On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.Comment: 22 pages, 6 figure

Magnon-photon coupling in the noncollinear magnetic insulator Cu 2 OSeO 3

Anticrossing behavior between magnons in the noncollinear chiral magnet Cu2OSeO3 and a two-mode X-band microwave resonator was studied in the temperature range 5–100 K. In the field-induced ferrimagnetic phase, we observed a strong-coupling regime between magnons and two microwave cavity modes with a cooperativity reaching 3600. In the conical phase, cavity modes are dispersively coupled to a fundamental helimagnon mode, and we demonstrate that the magnetic phase diagram of Cu2OSeO3 can be reconstructed from the measurements of the cavity resonance frequency. In the helical phase, a hybridized state of a higher-order helimagnon mode and a cavity mode—a helimagnon polariton—was found. Our results reveal a class of magnetic systems where strong coupling of microwave photons to nontrivial spin textures can be observed

Coherent storage of photoexcited triplet states using 29Si nuclear spins in silicon

Pulsed electron paramagnetic resonance spectroscopy of the photoexcited, metastable triplet state of the oxygen-vacancy center in silicon reveals that the lifetime of the ms = \pm1 sub-levels differ significantly from that of the ms =0 state. We exploit this significant difference in decay rates to the ground singlet state to achieve nearly ~100% electron spin polarization within the triplet. We further demonstrate the transfer of a coherent state of the triplet electron spin to, and from, a hyperfine-coupled, nearest-neighbor 29Si nuclear spin. We measure the coherence time of the 29 Si nuclear spin employed in this operation and find it to be unaffected by the presence of the triplet electron spin and equal to the bulk value measured by nuclear magnetic resonance.Comment: 5 pages, 4 figure

Earth resources-regional transfer activity contracts review

A regional transfer activity contracts review held by the Earth Resources Office was summarized. Contracts in the earth resources field primarily directed toward applications of satellite data and technology in solution of state and regional problems were reviewed. A summary of the progress of each contract was given in order to share experiences of researchers across a seven state region. The region included Missouri, Kentucky, Tennessee, Mississippi, Alabama, Georgia, and North Carolina. Research in several earth science disciplines included forestry, limnology, water resources, land use, geology, and mathematical modeling. The use of computers for establishment of information retrieval systems was also emphasized

Novice Teachers: Do They Use What We Teach Them?

Teacher educators frequently engage in some rather agonizing soul searching regarding their effectiveness in preparing preservice teachers. Students pass through their classes, go on to other classes, and eventually they are in the real world of the classroom. Teacher educators seldom get direct feedback from students as to the relevance or the value of the instruction they received. Lacking this feedback, teacher educators who teach from a whole language perspective frequently question whether students actually use the instructional strategies they were taught in their reading courses, or whether they choose the more traditional basal reader approach