Possibility of the tunneling time determination

We show that it is impossible to determine the time a tunneling particle spends under the barrier. However, it is possible to determine the asymptotic time, i.e., the time the particle spends in a large area including the barrier. We propose a model of time measurements. The model provides a procedure for calculation of the asymptotic tunneling and reflection times. The model also demonstrates the impossibility of determination of the time the tunneling particle spends under the barrier. Examples for delta-form and rectangular barrier illustrate the obtained results.Comment: 8 figure

Inverse Problems of Determining Sources of the Fractional Partial Differential Equations

In this chapter, we mainly review theoretical results on inverse source problems for diffusion equations with the Caputo time-fractional derivatives of order $\alpha\in(0,1)$. Our survey covers the following types of inverse problems: 1. determination of time-dependent functions in interior source terms 2. determination of space-dependent functions in interior source terms 3. determination of time-dependent functions appearing in boundary condition

Office of Spaceflight Standard Spaceborne Global Positioning System (GPS) user equipment project

The Global Positioning System (GPS) provides the following: (1) position and velocity determination to support vehicle GN&C, precise orbit determination, and payload pointing; (2) time reference to support onboard timing systems and data time tagging; (3) relative position and velocity determination to support cooperative vehicle tracking; and (4) attitude determination to support vehicle attitude control and payload pointing

Determination of the spin-flip time in ferromagnetic SrRuO3 from time-resolved Kerr measurements

We report time-resolved Kerr effect measurements of magnetization dynamics in ferromagnetic SrRuO3. We observe that the demagnetization time slows substantially at temperatures within 15K of the Curie temperature, which is ~ 150K. We analyze the data with a phenomenological model that relates the demagnetization time to the spin flip time. In agreement with our observations the model yields a demagnetization time that is inversely proportional to T-Tc. We also make a direct comparison of the spin flip rate and the Gilbert damping coefficient showing that their ratio very close to kBTc, indicating a common origin for these phenomena

Source blending effects on microlensing time-histograms and optical depth determination

Source blending in microlensing experiments is known to modify the Einstein time of the observed events. In this paper, we have conducted Monte-Carlo calculations, using the analytical relationships derived by Han (1999) to quantify the effect of blending on the observed event time distribution and optical depth. We show that short-time events are affected significantly by source blending and that, for moderately blended sources, the optical depth $\tau$ is globally overestimated, because of an underestimation of the exposure. For high blending situations, on the opposite, blending leads to an {\it under}estimation of the optical depth. Our results are in agreement with the most recent optical depth determinations toward the Galactic Center of the MACHO collaboration (Popowski et al. 2004) and the OGLE-II collaboration (Sumi et al. 2005) that use clump giants (less affected by the blending effect) as sources. The blending-corrected, lower optical depth toward the Galactic Bulge is now in good agreement with the value inferred from galactic models, reconciling theoretical and observational determinations.Comment: Accepted in Astronomy Astrophysics. Note that these calculations were conducted in 2001, prior to the recent DIA analyses mentioned in the references (see Alibert, Y. SF2A-conference, 2001