Local stability analysis for a planar shock wave

A procedure to study the local stability of planar shock waves is presented. The procedure is applied to a Rankine-Hugoniot shock in a divergent/convergent nozzle, to an isentropic shock in a divergent/convergent nozzle, and to Rankine-Hugoniot shocks attached to wedges and cones. It is shown that for each case, the equation governing the shock motion is equivalent to the damped harmonic oscillator equation

Three-dimensional simulation of vortex breakdown

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state

Multiple steady states for characteristic initial value problems

The time dependent, isentropic, quasi-one-dimensional equations of gas dynamics and other model equations are considered under the constraint of characteristic boundary conditions. Analysis of the time evolution shows how different initial data may lead to different steady states and how seemingly anamolous behavior of the solution may be resolved. Numerical experimentation using time consistent explicit algorithms verifies the conclusions of the analysis. The use of implicit schemes with very large time steps leads to erroneous results

Spectral methods for inviscid, compressible flows

Report developments in the application of spectral methods to two dimensional compressible flows are reviewed. A brief introduction to spectral methods -- their history and especially their implementation -- is provided. The stress is on those techniques relevant to transonic flow computation. The spectral multigrid iterative methods are discussed with application to the transonic full potential equation. Discontinuous solutions of the Euler equations are considered. The key element is the shock fitting technique which is briefly explained

Shock-fitted Euler solutions to shock vortex interactions

The interaction of a planar shock wave with one or more vortexes is computed using a pseudospectral method and a finite difference method. The development of the spectral method is emphasized. In both methods the shock wave is fitted as a boundary of the computational domain. The results show good agreement between both computational methods. The spectral method is, however, restricted to smaller time steps and requires use of filtering techniques

Pseudospectral solution of two-dimensional gas-dynamic problems

Chebyshev pseudospectral methods are used to compute two dimensional smooth compressible flows. Grid refinement tests show that spectral accuracy can be obtained. Filtering is not needed if resolution is sufficiently high and if boundary conditions are carefully prescribed

A comparative study of the nonuniqueness problem of the potential equation

The nonuniqueness problem occurring at transonic speeds with the conservative potential equation is investigated numerically. The study indicates that the problem is not an inviscid phenomenon, but results from approximate treatment of shock waves inherent in the conservative potential model. A new bound on the limit of validity of the conservative potential model is proposed

Real-time Monocular Object SLAM

We present a real-time object-based SLAM system that leverages the largest object database to date. Our approach comprises two main components: 1) a monocular SLAM algorithm that exploits object rigidity constraints to improve the map and find its real scale, and 2) a novel object recognition algorithm based on bags of binary words, which provides live detections with a database of 500 3D objects. The two components work together and benefit each other: the SLAM algorithm accumulates information from the observations of the objects, anchors object features to especial map landmarks and sets constrains on the optimization. At the same time, objects partially or fully located within the map are used as a prior to guide the recognition algorithm, achieving higher recall. We evaluate our proposal on five real environments showing improvements on the accuracy of the map and efficiency with respect to other state-of-the-art techniques

Tropical Pacific spatial trend patterns in observed sea level: internal variability and/or anthropogenic signature?

In this study we focus on the sea level trend pattern observed by satellite altimetry in the tropical Pacific over the 1993–2009 time span (i.e. 17 yr). Our objective is to investigate whether this 17-yr-long trend pattern was different before the altimetry era, what was its spatio-temporal variability and what have been its main drivers. We try to discriminate the respective roles of the internal variability of the climate system and of external forcing factors, in particular anthropogenic emissions (greenhouse gases and aerosols). On the basis of a 2-D past sea level reconstruction over 1950–2009 (based on a combination of observations and ocean modelling) and multi-century control runs (i.e. with constant, preindustrial external forcing) from eight coupled climate models, we have investigated how the observed 17-yr sea level trend pattern evolved during the last decades and centuries, and try to estimate the characteristic time scales of its variability. For that purpose, we have computed sea level trend patterns over successive 17-yr windows (i.e. the length of the altimetry record), both for the 60-yr long reconstructed sea level and the model runs. We find that the 2-D sea level reconstruction shows spatial trend patterns similar to the one observed during the altimetry era. The pattern appears to have fluctuated with time with a characteristic time scale of the order of 25–30 yr. The same behaviour is found in multi-centennial control runs of the coupled climate models. A similar analysis is performed with 20th century coupled climate model runs with complete external forcing (i.e. solar plus volcanic variability and changes in anthropogenic forcing). Results suggest that in the tropical Pacific, sea level trend fluctuations are dominated by the internal variability of the ocean–atmosphere coupled system. While our analysis cannot rule out any influence of anthropogenic forcing, it concludes that the latter effect in that particular region is stillhardly detectable

Status of neutrino oscillations 2018: first hint for normal mass ordering and improved CP sensitivity

We present a new global fit of neutrino oscillation parameters within the simplest three-neutrino picture, including new data which appeared since our previous analysis~\cite{Forero:2014bxa}. In this update we include new long-baseline neutrino data involving the antineutrino channel in T2K, as well as new data in the neutrino channel, data from NO$\nu$A, as well as new reactor data, such as the Daya Bay 1230 days electron antineutrino disappearance spectrum data and the 1500 live days prompt spectrum from RENO, as well as new Double Chooz data. We also include atmospheric neutrino data from the IceCube DeepCore and ANTARES neutrino telescopes and from Super-Kamiokande. Finally, we also update our solar oscillation analysis by including the 2055-day day/night spectrum from the fourth phase of the Super-Kamiokande experiment. With the new data we find a preference for the atmospheric angle in the upper octant for both neutrino mass orderings, with maximal mixing allowed at $\Delta\chi^2 = 1.6 \, (3.2)$ for normal (inverted) ordering. We also obtain a strong preference for values of the CP phase $\delta$ in the range $[\pi,2\pi]$, excluding values close to $\pi/2$ at more than 4$\sigma$. More remarkably, our global analysis shows for the first time hints in favour of the normal mass ordering over the inverted one at more than 3$\sigma$. We discuss in detail the origin of the mass ordering, CP violation and octant sensitivities, analyzing the interplay among the different neutrino data samples.Comment: Updated neutrino oscillation analysis using the most recent results from T2K, NO$\nu$A, RENO and Super-Kamiokande. 17 pages, 8 figures, 1 tabl