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We introduce a homogenization approach to characterize the dynamical response of a generic dispersive spacetime crystal in the long-wavelength limit. The theory is applied to dispersive spacetime platforms with a travelling-wave modulation.…
In periodically sheared suspensions there is a dynamical phase transition characterized by a critical strain amplitude $\gamma_c$ between an absorbing state where particle trajectories are reversible and an active state where trajectories…
The Adler equation with time-periodic frequency modulation is studied. A series of resonances between the period of the frequency modulation and the time scale for the generation of a phase slip is identified. The resulting parameter space…
We develop a dynamical effective medium theory to accurately predict the unusual properties of elastic metamaterials in two dimensions near the resonant frequencies. The theory shows that the effective bulk modulus, shear modulus, and mass…
In this paper the relaxed micromorphic material model for anisotropic elasticity is used to describe the dynamical behavior of a band-gap metamaterial with tetragonal symmetry. Unlike other continuum models (Cauchy, Cosserat, second…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian…
We uncover the existence of Dirac and exceptional points in waveguides made of anisotropic materials, and study the transition between them. Dirac points in the dispersion diagram appear at propagation directions where the matrix describing…
Plasmon opens up the possibility to efficiently couple light and matter at sub-wavelength scales. In general, the plasmon frequency is dependent of carrier density. This dependency, however, renders fundamentally a weak plasmon intensity at…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
At zero energy the Dirac equation has interesting behaviour. The asymmetry in the number of spin up and spin down modes is determined by the topology of both space and the gauge field in which the system sits. An analogous phenomenon also…
We study analytically the dynamics of two-dimensional rectangular lattices with periodic boundary conditions. We consider anisotropic initial data supported on one low-frequency Fourier mode. We show that, in the continuous approximation,…
The Dirac materials, such as graphene and three-dimensional topological insulators, have attracted much attention because they exhibit novel quantum phenomena with their low energy electrons governed by the relativistic Dirac equations. One…
The effective low energy description of interacting Dirac and Weyl semimetals is that of massless quantum electrodynamics with several Lorentz breaking material parameters. We perform a renormalization group analysis of Coulomb interaction…
Interpreting the vibrational properties of amorphous solids beyond Debye's theory is challenging due to the presence of inhomogeneity on the mesoscopic scale. In this work, we model this inhomogeneity by real-space fluctuating elasticity…
In this work the spontaneous symmetry breaking in certain nonlinear theories with second-class constraints is explored. Using the Dirac's method we perform an analysis of the constraints and the counting of the degrees of freedom. The…
Electromagnetic properties of periodic two-dimensional sub-wavelength structures consisting of closely-packed inclusions of materials with negative dielectric permittivity $\epsilon$ in a dielectric host with positive $\epsilon_h$ can be…
Important insights into the dynamics of spherically symmetric AdS-scalar field perturbations can be obtained by considering a simplified time-averaged theory accurately describing perturbations of amplitude epsilon on time-scales of order…
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…
We consider the finite difference discretization of isotropic elastic wave equations on nonuniform grids. The intended applications are seismic studies, where heterogeneity of the earth media can lead to severe oversampling for simulations…