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.

Correlating flow induced shear stress and chondrocytes activity in micro-porous scaffold using computational fluid dynamics and rapid prototyping

Flow induced shear stress plays an important role in regulating cell growth and distribution in scaffolds. This study sought to correlate wall shear stress and chondrocytes activity for engineering design of micro-porous osteochondral grafts based on the hypothesis that it is possible to capture and discriminate between the transmitted force and cell response at the inner irregularities. Unlike common tissue engineering therapies with perfusion bioreactors in which flow-mediated stress is the controlling parameter, this work assigned the associated stress as a function of porosity to influence in vitro proliferation of chondrocytes. D-optimality criterion was used to accommodate three pore characteristics for appraisal in a mixed level fractional design of experiment (DOE); namely, pore size (4 levels), distribution pattern (2 levels) and density (3 levels). Micro-porous scaffolds (n=12) were fabricated according to the DOE using rapid prototyping of an acrylic-based bio-photopolymer. Computational fluid dynamics (CFD) models were created correspondingly and used on an idealized boundary condition with a Newtonian fluid domain to simulate the dynamic microenvironment inside the pores. In vitro condition was reproduced for the 3D printed constructs seeded by high pellet densities of human chondrocytes and cultured for 72 hours. The results showed that cell proliferation was significantly different in the constructs (p<0.05). Inlet fluid velocity of 3×10-2mms-1 and average shear stress of 5.65×10-2 Pa corresponded with increased cell proliferation for scaffolds with smaller pores in hexagonal pattern and lower densities. Although the analytical solution of a Poiseuille flow inside the pores was found insufficient for the description of the flow profile probably due to the outside flow induced turbulence, it showed that the shear stress would increase with cell growth and decrease with pore size. This correlation demonstrated the basis for determining the relation between the induced stress and chondrocyte activity to optimize microfabrication of engineered cartilaginous constructs.

High-growth firms : characteristics, job contribution and method observations

Largely as a result of mass unemployment problems in many European countries, the dynamics of job creation has in recent years attracted increased interest on the part of academics as well as policy-makers. In connection to this, a large number of studies carried out in various countries have concluded that SMEs play a very large and/or growing role as job creators (Birch, 1979; Baldwin and Picot, 1995; Davidsson, 1995a; Davidsson, Lindmark and Olofsson, 1993; 1994; 1995; 1997a; 1997b; Fumagelli and Mussati, 1993; Kirchhoff and Phillips, 1988; Spilling, 1995; for further reference to studies carried out in a large number of countries see also Aiginger and Tichy, 1991; ENSR, 1994; Loveman and Sengenberger, 1991; OECD, 1987; Storey and Johnson, 1987). While most researchers agree on the importance of SMEs, there is some controversy as regards whether this is mainly a result of many small start-ups and incremental expansions, or if a small minority of high growth SMEs contribute the lion’s share of new employment. This is known as the ‘mice vs. gazelles’ or ‘flyers vs. trundlers’ debate. Storey strongly advocates the position that the small group of high growth SMEs are the ‘real’ job creators (Storey, 1994; Storey & Johnson, 1987), whereas, e.g., the Davidsson et al research in Sweden (cf. above) gives more support for the ‘mice’ hypothesis.

Characteristics of spatial variation, size distribution, formation and growth of particles in urban environments

This thesis is the first comprehensive study of important parameters relating to aerosols' impact on climate and human health, namely spatial variation, particle size distribution and new particle formation. We determined the importance of spatial variation of particle number concentration in microscale environments, developed a method for particle size parameterisation and provided knowledge about the chemistry of new particle formation. This is a significant contribution to our understanding of processes behind the transformation and dynamics of urban aerosols. This PhD project included extensive measurements of air quality parameters using state of the art instrumentation at each of the 25 sites within the Brisbane metropolitan area and advanced statistical analysis.

Simulation of gas-phase nanoparticle dynamics in the plasma-enhanced chemical vapor deposition of carbon nanostructures

The results of 1D simulation of nanoparticle dynamics in the areas adjacent to nanostructured carbon-based films exposed to chemically active complex plasma of CH4 + H2 + Ar gas mixtures are presented. The nanoparticle-loaded near-substrate (including sheath and presheath) areas of a low-frequency (0.5 MHz) inductively coupled plasma facility for the PECVD growth of the ordered carbon-based nanotip structures are considered. The conditions allowing one to predict the size of particles that can pass through the plasma sheath and softly land onto the surface are formulated. The possibility of soft nano-cluster deposition without any additional acceleration common for some existing nano-cluster deposition schemes is demonstrated. The effect of the substrate heating power and the average atomic mass of neutral species is studied numerically and verified experimentally.

