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The magnetohydrodynamic (MHD) equations of incompressible viscous fluids with finite electrical conductivity describe the motion of viscous electrically conducting fluids in a magnetic field. In this paper, we find twelve families of…
Recently it was shown that the exact cosmological solutions known as the vacuum plane-wave solutions are late-time attractors for an open set of the spatially homogeneous Bianchi universes containing a non-inflationary $\gamma$-law perfect…
This work is concerned with the study of fundamental models from nonlinear acoustics. In Part~I, a hierarchy of nonlinear damped wave equations arising in the description of sound propagation in thermoviscous fluids is deduced. In…
We have re-examined the Andreev-Lifshitz theory of supersolids. This theory implicitly neglects uniform bulk processes that change the vacancy number, and assumes an internal pressure $P$ in addition to lattice stress $\lambda_{ik}$. Each…
We explore electromagnetic wave modes that can exist in a cosmological plasma dominated by dark energy due to a cosmological constant. It is found that, in the cold and hot plasma cases, electromagnetic plasma wave modes can be found…
The excitation of internal gravity waves by an entropy bubble oscillating in an isothermal atmosphere is investigated using direct two-dimensional numerical simulations. The oscillation field is measured by a projection of the simulated…
Hierarchical dynamics in glass-forming systems span multiple timescales, from fast vibrations to slow structural rearrangements, appearing in both supercooled fluids and glassy states. Understanding how these diverse processes interact…
Vertical thermal convection system exhibits weak turbulence and spatio-temporally chaotic behaviour. In this system, we report seven equilibria and 26 periodic orbits, all new and linearly unstable. These orbits, together with four…
Weakly ionized plasmas can be found in the lower layers of the solar and stellar atmospheres and in structures such as prominences and spicules. A variety of density perturbations and bulk flows detected in these environments have been…
The nonlinear amplitude modulation of known electrostatic plasma modes is examined in a generic manner, by applying a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are…
We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as model for the low-temperature vibrational properties of glass. Exact…
We define compressive and rarefactive waves and give the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential…
An opposite polarity dusty plasma system (containing a few micron size massive opposite polarity dust species and singly charged ion species following Boltzmann law) is considered. The nature of dust-acoustic (DA) wave electrostatic and…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
Equations describing the linear evolution of a non-dissipative Langmuir wave in inhomogeneous nonstationary anisotropic plasma without magnetic field are derived in the geometrical optics approximation. A continuity equation is obtained for…
We derive a family of similarity solutions to the nonlinear non-equilibrium Marshak wave problem for an inhomogeneous planar medium which is coupled to a time dependent radiation driving source. We employ the non-equilibrium gray diffusion…
A fifth--order nonlinear partial differential equation for the description of nonlinear waves in a liquid with gas bubbles is considered. Special solutions of this equation are studied. Some elliptic and simple periodic traveling waves…
To better understanding the principal features of collisionless damping/growing plasma waves we have implemented a demonstrative calculation for the simplest cases of electron waves in two-stream plasmas with the delta-function type…
We study the spectrum of the linearization around standing wave profiles for two quantum hydrodynamics systems with linear and nonlinear viscosity. The essential spectrum for such profiles is stable; we investigate the point spectrum using…
We develop the theory of hydrodynamics of an isotropic Fermi liquid of electrons coupled to isotropic acoustic phonons, assuming that umklapp processes may be neglected. At low temperatures, the fluid is approximately Galilean invariant; at…