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We study the transverse-size effect of a quasi-one-dimensional rectangular waveguide on the single-photon scattering on a two-level system. We calculate the transmission and reflection coefficients for single incident photons using the…

Results of forward modelling of acoustic wave propagation in a realistic solar sub-photosphere with two cases of steady horizontal flows are presented and analysed by the means of local helioseismology. The simulations are based on fully…

The aim of this lecture is to consider a concrete problem, namely the identification of situations of invisibility in waveguides, to present techniques and tools that may be useful in various fields of applied mathematics. To be more…

The hydrodynamic phonon transport was studied several decades ago for verifying the quantum theory of lattice thermal transport. Recent prediction of significant hydrodynamic phonon transport in graphitic materials shows its practical…

Despite the ubiquity of applications of heat transport across nanoscale interfaces, including integrated circuits, thermoelectrics, and nanotheranostics, an accurate description of phonon transport in these systems remains elusive. Here we…

This work considers the propagation of high-frequency waves in highly-scattering media where physical absorption of a nonlinear nature occurs. Using the classical tools of the Wigner transform and multiscale analysis, we derive semilinear…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

Wave propagation in complex media is a universal problem spanning optics, acoustics, mechanics, and condensed matter physics. While disorder usually causes strong scattering, recent theory predicts that a special class of correlated…

With the current revival of interest in astronomical intensity interferometry, it is interesting to revisit the associated theory, which was developed in the 1950s and 1960s. This paper argues that intensity interferometry can be understood…

We prove a quantum version of the Sabine law from acoustics describing the location of resonances in transmission problems. This work extends the author's previous work to a broader class of systems. Our main applications are to scattering…

Propagation of waves through Cantor-set media is investigated by renormalization-group analysis. For specific values of wave numbers, transmission coefficients are shown to be governed by the logistic map, and in the chaotic region, they…

The bubbles involved in sonochemistry and other applications of cavitation oscillate inertially. A correct estimation of the wave attenuation in such bubbly media requires a realistic estimation of the power dissipated by the oscillation of…

The thermal conductance by phonons of a quasi-one-dimensional solid with isotope or defect scattering is studied using the Landauer formalism for thermal transport. The conductance shows a crossover from localized to Ohmic behavior, just as…

Many astronomical sources produce transient phenomena at radio frequencies, but the transient sky at low frequencies (<300 MHz) remains relatively unexplored. Blind surveys with new widefield radio instruments are setting increasingly…

In this paper we analyze a time-reversal experiment in a random underwater acoustic channel. In this kind of waveguide with semi-infinite cross section a propagating field can be decomposed over three kinds of modes: the propagating modes,…

Scalar wave propagation across a semi-infinite step or step-like discontinuity on any one boundary of the square lattice waveguides is considered within nearest-neighbour interaction approximation. An application of the Wiener-Hopf method…

Problem of long-range sound propagation in the randomly-inhomogeneous deep ocean is considered. We examine a novel approach for modeling of wave propagation, developed by K.C.Hegewisch and S.Tomsovic. This approach relies on construction of…

Diffusion is the result of repeated random scattering. It governs a wide range of phenomena from Brownian motion, to heat flow through window panes, neutron flux in fuel rods, dispersion of light in human tissue, and electronic conduction.…

Using a parabolic equation, we consider ray propagation in a waveguide with the sound speed profile that corresponds to the dynamics of a nonlinear oscillator. An analytical consideration of the dependence of the travel time on the initial…

Starting with Maxwell's equations, we derive the fundamental results of the Huygens-Fresnel-Kirchhoff and Rayleigh-Sommerfeld theories of scalar diffraction and scattering. These results are then extended to cover the case of vector…