Nonlinear Longitudinal Bulk Strain Waves in Layered Elastic Wavegudes

We consider long longitudinal bulk strain waves in layered waveguides using Boussinesq-type equations. The equations are developed using lattice models, and this is viewed as an extension of the Fermi-Pasta-Ulam problem. We describe semi-analytical approaches to the solution of scattering problems in delaminated waveguides, and to the construction of the solution of an initial-value problem in the class of periodic functions, motivated by the scattering problems.Comment: 24 pages, 11 figure

Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves

We study solitary wave solutions of the fifth-order Korteweg–de Vries equation which contains, besides the traditional quadratic nonlinearity and third-order dispersion, additional terms including cubic nonlinearity and fifth order linear dispersion, as well as two nonlinear dispersive terms. An exact solitary wave solution to this equation is derived, and the dependence of its amplitude, width, and speed on the parameters of the governing equation is studied. It is shown that the derived solution can represent either an embedded or regular soliton depending on the equation parameters. The nonlinear dispersive terms can drastically influence the existence of solitary waves, their nature (regular or embedded), profile, polarity, and stability with respect to small perturbations. We show, in particular, that in some cases embedded solitons can be stable even with respect to interactions with regular solitons. The results obtained are applicable to surface and internal waves in fluids, as well as to waves in other media (plasma, solid waveguides, elastic media with microstructure, etc.)

Nonlinear longitudinal bulk strain waves in layered elastic waveguides

We consider long longitudinal bulk strain waves in layered waveguides using Boussinesq-type equations. The equations are developed using lattice models, and this is viewed as an extension of the Fermi-Pasta-Ulam problem. We describe semi-analytical approaches to the solution of scattering problems in delaminated waveguides, and to the construction of the solution of an initial-value problem in the class of periodic functions, motivated by the scattering problems

Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves

Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in which case the system can support radiating solitary waves. We construct a weakly-nonlinear d'Alembert-type solution of this system, considering the problem in the class of periodic functions on an interval of finite length. The solution is constructed using a novel multiple-scales procedure involving fast characteristic variables and two slow time variables. Asymptotic validity of the solution is carefully examined numerically. We also discuss the limiting case of an infinite interval for localised initial conditions. The solution is applied to study interactions of radiating solitary waves

A recent bottleneck of Y chromosome diversity coincides with a global change in culture

Contains fulltext : 153022.pdf (publisher's version ) (Open Access)It is commonly thought that human genetic diversity in non-African populations was shaped primarily by an out-of-Africa dispersal 50-100 thousand yr ago (kya). Here, we present a study of 456 geographically diverse high-coverage Y chromosome sequences, including 299 newly reported samples. Applying ancient DNA calibration, we date the Y-chromosomal most recent common ancestor (MRCA) in Africa at 254 (95% CI 192-307) kya and detect a cluster of major non-African founder haplogroups in a narrow time interval at 47-52 kya, consistent with a rapid initial colonization model of Eurasia and Oceania after the out-of-Africa bottleneck. In contrast to demographic reconstructions based on mtDNA, we infer a second strong bottleneck in Y-chromosome lineages dating to the last 10 ky. We hypothesize that this bottleneck is caused by cultural changes affecting variance of reproductive success among males