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Imre F. Barna

Publications and source records attributed to Imre F. Barna.

8 recordsLinked to original sources
arXiv2023

Analytical investigation of time-dependent two-dimensional non-Newtonian boundary layer equations

In this study, five different time-dependent incompressible non-Newtonian boundary layer models in two dimensions are investigated, including external magnetic field effects. The power law, the Casson fluid, the Oldroyd-B model, the Walter fluid B model and the Williamson fluid are analyzed. For the first two models, analytical results are given for the velocity and pressure distributions, which can be expressed by different types of hypergeometric functions. Depending on the parameters involved in the analytical solutions of the nonlinear ordinary differential equation obtained by the similarity transformation, a very wide range of solution types is presented.

physics.flu-dyn↗
arXiv2023

Diatomic molecule in a strong infrared laser field: level-shifts and bond-length change due to laser-dressed Morse potential

We present a general mathematical procedure to handle interactions described by a Morse potential in the presence of a strong harmonic excitation. We account for permanent and field-induced terms and their gradients in the dipole moment function, and we derive analytic formulae for the bond-length change and for the shifted energy eigenvalues of the vibrations, by using the Kramers-Henneberger frame. We apply these results to the important cases of $\mathrm{H}_{2}$ and $\mathrm{LiH}$, driven by a near- or mid-infrared laser in the $10^{13}$ $\mathrm{ W/cm^2}$ intensity range.

physics.atom-ph↗
arXiv2021

Scaling Hydrodynamical Evolution of a Gravitating Dark-fluid Universe

We present a dark fluid model which contains the general linear equation of state including the gravitation term. The obtained spherical symmetric Euler equation and the continuity equation was investigated with the Sedov-type time-dependent self-similar {\it ansatz} which is capable to describe physically relevant diffusive and dispersive solutions. %The role of the parameter in the equation of state is investigated. As results the space and time dependent fluid density and radial velocity fields are presented and analyzed. Additionally, the role of the initial velocity on the kinetic and total energy densities of the fluid is discussed.

gr-qc↗
arXiv2021

General self-similar solutions of diffusion equation and related constructions

Transport phenomena plays an important role in science and technology. In the wide variety of applications both advection and diffusion may appear. Regarding diffusion, for long times, different type of decay rates are possible for different non-equilibrium systems. After summarizing the existing solutions of the regular diffusion equation, we present not so well known solution derived from three different trial functions, as a key point we present a family of solutions for the case of infinite horizon. By this we tried to make a step toward understanding the different long time decays for different diffusive systems.

physics.class-ph↗
arXiv2021

Self-similar analysis of the time-dependent compressible and incompressible boundary layers including heat conduction

We investigate the incompressible and compressible heat conducting boundary layer with applying the two-dimensional self-similar Ansatz. Analytic solutions can be found for the incompressible case which can be expressed with special functions. The parameter dependencies are studied and discussed in details. In the last part of our study we present the ordinary differential equation (ODE) system which is obtained for compressible boundary layers.

physics.flu-dyn↗
arXiv2018

Self-similarity analysis of the non-linear Schrödinger equation in the Madelung form

In the present study a particular case of Gross-Pitaevskii or non-linear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation. The obtained system of differential equations is highly nonlinear. Regarding solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.

quant-ph↗
arXiv2017

Analytic solutions of the Madelung equation

We present analytic self-similar solutions for the one, two and three dimensional Madelung hydrodynamical equation for a free particle. There is a direct connection between the zeros of the Madelung fluid density and the magnitude of the quantum potential.

quant-ph↗