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We perform a short review of the history of quantum mechanics, with a focus on the historical problems with describing ionization theoretically in the context of quantum mechanics. The essentials of the theory of resonances are presented.…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
The linearized Boltzmann equation is considered to describe small spatial perturbations of the homogeneous cooling state. The corresponding macroscopic balance equations for the density, temperature, and flow velocity are derived from it as…
Starting with a brief introduction into the basics of relativistic fluid dynamics, I discuss our current knowledge of a relativistic theory of fluid dynamics in the presence of (mostly shear) viscosity. Derivations based on the generalized…
The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in $\mathbb{R}^2$. The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence…
We derive and investigate several hydrodynamic formalisms that emerge from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. The specific form of the total cross-section enables the…
We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…
This contribution presents a theoretical overview of hydrodynamic modelling of heavy-ion collisions, with highlights on some recent developments. In particular, the formulation of anisotropic hydrodynamics, the role of hydrodynamic…
Fluid flows hosting electrical phenomena make the subject of a fascinating and highly interdisciplinary scientific field. In recent years, the extraordinary success of electrospinning and solution blowing technologies for the generation of…
We consider a thin horizontal layer of a non-magnetic electrolyte containing a bulk solution of salt and carrying an electric current. The layer is bounded by two deformable free surfaces loaded with an insoluble surfactant and is placed in…
In contrast to the commonly used lattice Boltzmann method, off-lattice Boltzmann methods decouple the velocity discretization from the underlying spatial grid, thus allowing for more efficient geometric representations of complex…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
Spatial interaction effects between charge carriers in ionic systems play a sizable role beyond a classical Maxwellian description. We develop a nonlocal, two-fluid, hydrodynamic theory of charges and study ionic plasmon effects, i. e.…
We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity $u_\infty$ at infinity. The main result shows the existence of unique solutions for arbitrary…
We introduce a theoretical and numerical method to investigate the flow of charged fluid mixtures under extreme confinement. We model the electrolyte solution as a ternary mixture, comprising two ionic species of opposite charge and a third…
In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…
We show weak-strong uniqueness and stability results for the motion of a two or three dimensional fluid governed by the Navier-Stokes equation interacting with a flexible, elastic plate of Koiter type. The plate is situated at the top of…
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated…
We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through…
We report a novel algorithm of constructing linear and nonlinear potentials in the two-dimensional Gross-Pitaevskii equation subject to given boundary conditions, which allow for exact analytic solutions. The obtained solutions represent…