Discrete families of Saffman–Taylor fingers with exotic shapes

The mathematical problem of determining the shape of a steadily propagating Saffman–Taylor finger in a rectangular Hele-Shaw cell is known to have a countably infinite number of solutions for each fixed surface tension value. For sufficiently large surface tension values, we find that fingers on higher solution branches are non-convex. The tips of the fingers have increasingly exotic shapes as the branch number increases.

Persistent anterior chamber silicone oil and myopia

A 60-year-old male experienced a marked unilateral myopic shift of 20 D following attempted removal of intravitreal heavy silicone oil (HSO) used in the treatment of inferior proliferative vitreous retinopathy following retinal detachment. Examination revealed HSO adherent to the corneal endothelium forming a convex interface with the aqueous, obscuring the entire pupil, which required surgical intervention to restore visual acuity. This case highlights the potential ocular complications associated with silicone oil migration into the anterior chamber, which include corneal endothelial decompensation and a significant increase in myopia.

Tuning the resonance properties of 2D carbon nanotube networks towards a mechanical resonator

The capabilities of the mechanical resonator-based nanosensors in detecting ultra-small mass or force shifts have driven a continuing exploration of the palette of nanomaterials for such application purposes. Based on large-scale molecular dynamics simulations, we have assessed the applicability of a new class of carbon nanomaterials for nanoresonator usage, i.e. the single-wall carbon nanotube (SWNT) network. It is found that SWNT networks inherit excellent mechanical properties from the constituent SWNTs, possessing a high natural frequency. However, although a high quality factor is suggested from the simulation results, it is hard to obtain an unambiguous Q-factor due to the existence of vibration modes in addition to the dominant mode. The nonlinearities resulting from these extra vibration modes are found to exist uniformly under various testing conditions including different initial actuations and temperatures. Further testing shows that these modes can be effectively suppressed through the introduction of axial strain, leading to an extremely high quality factor in the order of 109 estimated from the SWNT network with 2% tensile strain. Additional studies indicate that the carbon rings connecting the SWNTs can also be used to alter the vibrational properties of the resulting network. This study suggests that the SWNT network can be a good candidate for applications as nanoresonators.

A new method of detecting changes in corneal health in response to toxic insults

The size and arrangement of stromal collagen fibrils (CFs) influence the optical properties of the cornea and hence its function. The spatial arrangement of the collagen is still questionable in relation to the diameter of collagen fibril. In the present study, we introduce a new parameter, edge-fibrillar distance (EFD) to measure how two collagen fibrils are spaced with respect to their closest edges and their spatial distribution through normalized standard deviation of EFD (NSDEFD) accessed through the application of two commercially available multipurpose solutions (MPS): ReNu and Hippia. The corneal buttons were soaked separately in ReNu and Hippia MPS for five hours, fixed overnight in 2.5% glutaraldehyde containing cuprolinic blue and processed for transmission electron microscopy. The electron micrographs were processed using ImageJ user-coded plugin. Statistical analysis was performed to compare the image processed equivalent diameter (ED), inter-fibrillar distance (IFD), and EFD of the CFs of treated versus normal corneas. The ReNu-soaked cornea resulted in partly degenerated epithelium with loose hemidesmosomes and Bowman’s collagen. In contrast, the epithelium of the cornea soaked in Hippia was degenerated or lost but showed closely packed Bowman’s collagen. Soaking the corneas in both MPS caused a statistically significant decrease in the anterior collagen fibril, ED and a significant change in IFD, and EFD than those of the untreated corneas (p < 0.05, for all comparisons). The introduction of EFD measurement in the study directly provided a sense of gap between periphery of the collagen bundles, their spatial distribution; and in combination with ED, they showed how the corneal collagen bundles are spaced in relation to their diameters. The spatial distribution parameter NSDEFD indicated that ReNu treated cornea fibrils were uniformly distributed spatially, followed by normal and Hippia. The EFD measurement with relatively lower standard deviation and NSDEFD, a characteristic of uniform CFs distribution, can be an additional parameter used in evaluating collagen organization and accessing the effects of various treatments on corneal health and transparency.

Estimating link-dependent origin-destination matrices from sample trajectories and traffic counts

Origin-Destination matrices (ODM) estimation can benefits of the availability of sample trajectories which can be measured thanks to recent technologies. This paper focus on the case of transport networks where traffic counts are measured by magnetic loops and sample trajectories available. An example of such network is the city of Brisbane, where Bluetooth detectors are now operating. This additional data source is used to extend the classical ODM estimation to a link-specific ODM (LODM) one using a convex optimisation resolution that incorporates networks constraints as well. The proposed algorithm is assessed on a simulated network.

