On a Dirichlet problem related to the invertibility of mappings arising in 2D grid generation problems

this paper depends strongly on a theorem of Carleman-HartmanWintner. This theorem is only true in two dimensional domains. In fact a straightforward generalization to more than two dimensional domains cannot be true. A counterexample to the proof of [15]forthe three dimensional case can be found by using a special harmonic function due to Kellogg [12]. This function is shown in [2]. A direct counterexample can be found in [13]. 2 Main result on smooth domain

On the invertibility of mappings arising in 2D grid generation problems

In adapting a grid for a Computational Fluid Dynamics problem one uses a mapping from the unit square onto itself that is the solution of an elliptic partial differential equation with rapidly varying coefficients. For a regular discretization this mapping has to be invertible. We will show that such result holds for general elliptic operators (in two dimensions). The Carleman-Hartman-Wintner Theorem will be fundamental in our proof. We will also explain why such a general result cannot be expected to hold for the (three-dimensional) cube

Scaling properties of velocity and temperature spectra above the surface friction layer in a convective atmospheric boundary layer

International audienceWe report velocity and temperature spectra measured at nine levels from 1.42 meters up to 25.7 m over a smooth playa in Western Utah. Data are from highly convective conditions when the magnitude of the Obukhov length (our proxy for the depth of the surface friction layer) was less than 2 m. Our results are somewhat similar to the results reported from the Minnesota experiment of Kaimal et al. (1976), but show significant differences in detail. Our velocity spectra show no evidence of buoyant production of kinetic energy at at the scale of the thermal structures. We interpret our velocity spectra to be the result of outer eddies interacting with the ground, not "local free convection". We observe that velocity spectra represent the spectral distribution of the kinetic energy of the turbulence, so we use energy scales based on total turbulence energy in the convective boundary layer (CBL) to collapse our spectra. For the horizontal velocity spectra this scale is (zi ?o)2/3, where zi is inversion height and ?o is the dissipation rate in the bulk CBL. This scale functionally replaces the Deardorff convective velocity scale. Vertical motions are blocked by the ground, so the outer eddies most effective in creating vertical motions come from the inertial subrange of the outer turbulence. We deduce that the appropriate scale for the peak region of the vertical velocity spectra is (z ?o)2/3 where z is height above ground. Deviations from perfect spectral collapse under these scalings at large and small wavenumbers are explained in terms of the energy transport and the eddy structures of the flow. We find that the peaks of the temperature spectra collapse when wavenumbers are scaled using (z1/2 zi1/2). That is, the lengths of the thermal structures depend on both the lengths of the transporting eddies, ~9z, and the progressive aggregation of the plumes with height into the larger-scale structures of the CBL. This aggregation depends, in top-down fashion, on zi. The whole system is therefore highly organized, with even the smallest structures conforming to the overall requirements of the whole flow

Soft singularity and the fundamental length

It is shown that some regular solutions in 5D Kaluza-Klein gravity may have interesting properties if one from the parameters is in the Planck region. In this case the Kretschman metric invariant runs up to a maximal reachable value in nature, i.e. practically the metric becomes singular. This observation allows us to suppose that in this situation the problems with such soft singularity will be much easier resolved in the future quantum gravity then by the situation with the ordinary hard singularity (Reissner-Nordstr\"om singularity, for example). It is supposed that the analogous consideration can be applied for the avoiding the hard singularities connected with the gauge charges.Comment: 5 page

Integrity static analysis of COTS/SOUP

This paper describes the integrity static analysis approach developed to support the justification of commercial off-the-shelf software (COTS) used in a safety-related system. The static analysis was part of an overall software qualification programme, which also included the work reported in our paper presented at Safecomp 2002. Integrity static analysis focuses on unsafe language constructs and “covert” flows, where one thread can affect the data or control flow of another thread. The analysis addressed two main aspects: the internal integrity of the code (especially for the more critical functions), and the intra-component integrity, checking for covert channels. The analysis process was supported by an aggregation of tools, combined and engineered to support the checks done and to scale as necessary. Integrity static analysis is feasible for industrial scale software, did not require unreasonable resources and we provide data that illustrates its contribution to the software qualification programme

Bounds on the force between black holes

We treat the problem of N interacting, axisymmetric black holes and obtain two relations among physical parameters of the system including the force between the black holes. The first relation involves the total mass, the angular momenta, the distances and the forces between the black holes. The second one relates the angular momentum and area of each black hole with the forces acting on it.Comment: 13 pages, no figure

Analysis of pilot control strategy

Methods for nonintrusive identification of pilot control strategy and task execution dynamics are presented along with examples based on flight data. The specific analysis technique is Nonintrusive Parameter Identification Procedure (NIPIP), which is described in a companion user's guide (NASA CR-170398). Quantification of pilot control strategy and task execution dynamics is discussed in general terms followed by a more detailed description of how NIPIP can be applied. The examples are based on flight data obtained from the NASA F-8 digital fly by wire airplane. These examples involve various piloting tasks and control axes as well as a demonstration of how the dynamics of the aircraft itself are identified using NIPIP. Application of NIPIP to the AFTI/F-16 flight test program is discussed. Recommendations are made for flight test applications in general and refinement of NIPIP to include interactive computer graphics

Adaptive Filters Revisited - RFI Mitigation in pulsar observations

Pulsar detection and timing experiments are applications where adaptive filters seem eminently suitable tools for radio-frequency-interference (RFI) mitigation. We describe a novel variant which works well in field trials of pulsar observations centred on an observing frequency of 675 MHz, a bandwidth of 64 MHz and with 2-bit sampling. Adaptive filters have generally received bad press for RFI mitigation in radio astronomical observations with their most serious drawback being a spectral echo of the RFI embedded in the filtered signals. Pulsar observations are intrinsically less sensitive to this as they operate in the (pulsar period) time domain. The field trials have allowed us to identify those issues which limit the effectiveness of the adaptive filter. We conclude that adaptive filters can significantly improve pulsar observations in the presence of RFI.Comment: Accepted for publication in Radio Scienc

Mission-oriented requirements for updating MIL-H-8501. Volume 2: STI background and rationale

A supplement to the structure of a new flying and ground handling qualities specification for military rotorcraft structure is presented in order to explain the background and rationale for the specification structure, the proposed forms of criteria, and the status of the existing data base. Critical gaps in the data base for the new structure are defined, and recommendations are provided for the research required to address the most important of these gaps