A test of the standard dark matter density evolution law using galaxy clusters and cosmic chronometers

In this paper, we implement a test of the standard law for the dark matter density evolution as a function of redshift. For this purpose, only a flat universe and the validity of the FRW metric are assumed. A deformed dark matter density evolution law is considered, given by $$\rho _c(z) \propto (1+z)^{3+\epsilon }$$ ρ c ( z ) ∝ ( 1 + z ) 3 + ϵ , and constraints on $$\epsilon $$ ϵ are obtained by combining the galaxy cluster gas mass fractions with cosmic chronometers measurements. We find that $$\epsilon =0$$ ϵ = 0 within 2$$\sigma $$ σ c.l., in full agreement with other recent analyses.

Numerical Simulation and Experimental Analysis of Volume Alternate Cavitation (VAC) - A new Cavitation Generation Method

Cavitation generation methods have been applied in multifarious directions due to their diversity. And scholars have carried out numerous researches and discussions on cavitation generation methods. The purpose of this study is to explore the generating mechanism and evolution law of volumetric alternate cavitation (VAC). In the VAC, the liquid water is placed in an airtight container with variable volume. With the volume alternately changes, the liquid water inside the container continues to cavitate. In this study, the mixture turbulence model and in-cylinder dynamic grid model were used to apply computational fluid dynamics (CFD) simulation of volume alternate cavitation. In the simulation, the cloud images at 7 heights on the central axis are monitored, and the phenomenon and mechanism of height and eccentricity are analyzed detailedly. By using the method of cavitation flow visualization (CFV), the generating mechanism and evolution law of cavitation are clarified. The synergistic effects of experiments and high-speed camera capture confirm the simulation. In the experiment, the volume change stroke of the airtight container is 20 mm, the volume change frequency is 18 Hz, and the shooting frequency of the high-speed camera is set to 10000 fps. The results show that the position of occurring cavitation phenomenon has a reasonable law during the whole evolution cycle of the cavitation cloud. It is evident that a cycle of volume alternation corresponds to the generation, development and collapse stages of cavitation bubbles.

Spectral and numerical analysis for a thermoelastic problem with double porosity and second sound

We study some spectral and numerical properties of the solutions to a thermoelastic problem with double porosity. The model includes Cattaneo-type evolution law for the heat flux to remove the physical paradox of infinite propagation speed of the classical Fourier’s law. Firstly, we prove that the operator determined by the considered problem has compact resolvent and generates a C 0 -semigroup in an appropriate Hilbert space. We also show that there is a sequence of generalized eigenfunctions of the linear operator that forms a Riesz basis. By a detailed spectral analysis, we obtain the expressions of the spectrum and we deduce that the spectrum determined growth condition holds. Therefore we prove that the energy of the considered problem decays exponentially to a rate determined explicitly by the physical parameters. Finally, some numerical simulations based on Chebyshev spectral method for spatial discretization are given to confirm the exponential stability result and to show the distribution of the eigenvalues and the variables of the problem.

Dynamic Evolution Law of Overburden Rock in Shallow-Buried Super-High Fully Mechanized Working Face and Determination of Support Strength

The objective of this study was to reveal the law of overburden movement and stress evolution during the mining of super-high fully mechanized mining faces. Based on the 12401 fully mechanized mining face of Shangwan Coal Mine in Shendong, this study conducted research and analysis using the methods of similarity simulation experiment, numerical simulation, and field measurement. The results showed that the maximum and minimum principal stresses in the coal seam in front of the working face are concentrated with the advance of the working face. The degree of stress concentration increases with the increase in the advancing range, and the concentration degree of the maximum principal stress and the change gradient is greater than that of the minimum principal stress. But the range of the peak lead coal wall is lower than that of the minimum principal stress of the peak lead coal wall. The phenomenon of stress recovery exists in the goaf. With the increase in the advancing range of the working face, the degree of stress recovery gradually increases, and the degree of maximum principal stress recovery is higher than that of the minimum principal stress recovery. The large fractures observed near the working face are closely related to the underground pressure, relatively large fractures appear on the surface, and the fractures become narrower near the two pathways. Only caving and fissure zones exist in the thin bedrock overburden, and the bending subsidence zone changes with the bedrock thickness. The support strength of the hydraulic support should not be less than 1.47 MPa. This research on the overburden movement and stress evolution law of a super-high fully mechanized mining face can provide theoretical guidance for the exploitation and utilization of extrathick coal seam resources. It has broad engineering prospects.