scholarly journals Beyond Mapping Functions and Gradients

2021 ◽  
Author(s):  
Jean-Pierre Barriot ◽  
Peng Feng
Keyword(s):  
Perturbation Theory ◽  
Exponential Decay ◽  
Base Case ◽  
Microwave Propagation ◽  
Orthogonal Functions ◽  
Mathematical Basis ◽  
Mapping Functions ◽  
Alternative Approach ◽  
Propagation Delays ◽  
The Sixties

Mapping functions and gradients in GNSS and VLBI applications were introduced in the sixties and seventies to model the microwave propagation delays in the troposphere, and they were proven to be the perfect tools for these applications. In this work, we revisit the physical and mathematical basis of these tools in the context of meteorology and climate applications and propose an alternative approach for the wet delay part. This alternative approach is based on perturbation theory, where the base case is an exponential decay of the wet refractivity with altitude. The perturbation is modeled as a set of orthogonal functions in space and time, with the ability to separate eddy-scale variations of the wet refractivity.

A Deconvolution Technique for Determining the Intrinsic Fluorescence Decay Lifetimes of Crude Oils

1988 ◽  
Vol 42 (3) ◽  
pp. 406-410 ◽  
Author(s):  
M. F. Quinn ◽  
S. Joubian ◽  
F. Al-Bahrani ◽  
S. Al-Aruri ◽  
Oussama Alameddine
Keyword(s):  
Fourier Transform ◽  
Impulse Response ◽  
Exponential Decay ◽  
Fluorescence Decay ◽  
Average Lifetime ◽  
Nitrogen Laser ◽  
Alternative Approach ◽  
Deconvolution Technique ◽  
The Fourier Transform ◽  
Single Exponential

A simple deconvolution procedure using FT was developed for determining the average lifetime of samples excited by a nitrogen laser pumped dye laser operating at 428 nm. To overcome the noise limitations imposed by including higher frequency harmonics in the analysis, we used an alternative approach. This approach relied on taking the Fourier transform at 21 subharmonic frequencies and using an appropriate weighting procedure in the calculation of amplitude and lifetime of the sample impulse response. A single exponential decay was assumed.

Field experimentation on rough land: the method of Papadakis reconsidered

1998 ◽  
Vol 131 (1) ◽  
pp. 1-11 ◽  
Author(s):  
S. C. PEARCE
Keyword(s):  
Correct Answer ◽  
Iterative Procedure ◽  
Experimental Error ◽  
Field Experiments ◽  
Analysis Of Covariance ◽  
Mathematical Basis ◽  
Alternative Approach ◽  
Special Weight ◽  
Field Experimentation ◽  
Fertility Pattern

Much of the error in field experiments comes from environmental differences, which traditional methods (e.g. blocks or rows and columns) sometimes fail to control, especially if the fertility pattern is complex or unexpected. In 1937 Papadakis proposed an alternative approach in which the performance of each plot was judged by that of its neighbours. If a plot was situated in an area of generally high cropping, its own high crop was partly discounted but if surrounding plots were yielding poorly, it was given special weight. Adjustment was by the analysis of covariance. The method has not been much used, partly because it still lacks a mathematical basis and partly because it is suspected of bias in the estimation of contrasts between treatments.It has been studied here by simulation, i.e. bodies of data have been generated on the computer with known characteristics and then analysed by Papadakis's method to see if a correct answer was returned. Also, an improvement in the covariate is suggested and an iterative procedure developed to ensure more consistent results.It emerges that the suspicion of bias was unjustified. Also, the method can be extremely effective in reducing experimental error. In all its variant forms it has difficulty with outside plots, and for that reason is more effective on compact areas than on strips. Also, interference between plots is especially serious, because the neighbours affected are those needed to form the adjusting covariate. Discontinuities arising from past use of the land can cause problems but a method is suggested for minimizing their effect.

scholarly journals CHIRAL PERTURBATION THEORY WITH NUCLEONS

1992 ◽  
Vol 01 (03) ◽  
pp. 561-601 ◽  
Author(s):  
Ulf-G. Meißner
Keyword(s):  
Perturbation Theory ◽  
Chiral Symmetry ◽  
Chiral Perturbation Theory ◽  
Chiral Limit ◽  
Nuclear Forces ◽  
Chiral Perturbation ◽  
Chiral Structure ◽  
Quark Masses ◽  
Alternative Approach ◽  
Working Out

I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external momenta and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward–identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the method. Some processes which are discussed are threshold photopion production, low-energy Compton scattering off nucleons, πN scattering and the σ–term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon.

The role of dissipation in macroscopic quantum tunneling and in near-field propagation

2019 ◽  
Vol 33 (11) ◽  
pp. 1950131
Author(s):  
A. Ranfagni ◽  
G. P. Pazzi ◽  
I. Cacciari
Keyword(s):  
Quantum Tunneling ◽  
Wave Attenuation ◽  
Near Field ◽  
Superconducting Devices ◽  
Transition Elements ◽  
Microwave Propagation ◽  
Dissipative Effects ◽  
Alternative Approach ◽  
Macroscopic Quantum Tunneling

A stochastic model, which demonstrated to be capable of determining dissipative effects in the microwave circuits loading superconducting devices, is found to be suitable also for analyzing near-field microwave propagation when the wave attenuation is interpreted as a dissipative effect. An alternative approach to the problem is offered by Feynman’s transition elements.

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