Classifying general nonlinear force laws in cell-based models via the continuum limit

though discrete cell-based frameworks are now commonly used to simulate a whole range of biological phenomena, it is typically not obvious how the numerous different types of model are related to one another, nor which one is most appropriate in a given context. Here we demonstrate how individual cell movement on the discrete scale modeled using nonlinear force laws can be described by nonlinear diffusion coefficients on the continuum scale. A general relationship between nonlinear force laws and their respective diffusion coefficients is derived in one spatial dimension and, subsequently, a range of particular examples is considered. For each case excellent agreement is observed between numerical solutions of the discrete and corresponding continuum models. Three case studies are considered in which we demonstrate how the derived nonlinear diffusion coefficients can be used to (a) relate different discrete models of cell behavior; (b) derive discrete, intercell force laws from previously posed diffusion coefficients, and (c) describe aggregative behavior in discrete simulations

On the formation time scale and core masses of gas giant planets

Numerical simulations show that the migration of growing planetary cores may be dominated by turbulent fluctuations in the protoplanetary disk, rather than by any mean property of the flow. We quantify the impact of this stochastic core migration on the formation time scale and core mass of giant planets at the onset of runaway gas accretion. For standard Solar Nebula conditions, the formation of Jupiter can be accelerated by almost an order of magnitude if the growing core executes a random walk with an amplitude of a few tenths of an au. A modestly reduced surface density of planetesimals allows Jupiter to form within 10 Myr, with an initial core mass below 10 Earth masses, in better agreement with observational constraints. For extrasolar planetary systems, the results suggest that core accretion could form massive planets in disks with lower metallicities, and shorter lifetimes, than the Solar Nebula.Comment: ApJL, in pres

Molecular characterisation of four double-flowered mutants of Silene dioica representing four centuries of variation

Records of double-flowered Silene dioica date from the late sixteenth century and four named varieties are grown today, as previously, for their horticultural interest. Although double-flowered mutants have been characterized in several plants, their study in dioecious species is of particular interest due to influences of the homeotic mutation on the different floral whorl configurations in males and females. We have analysed four double-flowered varieties of Silene dioica: Flore Pleno and Rosea Plena date back to the seventeenth and nineteenth centuries, Thelma Kay and Firefly were recognized in the latter part of the twentieth and early twenty-first centuries. We have analysed the floral structure of the four varieties, which have distinct floral architectures. Based on Y chromosome-specific PCR analysis we show that Firefly is male and that the other three varieties are female: Random Amplification of Polymorphic DNA (RAPD) analyses suggested a common origin for the three female varieties. The double-flowered phenotype in all four varieties is caused by mutation of the C-function MADS-box transcription factor gene SDM1. We show that Firefly carries a unique 44bp insertion into SDM1, revealing an independent origin for this variety. Comparative analysis of SDM1 cDNA and genomic sequences in Flore Pleno, Rosea Plena and Thelma Kay shows that all three are caused by the same 7bp insertion within SDM1 and therefore share a common origin. The three alleles also differ by several single nucleotide polymorphisms, which represent somatic mutations accumulated over four centuries of asexual propagation

Thermoelectric and Magnetothermoelectric Transport Measurements of Graphene

The conductance and thermoelectric power (TEP) of graphene is simultaneously measured using microfabricated heater and thermometer electrodes. The sign of the TEP changes across the charge neutrality point as the majority carrier density switches from electron to hole. The gate dependent conductance and TEP exhibit a quantitative agreement with the semiclassical Mott relation. In the quantum Hall regime at high magnetic field, quantized thermopower and Nernst signals are observed and are also in agreement with the generalized Mott relation, except for strong deviations near the charge neutrality point

Mesoscopic and continuum modelling of angiogenesis

Angiogenesis is the formation of new blood vessels from pre-existing ones in response to chemical signals secreted by, for example, a wound or a tumour. In this paper, we propose a mesoscopic lattice-based model of angiogenesis, in which processes that include proliferation and cell movement are considered as stochastic events. By studying the dependence of the model on the lattice spacing and the number of cells involved, we are able to derive the deterministic continuum limit of our equations and compare it to similar existing models of angiogenesis. We further identify conditions under which the use of continuum models is justified, and others for which stochastic or discrete effects dominate. We also compare different stochastic models for the movement of endothelial tip cells which have the same macroscopic, deterministic behaviour, but lead to markedly different behaviour in terms of production of new vessel cells.Comment: 48 pages, 13 figure

Heavy landings of whelks, Babylonia spp. in trawl catches off Quilon, southwest coast of India

Whelks are recently being exploited from east and west coasts of India on a commercial basis for meat export trade. Babylonia spirata and B. zeylanica are the two species of whelks which form bycatch of shrimp trawlers in Sakthikulangara-Neendakara area along the southwest coast of India and the former species contributes to the fishery along Annappanpettai, near Portonovo along the southeast coast of India