Work Fluctuations in Bosonic Josephson Junctions

We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In the instantaneous case, we show how the irreversible work scales differently depending on whether the system is driven to the Josephson or Fock regime of the bosonic Josephson junction. In the finite-time case, we use optimal control techniques to substantially decrease the irreversible work to negligible values. Our analysis can be implemented in present-day experiments with ultracold atoms and we show how to relate the work statistics to that of the population imbalance of the two modes.

Guided Migration and Collective Behavior: Cell Dynamics during Cancer Progression

This dissertation focuses on gaining understanding of cell migration and collective behavior through a combination of experiment, analysis, and modeling techniques. Cell migration is a ubiquitous process that plays an important role during embryonic development and wound healing as well as in diseases like cancer, which is a particular focus of this work. As cancer cells become increasingly malignant, they acquire the ability to migrate away from the primary tumor and spread throughout the body to form metastatic tumors. During this process, changes in gene expression and the surrounding tumor environment can lead to changes in cell migration characteristics. In this thesis, I analyze how cells are guided by the texture of their environment and how cells cooperate with their neighbors to move collectively. The emergent properties of collectively moving groups are a particular focus of this work as collective cell dynamics are known to change in diseases such as cancer. The internal machinery for cell migration involves polymerization of the actin cytoskeleton to create protrusions that---in coordination with retraction of the rear of the cell---lead to cell motion. This actin machinery has been previously shown to respond to the topography of the surrounding surface, leading to guided migration of amoeboid cells. Here we show that epithelial cells on nanoscale ridge structures also show changes in the morphology of their cytoskeletons; actin is found to align with the ridge structures. The migration of the cells is also guided preferentially along the ridge length. These ridge structures are on length scales similar to those found in tumor microenvironments and as such provide a system for studying the response of the cells' internal migration machinery to physiologically relevant topographical cues. In addition to sensing surface topography, individual cells can also be influenced by the pushing and pulling of neighboring cells. The emergent properties of collectively migrating cells show interesting dynamics and are relevant for cancer progression, but have been less studied than the motion of individual cells. We use Particle Image Velocimetry (PIV) to extract the motion of a collectively migrating cell sheet from time lapse images. The resulting flow fields allow us to analyze collective behavior over multiple length and time scales. To analyze the connection between individual cell properties and collective migration behavior, we compare experimental flow fields with the migration of simulated cell groups. Our collective migration metrics allow for a quantitative comparison between experimental and simulated results. This comparison shows that tissue-scale decreases in collective behavior can result from changes in individual cell activity without the need to postulate the existence of subpopulations of leader cells or global gradients. In addition to tissue-scale trends in collective behavior, the migration of cell groups includes localized dynamic features such as cell rearrangements. An individual cell may smoothly follow the motion of its neighbors (affine motion) or move in a more individualistic manner (non-affine motion). By decomposing individual motion into both affine and non-affine components, we measure cell rearrangements within a collective sheet. Finally, finite-time Lyapunov exponent (FTLE) values capture the stretching of the flow field and reflect its chaotic character. Applying collective migration analysis techniques to experimental data on both malignant and non-malignant human breast epithelial cells reveals differences in collective behavior that are not found from analyzing migration speeds alone. Non-malignant cells show increased cooperative motion on long time scales whereas malignant cells remain uncooperative as time progresses. Combining multiple analysis techniques also shows that these two cell types differ in their response to a perturbation of cell-cell adhesion through the molecule E-cadherin. Non-malignant MCF10A cells use E-cadherin for short time coordination of collective motion, yet even with decreased E-cadherin expression, the cells remain coordinated over long time scales. In contrast, the migration behavior of malignant and invasive MCF10CA1a cells, which already shows decreased collective dynamics on both time scales, is insensitive to the change in E-cadherin expression.

