Non-Boolean almost perfect nonlinear functions on non-Abelian groups

The purpose of this paper is to present the extended definitions and characterizations of the classical notions of APN and maximum nonlinear Boolean functions to deal with the case of mappings from a finite group K to another one N with the possibility that one or both groups are non-Abelian.Comment: 17 page

Nonlocal effects in the shot noise of diffusive superconductor - normal-metal systems

A cross-shaped diffusive system with two superconducting and two normal electrodes is considered. A voltage $eV < \Delta$ is applied between the normal leads. Even in the absence of average current through the superconducting electrodes their presence increases the shot noise at the normal electrodes and doubles it in the case of a strong coupling to the superconductors. The nonequilibrium noise at the superconducting electrodes remains finite even in the case of a vanishingly small transport current due to the absence of energy transfer into the superconductors. This noise is suppressed by electron-electron scattering at sufficiently high voltages.Comment: 4 pages, RevTeX, 2 eps figure

Large-eddy simulation and experimental study of heat transfer, nitric oxide emissions and combustion instability in a swirled turbulent high-pressure burner

Nitric oxide formation in gas turbine combustion depends on four key factors: flame stabilization, heat transfer, fuel-air mixing and combustion instability. The design of modern gas turbine burners requires delicate compromises between fuel efficiency, emissions of oxides of nitrogen (NOx) and combustion stability. Burner designs allowing substantial NOx reduction are often prone to combustion oscillations. These oscillations also change the NOx fields. Being able to predict not only the main species field in a burner but also the pollutant and the oscillation levels is now a major challenge for combustion modelling. This must include a realistic treatment of unsteady acoustic phenomena (which create instabilities) and also of heat transfer mechanisms (convection and radiation) which control NOx generation. In this work, large-eddy simulation (LES) is applied to a realistic gas turbine combustion chamber configuration where pure methane is injected through multiple holes in a cone-shaped burner. In addition to a non-reactive simulation, this article presents three reactive simulations and compares them to experimental results. The first reactive simulation neglects effects of cooling air on flame stabilization and heat losses by radiation and convection. The second reactive simulation shows how cooling air and heat transfer affect nitric oxide emissions. Finally, the third reactive simulation shows the effects of combustion instability on nitric oxide emissions. Additionally, the combustion instability is analysed in detail, including the evaluation of the terms in the acoustic energy equation and the identification of the mechanism driving the oscillation. Results confirm that LES of gas turbine combustion requires not only an accurate chemical scheme and realistic heat transfer models but also a proper description of the acoustics in order to predict nitric oxide emissions and pressure oscillation levels simultaneousl

Using LES to Study Reacting Flows and Instabilities in Annular Combustion Chambers

Great prominence is put on the design of aeronautical gas turbines due to increasingly stringent regulations and the need to tackle rising fuel prices. This drive towards innovation has resulted sometimes in new concepts being prone to combustion instabilities. In the particular field of annular combustion chambers, these instabilities often take the form of azimuthal modes. To predict these modes, one must compute the full combustion chamber, which remained out of reach until very recently and the development of massively parallel computers. Since one of the most limiting factors in performing Large Eddy Simulation (LES) of real combustors is estimating the adequate grid, the effects of mesh resolution are investigated by computing full annular LES of a realistic helicopter combustion chamber on three grids, respectively made of 38, 93 and 336 million elements. Results are compared in terms of mean and fluctuating fields. LES captures self-established azimuthal modes. The presence and structure of the modes is discussed. This study therefore highlights the potential of LES for studying combustion instabilities in annular gas turbine combustors

Can Deflagration-Detonation-Transitions occur in Type Ia Supernovae?

The mechanism for deflagration-detonation-transition (DDT) by turbulent preconditioning, suggested to explain the possible occurrence of delayed detonations in Type Ia supernova explosions, is argued to be conceptually inconsistent. It relies crucially on diffusive heat losses of the burned material on macroscopic scales. Regardless of the amplitude of turbulent velocity fluctuations, the typical gradient scale for temperature fluctuations is shown to be the laminar flame width or smaller, rather than the factor of thousand more required for a DDT. Furthermore, thermonuclear flames cannot be fully quenched in regions much larger than the laminar flame width as a consequence of their simple ``chemistry''. Possible alternative explosion scenarios are briefly discussed.Comment: 8 pages, uses aastex; added references. Accepted by ApJ Letter

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Impact of Locally Suppressed Wave sources on helioseismic travel times

Wave travel-time shifts in the vicinity of sunspots are typically interpreted as arising predominantly from magnetic fields, flows, and local changes in sound speed. We show here that the suppression of granulation related wave sources in a sunspot can also contribute significantly to these travel-time shifts, and in some cases, an asymmetry between in and outgoing wave travel times. The tight connection between the physical interpretation of travel times and source-distribution homogeneity is confirmed. Statistically significant travel-time shifts are recovered upon numerically simulating wave propagation in the presence of a localized decrease in source strength. We also demonstrate that these time shifts are relatively sensitive to the modal damping rates; thus we are only able to place bounds on the magnitude of this effect. We see a systematic reduction of 10-15 seconds in $p$-mode mean travel times at short distances ($\sim 6.2$ Mm) that could be misinterpreted as arising from a shallow (thickness of 1.5 Mm) increase ($\sim$ 4%) in the sound speed. At larger travel distances ($\sim 24$ Mm) a 6-13 s difference between the ingoing and outgoing wave travel times is observed; this could mistakenly be interpreted as being caused by flows.Comment: Revised version. Submitted to Ap