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A mesoscopic model of amorphous plasticity is discussed in the context of depinning models. After embedding in a d + 1 dimensional space, where the accumulated plastic strain lives along the additional dimension, the gradual plastic…
The fully nonlinear notion of resonance$-$\textit{geometrical resonance}$-$in the general context of dissipative systems subjected to spatially periodic \textit{phase-modulated} potentials is discussed. It is demonstrated that there is an…
Recent progress of symbolic dynamics of one- and especially two-dimensional maps has enabled us to construct symbolic dynamics for systems of ordinary differential equations (ODEs). Numerical study under the guidance of symbolic dynamics is…
Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…
A periodically-uneven (in one horizontal direction) stress-free boundary covering a linear, isotropic, homogeneous, lossless solid half space is submitted to a vertically-propagating shear-horizontal plane, body wave. The rigorous theory of…
The orientational dynamics of inertialess anisotropic particles transported by two-dimensional convective turbulent flows display a coexistence of regular and chaotic features. We numerically demonstrate that very elongated particles (rods)…
The problem of a rigid disk rolling down a ramp is a classic problem given to students in introductory mechanics courses. In contrast, systematic studies on the rolling behavior of an ellipse have only recently emerged. Unlike a rolling…
Perturbative analyses of planetary resonances commonly predict singularities and/or divergences of resonance widths at very low and very high eccentricities. We have recently re-examined the nature of these divergences using…
We show that the ideal hydrodynamics of an eccentric astrophysical disc can be derived from a variational principle. The nonlinear secular theory describes the slow evolution of a continuous set of nested elliptical orbits as a result of…
We describe the families of periodic orbits in the 2-dimensional 1/2 retrograde resonance at mass ratio 0.001, analyzing their stability and bifurcations into 3-dimensional periodic orbits. We explain the role played by periodic orbits in…
Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and…
The slow dynamics for a colloidal suspension of particles interacting with a hard-core repulsion complemented by a short-ranged attraction is discussed within the frame of mode-coupling theory for ideal glass transitions for parameter…
We initiate the development of a theory of the elasticity of nanoscale objects based upon new physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in…
The temporal response of open systems is marked by damped oscillations. These oscillations, often referred to as ringings, are the signature of the decay of quasinormal modes (QNMs). A major research objective across various fields is to…
We study the motion of test particles around a center of attraction represented by a monopole (with and without spheroidal deformation) surrounded by a ring, given as a superposition of Morgan & Morgan discs. We deal with two kinds of…
The study of wave propagation outside bounded obstacles uncovers the existence of resonances for the Laplace operator, which are complex-valued generalized eigenvalues, relevant to estimate the long time asymptotics of the wave. In order to…
The vortex-like solutions are studied in the framework of the gauge model of disclinations in elastic continuum. A complete set of model equations with disclination driven dislocations taken into account is considered. Within the linear…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
Acoustic and elastic metamaterials with time- and space-dependent material properties have received great attention recently as a means to break reciprocity for propagating mechanical waves, achieving greater directional control. One…
The phase--space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, sudden reductions in the phase-space volume or gaps…