Drug diffusion from polymeric delivery devices : a problem with two moving boundaries

An existing model for solvent penetration and drug release from a spherically-shaped polymeric drug delivery device is revisited. The model has two moving boundaries, one that describes the interface between the glassy and rubbery states of polymer, and another that defines the interface between the polymer ball and the pool of solvent. The model is extended so that the nonlinear diffusion coefficient of drug explicitly depends on the concentration of solvent, and the resulting equations are solved numerically using a front-fixing transformation together with a finite difference spatial discretisation and the method of lines. We present evidence that our scheme is much more accurate than a previous scheme. Asymptotic results in the small-time limit are presented, which show how the use of a kinetic law as a boundary condition on the innermost moving boundary dictates qualitative behaviour, the scalings being very different to the similar moving boundary problem that arises from modelling the melting of an ice ball. The implication is that the model considered here exhibits what is referred to as ``non-Fickian'' or Case II diffusion which, together with the initially constant rate of drug release, has certain appeal from a pharmaceutical perspective.

Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.

Natural convection from a plane vertical porous surface in non-isothermal surroundings

In this paper, laminar natural convection flow from a permeable and isothermal vertical surface placed in non-isothermal surroundings is considered. Introducing appropriate transformations into the boundary layer equations governing the flow derives non-similar boundary layer equations. Results of both the analytical and numerical solutions are then presented in the form of skin-friction and Nusselt number. Numerical solutions of the transformed non-similar boundary layer equations are obtained by three distinct solution methods, (i) the perturbation solutions for small � (ii) the asymptotic solution for large � (iii) the implicit finite difference method for all � where � is the transpiration parameter. Perturbation solutions for small and large values of � are compared with the finite difference solutions for different values of pertinent parameters, namely, the Prandtl number Pr, and the ambient temperature gradient n.

An effective approach to verbose queries using a limited dependencies language model

Intuitively, any ‘bag of words’ approach in IR should benefit from taking term dependencies into account. Unfortunately, for years the results of exploiting such dependencies have been mixed or inconclusive. To improve the situation, this paper shows how the natural language properties of the target documents can be used to transform and enrich the term dependencies to more useful statistics. This is done in three steps. The term co-occurrence statistics of queries and documents are each represented by a Markov chain. The paper proves that such a chain is ergodic, and therefore its asymptotic behavior is unique, stationary, and independent of the initial state. Next, the stationary distribution is taken to model queries and documents, rather than their initial distributions. Finally, ranking is achieved following the customary language modeling paradigm. The main contribution of this paper is to argue why the asymptotic behavior of the document model is a better representation then just the document’s initial distribution. A secondary contribution is to investigate the practical application of this representation in case the queries become increasingly verbose. In the experiments (based on Lemur’s search engine substrate) the default query model was replaced by the stable distribution of the query. Just modeling the query this way already resulted in significant improvements over a standard language model baseline. The results were on a par or better than more sophisticated algorithms that use fine-tuned parameters or extensive training. Moreover, the more verbose the query, the more effective the approach seems to become.

Free surface flow past topography : a beyond-all-orders approach

The problem of steady subcritical free surface flow past a submerged inclined step is considered. The asymptotic limit of small Froude number is treated, with particular emphasis on the effect that changing the angle of the step face has on the surface waves. As demonstrated by Chapman & Vanden-Broeck (2006), the divergence of a power series expansion in powers of the square of the Froude number is caused by singularities in the analytic continuation of the free surface; for an inclined step, these singularities may correspond to either the corners or stagnation points of the step, or both, depending on the angle of incline. Stokes lines emanate from these singularities, and exponentially small waves are switched on at the point the Stokes lines intersect with the free surface. Our results suggest that for a certain range of step angles, two wavetrains are switched on, but the exponentially subdominant one is switched on first, leading to an intermediate wavetrain not previously noted. We extend these ideas to the problem of flow over a submerged bump or trench, again with inclined sides. This time there may be two, three or four active Stokes lines, depending on the inclination angles. We demonstrate how to construct a base topography such that wave contributions from separate Stokes lines are of equal magnitude but opposite phase, thus cancelling out. Our asymptotic results are complemented by numerical solutions to the fully nonlinear equations.

Ergodic capacity of the exponentially correlated slotted amplify and forward relay channel

In this paper we analyze the performance degradation of slotted amplify-and-forward protocol in wireless environments with high node density where the number of relays grows asymptotically large. Channel gains between source-destination pairs in such networks can no longer be independent. We analyze the degradation of performance in such wireless environments where channel gains are exponentially correlated by looking at the capacity per channel use. Theoretical results for eigenvalue distribution and the capacity are derived and compared with the simulation results. Both analytical and simulated results show that the capacity given by the asymptotic mutual information decreases with the network density.

Wound healing angiogenesis : the clinical implications of a simple mathematical model

Nonhealing wounds are a major burden for health care systems worldwide. In addition, a patient who suffers from this type of wound usually has a reduced quality of life. While the wound healing process is undoubtedly complex, in this paper we develop a deterministic mathematical model, formulated as a system of partial differential equations, that focusses on an important aspect of successful healing: oxygen supply to the wound bed by a combination of diffusion from the surrounding unwounded tissue and delivery from newly formed blood vessels. While the model equations can be solved numerically, the emphasis here is on the use of asymptotic methods to establish conditions under which new blood vessel growth can be initiated and wound-bed angiogenesis can progress. These conditions are given in terms of key model parameters including the rate of oxygen supply and its rate of consumption in the wound. We use our model to discuss the clinical use of treatments such as hyperbaric oxygen therapy, wound bed debridement, and revascularisation therapy that have the potential to initiate healing in chronic, stalled wounds.

