Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients

Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the existence of spatial inhomogeneities in various biological systems, most models have only been considered in a spatially homogeneous environment. The authors consider a two-chemical reaction-diffusion mechanism in one space dimension in which one of the diffusion coefficients depends explicitly on the spatial variable. The model is analysed in the case of a step function diffusion coefficient and the insight gained for this special case is used to discuss pattern generation for smoothly varying diffusion coefficients. The results show that spatial inhomogeneity may be an important biological pattern regulator, and possible applications of the model to chondrogenesis in the vertebrate limb are suggested

Unravelling the Turing bifurcation using spatially varying diffusion coefficients

The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper the authors determine the structure of this bifurcation for two coupled reaction diffusion equations on a two-dimensional square spatial domain when the diffusion coefficients have a small explicit variation in space across the domain. In the case of homogeneous diffusivities, the Turing bifurcation is highly degenerate. Using a two variable perturbation method, the authors show that the small explicit spatial inhomogeneity splits the bifurcation into two separate primary and two separate secondary bifurcations, with all solution branches distinct. This splitting of the bifurcation is more effective than that given by making the domain slightly rectangular, and shows clearly the structure of the Turing bifurcation and the way in which the! var ious solution branches collapse together as the spatial variation is reduced. The authors determine the stability of the solution branches, which indicates that several new phenomena are introduced by the spatial variation, including stable subcritical striped patterns, and the possibility that stable stripes lose stability supercritically to give stable spotted patterns

Terrestrial planets across space and time

The study of cosmology, galaxy formation and exoplanets has now advanced to a stage where a cosmic inventory of terrestrial planets may be attempted. By coupling semi-analytic models of galaxy formation to a recipe that relates the occurrence of planets to the mass and metallicity of their host stars, we trace the population of terrestrial planets around both solar-mass (FGK type) and lower-mass (M dwarf) stars throughout all of cosmic history. We find that the mean age of terrestrial planets in the local Universe is $7\pm{}1$ Gyr for FGK hosts and $8\pm{}1$ Gyr for M dwarfs. We estimate that hot Jupiters have depleted the population of terrestrial planets around FGK stars by no more than $\approx 10\%$, and that only $\approx 10\%$ of the terrestrial planets at the current epoch are orbiting stars in a metallicity range for which such planets have yet to be confirmed. The typical terrestrial planet in the local Universe is located in a spheroid-dominated galaxy with a total stellar mass comparable to that of the Milky Way. When looking at the inventory of planets throughout the whole observable Universe, we argue for a total of $\approx 1\times 10^{19}$ and $\approx 5\times 10^{20}$ terrestrial planets around FGK and M stars, respectively. Due to light travel time effects, the terrestrial planets on our past light cone exhibit a mean age of just $1.7\pm 0.2$ Gyr. These results are discussed in the context of cosmic habitability, the Copernican principle and searches for extraterrestrial intelligence at cosmological distances.Comment: 11 pages, 8 figures. v.2: Accepted for publication in ApJ. Some changes in quantitative results compared to v.1, mainly due to differences in IMF assumption

Charge Violation and Alice Behavior in Global and Textured Strings

Spontaneous breaking of global symmetries can produce ``Alice'' strings: line defects which make unbroken symmetries multivalued, induce apparent charge violation via Aharonov-Bohm interactions, and form point defects when twisted into loops. We demonstrate this behavior for both divergent and textured global Alice strings. Both adiabatically scatter charged particles via effective Wilson lines. For textured Alice strings, such Wilson lines occur at all radii, and are multivalued only inside the string. This produces measurable effects, including path-dependent charge violation.Comment: 32 pages, 2 epsfigs, Revte

Explicit Solution of the Time Domain Volume Integral Equation Using a Stable Predictor-Corrector Scheme

An explicit marching-on-in-time (MOT) scheme for solving the time domain volume integral equation is presented. The proposed method achieves its stability by employing, at each time step, a corrector scheme, which updates/corrects fields computed by the explicit predictor scheme. The proposedmethod is computationally more efficient when compared to the existing filtering techniques used for the stabilization of explicit MOT schemes. Numerical results presented in this paper demonstrate that the proposed method maintains its stability even when applied to the analysis of electromagnetic wave interactions with electrically large structures meshed using approximately half a million discretization elements

Midpalatal implants vs headgear for orthodontic anchorage - a randomized clinical trial: Cephalometric results

