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Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
Dynamics of linear perturbations in a differentially rotating accretion disk with non-homogeneous vertical structure is investigated. It has been found that turbulent viscosity results in instability of both pinching oscillations, and…
The dynamics of a single crack moving through a heterogeneous medium is studied in the quasi-static approximation. Equations of motion for the crack front are formulated and the resulting scaling behaviour analyzed. In a model scalar system…
The quasi-one-dimensional rhombic array of the waveguides is considered. System of equations describing coupled waves in the waveguide in the linear limit is solved exactly. The electric field distribution was found both for the…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
We present two alternative complete sets of static modes of a homogeneous dielectric sphere, for their use in the resonant-state expansion (RSE), a rigorous perturbative method in electrodynamics. Physically, these modes are needed to…
A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing…
We demonstrate a single-mode phononic waveguide that enables robust propagation of mechanical waves. The waveguide is a highly-stressed silicon nitride membrane that supports the propagation of out-of-plane modes. In direct analogy to…
Plane-wave reflection and refraction at an interface with a double wire medium is considered. The problem of additional boundary conditions (ABC) in application to wire media is discussed and an ABC-free approach, known in the solid state…
The propagation of waves in highly inhomogeneous media is a problem of interest in multiple fields including seismology, acoustics and electromagnetism. It is also relevant for technological applications such as the design of sound…
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…
In this work, we study wave propagation in generic Hermitian local periodic baths, and investigate the effects of anisotropy and quasi-breaking of periodicity on resonant emission into the band of the bath. We asymptotically decompose the…
We discuss the properties of an analytical solution for waves in radiating fluids, with a view towards its implementation as a quantitative test of radiation hydrodynamics codes. A homogeneous radiating fluid in local thermodynamic…
A solid object's geometry, density, and elastic moduli completely determine its spectrum of normal modes. Solving the inverse problem - determining a material's elastic moduli given a set of resonance frequencies and sample geometry -…
We report on the theoretical investigation of the plasmonic wave propagation in the coaxial cylindrical cables fabricated of both right-handed medium (RHM) [with $\epsilon >0$, $\mu >0$] and left-handed medium (LHM) [with $\epsilon(\omega)…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
We report a detailed and systematic numerical study of wave propagation through a coherently amplifying random one-dimensional medium. The coherent amplification is modeled by introducing a uniform imaginary part in the site energies of the…
We employ numerical simulations to understand the evolution of elastic standing waves in disordered frictional disk systems, where the dispersion relations of rotational sound modes are analyzed in detail. As in the case of frictional…
We analytically compute the time evolution of an initial infinite plane wave in the presence of a 1-dimensional square quantum barrier. This calculation generalizes the analysis of the shutter problem and sets the basis for the calculation…
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…