Local uniqueness of vortices for 2D steady Euler flow

We study the steady planar Euler flow in a bounded simply connected domain, where the vortex function is $f=t_+^p$ with $p>0$ and the vorticity strength is prescribed. By studying the location and local uniqueness of vortices, we prove that the vorticity method and the stream function method actually give the same solution. We also show that if the vorticity of flow is located near an isolated minimum point and non-degenerate critical point of the Kirchhoff-Routh function, it must be stable in the nonlinear sense.Comment: 47 pages. arXiv admin note: text overlap with arXiv:1703.0986

Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

A stationary and spherically symmetric black hole (For example, Reissner-Nordstrom black hole or Kerr-Newman black hole) has at most one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? De Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves.Comment: 14 pages, 7 figures. The Penrose diagrams are corrected. PRD accepte

Suppressing excitation effects in microwave induced thermoacoustic tomography by multi-view Hilbert transformation

Microwave induced thermoacoustic tomography (TAT) images usually suffer from distortions arising from the microwave polarization effect and standing wave effect. The microwave polarization effect, resulting from linearly polarized microwave illumination, splits the image of the object along the polarization direction, while the standing wave effect, when the object size is larger than the microwave wavelength within the object, modulates the image of the object. Both effects cause non-uniform energy distribution in a uniformly absorbing object and create artifacts in the reconstructed images. To address these problems in TAT, we propose an image reconstruction method that combines multi-view Hilbert transformation with the back-projection algorithm. We experimentally validate this method by imaging breast and brain tumor phantoms, showing that the aforementioned distortions are significantly suppressed. We anticipate that this method will contribute to clinical tumor diagnosis