for writing, whose intensity profile is modified by an amplitudemask which contains a pattern of the information to be stored, illuminates the lithium niobate crystal and the photorefractive effect causes the patterns to be stored as refractive index changes in the medium. These patterns are read out non-destructively using a low intensity probe beam and a CCD camera. A common complication of information storage in photorefractive crystals is the issue of destructive readout. This is a problem particularly for holographic data storage, where the readout beam should be at the same wavelength as the beam used for writing. Since the charge carriers in the medium are still sensitive to the read light field, the readout beam erases the stored information. A method to avoid this is by using thermal fixing. Here the photorefractive medium is heated to temperatures above 150�C; this process forms an ionic grating in the medium. This ionic grating is insensitive to the readout beam and therefore the information is not erased during readout. A non-contact method for determining temperature change in a lithium niobate crystal is presented in this thesis. The temperature-dependent birefringent properties of the medium cause intensity oscillations to be observed for a beam propagating through the medium during a change in temperature. It is shown that each oscillation corresponds to a particular temperature change, and by counting the number of oscillations observed, the temperature change of the medium can be deduced. The presented technique for measuring temperature change could easily be applied to a situation where thermal fixing of data in a photorefractive medium is required. Furthermore, by using an expanded beam and monitoring the intensity oscillations over a wide region, it is shown that the temperature in various locations of the crystal can be monitored simultaneously. This technique could be used to deduce temperature gradients in the medium. It is shown that the three dimensional nature of the recording medium causes interesting degradation effects to occur when the patterns are written for a longer-than-optimal time. This degradation results in the splitting of the vertical stripes in the data pattern, and for long writing exposure times this process can result in the complete deterioration of the information in the medium. It is shown in that simply by using incoherent illumination, the original pattern can be recovered from the degraded state. The reason for the recovery is that the refractive index changes causing the degradation are of a smaller magnitude since they are induced by the write field components scattered from the written structures. During incoherent erasure, the lower magnitude refractive index changes are neutralised first, allowing the original pattern to be recovered. The degradation process is shown to be reversed during the recovery process, and a simple relationship is found relating the time at which particular features appear during degradation and recovery. A further outcome of this work is that the minimum stripe width of 30 ìm is required for accurate storage and recovery of the information in the medium, any size smaller than this results in incomplete recovery. The degradation and recovery process could be applied to an application in image scrambling or cryptography for optical information storage. A two dimensional numerical model based on the finite-difference beam propagation method (FD-BPM) is presented and used to gain insight into the pattern storage process. The model shows that the degradation of the patterns is due to the complicated path taken by the write beam as it propagates through the crystal, and in particular the scattering of this beam from the induced refractive index structures in the medium. The model indicates that the highest quality pattern storage would be achieved with a thin 0.5 mm medium; however this type of medium would also remove the degradation property of the patterns and the subsequent recovery process. To overcome the simplistic treatment of the refractive index change in the FD-BPM model, a fully three dimensional photorefractive model developed by Devaux is presented. This model shows significant insight into the pattern storage, particularly for the degradation and recovery process, and confirms the theory that the recovery of the degraded patterns is possible since the refractive index changes responsible for the degradation are of a smaller magnitude. Finally, detailed analysis of the pattern formation and degradation dynamics for periodic patterns of various periodicities is presented. It is shown that stripe widths in the write beam of greater than 150 ìm result in the formation of different types of refractive index changes, compared with the stripes of smaller widths. As a result, it is shown that the pattern storage method discussed in this thesis has an upper feature size limit of 150 ìm, for accurate and reliable pattern storage.

A Two-stage information filtering based on rough decision rule and pattern mining

Information Overload and Mismatch are two fundamental problems affecting the effectiveness of information filtering systems. Even though both term-based and patternbased approaches have been proposed to address the problems of overload and mismatch, neither of these approaches alone can provide a satisfactory solution to address these problems. This paper presents a novel two-stage information filtering model which combines the merits of term-based and pattern-based approaches to effectively filter sheer volume of information. In particular, the first filtering stage is supported by a novel rough analysis model which efficiently removes a large number of irrelevant documents, thereby addressing the overload problem. The second filtering stage is empowered by a semantically rich pattern taxonomy mining model which effectively fetches incoming documents according to the specific information needs of a user, thereby addressing the mismatch problem. The experimental results based on the RCV1 corpus show that the proposed twostage filtering model significantly outperforms the both termbased and pattern-based information filtering models.

Models of collective cell spreading with variable cell aspect ratio : a motivation for degenerate diffusion models

Continuum diffusion models are often used to represent the collective motion of cell populations. Most previous studies have simply used linear diffusion to represent collective cell spreading, while others found that degenerate nonlinear diffusion provides a better match to experimental cell density profiles. In the cell modeling literature there is no guidance available with regard to which approach is more appropriate for representing the spreading of cell populations. Furthermore, there is no knowledge of particular experimental measurements that can be made to distinguish between situations where these two models are appropriate. Here we provide a link between individual-based and continuum models using a multi-scale approach in which we analyze the collective motion of a population of interacting agents in a generalized lattice-based exclusion process. For round agents that occupy a single lattice site, we find that the relevant continuum description of the system is a linear diffusion equation, whereas for elongated rod-shaped agents that occupy L adjacent lattice sites we find that the relevant continuum description is connected to the porous media equation (pme). The exponent in the nonlinear diffusivity function is related to the aspect ratio of the agents. Our work provides a physical connection between modeling collective cell spreading and the use of either the linear diffusion equation or the pme to represent cell density profiles. Results suggest that when using continuum models to represent cell population spreading, we should take care to account for variations in the cell aspect ratio because different aspect ratios lead to different continuum models.

Pattern-Based Evaluation of Scientific Workflow Management Systems

In recent years several scientific Workflow Management Systems (WfMSs) have been developed with the aim to automate large scale scientific experiments. As yet, many offerings have been developed, but none of them has been promoted as an accepted standard. In this paper we propose a pattern-based evaluation of three among the most widely used scientific WfMSs: Kepler, Taverna and Triana. The aim is to compare them with traditional business WfMSs, emphasizing the strengths and deficiencies of both systems. Moreover, a set of new patterns is defined from the analysis of the three considered systems.