The general solutions of the convolution type weakly nonlinear Burgers equation with the initial Cauchy condition are studied. Specifically, if 𝑢𝑢𝑢𝑢0(𝑥𝑥𝑥𝑥) =𝑢𝑢𝑢𝑢(0,𝑥𝑥𝑥𝑥) is continuous and ∫0𝑥𝑢𝑢𝑢𝑢𝑢𝑥𝑥𝑥 𝑦𝑦𝑦𝑦) = 𝑑𝑑𝑑𝑑𝑑𝑦𝑦𝑦 = 𝑑𝑑𝑑𝑑(𝑥𝑥𝑥𝑥) as the problem | At the same time, it is also a model equation of the Navier-Stokes equations without a stress term.
The derivative of the initial condition is also discretized using the central finite difference method. Saadatmandi [27] has developed the shifted Legendre Tau technique for solving the studied model. 17] presented the solution of the one-dimensional wave equation using the Lagrangian meshless finite-difference particle method with variable smoothing length.
Hikmet et.al [7] present a numerical solution of the One-dimensional wave equation with an Integral conservation condition presented by the method of the non-polynomial cubic spline. Still, the accuracy and stability of the method need attention because the treatment of the method used to solve one-dimensional wave equation is not trivial distribution.
Let Z has a power series expansion in the power of variable 𝛿𝛿 as follow
Thus, using the above statement, the order of truncation error for the scheme in Eq. Because hyperbolic equations often describe the motion and development of waves, Fourier analysis is of great value in studying the accuracy of methods as well as their stability [34]. The modulus of 𝜆𝜆�𝑘𝑘� describes the damping and the argument describes the dispersion in the scheme, i.e. the extent to which the wave speed varies with the frequency [34].
The Fourier analysis (Von-Neumann) stability analysis technique is applied to investigate the stability of the proposed method. From this we see that the moduli of this amplification factor is less than one�| 𝜆𝜆�𝑘𝑘�| � 1�. Now using the idea of this statement, the arguments of the amplification factor in Eq.(23).
Therefore, the lax-Wendorff finite difference scheme given in Eq. 12) is stable for the wave equation.
Zhumakhanova 2,10
We investigate the motion of stars in the central region of the Milky Way Galaxy. Studies of the motion of S stars near the center of the Milky Way Galaxy (MWG) have recently shown that. In this work, we study the motion of test particles, in the form of stars, near the center of the MWG in the gravitational field of both a BH and DM core.
1 we show the density and mass profiles of the exponential sphere model given by Eqs. We consider here the motion of test particles in the gravitational fields of the SMBH and DM scattering with the aim of distinguishing the two sources from the observation of stars orbiting the galactic center. However to distinguish the two objects we adopt as initial conditions those for circular orbits in SMBH gravity and use them also for test particles in the DM core field.
The initial conditions were chosen in such a way as to obtain circular orbits in the gravitational field of the point mass (SMBH), which lead to prior elliptical orbits in the field of the DM core. The differences that arise in the motion of test particles may shed light on the nature of the central compact object in the MWG with future more accurate observations. Initial conditions are chosen in such a way that they always get circular trajectories in the DM field.
We analyzed the orbits of stars near the Galactic center in the gravitational field of the SMBH and the DM core. As expected, a significant divergence in the motion appears at distances less than 30 AU, and it increases as we approach the center of the galaxy. Geodesic motion of S2 and G2 as a test of the nature of fermionic dark matter in our galactic core.” Astron.
Rotation curve and mass distribution in the galactic center – from black hole to the entire galaxy.” Publications of the. That is, in action, in the role of the matter field, we consider the special case of the Lagrange function for the essence. S , where Sgr. is the action of the gravitational field, Smat is the action of matter.
VL mat . 2
V is more realistic and is able to describe the modern dynamics of the expansion of the Universe. Keywords: equivalent dose rate; pyrite polymetallic ore; radioactivity of minerals; geology of the earth. The maximum possible surface was chosen on the sample to cover the working sensitive part of the detector.
The statistical error in measuring the gamma background and gamma radiation of the samples did not exceed 10%. Figures 4-6 show the dependence of specific EDR measurement results on the percentage of lead, copper and zinc. Online) Figure 6 – Dependence of the specific EDR on the percentage of copper in the samples.
-6) that specific EDR values in ore samples show a stable excess of gamma background. As a result of the decay of the three natural radioactive families, stable isotopes of lead are ultimately formed. Figures 8, 9 show the results of radiometric measurements of beta and alpha radiation of the samples under study.
The influence on the EDR of the samples is indirectly influenced by the concentration of zinc. Such a transformation of the latter is quite possible under the conditions of formed planets. This process of radiation origin of Zn from Cu can explain the anti-correlation (-0.34) of zinc and copper content in the studied ore samples.
Nuclear-physical mechanisms of the effect of radon alpha radiation on the cell and the problem of cancer morbidity. Study of the factor of local accumulation of daughter decay products of radon in the body by beta-spectrometry. A study of the accumulation factor of daughter products of radon decay in the surface layer by beta spectrometry.
