Novel solutions for a model of wound healing angiogenesis

We prove the existence of novel, shock-fronted travelling wave solutions to a model of wound healing angiogenesis studied in Pettet et al (2000 IMA J. Math. App. Med. 17 395–413) assuming two conjectures hold. In the previous work, the authors showed that for certain parameter values, a heteroclinic orbit in the phase plane representing a smooth travelling wave solution exists. However, upon varying one of the parameters, the heteroclinic orbit was destroyed, or rather cut-off, by a wall of singularities in the phase plane. As a result, they concluded that under this parameter regime no travelling wave solutions existed. Using techniques from geometric singular perturbation theory and canard theory, we show that a travelling wave solution actually still exists for this parameter regime. We construct a heteroclinic orbit passing through the wall of singularities via a folded saddle canard point onto a repelling slow manifold. The orbit leaves this manifold via the fast dynamics and lands on the attracting slow manifold, finally connecting to its end state. This new travelling wave is no longer smooth but exhibits a sharp front or shock. Finally, we identify regions in parameter space where we expect that similar solutions exist. Moreover, we discuss the possibility of more exotic solutions.

Application of system dynamics for evaluating truck load regulations in Anhui, China

In the critical situation of prevailing overweight transportation and crag-fast enforcement in Chinese highway networks, this paper develops a methodological framework for truck weight regulation (TWR) evaluation using System Dynamics (SD). Composed of five interrelated subsystems, the framework is able to capture the highway, vehicle and freight variables that influence the effect of TWR and transportation efficiency over time. It specifically describes the development and use of the Truck Weight Regulation Evaluating Model (TWREM) for the highway freight system in Anhui province, China. Three policy alternatives are analyzed: 1) tolerant policy approach, which allows heavy-duty freight activity to continue in its current state, and is shown to lead to nearly catastrophic results; 2) rigid policy approach, which would terminate all heavy-duty freight activities immediately, and is shown to be economically infeasible; and 3) moderate policy approach, which advocates a gradual reduction of heavy-duty freight activities to a moderate state. The simulation results shows that the moderate policy approach is the most appropriate option to solve the social and economic problems arising from the activities of the heavy-duty freight transportation in Anhui. In addition, some suggestions of TWR policy in China are also made in this paper.

Fast reconstruction of aerodynamic shapes using evolutionary algorithms and virtual Nash strategies in a CFD design environment

This paper compares the performances of two different optimisation techniques for solving inverse problems; the first one deals with the Hierarchical Asynchronous Parallel Evolutionary Algorithms software (HAPEA) and the second is implemented with a game strategy named Nash-EA. The HAPEA software is based on a hierarchical topology and asynchronous parallel computation. The Nash-EA methodology is introduced as a distributed virtual game and consists of splitting the wing design variables - aerofoil sections - supervised by players optimising their own strategy. The HAPEA and Nash-EA software methodologies are applied to a single objective aerodynamic ONERA M6 wing reconstruction. Numerical results from the two approaches are compared in terms of the quality of model and computational expense and demonstrate the superiority of the distributed Nash-EA methodology in a parallel environment for a similar design quality.

The role of cardiopulmonary signals in the dynamics of the eye's wavefront aberrations

Abstract—The role of cardiopulmonary signals in the dynamics of wavefront aberrations in the eye has been examined. Synchronous measurement of the eye’s wavefront aberrations, cardiac function, blood pulse, and respiration signals were taken for a group of young, healthy subjects. Two focusing stimuli, three breathing patterns, as well as natural and cycloplegic eye conditions were examined. A set of tools, including time–frequency coherence and its metrics, has been proposed to acquire a detailed picture of the interactions of the cardiopulmonary system with the eye’s wavefront aberrations. The results showed that the coherence of the blood pulse and its harmonics with the eye’s aberrations was, on average, weak (0.4 ± 0.15), while the coherence of the respiration signal with eye’s aberrations was, on average, moderate (0.53 ± 0.14). It was also revealed that there were significant intervals during which high coherence occurred. On average, the coherence was high (>0.75) during 16% of the recorded time, for the blood pulse, and 34% of the time for the respiration signal. A statistically significant decrease in average coherence was noted for the eye’s aberrations with respiration in the case of fast controlled breathing (0.5 Hz). The coherence between the blood pulse and the defocus was significantly larger for the far target than for the near target condition. After cycloplegia, the coherence of defocus with the blood pulse significantly decreased, while this was not the case for the other aberrations. There was also a noticeable, but not statistically significant, increase in the coherence of the comatic term and respiration in that case. By using nonstationary measures of signal coherence, a more detailed picture of interactions between the cardiopulmonary signals and eye’s wavefront aberrations has emerged.

Improving team dynamics and innovation : the “Aspect Design” approach applied to interaction design

Interaction Design is a fast developing branch of Industrial Design. The availability of cheap microprocessors and sensor electronics allow interactions between people and products that were until recently impossible. This has added additional layers of complexity to the design process. Novice designers find it difficult to effectively juggle these complexities and typically tend to focus on one aspect at a time. They also tend to take a linear, step-by-step approach to the design process in contrast to expert designers who pursue “parallel lines of thought” whilst simultaneously co-evolving both problem and solution. (Lawson, 1993) This paper explores an approach that encourages designers (in this case novice designers) to take a parallel rather than linear approach to the design process. It also addresses the problem of social loafing that tends to occur in team activities.

