scholarly journals ANALYTIC SELF-SIMILAR SOLUTIONS OF THE KARDAR-PARISI-ZHANG INTERFACE GROWING EQUATION WITH VARIOUS NOISE TERMS

2020 ◽  
Vol 25 (2) ◽  
pp. 241-256 ◽  
Author(s):  
Imre F. Barna ◽  
Gabriella Bognár ◽  
Mohammed Guedda ◽  
László Mátyás ◽  
Krisztián Hriczó
Keyword(s):  
Special Functions ◽  
Mathematical Structure ◽  
Analytic Solutions ◽  
Distribution Functions ◽  
Point Of View ◽  
Growth Equation ◽  
Interface Growth ◽  
Self Similar ◽  
New Feature ◽  
Similar Solutions

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 are 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.

scholarly journals Analytic Solutions of the Rotating and Stratified Hydrodynamical Equations

2021 ◽  
pp. 14-26
Author(s):  
Imre F. Barna ◽  
L. Mátyás
Keyword(s):  
Euler Equations ◽  
Power Law ◽  
Mathematical Structure ◽  
Analytic Solutions ◽  
Velocity Fields ◽  
Pressure Fields ◽  
Starting Point ◽  
Self Similar ◽  
Explosive Properties ◽  
Scientific Fields

In this article we investigate the two-dimensional incompressible rotating and stratified, just rotating,  just stratified Euler equations, comparing with each other and with the normal Euler equations with  the self-similar Ansatz. The motivation of our study is the following the presented rotating stratified  fluid equations can be interpreted as a well-established starting point of various more complex and  more realistic meteorologic, oceanographic or geographic models. We present analytic solutions  for all four models for density, pressure and velocity fields, most of them are some kind of power-law  type of functions. In general the presented solutions have a rich mathematical structure. Some  solutions show nonphysical explosive properties others, however are physically acceptable and  have finite numerical values with power law decays. For a better transparency we present some figs  for the most complicated velocity and pressure fields. To our knowledge there are no such analytic  results available in the literature till today. Our results may attract attention in various scientific fields.   

scholarly journals A laser experiment for studying radiative shocks in astrophysics

2002 ◽  
Vol 20 (2) ◽  
pp. 263-268 ◽  
Author(s):  
X. FLEURY ◽  
S. BOUQUET ◽  
C. STEHLÉ ◽  
M. KOENIG ◽  
D. BATANI ◽  
...  
Keyword(s):  
Laser Pulse ◽  
Pulse Duration ◽  
Experimental Results ◽  
Laboratory Astrophysics ◽  
Laser Pulse Duration ◽  
Radiative Shocks ◽  
Self Similar ◽  
Laser Experiment ◽  
Similar Solutions

In this article, we present a laboratory astrophysics experiment on radiative shocks and its interpretation using simple modelization. The experiment is performed with a 100-J laser (pulse duration of about 0.5 ns) which irradiates a 1-mm3 xenon gas-filled cell. Descriptions of both the experiment and the associated diagnostics are given. The apparition of a radiation precursor in the unshocked material is evidenced from interferometry diagrams. A model including self-similar solutions and numerical ones is derived and fairly good agreements are obtained between the theoretical and the experimental results.

Self-similar solutions to stellar winds with cosmic rays

2005 ◽  
Vol 35 (12) ◽  
pp. 2115-2118 ◽  
Author(s):  
Chung-Ming Ko ◽  
Min-Hsu Chu
Keyword(s):  
Cosmic Rays ◽  
Stellar Winds ◽  
Self Similar ◽  
Similar Solutions

On a self-similar solution for the decay of turbulent bursts

1992 ◽  
Vol 3 (4) ◽  
pp. 319-341 ◽  
Author(s):  
S. P. Hastings ◽  
L. A. Peletier
Keyword(s):  
Asymptotic Behaviour ◽  
Physical Parameter ◽  
Dimensional Analysis ◽  
Existence And Uniqueness ◽  
The Self ◽  
Similar Solution ◽  
Self Similar Solution ◽  
Eigenvalue Parameter ◽  
Self Similar ◽  
Similar Solutions

We discuss the self-similar solutions of the second kind associated with the propagation of turbulent bursts in a fluid at rest. Such solutions involve an eigenvalue parameter μ, which cannot be determined from dimensional analysis. Existence and uniqueness are established and the dependence of μ on a physical parameter λ in the problem is studied: estimates are obtained and the asymptotic behaviour as λ → ∞ is established.

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