On the degrees of freedom of scattered fields

1989 ◽  
Vol 37 (7) ◽  
pp. 918-926 ◽  
Author(s):  
O.M. Bucci ◽  
G. Franceschetti
Keyword(s):  
Degrees Of Freedom ◽  
Scattered Fields

scholarly journals Resolution of Born Scattering in Curve Geometries: Aspect-Limited Observations and Excitations

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3089
Author(s):  
Ehsan Akbari Sekehravani ◽  
Giovanni Leone ◽  
Rocco Pierri
Keyword(s):  
Degrees Of Freedom ◽  
Plane Waves ◽  
Single Frequency ◽  
Limited Data ◽  
Scattering Problems ◽  
Approximation Accuracy ◽  
Imaging Results ◽  
Exact Evaluation ◽  
Spread Function ◽  
Scattered Fields

In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.

scholarly journals NDF of Scattered Fields for Strip Geometries

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 202
Author(s):  
Ehsan Akbari Sekehravani ◽  
Giovanni Leone ◽  
Rocco Pierri
Keyword(s):  
Degrees Of Freedom ◽  
Plane Waves ◽  
Singular Value ◽  
Scattering Operator ◽  
Scattering Problems ◽  
First Order ◽  
Incident Plane ◽  
Minimum Number ◽  
Scattered Fields ◽  
Value Decomposition

Solving inverse scattering problems by numerical methods requires investigating the number of independent pieces of information that can be reconstructed stably. To this end, we address the evaluation of the Number of Degrees of Freedom (NDF) of far-zone scattered fields for some strip geometries under the first-order Born approximation. The analysis is performed by employing the Singular Value Decomposition (SVD) of the scattering operator in the two-dimensional scalar geometry of one or more strips illuminated by a TM polarized plane wave. It is known that investigating the scattering scene at different incident plane waves (multi-view configuration) enhances the NDF. Therefore we mean to examine the minimum number of incident plane waves providing the NDF of the scattered fields both by theoretical estimations and numerical verifications.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

Das Experten-Novizen-Paradigma und die Vertrauenskrise in der Psychologie

2016 ◽  
Vol 23 (4) ◽  
pp. 131-140 ◽  
Author(s):  
Philip Furley ◽  
Karsten Schul ◽  
Daniel Memmert
Keyword(s):  
Degrees Of Freedom

Zusammenfassung. Das Ziel des vorliegenden Beitrages ist es anhand eines vielverwendeten Paradigmas in der Sportwissenschaft – dem Experten-Novizen-Vergleich – zu prüfen, ob die momentane Vertrauenskrise in der Psychologie ebenfalls die Sportpsychologie betreffen könnte. Anhand einer exemplarischen Studie zeigen wir, dass es innerhalb dieses Paradigmas zu kontroversen Befunden kommt, welche durch die vermuteten Ursachen der Vertrauenskrise (Researcher Degrees of Freedom, kleine Stichprobengrößen) erklärt sein könnten. Zusätzlich argumentieren wir, dass weitere Faktoren (Konfundierung, Stichprobengrößen, Rosenthal Effekt, Expertise-Definition) innerhalb dieses Paradigmas die Reproduzierbarkeit von Erkenntnissen in Frage stellen. Wir diskutieren mögliche Maßnahmen, wie die dargestellten Probleme des Experten-Novizen-Paradigmas in zukünftigen Forschungsarbeiten gelöst werden können.

Determination of Graft Forces for Cranial Cruciate Ligament Reconstruction in the Dog

1996 ◽  
Vol 09 (04) ◽  
pp. 165-171 ◽  
Author(s):  
D. A. Hulse ◽  
M. R. Slater ◽  
J. F. Hunter ◽  
W. A. Hyman ◽  
B. A. Shelley
Keyword(s):  
Degrees Of Freedom ◽  
Cruciate Ligament ◽  
Insertion Site ◽  
Graft Fixation ◽  
Flexion Angle ◽  
Patellar Ligament ◽  
Graft Material ◽  
Test Apparatus ◽  
Cranial Cruciate Ligament ◽  
Tibial Insertion

SummaryA test apparatus that allowed the stifle to move in five degrees of freedom was used to determine the effect of graft location, graft preload, and flexion angle at the time of graft fixation on the tensile graft forces experienced by a replacement graft material used to simulate reconstruction of the cranial cruciate ligament deficient stifle. Two graft locations (tibial insertion site of the patellar ligament and tibial insertion site of the cranial cruciate ligament), two graft preloads (5 N and 20 N), and three flexion angles at the time of graft fixation (15°, 30° and 90°) were examined. The tibial insertion site and preload did not have as great an effect on graft force as did the flexion angle of the limb at time of graft fixation. Graft forces were highest when reconstructions were performed with the limb in 90° of flexion (ρ <0.0001). This study supports the notion that intracapsular grafts should be fixed with the limb in a normal standing angle.A five degree of freedom test apparatus was used to evaluate the effect of graft location, graft preload, and limb flexion angle at time of graft fixation on reconstructions of the cranial cruciate ligament deficient stifle. Our results suggest that intracapsular grafts should not be fixed with the limb in 90° of flexion, but in a normal standing angle.

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