arXiv subjects

Imre Ferenc Barna

Publications and source records attributed to Imre Ferenc Barna.

At least 19 recordsLinked to original sources

arXiv2026

On the Stability of the Euler-Poisson Dark-Fluid Model

We present a stability analysis of a dark-fluid model described as a non-relativistic, rotating, non-viscous, self-gravitating fluid. We assume spherical symmetry and model the matter by a polytropic equation of state. The resulting coupled nonlinear partial differential equation system is solved using a self-similar ansatz known from the Guderley-Landau-Stanyukovich problem. We find that three of the four Lyapunov exponents are negative, while only one is positive. This indicates one unstable direction and three contracting directions in phase space. The single positive exponent is relatively small, suggesting that the self-similar solution is only weakly unstable and remains dynamically robust over the investigated interval.

gr-qc↗

arXiv2026

The Formulation of Scaling Expansion in an Euler-Poisson Dark-fluid Model

We present a dark fluid model described as a non-viscous, non-relativistic, rotating, and self-gravitating fluid. We assumed that the system has spherical symmetry and the matter can be described with the polytropic equation of state. The induced coupled non-linear partial differential equation system was solved by using a self-similar time-dependent ansatz introduced by L. Sedov and G. I. Taylor. These kinds of solutions were successfully used to describe blast waves induced by an explosion since the Guderley-Landau-Stanyukovich problem. We showed that these kinds of solutions can provide new solutions that are consistent with the Newtonian cosmological framework. We have found that such solutions can be applied to describe normal-to-dark energy on the cosmological scale.

physics.flu-dyn↗

arXiv2025

Asymptotic evolution of bulk-viscous, spherically symmetric spacetimes

The scale-free nature of gravitational interaction in both Newtonian gravity and the general theory of relativity gives rise to the concept of self-similarity, where solutions are scale invariant. As a result of this property, the governing partial differential equations are greatly simplified and can be transformed into ordinary ones. These solutions function as attractors, characterizing the asymptotic dynamics of more general solutions. There exist situations in which self-similarity is only partially realized, giving rise to kinematic self-similar solutions. Our study provides a systematic classification of kinematic self-similar solutions corresponding to the most general spherically symmetric spacetime in the presence of bulk viscous flows.

gr-qc↗

arXiv2025

Cylindrical Euler--Poisson Equation in a Chaplygin Gas Medium

We studied the Euler--Poisson equation system in the case of cylindrical symmetry with the von Neumann--Sedov--Taylor type of self-similar Ansatz and present scaling solutions. We have analyzed the scenario governed by Chaplygin's equation of state, which has historically been studied as a unifying framework of dark fluid for dark matter and dark energy.

math-ph↗

arXiv2025

Can Rotation Solve the Hubble Puzzle?

The discrepancy between low and high redshift Hubble constant $H_0$ measurements is the highest significance tension within the concordance $Λ$CDM paradigm. If not due to unknown systematics, the Hubble puzzle suggests a lack of understanding of the universe's expansion history despite the otherwise spectacular success of the theory. We show that a Gödel inspired slowly rotating dark-fluid variant of the concordance model resolves this tension with an angular velocity today $ω_0 \simeq 2\times 10^{-3}$~Gyr\textsuperscript{-1}. Curiously, this is close to the maximal rotation, avoiding closed time-like loops with a tangential velocity less than the speed of light at the horizon.

gr-qc↗

arXiv2022

Machine learning methods for Schlieren imaging of a plasma channel in tenuous atomic vapor

We investigate the usage of a Schlieren imaging setup to measure the geometrical dimensions of a plasma channel in atomic vapor. Near resonant probe light is used to image the plasma channel in a tenuous vapor and machine learning techniques are tested for extracting quantitative information from the images. By building a database of simulated signals with a range of plasma parameters for training Deep Neural Networks, we demonstrate that they can extract from the Schlieren images reliably and with high accuracy the location, the radius and the maximum ionization fraction of the plasma channel as well as the width of the transition region between the core of the plasma channel and the unionized vapor. We test several different neural network architectures with supervised learning and show that the parameter estimations supplied by the networks are resilient with respect to slight changes of the experimental parameters that may occur in the course of a measurement.

physics.plasm-ph↗

arXiv2022

Advanced self-similar solutions of regular and irregular diffusion equations

We study the diffusion equation with an appropriate change of variables. This equation is in general a partial differential equation (PDE). With the self-similar and related Ansatätze we transform the PDE of diffusion to an ordinary differential equation. The solutions of the PDE belong to a family of functions which are presented for the case of infinite horizon. In the presentation we accentuate the physically reasonable solutions. We also study time dependent diffusion phenomena, where the spreading may vary in time. To describe the process we consider time dependent diffusion coefficients. The obtained analytic solutions all can be expressed with Kummer's or Whittaker-type of functions.

physics.class-ph↗

arXiv2020

Analytic solutions of the rotating and stratified hydrodynamical equations

In this article we investigate the two-dimensional incompressible rotating and stratified, just rotating, just stratified Euler equations with each other and with the normal Euler equations with the self-similar Ansatz. There are analytic solutions available for all four models, for density, pressure and velocity fields, some of them are compound power-law dependent functions. In general the solutions have a rich mathematical structure. Some solutions show unphysical explosive properties others, however are physically acceptable and have finite numerical values with power law decays. For a better transparency we present some figures for the most complicated velocity and pressure fields.

physics.flu-dyn↗

arXiv2019

Analytic traveling-wave solutions of the Kardar-Parisi-Zhang interface growing equation with different kind of noise terms

