Numerical study of two ill-posed one-phase Stefan problems

We treat two related moving boundary problems. The first is the ill-posed Stefan problem for melting a superheated solid in one Cartesian coordinate. Mathematically, this is the same problem as that for freezing a supercooled liquid, with applications to crystal growth. By applying a front-fixing technique with finite differences, we reproduce existing numerical results in the literature, concentrating on solutions that break down in finite time. This sort of finite-time blow-up is characterised by the speed of the moving boundary becoming unbounded in the blow-up limit. The second problem, which is an extension of the first, is proposed to simulate aspects of a particular two-phase Stefan problem with surface tension. We study this novel moving boundary problem numerically, and provide results that support the hypothesis that it exhibits a similar type of finite-time blow-up as the more complicated two-phase problem. The results are unusual in the sense that it appears the addition of surface tension transforms a well-posed problem into an ill-posed one.

A Raman spectroscopic study of bukovskýite Fe2(AsO4)(SO4)(OH)•7H2O-a mineral phase with a significant role in arsenic migration

The Raman spectrum of bukovskýite, Fe3+2(OH)(SO4)(AsO4)•7H2O has been studied and compared with the Raman spectrum of an amorphous gel containing specifically Fe, As and S elements and is understood as an intermediate product in the formation of bukovskýite. Observed bands are assigned to the stretching and bending vibrations of (SO4)2- and (AsO4)3- units, stretching and bending vibrations and librational modes of hydrogen bonded water molecules, stretching and bending vibrations of hydrogen bonded (OH)- ions and Fe3+-(O,OH) units. Approximate range of O-H...O hydrogen bond lengths is inferred from the Raman spectra. Raman spectra of crystalline bukovskýite and of the amorphous gel differ in that the bukovskýite spectrum is more complex, observed bands are sharp, the degenerate bands of (SO4)2- and (AsO4)3- are split and more intense. Lower wavenumbers of  H2O bending vibration in the spectrum of the amorphous gel may indicate the presence of weaker hydrogen bonds compared with those in bukovskýite.

Inter-sector leader transitions and organisation transformation : a research agenda

Faced with the need for strategic change, structural and cultural realignment, innovation and value-adding, many public sector organisations are tapping into a wider senior leadership talent pool and attracting successful leaders from other sectors (Flynn and Thompson, 2009). Leadership renewal has resulted, in some cases, in the external recruitment of whole senior leadership teams (Hockridge, 2008), raising issues about the influence of context on leader success (Pawar and Eastman, 1997) and potential leader transition failure, a costly outcome for leaders and organisations (Howard, 2001). There is little research on inter-sector leader transitions, which is surprising given the significant costs associated with leader acquisition and failure(Conger, 2010; Day and Halpin, 2004). For example, it is not clear what organizations do (or do not do) to ensure the outcomes of their significant investment in inter sector transitions are realised. In addition, it is not clear how the individual leader manages the challenging transition into a new leadership context and how their approach to leadership facilitates or inhibits successful transition (Avolio, 2010). Leader assimilation programs have been developed to assimilate new leaders (Manderscheid, 2008); however, assimilation is not necessarily a desired organisational outcome (Denis and Pineault, 2000). In this paper we critically review the limited literature on inter-sector leader transitions and transformational change outcomes and argue for a mutual accommodation approach. We draw on our own initial empirical work to propose the elements of a program for achieving this outcome from the perspective of the public organisation and the inter-sector appointee.

Epithelial—mesenchymal and mesenchymal—epithelial transitions in carcinoma progression

Like a set of bookends, cellular, molecular, and genetic changes of the beginnings of life mirror those of one of the most common cause of death—metastatic cancer. Epithelial to mesenchymal transition (EMT) is an important change in cell phenotype which allows the escape of epithelial cells from the structural constraints imposed by tissue architecture, and was first recognized by Elizabeth Hay in the early to mid 1980's to be a central process in early embryonic morphogenesis. Reversals of these changes, termed mesenchymal to epithelial transitions (METs), also occur and are important in tissue construction in normal development. Over the last decade, evidence has mounted for EMT as the means through which solid tissue epithelial cancers invade and metastasize. However, demonstrating this potentially rapid and transient process in vivo has proven difficult and data connecting the relevance of this process to tumor progression is still somewhat limited and controversial. Evidence for an important role of MET in the development of clinically overt metastases is starting to accumulate, and model systems have been developed. This review details recent advances in the knowledge of EMT as it occurs in breast development and carcinoma and prostate cancer progression, and highlights the role that MET plays in cancer metastasis. Finally, perspectives from a clinical and translational viewpoint are discussed

A collagen network phase improves cell seeding of open-pore structure scaffolds under perfusion

Scaffolds with open-pore morphologies offer several advantages in cell-based tissue engineering, but their use is limited by a low cell seeding efficiency. We hypothesized that inclusion of a collagen network as filling material within the open-pore architecture of polycaprolactone-tricalcium phosphate (PCL-TCP) scaffolds increases human bone marrow stromal cells (hBMSC) seeding efficiency under perfusion and in vivo osteogenic capacity of the resulting constructs. PCL-TCP scaffolds, rapid prototyped with a honeycomb-like architecture, were filled with a collagen gel and subsequently lyophilized, with or without final crosslinking. Collagen-free scaffolds were used as controls. The seeding efficiency was assessed after overnight perfusion of expanded hBMSC directly through the scaffold pores using a bioreactor system. By seeding and culturing freshly harvested hBMSC under perfusion for 3 weeks, the osteogenic capacity of generated constructs was tested by ectopic implantation in nude mice. The presence of the collagen network, independently of the crosslinking process, significantly increased the cell seeding efficiency (2.5-fold), and reduced the loss of clonogenic cells in the supernatant. Although no implant generated frank bone tissue, possibly due to the mineral distribution within the scaffold polymer phase, the presence of a non crosslinked collagen phase led to in vivo formation of scattered structures of dense osteoids. Our findings verify that the inclusion of a collagen network within open morphology porous scaffolds improves cell retention under perfusion seeding. In the context of cell-based therapies, collagen-filled porous scaffolds are expected to yield superior cell utilization, and could be combined with perfusion-based bioreactor devices to streamline graft manufacture.

Asymptotic and numerical results for a model of solvent-dependent drug diffusion through polymeric spheres

A model for drug diffusion from a spherical polymeric drug delivery device is considered. The model contains two key features. The first is that solvent diffuses into the polymer, which then transitions from a glassy to a rubbery state. The interface between the two states of polymer is modelled as a moving boundary, whose speed is governed by a kinetic law; the same moving boundary problem arises in the one-phase limit of a Stefan problem with kinetic undercooling. The second feature is that drug diffuses only through the rubbery region, with a nonlinear diffusion coefficient that depends on the concentration of solvent. We analyse the model using both formal asymptotics and numerical computation, the latter by applying a front-fixing scheme with a finite volume method. Previous results are extended and comparisons are made with linear models that work well under certain parameter regimes. Finally, a model for a multi-layered drug delivery device is suggested, which allows for more flexible control of drug release.