Holder continuity of absolutely continuous spectral measures for one-frequency Schrodinger operators

We establish sharp results on the modulus of continuity of the distribution of the spectral measure for one-frequency Schrodinger operators with Diophantine frequencies in the region of absolutely continuous spectrum. More precisely, we establish 1/2-Holder continuity near almost reducible energies (an essential support of absolutely continuous spectrum). For non-perturbatively small potentials (and for the almost Mathieu operator with subcritical coupling), our results apply for all energies.Comment: 16 page

Stability of nonuniform rotor blades in hover using a mixed formulation

A mixed formulation for calculating static equilibrium and stability eigenvalues of nonuniform rotor blades in hover is presented. The static equilibrium equations are nonlinear and are solved by an accurate and efficient collocation method. The linearized perturbation equations are solved by a one step, second order integration scheme. The numerical results correlate very well with published results from a nearly identical stability analysis based on a displacement formulation. Slight differences in the results are traced to terms in the equations that relate moments to derivatives of rotations. With the present ordering scheme, in which terms of the order of squares of rotations are neglected with respect to unity, it is not possible to achieve completely equivalent models based on mixed and displacement formulations. The one step methods reveal that a second order Taylor expansion is necessary to achieve good convergence for nonuniform rotating blades. Numerical results for a hypothetical nonuniform blade, including the nonlinear static equilibrium solution, were obtained with no more effort or computer time than that required for a uniform blade

Harper operators, Fermi curves, and Picard-Fuchs equations

This paper is a continuation of the work on the spectral problem of Harper operator using algebraic geometry. We continue to discuss the local monodromy of algebraic Fermi curves based on Picard-Lefschetz formula. The density of states over approximating components of Fermi curves satisfies a Picard-Fuchs equation. By the property of Landen transformation, the density of states has a Lambert series as the quarter period. A $q$-expansion of the energy level can be derived from a mirror map as in the B-model.Comment: v2, 13 pages, minor changes have been mad

The rise of fully turbulent flow

Over a century of research into the origin of turbulence in wallbounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow. At slightly higher speeds the situation changes distinctly and the entire flow is turbulent. Neither the origin of the different states encountered during transition, nor their front dynamics, let alone the transformation to full turbulence could be explained to date. Combining experiments, theory and computer simulations here we uncover the bifurcation scenario organising the route to fully turbulent pipe flow and explain the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence and fully turbulent flows.Comment: 31 pages, 9 figure

Business and Information Technology Alignment Measurement -- a recent Literature Review

Since technology has been involved in the business context, Business and Information Technology Alignment (BITA) has been one of the main concerns of IT and Business executives and directors due to its importance to overall company performance, especially today in the age of digital transformation. Several models and frameworks have been developed for BITA implementation and for measuring their level of success, each one with a different approach to this desired state. The BITA measurement is one of the main decision-making tools in the strategic domain of companies. In general, the classical-internal alignment is the most measured domain and the external environment evolution alignment is the least measured. This literature review aims to characterize and analyze current research on BITA measurement with a comprehensive view of the works published over the last 15 years to identify potential gaps and future areas of research in the field.Comment: 12 pages, Preprint version, BIS 2018 International Workshops, Berlin, Germany, July 18 to 20, 2018, Revised Paper

Collapse of the Gd3+Gd^{3+} ESR fine structure throughout the coherent temperature of the Gd-doped Kondo Semiconductor CeFe4P12CeFe_{4}P_{12}

Experiments on the $Gd^{3+}$ Electron Spin Resonance (ESR) in the filled skutterudite $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$ ($x \approx 0.001$), at temperatures where the host resistivity manifests a smooth insulator-metal crossover, provides evidence of the underlying Kondo physics associated with this system. At low temperatures (below $T \approx K$), $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$ behaves as a Kondo-insulator with a relatively large hybridization gap, and the $Gd^{3+}$ ESR spectra displays a fine structure with lorentzian line shape, typical of insulating media. The electronic gap is attributed to the large hybridization present in the coherent regime of a Kondo lattice, when Ce 4f-electrons cooperate with band properties at half-filling. Mean-field calculations suggest that the electron-phonon interaction is fundamental at explaining the strong 4f-electron hybridization in this filled skutterudite. The resulting electronic structure is strongly temperature dependent, and at about $T^{*} \approx 160 K$ the system undergoes an insulator-to-metal transition induced by the withdrawal of 4f-electrons from the Fermi volume, the system becoming metallic and non-magnetic. The $Gd^{3+}$ ESR fine structure coalesces into a single dysonian resonance, as in metals. Still, our simulations suggest that exchange-narrowing via the usual Korringa mechanism, alone, is not capable of describing the thermal behavior of the ESR spectra in the entire temperature region ($4.2$ - $300$ K). We propose that temperature activated fluctuating-valence of the Ce ions is the missing ingredient that, added to the usual exchange-narrowing mechanism, fully describes this unique temperature dependence of the $Gd^{3+}$ ESR fine structure observed in $Ce_{1-x}Gd_{x}Fe_{4}P_{12}$.Comment: 19 pages, 6 figure

Turbulent dissipation in the ISM: the coexistence of forced and decaying regimes and implications for galaxy formation and evolution

We discuss the dissipation of turbulent kinetic energy Ek in the global ISM by means of 2-D, MHD, non-isothermal simulations in the presence of model radiative heating and cooling. We argue that dissipation in 2D is representative of that in three dimensions as long as it is dominated by shocks rather than by a turbulent cascade. Energy is injected at a few isolated sites in space, over relatively small scales, and over short time periods. This leads to the coexistence of forced and decaying regimes in the same flow. We find that the ISM-like flow dissipates its turbulent energy rapidly. In simulations with forcing, the input parameters are the radius l_f of the forcing region, the total kinetic energy e_k each source deposits into the flow, and the rate of formation of those regions, sfr_OB. The global dissipation time t_d depends mainly on l_f. In terms of measurable properties of the ISM, t_d >= Sigma_g u_rms^2/(e_k sfr_OB), where Sigma_g is the average gas surface density and u_rms is the rms velocity dispersion. For the solar neighborhood, t_d >= 1.5x10^7 yr. The global dissipation time is consistently smaller than the crossing time of the largest energy-containing scales. In decaying simulations, Ek decreases with time as t^-n, where n~0.8-0.9. This suggests a decay with distance d as Ek\propto d^{-2n/(2-n)} in the mixed forced+decaying case. If applicable to the vertical direction, our results support models of galaxy evolution in which stellar energy injection provides significant support for the gas disk thickness, but not models of galaxy formation in which this energy injection is supposed to reheat an intra-halo medium at distances of up to 10-20 times the optical galaxy size, as the dissipation occurs on distances comparable to the disk height.Comment: 23 pages, including figures. To appear in ApJ. Abstract abridge