Meteoroid trajectories from BRAMS data

Author(s):  
Hervé Lamy

<p>BRAMS (Belgian RAdio Meteor Stations) is a Belgian radio network using forward scatter observations to detect and characterize meteoroids. A dedicated transmitter located in south of Belgium emits a CW signal with no modulation at a frequency of 49.97 MHz and with a power of 130 W. The network comprises currently 35 similar receiving stations located in Belgium and neighboring countries. They use Yagi antennas with a wide sensitivity pattern which therefore provide no information about the directivity of the meteor echoes. One of these stations is however a radio interferometer using the classical Jones configuration and is able to retrieve the direction of the meteor echoes.</p><p>We discuss here a general method to retrieve meteoroid trajectories based solely on time delays measured between meteor echoes recorded at multiple receiving stations. It is based on solving at least 6 non-linear equations to solve for the position of one specular reflection point (3 unknowns) and the 3 components of the speed. This method has also been described recently in Mazur et al (2020) and applied to CMOR data. However, specificities of the CMOR configuration has allowed simplifications that cannot be made with the BRAMS network. In order to maximize the number of meteoroid trajectories with at least 6 stations detecting meteor echoes, a number of additional stations geographically close to each other have been installed in the Limburg province in 2020. Another method to retrieve meteoroid trajectories using data from the radio interferometer and from 3 other stations is also presented.</p><p>We show preliminary results from both methods using also complementary data from the optical CAMS Benelux network.  The CAMS trajectories are used to select specific meteor echoes in the BRAMS data. The time delays between them are computed and used to solve the set of non-linear equations to retrieve the meteoroid trajectory and speed, which are then compared to the CAMS values. This allows us to assess the accuracy of both methods.</p><p>Finally we simulate the impact of using additional information, not currently available but that might become in a near future. This includes data from a monostatic system (a radar nearby our BRAMS transmitter is currently built), from a second radio interferometer (to be located in Limburg and/or near the transmitter), or the total range traveled by the radio wave if a coded CW transmitter such as in Vierinen et al (2016) is used.</p>

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Guillaume Bossard ◽  
Axel Kleinschmidt ◽  
Ergin Sezgin

Abstract We construct a pseudo-Lagrangian that is invariant under rigid E11 and transforms as a density under E11 generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on E11 exceptional field theory and the inclusion of constrained fields that transform in an indecomposable E11-representation together with the E11 coset fields. We show that, in combination with gauge-invariant and E11-invariant duality equations, this pseudo-Lagrangian reduces to the bosonic sector of non-linear eleven-dimensional supergravity for one choice of solution to the section condi- tion. For another choice, we reobtain the E8 exceptional field theory and conjecture that our pseudo-Lagrangian and duality equations produce all exceptional field theories with maximal supersymmetry in any dimension. We also describe how the theory entails non-linear equations for higher dual fields, including the dual graviton in eleven dimensions. Furthermore, we speculate on the relation to the E10 sigma model.


Author(s):  
Vesa Mustonen

SynopsisThe existence of a variational solution is shown for the strongly non-linear elliptic boundary value problem in unbounded domains. The proof is a generalisation to Orlicz-Sobolev space setting of the idea introduced in [15] for the equations involving polynomial non-linearities only.


Author(s):  
N. Parhi

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.


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