Impulsive cylindrical gravitational wave: one possible radiative form emitted from cosmic strings and corresponding electromagnetic response

The cosmic strings(CSs) may be one important source of gravitational waves(GWs), and it has been intensively studied due to its special properties such as the cylindrical symmetry. The CSs would generate not only usual continuous GW, but also impulsive GW that brings more concentrated energy and consists of different GW components broadly covering low-, intermediate- and high-frequency bands simultaneously. These features might underlie interesting electromagnetic(EM) response to these GWs generated by the CSs. In this paper, with novel results and effects, we firstly calculate the analytical solutions of perturbed EM fields caused by interaction between impulsive cylindrical GWs (would be one of possible forms emitted from CSs) and background celestial high magnetic fields or widespread cosmological background magnetic fields, by using rigorous Einstein - Rosen metric. Results show: perturbed EM fields are also in the impulsive form accordant to the GW pulse, and asymptotic behaviors of the perturbed EM fields are fully consistent with the asymptotic behaviors of the energy density, energy flux density and Riemann curvature tensor of corresponding impulsive cylindrical GWs. The analytical solutions naturally give rise to the accumulation effect which is proportional to the term of distance^1/2, and based on it, we for the first time predict potentially observable effects in region of the Earth caused by the EM response to GWs from the CSs.Comment: 34 pages, 12 figure

A new effective interaction for the trapped Fermi gas

We apply the configuration-interaction method to calculate the spectra of two-component Fermi systems in a harmonic trap, studying the convergence of the method at the unitary interaction limit. We find that for a fixed regularization of the two-body interaction the convergence is exponential or better in the truncation parameter of the many-body space. However, the conventional regularization is found to have poor convergence in the regularization parameter, with an error that scales as a low negative power of this parameter. We propose a new regularization of the two-body interaction that produces exponential convergence for systems of three and four particles. From the systematics, we estimate the ground-state energy of the four-particle system to be (5.05 +- 0.024)hbar omega.Comment: 4 pages, 3 figure

Nonstationary seismic-well tying with time-varying wavelets

Seismic-well tying is an important technique for correlating well-logging curves in depth with seismic traces in time. An appropriate seismic-well tying technique must account for two types of nonstationarity: the nonstationary time errors in the synthetic seismic trace caused by the inaccurate time-depth relationship established based on sonic-logging velocity and the nonstationary seismic signals due to the time-varying wavelets during wave propagation. The nonstationary problems related to the time-depth relationship and the time-varying wavelets are interrelated in seismic-well tying procedure. We implemented a nonstationary seismic-well tying method by iteratively updating the time-depth relationship and estimating the time-varying wavelets. From the estimated time-varying wavelets, we also estimated a Q-value by assuming that the subsurface medium has a constant Q at depth and used the constant Q to constrain the variation of the seismic wavelet during propagation. Then, we used the improved time-depth relationship and time-varying wavelets with the Q constraint for further iterations. In the iterative procedure, we quantified the accuracy of the seismic-well tying result using the correlation coefficient between the synthetic and the true seismic trace in each iteration and evaluated the reliability using the normalized mean-square errors among the wavelets estimated in different iterations