Related papers: Some thoughts on dynamic effective properties -- a…
The problem of an electromagnetic wave scattered from a random medium layer with rough boundaries is formulated using integral equations which involve two kinds of Green functions. The first one describes the wave scattered by the random…
The paper provides a rigorous analysis of the dispersion spectrum of SH (shear horizontal) elastic waves in periodically stratified solids. The problem consists of an ordinary differential wave equation with periodic coefficients, which…
Electromagnetic waves and fluids have locally conserved mechanical properties associated with them and we may expect these to exist for matter waves. We present a semiclassical description of the continuity equations relating to these…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
The formalism of the scattering matrix is applied to describe the transmission properties of multilayered structures with deep variations of the refractive index and arbitrary arrangements of the layers. We show that there is an exact…
The emergence of nonequilibrium phenomena in individual complex wave systems has long been of fundamental interests. Its analytic studies remain notoriously difficult. Using the mathematical tool of the concentration of measure (CM), we…
We develop a computing framework that leverages wave propagation within an interconnected network, where nodes and edges possess wave manipulation capabilities, such as frequency mixing or time delay. This computing paradigm can not only…
Quantum particle transmission through locally periodic potentials surrounded by symmetric exterior potentials is analyzed. Closed-form conditions for locating energy peaks of total transmission are derived. Floquet/Bloch energy band types…
We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity in vacuum regions.…
We develop a method for computing the scattering of flexural waves off of a periodic wall or a periodic line of scatterers. These waves model the fluctuations of thin plates with periodic clamped, supported, or free edges. We use the…
In this study, we experimentally investigated the time dependence of the statistical properties of two-dimensional drying crack patterns to determine the functional form of fragment size distribution. Experiments using a thin layer of a…
We analyse the influence of pre-stress on the propagation of interfacial waves along the boundary of an incompressible hyperelastic half-space that is in contact with a viscous fluid extending to infinity in the adjoining half-space. One…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
We investigate how momentum and kinetic energy is transferred between Fourier components (the so-called triad interactions) in measured turbulent flow fields, i.e. in practical, discretely sampled signals with limited temporal and spatial…
In this work we present the mathematical model and simulations of a particular wave energy converter, the so-called oscillating water column. In this device, waves governed by the one-dimensional nonlinear shallow water equations arrive…
The paper addresses a novel model of metamaterial structure. A system of spinners has been embedded into a two-dimensional periodic lattice system. The equations of motion of spinners are used to derive the expression for the chiral term in…
We present a one-dimensional model for diffusion in a fluctuating lattice; that is a lattice which can be in two or more states. Transitions between the lattice states are induced by a combination of two processes: one periodic…
Some relationships, fundamental to the resolution of interface wave problems, are presented. These equations allow for the derivation of explicit secular equations for problems involving waves localized near the plane boundary of…
We investigate in this chapter the mathematical models for electromagnetic wave propagation in dispersive isotropic passive linear media for which the dielectric permittivity $\varepsilon$ and magnetic permeability $\mu$ depend on the…
The data of simultaneous measurements of the surface displacement produced by propagating planar waves in experimental flume and of the dynamic pressure beneath the waves are compared with the theoretical predictions based on different…