Self-organization and dynamics of nanoparticles in chemically active plasmas for low-temperature deposition of silicon and carbon-based nanostructured films

Self-organization and dynamic processes of nano/micron-sized solid particles grown in low-temperature chemically active plasmas as well as the associated physico-chemical processes are reviewed. Three specific reactive plasma chemistries, namely, of silane (SiH4), acetylene (C 2H2), and octafluorocyclobutane (c-C4F 8) RF plasma discharges for plasma enhanced chemical vapor deposition of amorphous hydrogenated silicon, hydrogenated and fluorinated carbon films, are considered. It is shown that the particle growth mechanisms and specific self-organization processes in the complex reactive plasma systems are related to the chemical organization and size of the nanoparticles. Correlation between the nanoparticle origin and self-organization in the ionized gas phase and improved thin film properties is reported. Self-organization and dynamic phenomena in relevant reactive plasma environments are studied for equivalent model systems comprising inert buffer gas and mono-dispersed organic particulate powders. Growth kinetics and dynamic properties of the plasma-assembled nanoparticles can be critical for the process quality in microelectronics as well as a number of other industrial applications including production of fine metal or ceramic powders, nanoparticle-unit thin film deposition, nanostructuring of substrates, nucleating agents in polymer and plastics synthesis, drug delivery systems, inorganic additives for sunscreens and UV-absorbers, and several others. Several unique properties of the chemically active plasma-nanoparticle systems are discussed as well.

Determinants of plant performance dynamics : empirical analysis of the manufacturing sector in Indonesia, 1990-2000

We identify determinants of plant dynamics and find their differences before, during, and after the Asian financial crisis. The results show that the distinction of the crisis is important and the effects of the crisis do not seem to persist after 1998. Furthermore, we reject Gibrat's law as the right functional form to describe plant growth. We are not able to support empirically the theoretical results that smaller and efficient plants tend to grow faster than larger and inefficient plants with the exception of the crisis period. The results reflect that there was a trickle down effect of economic development.

Pathways to peace : a phenomenological exploration of the processes of healing and posttraumatic growth following childhood sexual assault

This thesis explored pathways to healing in men and women who experienced traumatic sexual abuse in childhood and considered themselves to be in a place of wellness. The thesis synthesises current knowledge in this area and has produced a number of models with direct implications for clinical practice. This unique work has also contributed to advancing theoretical understanding of healing following sexual assault.

Dynamics of industry architecture and firm’s capability development : role of knowledge integration within product innovation

Aligned with the decline of Marshalian view of industry as constituting homogeneous set of firms, the new perspective is emerging by concentrating more on dynamics of sectors as the building block of industrial changes. Based on new assumptions, much of the action in terms of strategy, technology, and knowledge development does not happen either among firms within a stable industry, or through the growth or decline of certain sectors compared to others. Instead, the action happens in terms of the definition, redefinition, drawing, and redrawing of the very nature of these sectors. Technology does not progress and develop within a sector; rather it shapes (and is shaped by) the encompassing architecture of multiple sectors.

Using culture to manage the transition into university: Conceptualising the dynamics of withdrawal and engagement

This conceptual paper explored the purposes of using culture in the process of coping with stress by looking how first year undergraduate students used cultural elements and activities to aid their transition into university. Results supported two key conceptualisations of the use of culture. Firstly, results indicated that students used culture either for withdrawal purposes, i.e., for escaping from the stressful situation, or for engagement purposes, i.e., for actively engaging with the stressful situation. Secondly, the results suggested three different forms of using culture to engage with stressful situations: mood management, learning, and personal interaction. While the results of the study resonate with the distinction between avoidance versus approach-oriented coping strategies that are widely explored in the stress and coping literature, they also suggest that the relationship between withdrawal and engagement might be dynamic with those two strategies serving distinct purposes in the process of coping with stress. The paper thus suggests that there is a need to develop process-oriented models of coping that would allow identifying patterns in the way people fluctuate between withdrawal and engagement that support and facilitate their personal growth and development.

