We propose and study two second-order in time implicit-explicit (IMEX) methods for the coupled Stokes-Darcy system that governs flows in karst aquifers. The first is a combination of a second-order backward differentiation formula and the second-orde
r Gears extrapolation approach. The second is a combination of the second-order Adams-Moulton and second-order Adams-Bashforth methods. Both algorithms only require the solution of two decoupled problems at each time step, one Stokes and the other Darcy. Hence, these schemes are very efficient and can be easily implemented using legacy codes. We establish the unconditional and uniform in time stability for both schemes. The uniform in time stability leads to uniform in time control of the error which is highly desirable for modeling physical processes, e.g., contaminant sequestration and release, that occur over very long time scales. Error estimates for fully-discretized schemes using finite element spatial discretizations are derived. Numerical examples are provided that illustrate the accuracy, efficiency, and long-time stability of the two schemes.
Our work is based on the collision-induced coherence of two decay channels along two optical transitions.The quantum interference of pumping processes creates the dark state and the more atoms are pumped in this collision-induced dark state the stron
ger the suppression of the spontaneous emission. The efficiency of this suppression is quantified by putting it in comparison with the spontaneous emission on the ultraviolet transition which proceeds in a regular fashion. The branching ratio of these two(visible and ultraviolet) transitions is introduced as the effective measure of the degree of the suppression of the spontaneous emission on the visible transition. Our preliminary calculations show that a significant decrease of the branching ratio with increase of electron densities is reproduced in the theory.
The unusual electrical and optical properties of graphene make it a promising candidate for optoelectronic applications. An important, but as yet unexplored aspect is the role of photo-excited hot carriers in charge and energy transport at graphene i
nterfaces. Here, we perform time-resolved (~250 fs) scanning photocurrent microscopy on a tunable graphene pn junction. The ultrafast pump-probe measurements yield a photocurrent response time of ~1.5 ps at room temperature increasing to ~4 ps at 20 K. Combined with the negligible dependence of photocurrent amplitude on environmental temperature this implies that hot carriers rather than phonons dominate energy transport at high frequencies. Gate-dependent pump-probe measurements demonstrate that both thermoelectric and built-in electric field effects contribute to the photocurrent excited by laser pulses. The relative weight of each contribution depends on the junction configuration. A single laser beam excitation also displays multiple polarity-reversals as a function of carrier density, a signature of impact ionization. Our results enhance the understanding of non-equilibrium electron dynamics, electron-electron interactions, and electron-phonon interactions in graphene. They also determine fundamental limits on ultrafast device operation speeds (~500 GHz) for potential graphene-based photon detection, sensing, and communication.
We investigate the ultrafast relaxation dynamics of hot Dirac fermionic quasiparticles in multilayer epitaxial graphene using ultrafast optical differential transmission spectroscopy. We observe DT spectra which are well described by interband transi
tions with no electron-hole interaction. Following the initial thermalization and emission of high-energy phonons, the electron cooling is determined by electron-acoustic phonon scattering, found to occur on the time scale of 1 ps for highly doped layers, and 4-11 ps in undoped layers. The spectra also provide strong evidence for the multilayer stucture and doping profile of thermally grown epitaxial graphene on SiC.
