Classical Electrodynamics, 2nd edition

Double-Mode Stellar Pulsations

“…The imaginary parts(t) of a(t) can then be obtained via a Cauchy integral, which through contour deformation becomes a Hilbert transform. Physicists are generally familiar with this analytic signal concept through the Kramers-Kronig dispersion relations (Jackson 1975).…”

Experimental observations of in situ secondary electron yield reduction in the PEP-II particle accelerator beam line

“…(1) represents the total number of photons emitted by a beam particle while traversing a dipole. To estimate the photon dose on the sample, we need to calculate the number of photons hitting the sample and thus integrate the spectrum of synchrotron radiation [21], (3) where e is the positron charge and the beam current varies with time I = I(t), as shown for example in Figure 6. Eq.…”

An off-lattice model for Br electrodeposition on Au(100): from DFT to experiment

“…3, it would appear that the dipole moment is dependent on the seemingly arbitrary center of the dipole; however, we note that when the charge density goes to zero at the limits of integration, p is independent of Z [26]. Since all charge distributions considered in this paper go to zero in the vacuum region, we choose the limits of integration in the z direction to be [−3.2, 9.4]Å, and the integration in the surface tangent directions obviously extend over the full x and y ranges of the cell.…”