Related papers: The discrete Lamb problem: Elastic lattice waves i…
A Rayleigh wave is a type of surface wave that propagates in the boundary of an elastic solid with traction (or Neumann) boundary conditions. Since the 1980s much work has been done on the problem of constructing a leading term in an…
In this paper we discuss the uniaxial propagation of transient waves within a semi-infinite viscoelastic Bessel medium. First, we provide the analytic expression for the response function of the material as we approach the wave-front. To do…
The standing wave solution on an idealized mass spring system can be found using straight forward algebra. The solution is found when this system makes jump rope like rotations around an axis.The standing wave forms a constant shape in a…
We address an important issue of a dynamic homogenisation in vector elasticity for a doubly periodic mass-spring elastic lattice. The notion of logarithmically growing resonant waves is used in a complete analysis of star-shaped wave forms…
We derive the general solution of the unsteady Stokes equations for an unbounded fluid in spherical polar coordinates, in both time and frequency domains. The solution is an expansion in vector spherical harmonics and given as a sum of a…
The system of Lama's equations is investigated, describing the motion of the elastic media under subsonic, transonic and supersonic velocities of the moving source of distributions, and its decisions in space of generalized…
This paper is concerned with the time-dependent acoustic-elastic interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above an unbounded rough surface. The well-posedness and stability of the…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices of point masses connected by Voigt elements, under an antiplane concentrated loading. The emphasis is on obtaining analytical estimates for…
The object of the numerical study is the travel of pendulum waves in a blocky medium under nonstationary impact of deep-seated charge blasting on the surface of the expansion chamber. The blocky model is simulated by a two-dimensional…
The analytical solution is given for a vibrating rigid core sphere, oscillating up and down without volume change, situated at the center of an elastic material spherical shell, which in turn is situated inside an infinite (possible…
The hydrodynamic limit of a discrete kinetic equation is intrinsically connected with the symmetry of the lattices used in construction of a discrete velocity model. On mixed lattices composed of standard lattices the sixth-order (and…
This article delves into the intricate dynamics of Rayleigh wave propagation within a nonlocal orthotropic medium, where the presence of void and diffusion adds an intriguing layer to the analysis. Grounded in Eringen nonlocal elasticity…
Leaky waves are an important class of waves, particularly for guiding waves along structures embedded within another medium; a mismatch in wavespeeds often leads to leakage of energy from the waveguide, or interface, into the medium, which…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
The problem of an electromagnetic wave scattering by a slab with two rough boundaries is solved by a small-perturbation method under the Rayleigh hypothesis. In order to obtain a perturbative development, we use a systematic procedure which…
In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive…
In this work, the lattice Boltzmann method (LBM) is assessed as a time-domain numerical approach for electromagnetic wave scattering. Owing to its explicit formulation and suitability for parallel computation on structured grids, LBM…
The discrete periodic lattice of masses and springs with line and point defects is considered. The dispersion equations for propagative, guided and localised waves are obtained. The detailed analysis of example with three masses is…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
Rotating waves are a fascinating feature of a wide array of complex systems, particularly those arising in the study of many chemical and biological processes. With many rigorous mathematical investigations of rotating waves relying on the…