Guided Migration and Collective Behavior: Cell Dynamics during Cancer Progression

This dissertation focuses on gaining understanding of cell migration and collective behavior through a combination of experiment, analysis, and modeling techniques. Cell migration is a ubiquitous process that plays an important role during embryonic development and wound healing as well as in diseases like cancer, which is a particular focus of this work. As cancer cells become increasingly malignant, they acquire the ability to migrate away from the primary tumor and spread throughout the body to form metastatic tumors. During this process, changes in gene expression and the surrounding tumor environment can lead to changes in cell migration characteristics. In this thesis, I analyze how cells are guided by the texture of their environment and how cells cooperate with their neighbors to move collectively. The emergent properties of collectively moving groups are a particular focus of this work as collective cell dynamics are known to change in diseases such as cancer. The internal machinery for cell migration involves polymerization of the actin cytoskeleton to create protrusions that---in coordination with retraction of the rear of the cell---lead to cell motion. This actin machinery has been previously shown to respond to the topography of the surrounding surface, leading to guided migration of amoeboid cells. Here we show that epithelial cells on nanoscale ridge structures also show changes in the morphology of their cytoskeletons; actin is found to align with the ridge structures. The migration of the cells is also guided preferentially along the ridge length. These ridge structures are on length scales similar to those found in tumor microenvironments and as such provide a system for studying the response of the cells' internal migration machinery to physiologically relevant topographical cues. In addition to sensing surface topography, individual cells can also be influenced by the pushing and pulling of neighboring cells. The emergent properties of collectively migrating cells show interesting dynamics and are relevant for cancer progression, but have been less studied than the motion of individual cells. We use Particle Image Velocimetry (PIV) to extract the motion of a collectively migrating cell sheet from time lapse images. The resulting flow fields allow us to analyze collective behavior over multiple length and time scales. To analyze the connection between individual cell properties and collective migration behavior, we compare experimental flow fields with the migration of simulated cell groups. Our collective migration metrics allow for a quantitative comparison between experimental and simulated results. This comparison shows that tissue-scale decreases in collective behavior can result from changes in individual cell activity without the need to postulate the existence of subpopulations of leader cells or global gradients. In addition to tissue-scale trends in collective behavior, the migration of cell groups includes localized dynamic features such as cell rearrangements. An individual cell may smoothly follow the motion of its neighbors (affine motion) or move in a more individualistic manner (non-affine motion). By decomposing individual motion into both affine and non-affine components, we measure cell rearrangements within a collective sheet. Finally, finite-time Lyapunov exponent (FTLE) values capture the stretching of the flow field and reflect its chaotic character. Applying collective migration analysis techniques to experimental data on both malignant and non-malignant human breast epithelial cells reveals differences in collective behavior that are not found from analyzing migration speeds alone. Non-malignant cells show increased cooperative motion on long time scales whereas malignant cells remain uncooperative as time progresses. Combining multiple analysis techniques also shows that these two cell types differ in their response to a perturbation of cell-cell adhesion through the molecule E-cadherin. Non-malignant MCF10A cells use E-cadherin for short time coordination of collective motion, yet even with decreased E-cadherin expression, the cells remain coordinated over long time scales. In contrast, the migration behavior of malignant and invasive MCF10CA1a cells, which already shows decreased collective dynamics on both time scales, is insensitive to the change in E-cadherin expression.

Rock slope stability analyses using extreme learning neural network and terminal steepest descent algorithm

The analysis of rock slope stability is a classical problem for geotechnical engineers. However, for practicing engineers, proper software is not usually user friendly, and additional resources capable of providing information useful for decision-making are required. This study developed a convenient tool that can provide a prompt assessment of rock slope stability. A nonlinear input-output mapping of the rock slope system was constructed using a neural network trained by an extreme learning algorithm. The training data was obtained by using finite element upper and lower bound limit analysis methods. The newly developed techniques in this study can either estimate the factor of safety for a rock slope or obtain the implicit parameters through back analyses. Back analysis parameter identification was performed using a terminal steepest descent algorithm based on the finite-time stability theory. This algorithm not only guarantees finite-time error convergence but also achieves exact zero convergence, unlike the conventional steepest descent algorithm in which the training error never reaches zero.