Single layer lead iodide: Computational exploration of structural, electronic and optical properties, strain induced band modulation and the role of spin-orbital-coupling

Graphitic like layered materials exhibit intriguing electronic structures and thus the search for new types of two-dimensional (2D) monolayer materials is of great interest for developing novel nano-devices. By using density functional theory (DFT) method, here we for the first time investigate the structure, stability, electronic and optical properties of monolayer lead iodide (PbI2). The stability of PbI2 monolayer is first confirmed by phonon dispersion calculation. Compared to the calculation using generalized gradient approximation, screened hybrid functional and spin–orbit coupling effects can not only predicts an accurate bandgap (2.63 eV), but also the correct position of valence and conduction band edges. The biaxial strain can tune its bandgap size in a wide range from 1 eV to 3 eV, which can be understood by the strain induced uniformly change of electric field between Pb and I atomic layer. The calculated imaginary part of the dielectric function of 2D graphene/PbI2 van der Waals type hetero-structure shows significant red shift of absorption edge compared to that of a pure monolayer PbI2. Our findings highlight a new interesting 2D material with potential applications in nanoelectronics and optoelectronics.

Behaviour and strength of hollow flange channel sections under torsion and bending

Hollow flange channel section is a cold-formed high-strength and thin-walled steel section with a unique shape including two rectangular hollow flanges and a slender web. Due to its mono-symmetric characteristics, it will also be subjected to torsion when subjected to transverse loads in practical applications. Past research on steel beams subject to torsion has concentrated on open sections while very few steel design standards give suitable design rules for torsion design. Since the hollow flange channel section is different from conventional open sections, its torsional behaviour remains unknown to researchers. Therefore the elastic behaviour of hollow flange channel sections subject to uniform and non-uniform torsion, and combined torsion and bending was investigated using the solutions of appropriate differential equilibrium equations. The section torsion shear flow, warping normal stress distribution, and section constants including torsion constant and warping constant were obtained. The results were compared with those from finite element analyses that verified the accuracy of analytical solutions. Parametric studies were undertaken for simply supported beams subject to a uniformly distributed torque and a uniformly distributed transverse load applied away from the shear centre. This paper presents the details of this research into the elastic behaviour and strength of hollow flange channel sections subject to torsion and bending and the results.

Catalyst engineering for lithium ion batteries: The catalytic role of Ge in enhancing the electrochemical performance of SnO2(GeO2)0.13/G anodes

The catalytic role of germanium (Ge) was investigated to improve the electrochemical performance of tin dioxide grown on graphene (SnO(2)/G) nanocomposites as an anode material of lithium ion batteries (LIBs). Germanium dioxide (GeO(20) and SnO(2) nanoparticles (<10 nm) were uniformly anchored on the graphene sheets via a simple single-step hydrothermal method. The synthesized SnO(2)(GeO(2))0.13/G nanocomposites can deliver a capacity of 1200 mA h g(-1) at a current density of 100 mA g(-1), which is much higher than the traditional theoretical specific capacity of such nanocomposites (∼ 702 mA h g(-1)). More importantly, the SnO(2)(GeO(2))0.13/G nanocomposites exhibited an improved rate, large current capability (885 mA h g(-1) at a discharge current of 2000 mA g(-1)) and excellent long cycling stability (almost 100% retention after 600 cycles). The enhanced electrochemical performance was attributed to the catalytic effect of Ge, which enabled the reversible reaction of metals (Sn and Ge) to metals oxide (SnO(2) and GeO(2)) during the charge/discharge processes. Our demonstrated approach towards nanocomposite catalyst engineering opens new avenues for next-generation high-performance rechargeable Li-ion batteries anode materials.

Linear programming for large-scale Markov decision problems

We consider the problem of controlling a Markov decision process (MDP) with a large state space, so as to minimize average cost. Since it is intractable to compete with the optimal policy for large scale problems, we pursue the more modest goal of competing with a low-dimensional family of policies. We use the dual linear programming formulation of the MDP average cost problem, in which the variable is a stationary distribution over state-action pairs, and we consider a neighborhood of a low-dimensional subset of the set of stationary distributions (defined in terms of state-action features) as the comparison class. We propose a technique based on stochastic convex optimization and give bounds that show that the performance of our algorithm approaches the best achievable by any policy in the comparison class. Most importantly, this result depends on the size of the comparison class, but not on the size of the state space. Preliminary experiments show the effectiveness of the proposed algorithm in a queuing application.