The lived experience of PTSD for children of Australian Vietnam veterans in Australia

There is a growing area of scholarship that attests to the importance of understanding the impact of Post Traumatic Stress Disorder (PTSD) on the military family (Cozza, Chun, & Polo, 2005; Peach, 2005; Riggs, 2009; Siebler, 2003). Recent research highlights the critical role that the family plays in mitigating the effects of this condition for its members (Chase-Lansdale, Wakschlag, & Brooks-Gunn, 1995; Fiese, Foley, & Spagnola, 2006; Hetherington & Blechman, 1996; Pinkerton & Dolan, 2007; Seedat, Niehaus, & Stein, 2001; Serbin & Karp, 2003; Walsh, 2003), society (Jenson & Fraser, 2006; Seedat, Kaminer, Lockhat, & Stein, 2000; Wood & Geismar, 1989) and the next generation (Davidson & Mellor, 2001; Ender, 2006; Weber, 2005; Westerink & Giarratano, 1999). However, little is understood about the way people who grew up in Australlian military families affected by PTSD describe their experiences and what the implications are for their participation in family life. This study addressed the following research questions: (1) ‘How does a child of a Vietnam veteran understand and describe the experience of PTSD in the family?’ and (2) ‘What are the implications of this understanding on their current participation in family life?’ These questions were addressed through a qualitative analysis of focus-group data collected from adults with a Vietnam veteran parent with PTSD. The key rationale for a qualitative approach was to develop an understanding of these questions in a way which was as faithful as possible to the way they talked about their past and present family experiences. A number of experiential themes common to participants were identified through the data analysis. Participants’ experiences linked together to form a central theme of control, which revealed the overarching narrative of ‘It’s all about control and the fear of losing it’, that responds to the first research queston. The second research question led to a deeper analysis of the ‘control experiences’ to identify the ways in which participants responded to and managed these problematic aspects of family life, and the implications for their current sense of participation in family life. These responses can be understood through the overarching narrative of: ‘Soldier on despite the differences’ which assists them to optimise the impact of control and develop strategies required to maintain a semblance of personal normality and a normal family life. This intensive research has led to the development of theoretical propositions about this group’s experiences and responses that can be tested further in subsequent research to assist families and their members who may be experiencing the intergenerational impacts of psychological trauma acquired from military service.

Rebuilding housing after a disaster : factors for failure

Disasters, particularly those triggered by nature are often followed by a swift humanitarian relief response to address the resultant emergencies. These efforts are then transitioned through the medium recovery stage, eventually aimed at providing a long term post-disaster reconstruction solution. Emergency humanitarian relief focuses on responding to the immediate need for restoration of basic services, medical treatment and medical supplies, food and temporary shelter, and is a short term strenuous effort. Reconstruction of permanent houses, on the other hand, is a continuous process that often requires decades of effort to return a community to normality. Whilst emergency relief is generally perceived to be very effective, post-disaster housing reconstruction projects often fail to meet their set objectives. This paper outlines and discusses factors that contribute to the failure of post-disaster housing reconstruction projects and the subsequent immediate and long term negative impacts of failure on project outcomes.

Double diffusive magneto-convection fluid flow in a strong cross magnetic field with uniform surface heat and mass flux

In this study, magnetohydrodynamic natural convection boundary layer flow of an electrically conducting and viscous incompressible fluid along a heated vertical flat plate with uniform heat and mass flux in the presence of strong cross magnetic field has been investigated. For smooth integrations the boundary layer equations are transformed in to a convenient dimensionless form by using stream function formulation as well as the free variable formulation. The nonsimilar parabolic partial differential equations are integrated numerically for Pr ≪1 that is appropriate for liquid metals against the local Hartmann parameter ξ . Further, asymptotic solutions are obtained near the leading edge using regular perturbation method for smaller values of ξ . Solutions for values of ξ ≫ 1 are also obtained by employing the matched asymptotic technique. The results obtained for small, large and all ξ regimes are examined in terms of shear stress, τw, rate of heat transfer, qw, and rate of mass transfer, mw, for important physical parameter. Attention has been given to the influence of Schmidt number, Sc, buoyancy ratio parameter, N and local Hartmann parameter, ξ on velocity, temperature and concentration distributions and noted that velocity and temperature of the fluid achieve their asymptotic profiles for Sc ≥ 10:0.

Building community resilience – learning from the 2011 floods in Southeast Queensland, Australia

The year 2010 was the wettest year on record for Queensland, Australia and the wettest year since 1974 for Southeast Queensland. The extremely heavy rain in early January 2011 fell on the catchments of heavily saturated Brisbane and Stanley Rivers systems resulting in significant runoff which rapidly produced a widespread and devastating flood event. The area of inundation was equivalent to the total land area of France and Germany combined. Over 200,000 people were affected leaving 35 people dead and 9 missing. The damage bill was estimated at over $1B and cost to the economy at over $10B with over 30,000 homes and 6,000 business flooded and 86 towns and regional centres affected. The need to disburse disaster funding in a prompt manner to the affected population was paramount to facilitate individuals getting their lives back to some normality. However, the payout of insurance claims has proved to be a major area of community anger. The ongoing impasse in payment of insurance compensation is attributed to the nature and number of claims, confusing definition of flooding and the lack or accuracy of information needed to determine individually the properties affected and legitimacy of claims. Information was not readily available at the micro-level including, extent and type of inundation, flood heights at property level and cause of damage. Events during the aftermath highlighted widespread community misconceptions concerning the technical factors associated with the flood event and the impact of such on access to legitimate compensation and assistance. Individual and community wide concerns and frustration, anger and depression, have arisen resulting from delays in the timely settlement of insurance claims. Lessons learnt during the aftermath are presented in the context of their importance as a basis for inculcating communities impacted by the flood event with resilience for the future.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.