OBJECTIVE: To compare the clinical effectiveness of the mid-palatal implant as a method of reinforcing anchorage during orthodontic treatment with that of conventional extra-oral anchorage. DESIGN: A prospective, randomized, clinical trial Setting: Chesterfield and North Derbyshire Royal Hospital NHS Trust and the Charles Clifford Dental Hospital, Sheffield. SUBJECTS AND METHODS: 51 orthodontic patients between the ages of 12 and 39, with a class II division 1 malocclusion and ‘absolute anchorage’ requirements were randomly allocated to either receive a mid-palatal implant or headgear to reinforce orthodontic anchorage. The main outcome of the trial was to compare the mesial movement of the molars and incisors of the two treatment groups between T1 (start) and T2 (end of anchorage reinforcement) as measured from cephalometric radiographs. RESULTS: The reproducibility of the measuring technique was acceptable. There were significant differences between the T1 and T2 measurements within the implant group for the position of the maxillary central incisor (p<0.001), position of the maxillary molar (p=0.009) and position of the mandibular molar (p<0.001). There were significant differences within the headgear group for the position of the mandibular central incisor (p<0.045), position of the maxillary molar (p=<0.001) and position of the mandibular molar (p<0.001). All the skeletal and dental points moved mesially more in the headgear group during treatment than in the implant group. These ranged from an average of 0.5mm more mesial for the mandibular permanent molar to 1.5mm more mesial for the maxillary molar and mandibular base. None of the treatment changes between the implant and headgear groups were statistically significant. CONCLUSIONS: Mid-palatal implants are an acceptable technique for reinforcing anchorage in the orthodontic patient

Topologically Alice Strings and Monopoles

Symmetry breaking can produce ``Alice'' strings, which alter scattered charges and carry monopole number and charge when twisted into loops. Alice behavior arises algebraically, when strings obstruct unbroken symmetries -- a fragile criterion. We give a topological criterion, compelling Alice behavior or deforming it away. Our criterion, that \pi_o(H) acts nontrivially on \pi_1(H), links topologically Alice strings to topological monopoles. We twist topologically Alice loops to form monopoles. We show that Alice strings of condensed matter systems (nematic liquid crystals, helium 3A, and related non-chiral Bose condensates and amorphous chiral superconductors) are topologically Alice, and support fundamental monopole charge when twisted into loops. Thus they might be observed indirectly, not as strings, but as loop-like point defects. We describe other models, showing Alice strings failing our topological criterion; and twisted Alice loops supporting deposited, but not fundamental, monopole number.Comment: 2 figures; this paper consolidates preprints hep-th/0304161 and hep-th/0304162, to appear in Phys. Rev.

Midpalatal implants vs headgear for orthodontic anchorage - a randomized clinical trial: Cephalometric results

OBJECTIVE: To compare the clinical effectiveness of the mid-palatal implant as a method of reinforcing anchorage during orthodontic treatment with that of conventional extra-oral anchorage. DESIGN: A prospective, randomized, clinical trial Setting: Chesterfield and North Derbyshire Royal Hospital NHS Trust and the Charles Clifford Dental Hospital, Sheffield. SUBJECTS AND METHODS: 51 orthodontic patients between the ages of 12 and 39, with a class II division 1 malocclusion and ‘absolute anchorage’ requirements were randomly allocated to either receive a mid-palatal implant or headgear to reinforce orthodontic anchorage. The main outcome of the trial was to compare the mesial movement of the molars and incisors of the two treatment groups between T1 (start) and T2 (end of anchorage reinforcement) as measured from cephalometric radiographs. RESULTS: The reproducibility of the measuring technique was acceptable. There were significant differences between the T1 and T2 measurements within the implant group for the position of the maxillary central incisor (p<0.001), position of the maxillary molar (p=0.009) and position of the mandibular molar (p<0.001). There were significant differences within the headgear group for the position of the mandibular central incisor (p<0.045), position of the maxillary molar (p=<0.001) and position of the mandibular molar (p<0.001). All the skeletal and dental points moved mesially more in the headgear group during treatment than in the implant group. These ranged from an average of 0.5mm more mesial for the mandibular permanent molar to 1.5mm more mesial for the maxillary molar and mandibular base. None of the treatment changes between the implant and headgear groups were statistically significant. CONCLUSIONS: Mid-palatal implants are an acceptable technique for reinforcing anchorage in the orthodontic patient

Investigating eye movement acquisition and analysis technologies as a causal factor in differential prevalence of crossed and uncrossed fixation disparity during reading and dot scanning

Previous studies examining binocular coordination during reading have reported conflicting results in terms of the nature of disparity (e.g. Kliegl, Nuthmann, &amp; Engbert (Journal of Experimental Psychology General 135:12-35, 2006); Liversedge, White, Findlay, &amp; Rayner (Vision Research 46:2363-2374, 2006). One potential cause of this inconsistency is differences in acquisition devices and associated analysis technologies. We tested this by directly comparing binocular eye movement recordings made using SR Research EyeLink 1000 and the Fourward Technologies Inc. DPI binocular eye-tracking systems. Participants read sentences or scanned horizontal rows of dot strings; for each participant, half the data were recorded with the EyeLink, and the other half with the DPIs. The viewing conditions in both testing laboratories were set to be very similar. Monocular calibrations were used. The majority of fixations recorded using either system were aligned, although data from the EyeLink system showed greater disparity magnitudes. Critically, for unaligned fixations, the data from both systems showed a majority of uncrossed fixations. These results suggest that variability in previous reports of binocular fixation alignment is attributable to the specific viewing conditions associated with a particular experiment (variables such as luminance and viewing distance), rather than acquisition and analysis software and hardware.<br/