A Variational Principle for the Asymptotic Speed of Fronts of the Density Dependent Diffusion--Reaction Equation

We show that the minimal speed for the existence of monotonic fronts of the equation $u_t = (u^m)_{xx} + f(u)$ with $f(0) = f(1) = 0$, $m >1$ and $f>0$ in $(0,1)$ derives from a variational principle. The variational principle allows to calculate, in principle, the exact speed for arbitrary $f$. The case $m=1$ when $f'(0)=0$ is included as an extension of the results.Comment: Latex, postcript figure availabl

River delta morphotypes emerge from multiscale characterization of shorelines

Delta shoreline structure has long been hypothesized to encode information on the relative influence of fluvial, wave, and tidal processes on delta formation and evolution. We introduce here a novel multiscale characterization of shorelines by defining three process-informed morphological metrics. We show that this characterization yields self-emerging classes of morphologically similar deltas, that is, delta morphotypes, and also predicts the dominant forcing of each morphotype. Then we show that the dominant forcings inferred from shoreline structure generally align with those estimated via relative sediment fluxes, while positing that misalignments arise from spatiotemporal heterogeneity in deltaic sediment fluxes not captured in their estimates. The proposed framework for shoreline characterization advances our quantitative understanding of how shoreline features reflect delta forcings, and may aid in deciphering paleoclimate from images of ancient deposits and projecting delta morphologic response to changes in sediment fluxes

Speed of reaction-transport processes

We present an approach to determining the speed of wave-front solutions to reaction-transport processes. This method is more accurate than previous ones. This is explicitly shown for several cases of practical interest: (i) the anomalous diffusion reaction, (ii) reaction diffusion in an advective field, and (iii) time-delayed reaction diffusion. There is good agreement with the results of numerical simulations