Dynamics of a dilute sheared inelastic fluid. I. Hydrodynamic modes and velocity correlation functions

The hydrodynamic modes and the velocity autocorrelation functions for a dilute sheared inelastic fluid are analyzed using an expansion in the parameter epsilon=(1-e)(1/2), where e is the coefficient of restitution. It is shown that the hydrodynamic modes for a sheared inelastic fluid are very different from those for an elastic fluid in the long-wave limit, since energy is not a conserved variable when the wavelength of perturbations is larger than the ``conduction length.'' In an inelastic fluid under shear, there are three coupled modes, the mass and the momenta in the plane of shear, which have a decay rate proportional to k(2/3) in the limit k -> 0, if the wave vector has a component along the flow direction. When the wave vector is aligned along the gradient-vorticity plane, we find that the scaling of the growth rate is similar to that for an elastic fluid. The Fourier transforms of the velocity autocorrelation functions are calculated for a steady shear flow correct to leading order in an expansion in epsilon. The time dependence of the autocorrelation function in the long-time limit is obtained by estimating the integral of the Fourier transform over wave number space. It is found that the autocorrelation functions for the velocity in the flow and gradient directions decay proportional to t(-5/2) in two dimensions and t(-15/4) in three dimensions. In the vorticity direction, the decay of the autocorrelation function is proportional to t(-3) in two dimensions and t(-7/2) in three dimensions.

Intermittent Dynamics, Stochastic Resonance and Dynamical Heterogeneity in Supercooled Liquid Water

Here we find through computer simulations and theoretical analysis that the low temperature thermodynamic anomalies of liquid water arises from the intermittent fluctuation between its high density and low density forms, consisting largely of 5-coordinated and 4-coordinated water molecules, respectively. The fluctuations exhibit strong dynamic heterogeneity (defined by the four point time correlation function), accompanied by a divergence like growth of the dynamic correlation length, of the type encountered in fragile supercooled liquids. The intermittency has been explained by invoking a two state model often employed to understand stochastic resonance, with the relevant periodic perturbation provided here by the fluctuation of the total volume of the system.

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.

Growth defect in Grg5 null mice is associated with reduced Ihh signaling in growth plates

Gene-targeted disruption of Grg5, a mouse homologue of Drosophila groucho (gro), results in postnatal growth retardation in mice. The growth defect, most striking in approximately half of the Grg5 null mice, occurs during the first 4-5 weeks of age, but most mice recover retarded growth later. We used the nonlinear mixed-effects model to fit the growth data of wild-type, heterozygous, and Grg5 null mice. On the basis of preliminary evidence suggesting an interaction between Grg5 and the transcription factor Cbfa1/Runx2, critical for skeletal development, we further investigated the skeleton in the mice. A long bone growth plate defect was identified, which included shorter zones of proliferative and hypertrophic chondrocytes and decreased trabecular bone formation. This decreased trabecular bone formation is likely caused by a reduced recruitment of osteoblasts into the growth plate region of Grg5 null mice. Like the growth defect, the growth plate and trabecular bone abnormality improved as the mice grew older. The growth plate defect was associated with reduced Indian hedgehog expression and signaling. We suggest that Grg5, a transcriptional coregulator, modulates the activities of transcription factors, such as Cbfa1/Runx2 in vivo to affect Ihh expression and the function of long bone growth plates.

Recruitment dynamics of invasive species in rainforest habitats following Cyclone Larry

In tropical forests, natural disturbance creates opportunities for species to claim previously utilized space and resources and is considered an important mechanism in the maintenance of species diversity. However, ecologists have long recognized that disturbance also promotes exotic plant invasions. Cyclones cause extensive defoliation, loss of major branches and multiple tree falls, resulting in a significantly more open canopy and increased light and heat levels in the understorey. The widespread and massive disturbance caused by cyclones provides ideal conditions for rapid recruitment and spread of invasive species. The ecological roles of invasive species in rainforest habitats following such a severe disturbance are poorly understood. Severe category 4 Cyclone Larry crossed the North Queensland coast in March 2006 causing massive disturbance to rainforest habitats from Tully to Cairns and west to the Atherton Tablelands. We established 10 plots in an area extensively damaged by this cyclone near El Arish in North Queensland. On each plot nine 2 × 2 m quadrats were established with three quadrats per plot in each of the following treatments: (i) complete debris removal down to the soil layer, (ii) removal of coarse woody debris only, and (iii) uncleared. We monitored recruitment, growth and mortality of all native and invasive species in the 90 quadrats every 3 months since the cyclone. Here we present the recruitment dynamics of invasive species across the study area in relation to the level of disturbance, the type of quadrat treatment, and the diversity and abundance of the native recruiting flora over the first 12 months post-cyclone. Our results suggest that invasive species will mostly comprise a transient component of the flora in the early stages of the successional response. However, some species may have longer-term effects on the successional trajectory of the rainforest and future forest composition and structure.