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For a nonlinear system of coupled PDEs, that describes evolution of a viscous thin liquid sheet and takes account of surface tension at the free surface, we show exponential $(H^1,\,L^2)$ asymptotic decay to the flat profile of its…
Symmetric instability (SI) is a frontal instability arising from the interaction of rotation with lateral and vertical shear of a frontal jet and is a generalization of shear, centrifugal, and gravitational instabilities. While the onset of…
A new condition for the linear dissipative instability of the strong plane shock wave in an arbitrary medium is obtained. The instability of the shock is realized due to the flow instability behind its front, which is similar to the known…
Complex elastic media such as biological membranes, in particular, blood vessels, may be described as fiber-reinforced solids in the framework of nonlinear hyperelasticity. Finite axially symmetric anti-plane shear displacements in such…
We present a phenomenological time-dependent Ginzburg-Landau theory of nonlinear plastic deformations in solids. Because the problem is very complex, we first give models in one and two dimensions without vacancies and interstitials, where…
We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly nonlinear regime. Such waves are generically found to be excited in simulations of turbulent accretion disks, in particular if said…
Wave propagation in real media is affected by various non-trivial physical phenomena, e.g., anisotropy, an-elasticity and dissipation. Assumptions on the stress-strain relationship are an integral part of seismic modeling and determine the…
It is the aim of the paper to present a new point of view on rotational elasticity in a nonlinear setting using orthogonal matrices. The proposed model, in the linear approximation, can be compared to the well known equilibrium equations of…
Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast,…
Acoustic perturbations to stellar envelopes can lead to the formation of weak shock waves via nonlinear wave-steepening. Close to the stellar surface, the weak shock wave increases in strength and can potentially lead to the expulsion of…
Nonlinear dynamics have long been exploited in order to damp vibrations in solid mechanics. The phenomenon of irreversible energy transfer from a linear primary system to a nonlinear absorber has driven great attention to the optimal design…
Regarding a recent dispute about the symmetry of the stress tensor of fluids, more considerations are presented. The usual proofs of this symmetry are reviewed, and contradictions between this symmetry and the mechanism of gas viscosity are…
We describe propagation of torsional elastic waves in cylindrical waveguide with wedge dislocation in the framework of geometric theory of defects. The defect changes the dispersion relation. For positive deficit angles, it increases the…
Whereas electromagnetic surface waves are confined to a planar interface between two media, line waves exist at the one-dimensional interface between three materials. Here we derive a non-local integral equation for computing the properties…
In this paper, we initiate the study of wave propagation in a recently proposed mathematical model for stretch-limited elastic strings. We consider the longitudinal motion of a simple class of uniform, semi-infinite, stretch-limited strings…
We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…
We study the energy decay properties of a pulse propagating in a strongly nonlinear granular chain with damping proportional to the relative velocity of the grains. We observe a wave disturbance that at low viscosities consists of two parts…
We study elastic shear waves of small but finite amplitude, composed of an anti-plane shear motion and a general in-plane motion. We use a multiple scales expansion to derive an asymptotic system of coupled nonlinear equations describing…
This paper formally analyses effects of nematic weak elasticity using the five parametric de Gennes (DG) potential. The analysis is trivialized in a specific (local) Cartesian coordinate system whose one axis is directed along the initial…
The propagation of nonlinear waves in one dimensional space, unsteady and compressible flow in Darcy-type porous media is analyzed. It is assumed that the weak discontinuity propagate long the characteristic path using the characteristics…