The Spectrum Power of Interstellar Plasma Inhomogeneities in the Direction of Eleven Radio Pulsars

We have analyzed two-dimensional correlation functions from the dynamic spectra of 11 pulsars using the archival data of the “Radioastron” project. The time-sections of these functions were approximated by exponential functions with a power $$\alpha $$. It is shown that this approximation describes the shape of the correlation function much better than the Gaussian. The temporal structure function $$D(\Delta t)$$ for small values of the delay $$\Delta t$$is a power law with an index $$\alpha $$. The spectrum power of spatial inhomogeneities of the interstellar plasma is related to the power of the structure function as $$n = \alpha + 2$$. We have determined the characteristic scintillation time and the power $$n$$ in the direction of 11 pulsars. In the direction of three pulsars (B0329+54, B0823+26, and B1929+10), the spectrum power of spatial inhomogeneities of the interstellar plasma turned out to be very close to the value for the Kolmogorov spectrum ($$n = 3.67$$). For other pulsars, it ranges from 3.18 to 3.86. It is shown that the measured scintillation parameters are significantly influenced by the duration of the observation session, expressed by its ratio to the characteristic scintillation time. If this parameter is less than 10, the parameter estimates may be biased: the values of $$\alpha $$ and the characteristic scintillation time $${{t}_{{{\text{scint}}}}}$$ may decrease.

Stable transition layer induced by degeneracy of the spatial inhomogeneities in the Allen-Cahn problem

<p style='text-indent:20px;'>In this article we consider a singularly perturbed Allen-Cahn problem <inline-formula><tex-math id="M1">\begin{document}$ u_t = \epsilon^2(a^2u_x)_x+b^2(u-u^3) $\end{document}</tex-math></inline-formula>, for <inline-formula><tex-math id="M2">\begin{document}$ (x,t)\in (0,1)\times\mathbb{R}^+ $\end{document}</tex-math></inline-formula>, supplied with no-flux boundary condition. The novelty here lies in the fact that the nonnegative spatial inhomogeneities <inline-formula><tex-math id="M3">\begin{document}$ a(\cdot) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ b(\cdot) $\end{document}</tex-math></inline-formula> are allowed to vanish at some points in <inline-formula><tex-math id="M5">\begin{document}$ (0,1) $\end{document}</tex-math></inline-formula>. Using the variational concept of <inline-formula><tex-math id="M6">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula>-convergence we prove that, for <inline-formula><tex-math id="M7">\begin{document}$ \epsilon $\end{document}</tex-math></inline-formula> small, such degeneracy of <inline-formula><tex-math id="M8">\begin{document}$ a(\cdot) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M9">\begin{document}$ b(\cdot) $\end{document}</tex-math></inline-formula> induces the existence of stable stationary solutions which develop internal transition layer as <inline-formula><tex-math id="M10">\begin{document}$ \epsilon\to 0 $\end{document}</tex-math></inline-formula>.</p>

Cluster dynamics in dense granular gases of rod-like particles

Granular gases are interesting multiparticle systems which, irrespective of the apparent simplicity of particle interactions, exhibit a rich scenario of so far only little understood features. We have numerically investigated a dense granular gas composed of frictional spherocylinders which are excited mechanically by lateral vibrating container walls. This study was stimulated by experiments in microgravity on parabolic flights. The formation of spatial inhomogeneities (clusters) was observed in a region near the corners of the container, about halfway from the excitation plates. The particles in the clusters show a tendency to align parallel to the container walls, seemingly increasing the stabilizing effect of friction. The simulation results provide hints that the phase difference of the vibrations of the two excitation walls might affect the cluster dynamics.

CFD Modeling of Spatial Inhomogeneities in a Vegetable Oil Carbonation Reactor

Fossil materials are widely used raw materials in polymerization processes; hence, in many cases, the primary goal of green and sustainable technologies is to replace them with renewables. An exciting and promising technology from this aspect is the isocyanate-free polyurethane production using vegetable oil as a raw material. Functional compounds can be formed by the epoxidation of vegetable oils in three reaction steps: epoxidation, carbonation, and aminolysis. In the case of vegetable oil carbonation, the material properties vary strongly, with the composition affecting the solubility of CO2 in the reaction mixture. Many attempts have been made to model these interactions, but they generally do not account for the changes in the material properties in terms of spatial coordinates. A 2D CFD model based on the combination of the k-ε turbulence model and component mass balances considering the spatial inhomogeneities on the performance of the reactor was created. After the evaluation of the mesh independence study, the simulator was used to calculate the carbonation reaction in a transient analysis with spatial coordinate-dependent density and viscosity changes. The model parameters (height-dependent mass transfer parameters and boundary flux parameters) were identified based on one physical experiment, and a set of 15 experiments were used for model validation. With the validated model, the optimal operating temperature, pressure, and catalyst concentration was proposed.

Random Field Modeling and Analysis of Rotor Bladed Disc Sector Using a Data Driven PCE Based Approach

Bladed disc systems, are designed to be rotationally periodic i.e. each sector repeats itself in an angular manner. This ensures that the response characteristics preserve this rotational periodicity and is defined as a tuned system. However, due to manufacturing limitations, there are invariably random spatial variations in the sectors which constitute the rotor. This in turn destroys the periodicity (angular symmetry) of the rotor. Such a system is defined as a mistuned system, leads to energy localization and makes the rotor susceptible to damage leading to a loss of its service life. This study focusses on developing a methodology for modeling the random spatial inhomogeneities and integrating with finite element analysis for estimating the behavior of a sector of a rotor blade assembly. Approximations for the non-Gaussian random fields for the spatial inhomogeneities are directly developed from the data set of measurements available from coordinate measuring machine (CMM). Subsequently, Rosenblatt’s transformations are applied to each component of the discrete measurement data set for polynomial chaos (PC) representation of the parameter to get the estimated probability density function (pdf). Spearman’s rank correlation coefficient (SRCC) is calculated to obtain the correlation parameter. Kullback–Liebler entropy (KLE) is used as a metric to compare the estimated pdf obtained through the PC representation of the measured data. The in-house PC based developed codes are subsequently integrated with commercially available finite element software which enable quantifying the propagation of the spatial random uncertainties into the response characteristics. Statistical processing of the response quantities is carried out to estimate probabilistic measures of the corresponding response quantities.