Right and Left Modules over the Frobenius Skew Polynomial Ring in the F-Finite Case

The main purposes of this paper are to establish and exploit the result that, over a complete (Noetherian) local ring $R$ of prime characteristic for which the Frobenius homomorphism $f$ is finite, the appropriate restrictions of the Matlis-duality functor provide an equivalence between the category of left modules over the Frobenius skew polynomial ring $R[x,f]$ that are Artinian as $R$-modules and the category of right $R[x,f]$-modules that are Noetherian as $R$-modules.Comment: 16 pages, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society. This revised version includes two additionl references and points out that some of the results have been obtained independently by M. Blickle and G. Boeckl

Depth of FF-singularities and base change of relative canonical sheaves

For a characteristic $p > 0$ variety $X$ with controlled $F$-singularities, we state conditions which imply that a divisorial sheaf is Cohen-Macaulay or at least has depth $\geq 3$ at certain points. This mirrors results of Koll\'ar for varieties in characteristic zero. As an application, we show that that relative canonical sheaves are compatible with arbitrary base change for certain families with sharply $F$-pure fibers.Comment: 18 pages, typos corrected, exposition improved, Corollary 3.3 added. To appear in Journal of the Institute of Mathematics of Jussie

Dynamical Decoupling of a single electron spin at room temperature

Here we report the increase of the coherence time T$_2$ of a single electron spin at room temperature by using dynamical decoupling. We show that the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence can prolong the T$_2$ of a single Nitrogen-Vacancy center in diamond up to 2.44 ms compared to the Hahn echo measurement where T$_2 = 390 \mu$s. Moreover, by performing spin locking experiments we demonstrate that with CPMG the maximum possible $T_2$ is reached. On the other hand, we do not observe strong increase of the coherence time in nanodiamonds, possibly due to the short spin lattice relaxation time $T_1=100 \mu$s (compared to T$_1$ = 5.93 ms in bulk). An application for detecting low magnetic field is demonstrated, where we show that the sensitivity using the CPMG method is improved by about a factor of two compared to the Hahn echo method.Comment: 4 pages, 4 figures, Two reference were added reporting results related to our wor

A Simulation of High Latitude F-Layer Instabilities in the Presence of Magnetosphere-Ionosphere Coupling

A magnetic-field-line-integrated model of plasma interchange instabilities is developed for the high latitude ionosphere including magnetospheric coupling effects. We show that primary magnetosphere-ionosphere coupling effect is to incorporate the inertia of the magnetospheric plasma in the analysis. As a specific example, we present the first simulation of the E x B instability in the inertial regime, i.e., nu sub i omega where nu sub i is the ion-neutral collision frequency and omega is the wave frequency. We find that the inertial E x B instability develops in a fundamentally different manner than in the collisional case ni sub i omega. Our results show that striations produced in the inertial regime are spread and retarded by ion inertial effects, and result in more isotropic irregularities than those seen in the collisional case

Integrated Diamond Optics for Single Photon Detection

Optical detection of single defect centers in the solid state is a key element of novel quantum technologies. This includes the generation of single photons and quantum information processing. Unfortunately the brightness of such atomic emitters is limited. Therefore we experimentally demonstrate a novel and simple approach that uses off-the-shelf optical elements. The key component is a solid immersion lens made of diamond, the host material for single color centers. We improve the excitation and detection of single emitters by one order of magnitude, as predicted by theory.Comment: 10 pages, 3 figure

Multifractal properties of growing networks

We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their parent's connections. We show that combination of these two features produces multifractal degree distributions, where degree is the number of connections of a vertex. An exact multifractal distribution is found for a nontrivial model of this class. The distribution tends to a power-law one, $\Pi (q) \sim q^{-\gamma}$, $\gamma =\sqrt{2}$ in the infinite network limit. Nevertheless, for finite networks's sizes, because of multifractality, attempts to interpret the distribution as a scale-free would result in an ambiguous value of the exponent $\gamma$.Comment: 7 pages epltex, 1 figur

Global Response to Local Ionospheric Mass Ejection

We revisit a reported "Ionospheric Mass Ejection" using prior event observations to guide a global simulation of local ionospheric outflows, global magnetospheric circulation, and plasma sheet pressurization, and comparing our results with the observed global response. Our simulation framework is based on test particle motions in the Lyon-Fedder-Mobarry (LFM) global circulation model electromagnetic fields. The inner magnetosphere is simulated with the Comprehensive Ring Current Model (CRCM) of Fok and Wolf, driven by the transpolar potential developed by the LFM magnetosphere, and includes an embedded plasmaspheric simulation. Global circulation is stimulated using the observed solar wind conditions for the period 24-25 Sept 1998. This period begins with the arrival of a Coronal Mass Ejection, initially with northward, but later with southward interplanetary magnetic field. Test particles are launched from the ionosphere with fluxes specified by local empirical relationships of outflow to electrodynamic and particle precipitation imposed by the MIlD simulation. Particles are tracked until they are lost from the system downstream or into the atmosphere, using the full equations of motion. Results are compared with the observed ring current and a simulation of polar and auroral wind outflows driven globally by solar wind dynamic pressure. We find good quantitative agreement with the observed ring current, and reasonable qualitative agreement with earlier simulation results, suggesting that the solar wind driven global simulation generates realistic energy dissipation in the ionosphere and that the Strangeway relations provide a realistic local outflow description