scholarly journals Simple and Exact Closed-Form Expression for Determination of a Penetrated Ray Path in a Ray Tracing

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Hyun Wook Moon ◽  
Woojoong Kim ◽  
Sewoong Kwon ◽  
Jaeheung Kim ◽  
Young Joong Yoon
Keyword(s):  
Closed Form ◽  
Approximate Method ◽  
Ray Tracing ◽  
Conventional Method ◽  
Closed Form Expression ◽  
Indoor Environments ◽  
Straight Line ◽  
Ray Path ◽  
Ray Tracing Simulation

A simple and exact closed-form equation to determine a penetrated ray path in a ray tracing is proposed for an accurate channel prediction in indoor environments. Whereas the penetrated ray path in a conventional ray tracing is treated as a straight line without refraction, the proposed method is able to consider refraction through the wall in the penetrated ray path. Hence, it improves the accuracy in ray tracing simulation. To verify the validation of the proposed method, the simulated results of conventional method, approximate method, and proposed method are compared with the measured results. The comparison shows that the proposed method is in better agreement with the measured results than the conventional method and approximate method, especially in high frequency bands.

Conditions for Translation and Rotation of Bodies on Frictional Surfaces

1991 ◽  
Vol 205 (5) ◽  
pp. 311-316
Author(s):  
D Nowell ◽  
D A Hills ◽  
R L Munisamy
Keyword(s):  
Closed Form ◽  
Numerical Technique ◽  
Closed Form Expression ◽  
Frictional Surface ◽  
Form Expression ◽  
Straight Line ◽  
Frictional Surfaces

This paper is concerned with the quasi-static motion of a body resting on a frictional surface when subjected to an arbitrary imposed displacement by a small frictionless finger. A simplified object with three distinct feet is used as an illustration but the method adopted can be generalized to bodies with more feet or distributed contact. A closed-form expression is found which enables the determination of the conditions necessary for a body to rotate about a point of support and a more general numerical technique for determining the instantaneous centre is presented. The indeterminacy that occurs when the points of support lie in a straight line is also discussed.

A multilinear interaction model: algorithms for Kalai-Smorodinsky solution

2017 ◽  
Vol 3 (1) ◽  
pp. 47 ◽  
Author(s):  
Alessia Donato
Keyword(s):  
Closed Form ◽  
Interaction Model ◽  
Critical Zone ◽  
Dimensional Case ◽  
Compromise Solution ◽  
3 Dimensional ◽  
Straight Line

We implement Matlab algorithms for the construction and representation of the payoff space in a certain applicable game models, in 2 and 3 dimensions. More- over our algorithms can find the Kalai-Smorodinsky solutions in the same game with some interfering elements. We write down the intersection of the critical zone and the Kalai-Smorodinsky straight-line for finding the compromise solution. We propose a software for the determination of the graphs. In the Appendix we solve the problem in closed form for the 2 and 3 dimensional case and numerical ly for n = 7.

scholarly journals An adjusted location model for SuperDARN backscatter echoes

2012 ◽  
Vol 30 (12) ◽  
pp. 1769-1779 ◽  
Author(s):  
E. X. Liu ◽  
H. Q. Hu ◽  
R. Y. Liu ◽  
Z. S. Wu ◽  
M. Lester
Keyword(s):  
Ray Tracing ◽  
Elevation Angle ◽  
Location Model ◽  
Data Sets ◽  
Data Set ◽  
Straight Line ◽  
The Difference ◽  
Adjusted Model ◽  
Standard Software

Abstract. The radars that form the Super Dual Auroral Radar Network (SuperDARN) receive scatter from ionospheric irregularities in both the E- and F-regions, as well as the Earth's surface, either ground or sea. For ionospheric scatter, the current SuperDARN standard software considers a straight-line propagation from the radar to the scattering zone with an altitude assigned by a standard height model. The knowledge of the group delay to a scatter volume is not sufficient for an exact determination of the location of the irregularities. In this study, the difference between the locations of the backscatter echoes determined by SuperDARN standard software and by ray tracing has been evaluated, using the ionosonde data collected at Sodankylä, which is in the field-of-view of Hankasalmi SuperDARN radar. By studying elevation angle information of backscattered echoes from the data sets of Hankasalmi radar in 2008, we have proposed an adjusted fitting location model determined by slant range and elevation angle. To test the reliability of the adjusted model, an independent data set is selected in 2009. The result shows that the difference between the adjusted model and the ray tracing is significantly reduced and the adjusted model could provide a more accurate location for backscatter targets.

Rotation–Vibration Coupling in Diatomic Molecules and the Factorization Method. II. Closed Form Formulas for the Morse–Pekeris Intensities

1974 ◽  
Vol 52 (2) ◽  
pp. 110-119 ◽  
Author(s):  
M. Badawi ◽  
N. Bessis ◽  
G. Bessis ◽  
G. Hadinger
Keyword(s):  
Dipole Moment ◽  
Closed Form ◽  
Explicit Expression ◽  
Factorization Method ◽  
Closed Form Expression ◽  
Matrix Elements ◽  
Moment Matrix ◽  
Form Expression ◽  
Vibration Coupling

It is shown that, by applying an "accelerated" ladder operatorial formalism or an equivalent matrix procedure, one can obtain, easily, for the case of a Morse–Pekeris potential, a closed form expression of the rotation–vibration nuclear dipole moment matrix elements. This explicit expression, which is valid for any degree k of the dipole moment Taylor's expansion, allows the determination of the rotation–vibration intensities for any ΩνJ → Ω′ν′J′ transition.

Determination of radar coverage diagrams in complex environments using closed form ray tracing

Radio Science ◽  
1991 ◽  
Vol 26 (1) ◽  
pp. 45-50
Author(s):  
Shakir Abdulla ◽  
Samir Raouf ◽  
Abdulamir Al-anbari ◽  
Ashraf Kadri
Keyword(s):  
Closed Form ◽  
Ray Tracing ◽  
Complex Environments

scholarly journals Analysis of Simulated and Measured Indoor Channels for mm-Wave Beamforming Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-17 ◽  
Author(s):  
Anders Karstensen ◽  
Wei Fan ◽  
Fengchun Zhang ◽  
Jesper Ø. Nielsen ◽  
Gert F. Pedersen
Keyword(s):  
Ray Tracing ◽  
Beam Steering ◽  
Horn Antenna ◽  
Indoor Environments ◽  
Channel Measurements ◽  
Single Beam ◽  
Multiple Beams ◽  
Single User ◽  
Ray Tracing Simulation ◽  
Receive Antenna

Ray tracing- (RT-) assisted beamforming, where beams are directly steered to dominant paths tracked by ray tracing simulations, is a promising beamforming strategy, since it avoids the time-consuming exhaustive beam searching adopted in conventional beam steering strategies. The performance of RT-assisted beamforming depends directly on how accurate the spatial profiles of the radio environment can be predicted by the RT simulation. In this paper, we investigate how ray tracing-assisted beamforming performs in both poorly furnished and richly furnished indoor environments. Single-user beamforming performance was investigated using both single beam and multiple beams, with two different power allocation schemes applied to multibeamforming. Channel measurements were performed at 28–30 GHz using a vector network analyzer equipped with a biconical antenna as the transmit antenna and a rotated horn antenna as the receive antenna. 3D ray tracing simulations were carried out in the same replicated propagation environments. Based on measurement and ray tracing simulation data, it is shown that RT-assisted beamforming performs well both for single and multibeamforming in these two representative indoor propagation environments.

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