26,314 research outputs found

    New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. II

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    In the first part of this paper math-ph/0612078, a complete description of Q-conditional symmetries for two classes of reaction-diffusion-convection equations with power diffusivities is derived. It was shown that all the known results for reaction-diffusion equations with power diffusivities follow as particular cases from those obtained in math-ph/0612078 but not vise versa. In the second part the symmetries obtained in are successfully applied for constructing exact solutions of the relevant equations. In the particular case, new exact solutions of nonlinear reaction-diffusion-convection (RDC) equations arising in application and their natural generalizations are found

    DISCUSSION PAPER: REFLECTIONS ON TECHNOLOGY IN LEXICOGRAPHY

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    Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74810/1/j.1749-6632.1973.tb49508.x.pd

    Truncation effects in superdiffusive front propagation with L\'evy flights

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    A numerical and analytical study of the role of exponentially truncated L\'evy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a λ\lambda-truncated fractional derivative of order α\alpha where 1/λ1/\lambda is the characteristic truncation length scale. For λ=0\lambda=0 there is no truncation and fronts exhibit exponential acceleration and algebraic decaying tails. It is shown that for λ0\lambda \neq 0 this phenomenology prevails in the intermediate asymptotic regime (χt)1/αx1/λ(\chi t)^{1/\alpha} \ll x \ll 1/\lambda where χ\chi is the diffusion constant. Outside the intermediate asymptotic regime, i.e. for x>1/λx > 1/\lambda, the tail of the front exhibits the tempered decay ϕeλx/x(1+α)\phi \sim e^{-\lambda x}/x^{(1+\alpha)} , the acceleration is transient, and the front velocity, vLv_L, approaches the terminal speed v=(γλαχ)/λv_* = (\gamma - \lambda^\alpha \chi)/\lambda as tt\to \infty, where it is assumed that γ>λαχ\gamma > \lambda^\alpha \chi with γ\gamma denoting the growth rate of the reaction kinetics. However, the convergence of this process is algebraic, vLvα/(λt)v_L \sim v_* - \alpha /(\lambda t), which is very slow compared to the exponential convergence observed in the diffusive (Gaussian) case. An over-truncated regime in which the characteristic truncation length scale is shorter than the length scale of the decay of the initial condition, 1/ν1/\nu, is also identified. In this extreme regime, fronts exhibit exponential tails, ϕeνx\phi \sim e^{-\nu x}, and move at the constant velocity, v=(γλαχ)/νv=(\gamma - \lambda^\alpha \chi)/\nu.Comment: Accepted for publication in Phys. Rev. E (Feb. 2009

    Multiple Components in Narrow Planetary Rings

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    The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.Comment: 4 pages, 7 figures (some in colors

    Postfledging Survival, Movements, and Dispersal of Ring Ouzels (Turdus torquatus)

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    We thank Invercauld Estate for cooperation with access to Glen Clunie. S. Redpath, J. Wilson, and S. Roos provided valuable comments on the manuscript. This study was funded by the Royal Society for the Protection of Birds, Scottish Natural Heritage, and the Cairngorms National Park Authority. J.L.L. was supported by the Natural Environment Research Council.Peer reviewedPublisher PD
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