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Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We study a class of partial differential equations (PDEs) in the family of the so-called Euler-Poincar\'e differential systems, with the aim of developing a foundation for numerical algorithms of their solutions. This requires particular…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We study the universality in gravitational waves emitted from non-rotating neutron stars characterized by different equations of state (EOS). We find that the quasi-normal mode frequencies of such waves, including the $w$-modes and the…
We propose a two parameter generalization for the dark energy equation of state (EOS) $w_X$ for thawing dark energy models which includes PNGB, CPL and Algebraic thawing models as limiting cases and confront our model with the latest…
We report a fully kinetic, quantum study of Kinetic Electrostatic Electron Nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrow harmonic locking to the fundamental, and…
We study wave propagation in a non-relativistic cold quark-gluon plasma immersed in a constant magnetic field. Starting from the Euler equation we derive linear wave equations and investigate their stability and causality. We use a generic…
The formation and evolution of stars depends on various physical aspects of stellar matter, including the equation of state (EOS) and transport properties. Although often dismissed as `ideal gas-like' and therefore simple, states occurring…
In this paper we present a simple and effective method, based on appropriate superpositions of Bessel-Gauss beams, which in the Fresnel regime is able to describe in analytic form the 3D evolution of important waves as Bessel beams, plane…
While accurate simulations of dense gas flows far from the equilibrium can be achieved by Direct Simulation adapted to the Enskog equation, the significant computational demand required for collisions appears as a major constraint. In order…
In this work, we present a method of generating a class of nonlinear ordinary differential equations (ODEs), representing the dynamics of appropriate nonlinear oscillators, that have the characteristics of either amplitude independent…
Efforts to understand the equation of state (EOS) of dense nuclear matter at supra-saturation densities have grown more sophisticated over the past decade, driven by a surge in high-precision data from both terrestrial experiments and…
Studying extreme events and how they evolve in a changing climate is one of the most important current scientific challenges. Starting from complex climate models, a key difficulty is to be able to run long enough simulations in order to…
We propose two new alternative numerical schemes to solve the coupled Einstein-Euler equations in the Generalized Harmonic formulation. The first one is a finite difference (FD) Central Weighted Essentially Non-Oscillatory (CWENO) scheme on…
We consider optimal experimental design (OED) for nonlinear inverse problems within the Bayesian framework. Optimizing the data acquisition process for large-scale nonlinear Bayesian inverse problems is a computationally challenging task…
We present a generalized nonlinear theory for large amplitude electrostatic (ES) ion shocks in collisional quantum plasmas composed of mildly coupled degenerate electron fluids of arbitrary degeneracy and non-degenerate strongly correlated…
We study the discrete nonlinear Schr\"odinger equation (DNLS) in an annular geometry with on-site defects. The dynamics of a traveling plane-wave maps onto an effective ''non-rigid pendulum'' Hamiltonian. The different regimes include the…
The necessary conditions to derive the quantum VdW EoS with hard-core repulsion from the quantum partition are discussed. On a plausible example it is shown that an alternative way to account correctly for the 3-rd virial coefficient of…
The inconsistency between the time-reversible Liouville equation and time-irreversible Boltzmann equation has been pointed out long ago by Loschmidt. To avoid Loschmidt's objection, here we propose a new dynamical system to model the motion…