Empirical studies of the genome-wide length distribution of duplicated sequences have revealed an algebraic tail common to nearly all clades. The decay of the tail is often well approximated by a single exponent that takes values within a limited range. We propose and study here scale-free duplication dynamics, a class of model for genome sequence evolution that generates the observed shapes of this distribution. A transition between self-similar and non-self-similar regimes is exhibited. Our model accounts plausibly for the observed form of the algebraic tail, which is not produced by standard models for generating long-range sequence correlations.
We analyse the disturbed flow in the subsonic laminar boundary layer, disturbances being generated by local heating elements, which are placed on the surface. It is exhibited that these flows are described in terms of free interaction theory for specific sizes of thermal sources. We construct the numerical solution for the case of a flat subsonic stream in the viscous asymptotic layer, in which the flow is described by nonlinear equations for vorticity, temperature and an interaction condition which provides the influence of perturbations to the pressure in the main order. The obtained solutions are compared with those for corresponding linear problems with small perturbations. It is demonstrated that strong temperature perturbations in some situations allow us to obtain the flow close to the separated flow.
Plane nonlinear fluid flows through a porous medium which simulate a sink located at the same distance from the roof and floor of the stratum for two nonlinear flow laws are constructed. The following flow laws are taken: a power law and a law of special form reducing to analytic functions in the hodograph plane.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.