A GPU-based ray tracing approach for the prediction of multireflections on measurement objects and the a priori estimation of low-reflection measurement poses

2021 ◽  
Author(s):  
Philipp Middendorf ◽  
Pascal Kern ◽  
Nils Melchert ◽  
Markus Kästner ◽  
Eduard Reithmeier
Keyword(s):  
Ray Tracing ◽  
A Priori ◽  
Reflection Measurement ◽  
A Priori Estimation

A priori estimation of solutions of a boundary problem for a pseudodifferential equation with degeneration

2021 ◽  
pp. 6-10
Author(s):  
Alexander Dmitrievich Baev ◽  
◽  
Dmitry Alexandrovich Chechin ◽  
Sergey Alexandrovich Shabrov ◽  
Natalya Ivanovna Rabotinskaya ◽  
...  
Keyword(s):  
Boundary Problem ◽  
A Priori ◽  
Pseudodifferential Equation ◽  
A Priori Estimation

Maximum a priori estimation of wavefront slopes using a Hartmann wavefront sensor

1996 ◽  
Author(s):  
Scott A. Sallberg ◽  
Byron M. Welsh ◽  
Michael C. Roggemann
Keyword(s):  
A Priori ◽  
Wavefront Sensor ◽  
A Priori Estimation

Genomic selection efficiency and a priori estimation of accuracy in a structured dent maize panel

2018 ◽  
Vol 132 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Simon Rio ◽  
Tristan Mary-Huard ◽  
Laurence Moreau ◽  
Alain Charcosset
Keyword(s):  
Genomic Selection ◽  
A Priori ◽  
Selection Efficiency ◽  
A Priori Estimation

scholarly journals Atmospheric bending effects in GNSS tomography

2019 ◽  
Vol 12 (1) ◽  
pp. 23-34 ◽  
Author(s):  
Gregor Möller ◽  
Daniel Landskron
Keyword(s):  
Ray Tracing ◽  
Electromagnetic Waves ◽  
Piecewise Linear ◽  
A Priori ◽  
Elevation Angle ◽  
Functional Relation ◽  
Satellite System ◽  
Neutral Atmosphere ◽  
Correct Treatment ◽  
Reconstructed Signal

Abstract. In Global Navigation Satellite System (GNSS) tomography, precise information about the tropospheric water vapor distribution is derived from integral measurements like ground-based GNSS slant wet delays (SWDs). Therefore, the functional relation between observations and unknowns, i.e., the signal paths through the atmosphere, have to be accurately known for each station–satellite pair involved. For GNSS signals observed above a 15∘ elevation angle, the signal path is well approximated by a straight line. However, since electromagnetic waves are prone to atmospheric bending effects, this assumption is not sufficient anymore for lower elevation angles. Thus, in the following, a mixed 2-D piecewise linear ray-tracing approach is introduced and possible error sources in the reconstruction of the bended signal paths are analyzed in more detail. Especially if low elevation observations are considered, unmodeled bending effects can introduce a systematic error of up to 10–20 ppm, on average 1–2 ppm, into the tomography solution. Thereby, not only the ray-tracing method but also the quality of the a priori field can have a significant impact on the reconstructed signal paths, if not reduced by iterative processing. In order to keep the processing time within acceptable limits, a bending model is applied for the upper part of the neutral atmosphere. It helps to reduce the number of processing steps by up to 85 % without significant degradation in accuracy. Therefore, the developed mixed ray-tracing approach allows not only for the correct treatment of low elevation observations but is also fast and applicable for near-real-time applications.

scholarly journals A priori estimation of sequencing effort in complex microbial metatranscriptomes

2020 ◽  
Vol 10 (23) ◽  
pp. 13382-13394 ◽  
Author(s):  
Toni Monleon‐Getino ◽  
Jorge Frias‐Lopez
Keyword(s):  
A Priori ◽  
A Priori Estimation

scholarly journals Bifurcation Behaviors of Steady-State Solution to a Discrete General Brusselator Model

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Ruyun Ma ◽  
Zhongzi Zhao
Keyword(s):  
A Priori ◽  
Global Bifurcation ◽  
Small Neighborhood ◽  
Steady State Solution ◽  
Solution Curve ◽  
Bifurcation Theorem ◽  
Brusselator Model ◽  
Constant Solution ◽  
A Priori Estimation ◽  
Increasing Function

We study the local and global bifurcation of nonnegative nonconstant solutions of a discrete general Brusselator model. We generalize the linear u in the standard Brusselator model to the nonlinear fu. Assume that f∈C0,∞,0,∞ is a strictly increasing function, and f′f−1a∈0,∞. Taking b as the bifurcation parameter, we obtain that the solution set of the problem constitutes a constant solution curve and a nonconstant solution curve in a small neighborhood of the bifurcation point b0j,f−1a,ab/f−1a2. Moreover, via the Rabinowitz bifurcation theorem, we obtain the global structure of the set of nonconstant solutions under the condition that fs/s2 is nonincreasing in 0,∞. In this process, we also make a priori estimation for the nonnegative nonconstant solutions of the problem.

scholarly journals A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism

2017 ◽  
Vol 473 (2205) ◽  
pp. 20170385 ◽  
Author(s):  
Ayoub Gouasmi ◽  
Eric J. Parish ◽  
Karthik Duraisamy
Keyword(s):  
Evolution Equations ◽  
Nonlinear Dynamical Systems ◽  
A Priori ◽  
Time History ◽  
Original System ◽  
Memory Kernel ◽  
Nonlinear Dynamical ◽  
History Of ◽  
Consistent Basis ◽  
A Priori Estimation

Reduced models of nonlinear dynamical systems require closure, or the modelling of the unresolved modes. The Mori–Zwanzig procedure can be used to derive formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the time history of the resolved variables. While this procedure does not reduce the complexity of the original system, these equations can serve as a mathematically consistent basis to develop closures based on memory approximations. In this scenario, knowledge of the memory kernel is paramount in assessing the validity of a memory approximation. Unravelling the memory kernel requires solving the orthogonal dynamics, which is a high-dimensional partial differential equation that is intractable, in general. A method to estimate the memory kernel a priori , using full-order solution snapshots, is proposed. The key idea is to solve a pseudo orthogonal dynamics equation, which has a convenient Liouville form, instead. This ersatz arises from the assumption that the semi-group of the orthogonal dynamics is a composition operator for one observable. The method is exact for linear systems. Numerical results on the Burgers and Kuramoto–Sivashinsky equations demonstrate that the proposed technique can provide valuable information about the memory kernel.

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