Ability of commonly used prediction equations to predict resting energy expenditure in children with inflammatory bowel disease

Background: Paediatric onset inflammatory bowel disease (IBD) may cause alterations in energy requirements and invalidate the use of standard prediction equations. Our aim was to evaluate four commonly used prediction equations for resting energy expenditure (REE) in children with IBD. Methods: Sixty-three children had repeated measurements of REE as part of a longitudinal research study yielding a total of 243 measurements. These were compared with predicted REE from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict equations using the Bland-Altman method. Results: Mean (±SD) age of the patients was 14.2 (2.4) years. Mean measured REE was 1566 (336) kcal per day compared with 1491 (236), 1441 (255), 1481 (232), and 1435 (212) kcal per day calculated from Schofield, Oxford, FAO/WHO/UNU, and Harris-Benedict, respectively. While the Schofield equation demonstrated the least difference between measured and predicted REE, it, along with the other equations tested, did not perform uniformly across all subjects, indicating greater errors at either end of the spectrum of energy expenditure. Smaller differences were found for all prediction equations for Crohn's disease compared with ulcerative colitis. Conclusions: Of the commonly used equations, the equation of Schofield should be used in pediatric patients with IBD when measured values are not able to be obtained. (Inflamm Bowel Dis 2010;) Copyright © 2010 Crohn's & Colitis Foundation of America, Inc.

On the efficacy of Fourier series approximations for pricing European options

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the halfrange cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together,these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Learning with symmetric label noise: The importance of being unhinged

Convex potential minimisation is the de facto approach to binary classification. However, Long and Servedio [2008] proved that under symmetric label noise (SLN), minimisation of any convex potential over a linear function class can result in classification performance equivalent to random guessing. This ostensibly shows that convex losses are not SLN-robust. In this paper, we propose a convex, classification-calibrated loss and prove that it is SLN-robust. The loss avoids the Long and Servedio [2008] result by virtue of being negatively unbounded. The loss is a modification of the hinge loss, where one does not clamp at zero; hence, we call it the unhinged loss. We show that the optimal unhinged solution is equivalent to that of a strongly regularised SVM, and is the limiting solution for any convex potential; this implies that strong l2 regularisation makes most standard learners SLN-robust. Experiments confirm the unhinged loss’ SLN-robustness.

Optical and surface characterization of radio frequency plasma polymerized 1-isopropyl-4-methyl-1,4-cyclohexadiene thin films

Low pressure radio frequency plasma-assisted deposition of 1-isopropyl-4-methyl-1,4-cyclohexadiene thin films was investigated for different polymerization conditions. Transparent, environmentally stable and flexible, these organic films are promising candidates for organic photovoltaics (OPV) and flexible electronics applications, where they can be used as encapsulating coatings and insulating interlayers. The effect of deposition RF power on optical properties of the films was limited, with all films being optically transparent, with refractive indices in a range of 1.57–1.58 at 500 nm. The optical band gap (Eg) of ~3 eV fell into the insulating Eg region, decreasing for films fabricated at higher RF power. Independent of deposition conditions, the surfaces were smooth and defect-free, with uniformly distributed morphological features and average roughness between 0.30 nm (at 10 W) and 0.21 nm (at 75 W). Films fabricated at higher deposition power displayed enhanced resistance to delamination and wear, and improved hardness, from 0.40 GPa for 10 W to 0.58 GPa for 75 W at a load of 700 μN. From an application perspective, it is therefore possible to tune the mechanical and morphological properties of these films without compromising their optical transparency or insulating property.

A curve shortening flow rule for closed embedded plane curves with a prescribed rate of change in enclosed area

Motivated by a problem from fluid mechanics, we consider a generalization of the standard curve shortening flow problem for a closed embedded plane curve such that the area enclosed by the curve is forced to decrease at a prescribed rate. Using formal asymptotic and numerical techniques, we derive possible extinction shapes as the curve contracts to a point, dependent on the rate of decreasing area; we find there is a wider class of extinction shapes than for standard curve shortening, for which initially simple closed curves are always asymptotically circular. We also provide numerical evidence that self-intersection is possible for non-convex initial conditions, distinguishing between pinch-off and coalescence of the curve interior.