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The atomic exchange effect will lead to a significant increase in the probability density of $\beta$ decays below a few keV. This effect is very important for scientific experiments that performed by low-energy electron spectroscopy measurements. However, the atomic exchange effect involves multi-electron interactions, especially for a system with 82 electrons such as lead. Different parameters will lead to different trends in the energy spectrum predicted by the theory, so it is urgent to carry out experimental measurements to provide parameter limits for the theory. The probability increase brought about by the atomic exchange effect is most obvious near 0keV, and the $\beta$ energy spectrum is accurately measured near this energy point, so as to provide constraints for the physical model of atomic exchange. However, it is extremely difficult to measure the $\beta$ energy spectrum at 0keV due to the limitations of electronic noise and internal conversion effects. The excited decay path of $^{210}$Pb was taken as the observation object,by measuring the total energy spectrum of $\beta$ rays and cascaded gamma rays, the precise measurement of the $\beta$ energy spectrum near 0keV has been completed. The analysis of the $\beta$ energy spectrum of $^{210}$Pb gives the following conclusions. The experimental results first verified the theory that the exchange effect causes the probability increase at the low energy end near 0keV. At the same time, the experimental results are higher than the existing predictions of the atomic exchange effect. At least for Pb element, all the electron shells have played a role in improving the probability density of the low end of the $\beta$ energy spectrum. This discovery will promote the theoretical calculation of the $\beta$ energy spectrum of $^{214}$Pb, at the same time, it also indicates that the reactor neutrinos have a higher probability density at the omnipotent end.

We investigate the spatial distribution and dynamics of the vortices in rotating Rayleigh-B\'enard convection in a reduced Rayleigh-number range $1.3{\le}Ra/Ra_{c}{\le}166$. Under slow rotations ($Ra{\gtrsim}10Ra_{c}$), the vortices are randomly distributed. The size-distribution of the Voronoi cells of the vortex centers is well described by the standard $\Gamma$ distribution. In this flow regime the vortices exhibit Brownian-type horizontal motion. The probability density functions of the vortex displacements are, however, non-Gaussian at short time scales. At modest rotating rates ($4Ra_{c}{\le}Ra{\lesssim}10Ra_{c}$) the centrifugal force leads to radial vortex motions, i.e., warm cyclones (cold anticyclones) moving towards (outward from) the rotation axis. The mean-square-displacements of the vortices increase faster than linearly at large time. This super-diffusive behavior can be satisfactorily explained by a Langevin model incorporating the centrifugal force. In the rapidly rotating regime ($1.6Ra_{c}{\le}Ra{\le}4Ra_{c}$) the vortices are densely distributed, with the size-distribution of their Voronoi cells differing significantly from the standard $\Gamma$ distribution. The hydrodynamic interaction of neighboring vortices results in formation of vortex clusters. Inside clusters the correlation of the vortex velocity fluctuations is scale free, with the correlation length being approximately $30\%$ of the cluster length. We examine the influence of cluster forming on the dynamics of individual vortex. Within clusters, cyclones exhibit inverse-centrifugal motion as they submit to the motion of strong anticyclones, while the velocity for outward motion of the anticyclones is increased. Our analysis show that the mobility of isolated vortices, scaled by their vorticity strength, is a simple power function of the Froude number.

The Transition Edge Sensor is extremely sensitive to the change of temperature, combined with the high-Z metal of a certain thickness, it can realize the high energy resolution measurement of particles such as X-rays. X-rays with energies below 10 keV have very weak penetrating ability, so only a few microns thick of gold or bismuth can obtain quantum efficiency higher than 70\%. Therefore, the entire structure of the TES X-ray detector in this energy range can be realized in the microfabrication process. However, for X-rays or gamma rays from 10 keV to 200 keV, sub-millimeter absorber layers are required, which cannot be realized by microfabrication process. This paper first briefly introduces a set of TES X-ray detectors and their auxiliary systems built by ShanghaiTech University, then focus on the introduction of the TES $\gamma$-ray detector, with absorber based on an sub-millimeter lead-tin alloy sphere. The detector has a quantum efficiency above 70\% near 100 keV, and an energy resolution of about 161.5eV@59.5keV., Comment: 13 pages, 12 figures