Contracting bubbles in Hele-Shaw cells with a power-law fluid

The problem of bubble contraction in a Hele-Shaw cell is studied for the case in which the surrounding fluid is of power-law type. A small perturbation of the radially symmetric problem is first considered, focussing on the behaviour just before the bubble vanishes, it being found that for shear-thinning fluids the radially symmetric solution is stable, while for shear-thickening fluids the aspect ratio of the bubble boundary increases. The borderline (Newtonian) case considered previously is neutrally stable, the bubble boundary becoming elliptic in shape with the eccentricity of the ellipse depending on the initial data. Further light is shed on the bubble contraction problem by considering a long thin Hele-Shaw cell: for early times the leading-order behaviour is one-dimensional in this limit; however, as the bubble contracts its evolution is ultimately determined by the solution of a Wiener-Hopf problem, the transition between the long-thin limit and the extinction limit in which the bubble vanishes being described by what is in effect a similarity solution of the second kind. This same solution describes the generic (slit-like) extinction behaviour for shear-thickening fluids, the interface profiles that generalise the ellipses that characterise the Newtonian case being constructed by the Wiener-Hopf calculation.

A two-compartment mechanochemical model of the roles of transforming growth factor-beta and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor-beta (TGF-beta) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGF-beta and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGF-beta in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGF-beta significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures.

Modelling cell separation during plant organ abscission

A simple mathematical model is presented to describe the cell separation process that plants undertake in order to deliberately shed organs. The focus here is on modelling the production of the enzyme polygalacturonase, which breaks down pectin that provides natural cell-to-cell adhesion in the localised abscission zone. A coupled system of three ordinary differential equations is given for a single cell, and then extended to hold for a layer of cells in the abscission zone. Simple observations are made based on the results of this preliminary model and, furthermore, a number of opportunities for applied mathematicians to make contributions in this subject area are discussed.

Catch me if you can : the effective service of bankruptcy documents in a changing world

This article discusses some recent judicial decisions to assist legal practitioners to overcome some of the problems encountered when serving Bankruptcy Notices and Creditor’s Petitions. Some of the issues covered in the discussion are: What the valid last-known address of the debtor can be, whether a Bankruptcy Notice can be validly served by email on a debtor who is located outside Australia, whether service of a Bankruptcy Notice is valid when the debtor is outside Australia when service on the debtor occurs in Australia, whether the creditor’s failure to obtain leave for service of a Bankruptcy Notice can be excused, what can be done regarding personal service of a Creditor’s Petition when a debtor is outside Australia and whether the Court can set aside a sequestration order. The article goes on to place the issues in the context of broader bankruptcy policies noting that effective service of bankruptcy documents is challenging in a world where mobility of debtors is global and new modes of communication ever changing.

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.

Age, muscle fatigue, and walking endurance in pre-menopausal women

Aging is associated with loss of endurance; however, aging is also associated with decreased fatigue during maximal isometric contractions. The aims of this study were to examine the relationship between age and walking endurance (WE) and maximal isometric fatigue (MIF) and to determine which metabolic/fitness components explain the expected age effects on WE and MIF. Subjects were 96 pre-menopausal women. Oxygen uptake (walking economy) was assessed during a 3-mph walk; aerobic capacity and WE by progressive treadmill test; knee extension strength by isometric contractions, MIF during a 90-s isometric plantar flexion (muscle metabolism measured by 31P MRS). Age was related to increased walking economy (low VO2, r = −0.19, P < 0.03) and muscle metabolic economy (force/ATP, 0.34, P = 0.01), and reduced MIF (−0.26, P < 0.03). However, age was associated with reduced WE (−0.28, P < 0.01). Multiple regression showed that muscle metabolic economy explained the age-related decrease in MIF (partial r for MIF and age −0.13, P = 0.35) whereas walking economy did not explain the age-related decrease in WE (partial r for WE and age −0.25, P < 0.02). Inclusion of VO2max and knee endurance strength accounted for the age-related decreased WE (partial r for WE and age = 0.03, P > 0.80). In premenopausal women, age is related to WE and MIF. In addition, these results support the hypothesis that age-related increases in metabolic economy may decrease MIF. However, decreased muscle strength and oxidative capacity are related to WE.

