An envelope method for analysing sequential pattern formation

We examine sequential spatial pattern formation in a tissue interaction model for skin organ morphogenesis. Pattern formation occurs as a front sweeps across the domain leaving in its wake a steady state spatial pattern. Extensive numerical simulations show that these fronts travel with constant wave speed. By considering the envelope of the solution profile we present a novel method of calculating its wave speed

<em>Yearworth v. North Bristol NHS Trust</em>:A Property Case of Uncertain Significance?

It has long been the position in law that, subject to some minor but important exceptions, property cannot be held in the human body, whether living or dead. In the recent case of Yearworth and Others v North Bristol NHS Trust, however, the Court of Appeal for England and Wales revisited the property debate and threw into doubt a number of doctrines with respect to property and the body. This brief article analyses Yearworth, (1) reviewing the facts and the Court's decision with respect to the originators' proprietary and contractual interests in their body and bodily products, (2) considering the significance of relying on property and its use a legal metaphor, (3) questioning the scope of the property right created, and (4) querying whether an alternate conceptual approach to extending rights and a remedy was warranted. It concludes that, while Yearworth engages with, and impacts on, important theoretical and practical issues--from legal, healthcare and research perspectives--it does not offer a great deal of guidance and, for that reason, its precedential significance is in doubt

A minimal model for chaotic shear banding in shear-thickening fluids

We present a minimal model for spatiotemporal oscillation and rheochaos in shear-thickening complex fluids at zero Reynolds number. In the model, a tendency towards inhomogeneous flows in the form of shear bands combines with a slow structural dynamics, modelled by delayed stress relaxation. Using Fourier-space numerics, we study the nonequilibrium `phase diagram' of the fluid as a function of a steady mean (spatially averaged) stress, and of the relaxation time for structural relaxation. We find several distinct regions of periodic behavior (oscillating bands, travelling bands, and more complex oscillations) and also regions of spatiotemporal rheochaos. A low-dimensional truncation of the model retains the important physical features of the full model (including rheochaos) despite the suppression of sharply defined interfaces between shear bands. Our model maps onto the FitzHugh-Nagumo model for neural network dynamics, with an unusual form of long-range coupling.Comment: Revised version (in particular, new section III.E. and Appendix A

Spectral degeneracy and escape dynamics for intermittent maps with a hole

We study intermittent maps from the point of view of metastability. Small neighbourhoods of an intermittent fixed point and their complements form pairs of almost-invariant sets. Treating the small neighbourhood as a hole, we first show that the absolutely continuous conditional invariant measures (ACCIMs) converge to the ACIM as the length of the small neighbourhood shrinks to zero. We then quantify how the escape dynamics from these almost-invariant sets are connected with the second eigenfunctions of Perron-Frobenius (transfer) operators when a small perturbation is applied near the intermittent fixed point. In particular, we describe precisely the scaling of the second eigenvalue with the perturbation size, provide upper and lower bounds, and demonstrate $L^1$ convergence of the positive part of the second eigenfunction to the ACIM as the perturbation goes to zero. This perturbation and associated eigenvalue scalings and convergence results are all compatible with Ulam's method and provide a formal explanation for the numerical behaviour of Ulam's method in this nonuniformly hyperbolic setting. The main results of the paper are illustrated with numerical computations.Comment: 34 page

Modeling scenarios for water allocation in the Gediz Basin, Turkey

Water management / Water allocation / Models / River basin development / Hydrology / Decision making / Environmental effects / Water use efficiency / Climate / Irrigation water / Irrigated farming / Stream flow / Surface water / Salt water intrusion / Turkey / Gediz Basin

On a model mechanism for the spatial patterning of teeth primordia in the Alligator

We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator,Alligator mississippiensis. Detailed embryological studies by Westergaard & Ferguson (1986, 1987, 1990) show that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a reaction-diffusion mechanism, which crucially includes domain growth. The model can reproduce the spatial pattern development of the first seven teeth primordia in the lower half jaw ofA. mississippiensis. The results for the precise spatio-temporal sequence compare well with detailed developmental experiments

Spatio-temporal patterns in a mechanical model for mesenchymal morphogenesis

We present an in-depth study of spatio-temporal patterns in a simplified version of a mechanical model for pattern formation in mesenchymal morphogenesis. We briefly motivate the derivation of the model and show how to choose realistic boundary conditions to make the system well-posed. We firstly consider one-dimensional patterns and carry out a nonlinear perturbation analysis for the case where the uniform steady state is linearly unstable to a single mode. In two-dimensions, we show that if the displacement field in the model is represented as a sum of orthogonal parts, then the model can be decomposed into two sub-models, only one of which is capable of generating pattern. We thus focus on this particular sub-model. We present a nonlinear analysis of spatio-temporal patterns exhibited by the sub-model on a square domain and discuss mode interaction. Our analysis shows that when a two-dimensional mode number admits two or more degenerate mode pairs, the solution of the full nonlinear system of partial differential equations is a mixed mode solution in which all the degenerate mode pairs are represented in a frequency locked oscillation