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A theory of the propagation of acoustic waves in a porous medium filled with superfluid solution is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations…

Acoustic black holes are fluid dynamic analogs of general relativistic black holes, wherein the behaviour of sound waves in a moving fluid acts as an analog for scalar fields propagating in a gravitational background. Acoustic horizons…

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…

This thesis investigates phenomena occurring in black-hole accretion discs which are likely to induce high-frequency quasi-periodic variability. Two classes of pseudo-relativistic theoretical models are studied. The first is based on the…

"Acoustic spacetimes", in which techniques of differential geometry are used to investigate sound propagation in moving fluids, have attracted considerable attention over the last few decades. Most of the models currently considered in the…

We present a self-consistent theory for sound propagation in a simple model of a disordered solid. The solid is modeled as a collection of randomly distributed particles connected by harmonic springs with strengths that depend on the…

We investigate the possibility of the acoustic superresonance phenomenon (analog to the superradiance in black hole physics), i.e., the amplification of a sound wave by reflection from the ergoregion of a rotating acoustic black hole with…

Using both multiple scattering theory and effective medium theory, we find that an acoustic metamaterial consisting of an array of spinning cylinders can possess a host of unusual properties including folded bulk and interface-state bands…

The problem of oscillating flows inside pipes under periodic forcing of viscoelastic fluids is addressed here. Starting from the linear Oldroyd-B model, a generalized Darcy's law is obtained in frequency domain and an explicit expression…

A fast rotating Bose-Einstein condensate confined in a quadratic-plus-quartic potential is found to dynamically generate a "giant vortex" that absorbs all phase singularities into a central low density hole, thereby sustaining a…

We introduce an analogue model for a nonglobally hyperbolic spacetime in terms of a two-dimensional fluid. This is done by considering the propagation of sound waves in a radial flow with constant velocity. We show that the equation of…

It was reported that the optical field fluctuations in self-defocusing media can be described by sound waves propagating in a two-dimensional photon-fluid which is controlled by the driving laser beam. The photon-fluid can be regarded as…

The stability of a rotating fluid disk to the formation of spiral arms is studied in the tightwinding approximation in the linear regime. The dispersion relation for spirals that was derived by Bertin et al. is shown to contain a new,…

A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating…

Active systems on curved geometries are ubiquitous in the living world. In the presence of curvature orientationally ordered polar flocks are forced to be inhomogeneous, often requiring the presence of topological defects even in the steady…

Linear analysis of vortex sheet stability in the rotating gaseous disk or shallow water layer shows that presence of a central reflecting surface changes system stability significantly. An effect of absence of vortex sheet stabilization has…

We study the axisymmetric propagation of a viscous gravity current over a deep porous medium into which it also drains. A model for the propagation and drainage of the current is developed and solved numerically in the case of constant…

Multiple scattering of waves leads to many peculiar phenomena such as complete band gaps in periodic structures and wave localization in disordered media. Within a band gap excitations are evanescent; when localized they remain confined in…

This paper concerns the structural stability of subsonic flows with a contact discontinuity in a finitely long axisymmetric cylinder. We establish the existence and uniqueness of axisymmetric subsonic flows with a contact discontinuity by…

The hallmark of superfluidity is the appearance of "vortex states" carrying a quantized metastable circulating current. Considering a unidirectional flow of particles in a ring, at first it appears that any amount of scattering will…