Dark humour invigorates familiar fables ; a review

THEATRE: Grimm Tales. By Carol Ann Duffy and Tim Supple. Queensland Theatre Company, Brisbane. November 16. QUEENSLAND Theatre Company concludes its season with Grimm Tales, Carol Ann Duffy and Tim Supple's adaptation of classic cautionary tales as set down by the Brothers Grimm in the 19th century. This programming decision is clearly designed to present fun family entertainment as Christmas approaches. In Grimm Tales, well-known stories such as Hansel and Gretel, Snow White and Rumpelstiltskin pack a little more punch than in your standard picture book. Duffy and Supple's play is by no means the sort of poetic, postmodern or politicised adaptation of the fairytale we see from writers such as Angela Carter, and it is not intended to be subversive or to question the social and gender assumptions that underpin the tales. Start of sidebar. Skip to end of sidebar. End of sidebar. Return to start of sidebar. Rather, a return to the grislier original incarnations of the tales - the wicked stepsisters who lop off parts of their feet to fit the slipper and win the prince, or the hare so confused by the hedgehog's stratagem to make him think he is losing the race, he runs himself to death - has a comic effect. In this production, directed by Michael Futcher, heightened performances from some of Brisbane's best comic and physical actors, live music and an open, acknowledged relationship with the audience establish the atmosphere for the piece. While the production is a little sombre and slow to start with the first tale, Hansel and Gretel, the knowingness and almost slapstick quality with which the cast plays out the gruesome, scatological or silly moments in the other tales are well pitched to carry the comedy. The action is supported by a fantastic set by Greg Clarke of wooden planked walls, stairs and walkways which, with the help of David Walter's lighting design, is transformed into forests, ballrooms and castles as the cast moves up, over and under it. The overall highlight is probably the cast Futcher has brought together. Established QTC actors Eugene Gilfedder, Lucas Stibbard and Scott Witt, and emerging QTC actor Melanie Zanetti, join Liz Buchanan, Dan Crestani and Emma Pursey, all well known for their independent work in Brisbane but making their mainstage debut for the QTC. Every one of them metamorphoses with ease from character to character, human to animal, and central player to support. There is nothing particularly new in Grimm Tales, and it doesn't try to do anything more (or, indeed, less) than entertain, but skilful direction and a strong cast ensure it succeeds on those terms.

Throwing frame and performance of elite male seated shot-putters

Seated shot-putters rely on a customized assistive device called a throwing frame. Currently, the construction of each individual throwing frame is mainly driven by an empirical approach. One way to refine the conception is to improve the basic understanding of performance of seated shot-putters. The relationship between performance and throwing technique has been well described. Remarkably, the relationship between performance and throwing frame characteristics has received limited attention. The primary objective of this study was to present a cataloguing of characteristics of throwing frames used by seated shot-putters. This cataloguing consisted of defining and grouping 26 characteristics into three main categories (i.e., whole body, foot and upper limb specific characteristics) and seven sub-categories. The secondary objective of this study was to provide raw characterisations of the throwing frames for a group of athletes who participated in a world-class event. The characterisation consisted of describing the characteristics of each throwing frame. Potential relationships between characteristics, performance and classification were also identified. The cataloguing was achieved using a 6-step heuristic approach, involving expert opinions and the analysis of 215 attempts produced by 55 male athletes during the 2006 IPC Athletics World Championships. The distribution of samples across characteristics suggested a relevant level of comprehensiveness for the proposed cataloguing. The raw data, the profile of best athletes and the frequency of characteristics provided key benchmark information for construction of a throwing frame as well as coaching, classification and officiating. Analysis of data sets relating to characteristics, performance and classification were inconclusive.

Bow and stern flows with constant vorticity

Free surface flows of a rotational fluid past a two-dimensional semi-infinite body are considered. The fluid is assumed to be inviscid, incompressible, and of finite depth. A boundary integral method is used to solve the problem for the case where the free surface meets the body at a stagnation point. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterized by a train of waves upstream. It is shown numerically that the amplitude of these waves increases as each of the Froude number, vorticity and height of the body above the bottom increases.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

Using routinely collected hospital data for child maltreatment surveillance : issues, methods and patterns

Background: International data on child maltreatment are largely derived from child protection agencies, and predominantly report only substantiated cases of child maltreatment. This approach underestimates the incidence of maltreatment and makes inter-jurisdictional comparisons difficult. There has been a growing recognition of the importance of health professionals in identifying, documenting and reporting suspected child maltreatment. This study aimed to describe the issues around case identification using coded morbidity data, outline methods for selecting and grouping relevant codes, and illustrate patterns of maltreatment identified. Methods: A comprehensive review of the ICD-10-AM classification system was undertaken, including review of index terms, a free text search of tabular volumes, and a review of coding standards pertaining to child maltreatment coding. Identified codes were further categorised into maltreatment types including physical abuse, sexual abuse, emotional or psychological abuse, and neglect. Using these code groupings, one year of Australian hospitalisation data for children under 18 years of age was examined to quantify the proportion of patients identified and to explore the characteristics of cases assigned maltreatment-related codes. Results: Less than 0.5% of children hospitalised in Australia between 2005 and 2006 had a maltreatment code assigned, almost 4% of children with a principal diagnosis of a mental and behavioural disorder and over 1% of children with an injury or poisoning as the principal diagnosis had a maltreatment code assigned. The patterns of children assigned with definitive T74 codes varied by sex and age group. For males selected as having a maltreatment-related presentation, physical abuse was most commonly coded (62.6% of maltreatment cases) while for females selected as having a maltreatment-related presentation, sexual abuse was the most commonly assigned form of maltreatment (52.9% of maltreatment cases). Conclusion: This study has demonstrated that hospital data could provide valuable information for routine monitoring and surveillance of child maltreatment, even in the absence of population-based linked data sources. With national and international calls for a public health response to child maltreatment, better understanding of, investment in and utilisation of our core national routinely collected data sources will enhance the evidence-base needed to support an appropriate response to children at risk.