Self-reference interferometry of optical vortices using a Michelson interferometer is investigated in this paper. It is found that the detection of topological charge (TC) for the optical vortices is constrained by some physical conditions. We present these conditions through the theoretical analyses, numerical simulation and experimental results. For different parameters, the maximal detectable TCs are different, which is helpful for the measurement of TC in the practical application. Within the range allowed by the constrained conditions, we also study the detection of TC using the interference pattern of two-way optical vortex by changing the inclined angle of one mirror of the Michelson interferometer.
We perform the potential analysis for the holographic Schwinger effect in a rotating deformed AdS black-hole background. We calculate the total potential of a quark-antiquark ($Q\bar{Q}$) pair in an external electric field and evaluate the critical electric field from Dirac-Born-Infeld (DBI) action. It is shown that the inclusion of angular velocity decreases the potential barrier thus enhancing the Schwinger effect, opposite to the effect of the confining scale. Moreover, by increasing angular velocity decreases the critical electric field above which the pairs are produced freely without any suppression. Furthermore, we conclude that producing $Q\bar{Q}$ pairs would be easier in rotating medium.
A conceptual model was established to study the patterns of flow in vadose and saturated zones system induced by a prescribed boundary. Richards’ equation was adopted to describe groundwater flow in the vadose zone. Laplace transform and cosine Fourier transform were chosen to derive a semi-analytical solution of the governing equations. A finite-element numerical solution built with COMSOL software was used to test the semi-analytical solution. The buildups of the hydraulic head were investigated for different hydraulic parameters. Some noteworthy conclusions were obtained. The vadose zone parameters (constitutive exponent (κD) and specific yield (Sy)) have a significant effect on the buildups in the vadose zone and saturated zone. A larger κD value and smaller Sy value both lead to higher buildups in the vadose zone, while a larger κD value and a larger Sy value resulted in smaller buildups. As for the specific storage (Ss) of the saturated zone, the influence on buildup is more obvious in the saturated zone rather than in the vadose zone. The analysis further indicates that Media Anisotropy (Kz/Kx) value exhibits opposite influences on the hydraulic head in vadose and saturated zone. The present solution offers a valuable basis for further research of groundwater recharge and better design of MAR engineering.
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