Biharmonic pattern selection

A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements $u$. The model is based on the biharmonic equation $\nabla^{4}u =0$ in two-dimensional isotropic defect-free media as follows from the Kuramoto-Sivashinsky equation for pattern formation -or, alternatively, from the theory of elasticity. As a difference with Laplacian and Poisson growth models, in the new model the Laplacian of $u$ is neither zero nor proportional to $u$. Its discretization allows to reproduce a transition from dense to multibranched growth at a point in which the growth velocity exhibits a minimum similarly to what occurs within Poisson growth in planar geometry. Furthermore, in circular geometry the transition point is estimated for the simplest case from the relation $r_{\ell}\approx L/e^{1/2}$ such that the trajectories become stable at the growing surfaces in a continuous limit. Hence, within the biharmonic growth model, this transition depends only on the system size $L$ and occurs approximately at a distance $60 \%$ far from a central seed particle. The influence of biharmonic patterns on the growth probability for each lattice site is also analysed.Comment: To appear in Phys. Rev. E. Copies upon request to [email protected]

Presupernova Structure of Massive Stars

Issues concerning the structure and evolution of core collapse progenitor stars are discussed with an emphasis on interior evolution. We describe a program designed to investigate the transport and mixing processes associated with stellar turbulence, arguably the greatest source of uncertainty in progenitor structure, besides mass loss, at the time of core collapse. An effort to use precision observations of stellar parameters to constrain theoretical modeling is also described.Comment: Proceedings for invited talk at High Energy Density Laboratory Astrophysics conference, Caltech, March 2010. Special issue of Astrophysics and Space Science, submitted for peer review: 7 pages, 3 figure

Collective dynamics of colloids at fluid interfaces

The evolution of an initially prepared distribution of micron sized colloidal particles, trapped at a fluid interface and under the action of their mutual capillary attraction, is analyzed by using Brownian dynamics simulations. At a separation \lambda\ given by the capillary length of typically 1 mm, the distance dependence of this attraction exhibits a crossover from a logarithmic decay, formally analogous to two-dimensional gravity, to an exponential decay. We discuss in detail the adaption of a particle-mesh algorithm, as used in cosmological simulations to study structure formation due to gravitational collapse, to the present colloidal problem. These simulations confirm the predictions, as far as available, of a mean-field theory developed previously for this problem. The evolution is monitored by quantitative characteristics which are particularly sensitive to the formation of highly inhomogeneous structures. Upon increasing \lambda\ the dynamics show a smooth transition from the spinodal decomposition expected for a simple fluid with short-ranged attraction to the self-gravitational collapse scenario.Comment: 13 pages, 12 figures, revised, matches version accepted for publication in the European Physical Journal

A mean-field kinetic lattice gas model of electrochemical cells

We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration, and oxido-reduction processes on the electrode surfaces to allow for growth and dissolution. We confirm the viability of our approach by simulating (i) the electrochemical equilibrium at flat electrodes, which displays the correct charged double-layer, (ii) the growth kinetics of one-dimensional electrochemical cells during growth and dissolution, and (iii) electrochemical dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure

Crucial Physical Dependencies of the Core-Collapse Supernova Mechanism

We explore with self-consistent 2D F{\sc{ornax}} simulations the dependence of the outcome of collapse on many-body corrections to neutrino-nucleon cross sections, the nucleon-nucleon bremsstrahlung rate, electron capture on heavy nuclei, pre-collapse seed perturbations, and inelastic neutrino-electron and neutrino-nucleon scattering. Importantly, proximity to criticality amplifies the role of even small changes in the neutrino-matter couplings, and such changes can together add to produce outsized effects. When close to the critical condition the cumulative result of a few small effects (including seeds) that individually have only modest consequence can convert an anemic into a robust explosion, or even a dud into a blast. Such sensitivity is not seen in one dimension and may explain the apparent heterogeneity in the outcomes of detailed simulations performed internationally. A natural conclusion is that the different groups collectively are closer to a realistic understanding of the mechanism of core-collapse supernovae than might have seemed apparent.Comment: 25 pages; 10 figure

An economic evaluation of the randomized controlled trial of topical corticosteroid and home-based narrowband ultraviolet B for active and limited vitiligo (the HI-Light Vitiligo Trial)

Background: Economic evidence for vitiligo treatments is absent. Objectives: To determine the cost-effectiveness of (i) handheld narrowband ultraviolet B (NB-UVB) and (ii) a combination of topical corticosteroid (TCS) and NB-UVB compared with TCS alone for localized vitiligo. Methods: Cost-effectiveness analysis alongside a pragmatic, three-arm, placebo-controlled randomized controlled trial with 9 months’ treatment. In total 517 adults and children (aged ≥ 5 years) with active vitiligo affecting < 10% of skin were recruited from secondary care and the community and were randomized 1: 1: 1 to receive TCS, NB-UVB or both. Cost per successful treatment (measured on the Vitiligo Noticeability Scale) was estimated. Secondary cost–utility analyses measured quality-adjusted life-years using the EuroQol 5 Dimensions 5 Levels for those aged ≥ 11 years and the Child Health Utility 9D for those aged 5 to < 18 years. The trial was registered with number ISRCTN17160087 on 8 January 2015. Results: The mean ± SD cost per participant was £775 ± 83·7 for NB-UVB, £813 ± 111.4 for combination treatment and £600 ± 96·2 for TCS. In analyses adjusted for age and target patch location, the incremental difference in cost for combination treatment compared with TCS was £211 (95% confidence interval 188–235), corresponding to a risk difference of 10·9% (number needed to treat = 9). The incremental cost was £1932 per successful treatment. The incremental difference in cost for NB-UVB compared with TCS was £173 (95% confidence interval 151–196), with a risk difference of 5·2% (number needed to treat = 19). The incremental cost was £3336 per successful treatment. Conclusions: Combination treatment, compared with TCS alone, has a lower incremental cost per additional successful treatment than NB-UVB only. Combination treatment would be considered cost-effective if decision makers are willing to pay £1932 per additional treatment success

Micro-mechanical damage of needle puncture on bovine annulus fibrosus fibrils studied using polarization-resolved Second Harmonic Generation(P-SHG) microscopy

Needle injection has been widely used in spinal therapeutic or diagnostic processes, such as discography. The use of needles has been suspected in causing mild disc degeneration which can lead to long-term back pain. However, the localised microscopic damage caused by needles has not been well studied. The local progressive damage on a microscopic level caused by needle punctures on the surface of bovine annulus fibrosus was investigated. Four different sizes of needle were used for the puncture and twenty-nine bovine intervertebral discs were studied. Polarization-resolved second harmonic generation and fluorescent microscopy were used to study the local microscopic structural changes in collagen and cell nuclei due to needle damage. Repeated 70 cyclic loadings at ±5% of axial strain were applied after the needle puncture in order to assess progressive damage caused by the needle. Puncture damage on annulus fibrosus were observed either collagen fibre bundles being pushed aside, being cut through or combination of both with part being lift or pushed in. The progressive damage was found less relevant to the needle size and more progressive damage was only observed using the larger needle. Two distinct populations of collagen, in which one was relatively more organised than the other population, were observed especially after the puncture from skewed distribution of polarization-SHG analysis. Cell shape was found rounder near the puncture site where collagen fibres were damaged