Related papers: Elastodynamics and resonances in elliptical geomet…
We use perturbation theory and bifurcation theory to analyze the dynamical behavior of resonances, associated to a model describing a particle moving within a ring around a celestial object. The central body is modeled as a homogeneous…
The electromagnetic modes and the resonances of homogeneous, finite size, two-dimensional bodies are examined in the frequency domain by a rigorous full wave approach based on an integro-differential formulation of the electromagnetic…
The resonance modes and the related effects to the transmission of elastic waves in a two dimensional phononic crystal formed by periodic arrangements of a two blocks unit cell in one direction are studied. The unit cell consists of two…
A method is presented for solving elastodynamic problems in radially inhomogeneous elastic materials with spherical anisotropy, i.e.\ materials such that $c_{ijkl}= c_{ijkl}(r)$ in a spherical coordinate system ${r,\theta,\phi}$. The time…
Elastic waves scattering off a periodic single and double array of thin cylindrical defects is considered for isotropic materials. An analytical expression for the scattering matrix is obtained by means of the Lippmann-Schwinger formalism…
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…
The relation between the elastic wave equation for plane, isotropic bodies and an underlying classical ray dynamics is investigated. We study in particular the eigenfrequencies of an elastic disc with free boundaries and their connection to…
Linearised relativistic elasticity equations of motion are considered for a rod and a spinning ring encountering a gravitational wave. In the case of the rod, the equations reduce to a wave equation with appropriate boundary conditions.…
Observation of resonance modes is the most straightforward way of studying mechanical oscillations because these modes have maximum response to stimuli. However, a deeper understanding of mechanical motion could be obtained by also looking…
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,…
Analytical expressions for the axial and transverse acoustic radiation forces as well as the radiation torque per length are derived for a rigid elliptical cylinder placed arbitrarily in the field of in plane progressive, quasi-standing or…
Physical systems with loss or gain feature resonant modes that are decaying or growing exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, a so-called "exceptional…
Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
The mobility of an overdamped particle, in a periodic potential tilted by a constant external field and moving in a medium with periodic friction coefficient is examined. When the potential and the friction coefficient have the same…
We consider the plasmon resonance for the elastostatic system in $\mathbb{R}^3$ associated with a very broad class of sources. The plasmonic device takes a general core-shell-matrix form with the metamaterial located in the shell. It is…
Interactions between fluids and elastic solids are ubiquitous in application ranging from aeronautical and civil engineering to physiological flows. Here we study the pulsatile flow through a two-dimensional Starling resistor as a simple…
This work investigates different models of rotational dynamics of two rigid bodies with the shape of an ellipsoid, moving under their gravitational influence. The focus of this study is on their behavior, their linear stability, and…
We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find…
We describe a method to extract resonant orbits from N-body simulations exploiting the fact that they close in a frame rotating with a constant pattern speed. Our method is applied to the N-body simulation of the Milky Way by Shen et al.…