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.

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.

Online discovery of similarity mappings

We consider the problem of choosing, sequentially, a map which assigns elements of a set A to a few elements of a set B. On each round, the algorithm suffers some cost associated with the chosen assignment, and the goal is to minimize the cumulative loss of these choices relative to the best map on the entire sequence. Even though the offline problem of finding the best map is provably hard, we show that there is an equivalent online approximation algorithm, Randomized Map Prediction (RMP), that is efficient and performs nearly as well. While drawing upon results from the "Online Prediction with Expert Advice" setting, we show how RMP can be utilized as an online approach to several standard batch problems. We apply RMP to online clustering as well as online feature selection and, surprisingly, RMP often outperforms the standard batch algorithms on these problems.

A plasmonic 'ac Wheatstone bridge' circuit for high-sensitivity phase measurement and single-molecule detection

In this paper, a plasmonic “ac Wheatstone bridge” circuit is proposed and theoretically modeled for the first time. The bridge circuit consists of three metallic nanoparticles, shaped as rectangular prisms, with two nanoparticles acting as parallel arms of a resonant circuit and the third bridging nanoparticle acting as an optical antenna providing an output signal. Polarized light excites localized surface plasmon resonances in the two arms of the circuit, which generate an optical signal dependent on the phase-sensitive excitations of surface plasmons in the antenna. The circuit is analyzed using a plasmonic coupling theory and numerical simulations. The analyses show that the plasmonic circuit is sensitive to phase shifts between the arms of the bridge and has the potential to detect the presence of single molecules.