A fast, two-point, three-dimensional raytracing algorithm using a simple step search method

1988 ◽  
Vol 78 (3) ◽  
pp. 1190-1198 ◽  
Author(s):  
W. A. Prothero ◽  
W. J. Taylor ◽  
J. A. Eickemeyer
Keyword(s):  
Simplex Method ◽  
Velocity Structure ◽  
Three Dimensional ◽  
Computer Time ◽  
Sine Wave ◽  
Search Method ◽  
Minimum Time ◽  
Circular Arc ◽  
Path Distance ◽  
Simple Step

Abstract The simplex method of function minimization is used to find the ray that follows the path of minimum time through an arbitrary three-dimensionally varying medium. The advantage of this method is that it is extremely fast, always converges, and lends itself to a variety of velocity parameterizations. The first step in the algorithm is to find the minimum time circular arc path between the source and receiver using an exhaustive search method. Then perturbations, consisting of a sum of N sine wave harmonics with their zero crossings at the endpoints, are made to the circular arc path. The simplex method searches for the amplitude coefficients that produce the path of least time. On a VAX-750 running the VMS operating system, the first arriving ray for a station receiver distance of 96 km is computed to an accuracy of 0.02 sec, computed in a southern California velocity structure using less than 26 sec of computer time. The required computer time decreases as the ray path distance decreases.

scholarly journals Comparison of Two-Equation Turbulence Models for Prediction of Heat Transfer on Film-Cooled Turbine Blades

1997 ◽  
Author(s):  
Vijay K. Garg ◽  
Ali A. Ameri
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Film Cooling ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Turbulence Models ◽  
Computer Time ◽  
Suction Surface ◽  
The Heat Transfer Coefficient

A three-dimensional Navier-Stokes code has been used to compute the heat transfer coefficient on two film-cooled turbine blades, namely the VKI rotor with six rows of cooling holes including three rows on the shower head, and the C3X vane with nine rows of holes including five rows on the shower head. Predictions of heat transfer coefficient at the blade surface using three two-equation turbulence models, specifically, Coakley’s q-ω model, Chien’s k-ε model and Wilcox’s k-ω model with Menter’s modifications, have been compared with the experimental data of Camci and Arts (1990) for the VKI rotor, and of Hylton et al. (1988) for the C3X vane along with predictions using the Baldwin-Lomax (B-L) model taken from Garg and Gaugler (1995). It is found that for the cases considered here the two-equation models predict the blade heat transfer somewhat better than the B-L model except immediately downstream of the film-cooling holes on the suction surface of the VKI rotor, and over most of the suction surface of the C3X vane. However, all two-equation models require 40% more computer core than the B-L model for solution, and while the q-ω and k-ε models need 40% more computer time than the B-L model, the k-ω model requires at least 65% more time due to slower rate of convergence. It is found that the heat transfer coefficient exhibits a strong spanwise as well as streamwise variation for both blades and all turbulence models.

Trajectory planning for coordinately operating robots

1990 ◽  
Vol 4 (3) ◽  
pp. 165-177 ◽  
Author(s):  
Y. P. Chien ◽  
Qing Xue
Keyword(s):  
Trajectory Planning ◽  
Three Dimensional ◽  
Initial Position ◽  
Minimum Time ◽  
Future Research ◽  
Rigid Object ◽  
Redundant Robots ◽  
Planning Algorithm ◽  
The Common ◽  
Joint Velocity

An efficient locally minimum-time trajectory planning algorithm for coordinately operating multiple robots is introduced. The task of the robots is to carry a common rigid object from an initial position to a final position along a given path in three-dimensional workspace in minimum time. The number of robots in the system is arbitrary. In the proposed algorithm, the desired motion of the common object carried by the robots is used as the key to planning of the trajectories of all the non-redundant robots involved. The search method is used in the trajectory planning. The planned robot trajectories satisfy the joint velocity, acceleration and torque constraints as well as the path constraints. The other constraints such as collision-free constraints, can be easily incorporated into the trajectory planning in future research.

Minimum time three dimensional interception

1978 ◽  
Vol 5 (7-8) ◽  
pp. 515-522 ◽  
Author(s):  
A.I.A. Salama ◽  
M.H. Hamza
Keyword(s):  
Three Dimensional ◽  
Minimum Time

scholarly journals P-wave crustal tomography of Greece with use of an accurate two-point ray tracer

1997 ◽  
Vol 40 (1) ◽  
Author(s):  
G. Drakatos ◽  
G. Karantonis ◽  
G. N. Stavrakakis
Keyword(s):  
Large Scale ◽  
Velocity Structure ◽  
Three Dimensional ◽  
Seismic Energy ◽  
Aegean Sea ◽  
P Wave ◽  
Low Velocity ◽  
Aegean Area ◽  
Arrival Times ◽  
Horizontal Variations

The three-dimensional velocity structure of the crust in the Aegean sea and the surrounding regions (34.0º-42.OºN, 19.0ºE-29.0ºE) is investigated by inversion of about 10000 residuals of arrival times of P-wave from local events. The resulting velocity structure shows strong horizontal variations due to the complicated crustal structure and the variations of crustal thickness. The northern part of the region generally shows high velocities. In the inner part of the volcanic arc (Southern Aegean area), relatively low velocities are observed, suggesting a large-scale absorption of seismic energy as confirmed by the low seismicity of the region. A low velocity zone was observed along the subduction zone of the region, up to a depth of 4 km. The existence of such a zone could be due to granitic or other intrusions in the crust during the uplift of the region during Alpidic orogenesis.

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