The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the traveling-wave Ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as various noise distribution functions. Six different cases were investigated among others Gaussian, Lorentzian, white or even pink noise. Analytic solutions are evaluated and analyzed for all cases. All results are expressible with various special functions Mathieu, Bessel, Airy or Whittaker functions showing a very rich mathematical structure with some common general characteristics. This study is the continuation of our former work, where the same physical phenomena was investigated with the self-similar Ansatz. The differences and similarities among the various solutions are enlightened.

nlin.PS↗

arXiv2019

Role of the laser chirp parameter in photoionisation

Nowadays the development of novel particle accelerators is a hot topic for both experimental and theoretical sciences. In the CERN-AWAKE experiment electrons are accelerated in a cold rubidium plasma, generated by a short, intense laser pulse. We describe the corresponding photoionisation process with ab initio quantum mechanical calculations. In this paper we primarily investigate how the frequency chirping of the applied laser pulse influences the photoionisation. Secondarily we also study how the results of the numerical simulations depend on the shape of the envelope of the laser pulse. Based on our results, we give a recommendation to fine-tune the physical parameters of the applied laser pulse in order to improve the homogeneity of the rubidium plasma.

physics.atom-ph↗

arXiv2019

Self-similar analysis of a viscous heated Oberbeck-Boussinesq flow system

The simplest model to couple the heat conduction and Navier-Stokes equations together is the Oberbeck-Boussinesq(OB)system which were investigated by E.N. Lorenz and opened the paradigm of chaos. In our former studies - Chaos, Solitons and Fractals 78, 249 (2015), ibid, 103, 336 (2017) - we derived analytic solutions for the velocity, pressure and temperature fields. Additionally, we gave a possible explanation of the Rayleigh-Bènard convection cells with the help of the self-similar Ansatz. Now we generalize the OB hydrodynamical system, including a viscous source term in the heat conduction equation. Our results may attract the interest of various fields like micro or nanofluidics or climate studies.

physics.flu-dyn↗

arXiv2019

Analytic self-similar solutions of the Kardar-Parisi-Zhang interface growing equation with various noise term

The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar Ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as various noise distribution functions. Six different cases were investigated among others Gaussian, Lorentzian, white or even pink noise. Analytic solutions were evaluated and analyzed for all cases. All results are expressible with various special functions like Kummer, Heun, Whittaker or error functions showing a very rich mathematical structure with some common general characteristics.

nlin.PS↗

arXiv2019

Interaction of antiproton with helium based on ab-initio calculations

We present ionization cross sections for antiproton and helium collisions based on ab-initio time-dependent coupled channel method. In our calculations a finite basis set of regular helium Coulomb wave packets and Slater function were used. The semiclassical approximation was applied with the time-dependent Coulomb potential to describe the antiproton electron interaction. Three different projectile energies were considered as 10, 50 and 100 keV. We found clear evidence for the formation of the anti-cusp in the differential distributions.

physics.atom-ph↗

arXiv2019

Photoionisation of Rubidium in strong laser fields

The photoionisation of rubidium in strong infra-red laser fields based on ab initio calculations was investigated. The bound and the continuum states are described with Slater orbitals and Coulomb wave packets, respectively. The bound state spectra were calculated with the variational method and we found it reproduced the experimental data within a few percent accuracy. Using the similar approach, ionisation of Rb was also successfully investigated. The effects of the shape and the parameters of the pulse to the photoionisation probabilities and the energy spectrum of the ionised electron are shown. These calculations may provide a valuable contribution at the design of laser and plasma based novel accelerators, the CERN AWAKE experiment.

physics.atom-ph↗

arXiv2018

Laser induced distortion of band structure in solids: an analytic model

We consider a spatially periodic (cosine) potential as a model for a crystalline solid that interacts with a harmonically oscillating external electric field. This problem is periodic both in space and time and can be solved analytically using the Kramers-Henneberger co-moving frame. By analyzing the stability of the closely related Mathieu-type differential equation, the electronic band structure can be obtained. We demonstrate that by changing the field intensity, the width of the zero-field band gaps can be drastically modified, including the special case when the external field causes the band gaps to disappear

cond-mat.mes-hall↗

arXiv2015

Electron Acceleration by a Bichromatic Chirped Laser Pulse in Underdense Plasmas

A theoretical study of laser and plasma based electron acceleration is presented. An effective model has been used, in which the presence of an underdense plasma has been taken account via its index of refraction $n_{m}$. In the confines of this model, the basic phenomena can be studied by numerically solving the classical relativistic equations of motion. The key idea of this paper is the application of chirped, bichromatic laser fields. We investigated the advantages and disadvantages of mixing the second harmonic to the original $λ= 800 \, \mathrm{nm}$ wavelength pulse. We performed calculations both for plane wave and Gaussian pulses.

physics.plasm-ph↗

arXiv2015

Electron Acceleration in Underdense Plasmas Described with a Classical Effective Theory

An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this model, we did not need to perform PIC simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analysed. We compared our results to PIC simulations and experimental data. Keywords: Underdense plasma; Electron acceleration; Classical electrodynamics; Relativistic equation of motion; Ultrashort laser pulses

physics.plasm-ph↗

arXiv2014

Self-similar analytic solution of the two dimensional Navier-Stokes equation with a non-Newtonian type of viscosity

We investigate the two dimensional incompressible Navier-Stokes(NS) and the continuity equations in Cartesian coordinates and Eulerian description for non-Newtonian fluids. As a non-Newtonian viscosity we consider the Ladyzenskaya model with a non-linear velocity dependent stress tensor. The key idea is the multi-dimensional generalization of the well-known self-similar Ansatz, which was already used for non-compressible and compressible viscous flow studies. The geometrical interpretations of the trial function is also discussed. We compare our recent results to the former Newtonian ones.

physics.flu-dyn↗