Strategy for succession in family owned small businesses as a wicked problem to be tamed

Contemporary strategic-planning processes don’t help family businesses cope with some of the big problems they face. Owner managers admit that they are confronted with issues, such as those associated with succession and inter-generational transfer that cannot be resolved merely by gathering additional data, defining issues more clearly, or breaking them down into small problems. Preparing for succession is often put off or ignored, many planning techniques don’t generate fresh ideas and implementing solutions is often fraught with political peril. This paper presents a framework to explore the idea of wicked problems, its relevance to succession planning in family businesses and its implications for practice and policy. A wicked problem has many and varied elements, and is complex as well as challenging. These problems are different to hard but ordinary problems, which people can solve in a finite time period by applying standard techniques. In this paper the authors argue that the wicked problem of family business succession requires a different approach to strategy, founded on social planning processes to engage multiple stakeholders and reconcile family/business interests to foster a joint commitment to possible ways of resolution. This requires academics and practitioners to re-frame traditional business strategic planning processes to achieve more sustainable family business futures.

Real-time vision, tracking and control

This paper, which serves as an introduction to the mini-symposium on Real-Time Vision, Tracking and Control, provides a broad sketch of visual servoing, the application of real-time vision, tracking and control for robot guidance. It outlines the basic theoretical approaches to the problem, describes a typical architecture, and discusses major milestones, applications and the significant vision sub-problems that must be solved.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

The field of fractional differential equations provides a means for modelling transport processes within complex media which are governed by anomalous transport. Indeed, the application to anomalous transport has been a significant driving force behind the rapid growth and expansion of the literature in the field of fractional calculus. In this paper, we present a finite volume method to solve the time-space two-sided fractional advection dispersion equation on a one-dimensional domain. Such an equation allows modelling different flow regime impacts from either side. The finite volume formulation provides a natural way to handle fractional advection-dispersion equations written in conservative form. The novel spatial discretisation employs fractionally-shifted Gr¨unwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes, while the L1-algorithm is used to discretise the Caputo time fractional derivative. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Over time assessment data analysis tracking a school's on-going performance

In Australia, as in some other western nations, governments impose accountability measures on educational institutions (Earl, 2005). One such accountability measure is the National Assessment Program - Literacy and Numeracy (NAPLAN) from which high-stakes assessment data is generated. In this article, a practical method of data analysis known as the Over Time Assessment Data Analysis (OTADA) is offered as an analytical process by which schools can monitor their current and over time performances. This analysis developed by the author, is currently used extensively in schools throughout Queensland. By Analysing in this way, teachers, and in particular principals, can obtain a quick and insightful performance overview. For those seeking to track the achievements and progress of year level cohorts, the OTADA should be considered.

A finite volume method with linearisation in time for the solution of advection-reaction-diffusion systems

The numerical solution in one space dimension of advection--reaction--diffusion systems with nonlinear source terms may invoke a high computational cost when the presently available methods are used. Numerous examples of finite volume schemes with high order spatial discretisations together with various techniques for the approximation of the advection term can be found in the literature. Almost all such techniques result in a nonlinear system of equations as a consequence of the finite volume discretisation especially when there are nonlinear source terms in the associated partial differential equation models. This work introduces a new technique that avoids having such nonlinear systems of equations generated by the spatial discretisation process when nonlinear source terms in the model equations can be expanded in positive powers of the dependent function of interest. The basis of this method is a new linearisation technique for the temporal integration of the nonlinear source terms as a supplementation of a more typical finite volume method. The resulting linear system of equations is shown to be both accurate and significantly faster than methods that necessitate the use of solvers for nonlinear system of equations.

A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.