Perturbation Theory of Wave Propagation Based on the Method of Characteristics

1955 ◽  
Vol 34 (1-4) ◽  
pp. 133-151 ◽  
Author(s):  
Phyllis A. Fox
Keyword(s):  
Wave Propagation ◽  
Perturbation Theory ◽  
Method Of Characteristics ◽  
The Method Of Characteristics

Verification of UDEC Modeling 1-D Wave Propagation in Rocks

2011 ◽  
Vol 90-93 ◽  
pp. 1998-2001
Author(s):  
Wei Dong Lei ◽  
Xue Feng He ◽  
Rui Chen
Keyword(s):  
Wave Propagation ◽  
Analytical Solution ◽  
Transmission Coefficient ◽  
Method Of Characteristics ◽  
Rock Joint ◽  
Rock Joints ◽  
Dynamic Problems ◽  
The Method Of Characteristics ◽  
Elastic Rock ◽  
D Wave

Three cases for 1-D wave propagation in ideal elastic rock, through single rock joint and multiple parallel rock joints are used to verify 1-D wave propagation in rocks. For the case for 1-D wave propagation through single rock joint, the magnitude of transmission coefficient obtained from UDEC results is compared with that obtained from the analytical solution. For 1-D wave propagation through multiple parallel joints, the magnitude of transmission coefficient obtained from UDEC results is compared with that obtained from the method of characteristics. For all these cases, UDEC results agree well with results from the analytical solutions and the method of characteristics. From these verification studies, it can be concluded that UDEC is capable of modeling 1-D dynamic problems in rocks.

Turbomachinery Waves

1977 ◽  
Vol 28 (1) ◽  
pp. 1-14 ◽  
Author(s):  
J H Horlock ◽  
H Daneshyar
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Infinite Number ◽  
Method Of Characteristics ◽  
Wave Flow ◽  
Flow Properties ◽  
The Method Of Characteristics ◽  
Flow Through ◽  
Instantaneous Values

SummaryTwo methods of analysis are developed for the unsteady wave flow through axial turbomachinery of high hub-tip ratio. In the first method, the machine is supposed to consist of an infinite number of small stages. Differential equations for the instantaneous values of flow properties are derived which may be solved directly or by the method of characteristics. Conditions for wave propagation are discussed. Secondly, a model is used in which actuator discs replace the stages and the flow is axial between the stages. This is a good approximation in many compressors in which the leaving angle from the stators is small. Again the method of characteristics may then be used for solving the equations of unsteady flow between the discs.

scholarly journals Optimal Renormalization-Group Improvement of R(s) via the Method of Characteristics

2003 ◽  
Vol 18 (19) ◽  
pp. 3417-3426 ◽  
Author(s):  
V. Elias ◽  
D. G. C. McKeon ◽  
T. G. Steele
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Closed Form ◽  
Cross Section ◽  
Method Of Characteristics ◽  
Renormalization Group Equation ◽  
Group Equation ◽  
The Method Of Characteristics ◽  
Electron Positron Annihilation ◽  
Electron Positron

We discuss the application of the method of characteristics to the renormalization-group equation for the perturbative QCD series within the electron–positron annihilation cross-section. We demonstrate how one such renormalization-group improvement of this series is equivalent to a closed-form summation of the first four towers of renormalization-group accessible logarithms to all orders of perturbation theory.

Perturbation Theory in the Method of Characteristics

Atomic Energy ◽  
2020 ◽  
Vol 127 (4) ◽  
pp. 255-258
Author(s):  
I. R. Suslov ◽  
I. V. Tormyshev
Keyword(s):  
Perturbation Theory ◽  
Method Of Characteristics ◽  
The Method Of Characteristics
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