Related papers: Deformations of one-dimensional block media
Stochastic models for the development of cracks in 1 and 2 dimensional objects are presented. In one dimension, we focus on particular scenarios for interacting and non-interacting fragments during the breakup process. For two dimensional…
The diffusion of electronic wave packets in one-dimensional systems with on-site, binary disorder is numerically investigated within the framework of a single-band tight-binding model. Fractal properties are incorporated by assuming that…
Time modulation of the physical parameters offers interesting new possibilities for wave control. Examples include amplification of waves, harmonic generation and non-reciprocity, without resorting to non-linear mechanisms. Most of the…
In this paper, we present a formula describing the formation and decay of shock wave type solutions in some special cases.
We provide a two dimensional deformation model to describe how soft squishy circular particles respond to external forces and collisions. This model involves formulating mathematical equations and algorithms for the shape of a deformed…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
The deformation and flow of disordered solids, such as metallic glasses and concentrated emulsions, involves swift localized rearrangements of particles that induce a long-range deformation field. To describe these heterogeneous processes,…
We study perfusion by a multiscale model coupling diffusion in the tissue and diffusion along the one-dimensional segments representing the vasculature. We propose a block-diagonal preconditioner for the model equations and demonstrate its…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
A discrete model describing defects in crystal lattices and having the standard linear anisotropic elasticity as its continuum limit is proposed. The main ingredients entering the model are the elastic stiffness constants of the material…
We numerically solve the propagation of a shock wave in a chain of elastic beads with no restoring forces under traction (no-tension elasticity). We find a sequence of peaks of decreasing amplitude and velocity. Analyzing the main peak at…
Fundamental concepts in the quasi-one-dimensional geometry of disordered wires and random waveguides in which ideas of scaling and the transmission matrix were first introduced are reviewed. We discuss the use of the transmission matrix to…
In current scientific and technological scenario, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The…
Presented here is the mathematical model describing the phenomenon of shock waves. The underlying concept is based on the time-space model of wave propagation.
We compare two high order finite-difference methods that solve the elastic wave equation in two dimensional domains with curved boundaries and material discontinuities. Two numerical experiments are designed with focus on wave boundary…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
We study the dynamics of solitary waves traveling in a one-dimensional chain of bistable elements in the presence of a local inhomogeneity (defect). Numerical simulations reveal that depending upon its initial speed, an incoming solitary…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
This paper presents a simple ball-and-spring model for the propagation of small amplitude vibrations in a granular material. In this model, the positional disorder in the sample is ignored and the particles are placed on the vertices of a…
We consider the diffusion of independent particles experiencing random accelerations by a space- and time-dependent force as well as viscous damping. This model can exhibit several asymptotic behaviours, depending upon the limiting cases…