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The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general…
An Equation of State (\textit{EoS}) closes the set of fluid equations. Although an ideal EoS with a constant \textit{adiabatic index} $\Gamma$ is the preferred choice due to its simplistic implementation, many astrophysical fluid…
The equation of state (EOS) of dense nuclear matter is a key factor to determine the internal structure and properties of neutron stars. However, the EOS of high-density nuclear matter has great uncertainty mainly because the terrestrial…
Core-collapse supernovae are sources of powerful gravitational waves (GWs). We assess the possibility of extracting information about the equation of state (EOS) of high density matter from the GW signal. We use the bounce and early…
The Noh verification test problem is extended beyond the commonly studied ideal gamma-law gas to more realistic equations of state (EOSs) including the stiff gas, the Noble-Abel gas, and the Carnahan-Starling EOS for hard-sphere fluids.…
Numerical simulations of compressible fluid flows require an equation of state (EOS) to relate the thermodynamic variables of density, internal energy, temperature, and pressure. A valid EOS must satisfy the thermodynamic conditions of…
Gravitational waves from core-collapse supernovae provide a unique probe of the equation of state (EOS) of high density matter. In this work, we focus on the bounce signal from numerical simulations of rotating supernovae and explore its…
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of…
Strongly nonlinear models of internal wave propagation for incompressible stratified Euler fluids are investigated numerically and analytically to determine the evolution of a class of initial conditions of interest in laboratory…
Inference of the equation-of-state (EoS) of dense nuclear matter in neutron-star cores is a principal science goal of X-ray and gravitational-wave observations of neutron stars. In particular, gravitational-wave observations provide an…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
It is of great interest to understand the equation of state (EOS) of the neutron star (NS), whose core includes highly dense matter. However, there are large uncertainties in the theoretical predictions for the EOS of NS. It is useful to…
It is shown that the $\gamma$-van der Waals equation of state (eos) permits shock polars with supersonic critical points, corresponding to critical or strong-type shock reflections that are supersonic, which is not possible for ideal gas.…
In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or…
Equation-of-state (EOS) models underpin numerical simulations at the core of research in high energy density physics, inertial confinement fusion, laboratory astrophysics, and elsewhere. In these applications EOS models are needed that span…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
The relativistic equation of state (EOS) of the Van-der-Waals gas is suggested and analyzed. In contrast to the usual case, the Lorentz contraction of the sphere's volume is taken into account. It is proven that the suggested EOS obeys the…
We present modifications to the Athena++ framework to enable use of general equations of state (EOS). Part of our motivation for doing so is to model transient astrophysics phenomena, as these types of events are often not well approximated…
In this paper, we characterized resonant interaction of weakly nonlinear hyperbolic waves in gas dynamics with a real gas background. An asymptotic approach is used to study the interaction between waves, governed by the Euler equations of…
I describe a new algorithm for solving nonlinear wave equations. In this approach, evolution takes place on characteristic hypersurfaces. The algorithm is directly applicable to electromagnetic, Yang-Mills and gravitational fields and other…