What the experts think : fast bowling expertise acquisition and talent development

For applied sport scientists charged with developing talented performers an essential requirement is to identify components contributing to the development and maintenance of expertise. Previous qualitative analysis has revealed several psychological (e.g., mental focus, goal-setting and selfevaluation), socio-cultural (e.g. community and family support, cultural influence), physical (e.g., strength, height) and environmental (e.g., access to facilities and climate) constraints on successful Olympian development (Abbott et al., 2005). Open-ended interviews with expert athletes and/or expert coaches have been used to reveal competencies of elite performers to derive factors associated with success (Durand-Bush et al., 2002). However, the influence of these factors is likely to be sport-specific due to different task constraints and the changing nature of the performer-environment relationship through practice, coaching and competing (Vaeyens et al., 2008). So far, only one study on expertise acquisition in cricket has been undertaken. Weissensteiner, et al. (2009) found that development of expertise in cricket batting in Australia may be facilitated by early unstructured play (i.e. ‘backyard cricket’), a wide range of sport experience during development, and early exposure to playing with seniors.

Variables governing the dynamics of attacker-defender systems in team sport

This project was a step forward in the examination and identification of key variables on the perception, decision making and action of team sport athletes through theoretical insights provided by the ecological dynamics perspective. The methodology drew on experiential knowledge of elite coaches to drive further empirical investigation into the specific task, environmental and personal constraints that shape the behaviour of athletes in specific performance contexts. The thesis has provided an effective rationale for further investigation into the emergent perception, decision making and action demanded of athletes in these unpredictable, fluent, fast-paced environments.

Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

Distinguishing between mean-field, moment dynamics and stochastic descriptions of birth-death-movement processes

Mathematical descriptions of birth–death–movement processes are often calibrated to measurements from cell biology experiments to quantify tissue growth rates. Here we describe and analyze a discrete model of a birth–death-movement process applied to a typical two–dimensional cell biology experiment. We present three different descriptions of the system: (i) a standard mean–field description which neglects correlation effects and clustering; (ii) a moment dynamics description which approximately incorporates correlation and clustering effects, and; (iii) averaged data from repeated discrete simulations which directly incorporates correlation and clustering effects. Comparing these three descriptions indicates that the mean–field and moment dynamics approaches are valid only for certain parameter regimes, and that both these descriptions fail to make accurate predictions of the system for sufficiently fast birth and death rates where the effects of spatial correlations and clustering are sufficiently strong. Without any method to distinguish between the parameter regimes where these three descriptions are valid, it is possible that either the mean–field or moment dynamics model could be calibrated to experimental data under inappropriate conditions, leading to errors in parameter estimation. In this work we demonstrate that a simple measurement of agent clustering and correlation, based on coordination number data, provides an indirect measure of agent correlation and clustering effects, and can therefore be used to make a distinction between the validity of the different descriptions of the birth–death–movement process.

System dynamics model of the knowledge management process

To effectively manage the challenges being faced by construction organisations in a fast changing business environment, many organisations are attempting to integrate knowledge management (KM) into their business operations. KM activities interact with each other and form a process which receives input from its internal business environment and produces outputs that should be justified by its business performance. This paper aims to provide further understanding on the dynamic nature of the KM process. Through a combination of path analysis and system dynamic simulation, this study found that: 1) an improved business performance enables active KM activities and provide feedback and guidance for formulating learning-based policies; and 2) effective human resource recruitment policies can enlarge the pool of individual knowledge, which lead to a more conducive internal business environment, as well as a higher KM activity level. Consequently, the desired business performance level can be reached within a shorter time frame.

Stochastic dynamics of interacting haematopoietic stem cell niche lineages

Since we still know very little about stem cells in their natural environment, it is useful to explore their dynamics through modelling and simulation, as well as experimentally. Most models of stem cell systems are based on deterministic differential equations that ignore the natural heterogeneity of stem cell populations. This is not appropriate at the level of individual cells and niches, when randomness is more likely to affect dynamics. In this paper, we introduce a fast stochastic method for simulating a metapopulation of stem cell niche lineages, that is, many sub-populations that together form a heterogeneous metapopulation, over time. By selecting the common limiting timestep, our method ensures that the entire metapopulation is simulated synchronously. This is important, as it allows us to introduce interactions between separate niche lineages, which would otherwise be impossible. We expand our method to enable the coupling of many lineages into niche groups, where differentiated cells are pooled within each niche group. Using this method, we explore the dynamics of the haematopoietic system from a demand control system perspective. We find that coupling together niche lineages allows the organism to regulate blood cell numbers as closely as possible to the homeostatic optimum. Furthermore, coupled lineages respond better than uncoupled ones to random perturbations, here the loss of some myeloid cells. This could imply that it is advantageous for an organism to connect together its niche lineages into groups. Our results suggest that a potential fruitful empirical direction will be to understand how stem cell descendants communicate with the niche and how cancer may arise as a result of a failure of such communication.

Complex crystallization dynamics in amorphous germanium observed with dynamic transmission electron microscopy

Crystallization of amorphous germanium (a-Ge) by laser or electron beam heating is a remarkably complex process that involves several distinct modes of crystal growth and the development of intricate microstructural patterns on the nanosecond to ten microsecond time scales. Here we use dynamic transmission electron microscopy (DTEM) to study the fast, complex crystallization dynamics with 10 nm spatial and 15 ns temporal resolution. We have obtained time-resolved real-space images of nanosecond laser-induced crystallization in a-Ge with unprecedentedly high spatial resolution. Direct visualization of the crystallization front allows for time-resolved snapshots of the initiation and roughening of the dendrites on submicrosecond time scales. This growth is followed by a rapid transition to a ledgelike growth mechanism that produces a layered microstructure on a time scale of several microseconds. This study provides insights into the mechanisms governing this complex crystallization process and is a dramatic demonstration of the power of DTEM for studying time-dependent material processes far from equilibrium.