Related papers: Nonlinear interaction of waves in elastodynamics a…
Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…
The nonlinear mechanics of a flexible elastic rod constrained at its edges by a pair of sliding sleeves is analyzed. The planar equilibrium configurations of this variable-length elastica are found to have shape defined only by the…
In this article, we investigate the effects of the interplay between quadratic and cubic nonlinearities on the propagation of elastic waves in periodic waveguides. Through this framework, we unveil an array of wave control strategies that…
We study the weakly nonlinear evolution of acoustic instability of a plane- parallel polytrope with thermal dissipation in the form of Newton's law of cooling. The most unstable horizontal wavenumbers form a band around zero and this…
A number of important results of studying large deformations of hyper-elastic shells are obtained using discrete methods of mathematical physics. In the present paper, using the variational method for solving nonlinear boundary problems of…
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…
We consider a system of nonlinear Klein-Gordon equations with quadratic interaction in two and three space dimensions. The strong instability of standing wave solutions is studied for the system without assuming the mass resonance…
The stability of Marangoni roll convection in a liquid-gas system with deformable interface is studied in the case when there is a nonlinear interaction between two modes of Marangoni instability: long-scale surface deformations and…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
The nonlinear inviscid 1D blood flow equations are studied analytically using the method of characteristics. The boundary value problem with a triangle-shaped boundary data at the aortic outlet is considered. The pressure-velocity profile,…
In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape.…
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive…
Wave resonance is the fundamental mechanism of non-linear instabilities of fluid flows, and affects the long-time evolution of fluid motions and other physical problems described by non-linear differential equations. Some significant…
We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied…
Weak Wave Turbulence is a powerful theory to predict statistical observables of diverse relevant physical phenomena, such as ocean waves, magnetohydrodynamics and nonlinear optics. The theory is based upon an asymptotic closure permitted in…
The nonlinear dynamics of collisionless Alfven trains, including resonant particle effects is studied using the kinetic nonlinear Schroedinger (KNLS) equation model. Numerical solutions of the KNLS reveal the dynamics of Alfven waves to be…
We give a survey of recent results on flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are considered. The focus of…
We apply the framework of tempered fractional calculus to investigate the spatial dispersion of elastic waves in a one-dimensional elastic bar characterized by range-dependent nonlocal interactions. The measure of the interaction is given…
We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be…