scholarly journals Laplace transform inversion for late-time behavior of groundwater flow problems

2003 ◽  
Vol 39 (10) ◽  
Author(s):  
Simon A. Mathias ◽  
Robert W. Zimmerman
Keyword(s):  
Laplace Transform ◽  
Groundwater Flow ◽  
Late Time ◽  
Time Behavior ◽  
Flow Problems ◽  
Laplace Transform Inversion

Laplace transform inversion through the theta algorithm for power-system EMT analysis

2021 ◽  
Vol 197 ◽  
pp. 107342
Author(s):  
L.J. Castañón ◽  
J.L. Naredo ◽  
J.R. Zuluaga ◽  
E. Bañuelos-Cabral ◽  
Pablo Gómez
Keyword(s):  
Power System ◽  
Laplace Transform ◽  
Laplace Transform Inversion

scholarly journals Late Time Attractors of Some Varying Chaplygin Gas Cosmological Models

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 769
Author(s):  
Martiros Khurshudyan ◽  
Ratbay Myrzakulov
Keyword(s):  
Dark Energy ◽  
Gravitational Interaction ◽  
Chaplygin Gas ◽  
Cosmological Models ◽  
Late Time ◽  
Time Behavior ◽  
Coincidence Problem ◽  
Energy Models ◽  
Non Linear ◽  
Bayesian Machine Learning

The goal of this paper is to study new cosmological models where the dark energy is a varying Chaplygin gas. This specific dark energy model with non-linear EoS had been often discussed in modern cosmology. Contrary to previous studies, we consider new forms of non-linear non-gravitational interaction between dark matter and assumed dark energy models. We applied the phase space analysis allowing understanding the late time behavior of the models. It allows demonstrating that considered non-gravitational interactions can solve the cosmological coincidence problem. On the other hand, we applied Bayesian Machine Learning technique to learn the constraints on the free parameters. In this way, we gained a better understanding of the models providing a hint which of them can be ruled out. Moreover, the learning based on the simulated expansion rate data shows that the models cannot solve the H0 tension problem.

The solution of theoretical seismic problems by best rational function approximations for Laplace transform inversion

1975 ◽  
Vol 65 (4) ◽  
pp. 927-935
Author(s):  
I. M. Longman ◽  
T. Beer
Keyword(s):  
Laplace Transform ◽  
Rational Function ◽  
High Accuracy ◽  
Time Variable ◽  
Inversion Method ◽  
The Laplace Transform ◽  
Previously Treated ◽  
The Mean ◽  
Function Approximations ◽  
Laplace Transform Inversion

Abstract In a recent paper, the first author has developed a method of computation of “best” rational function approximations ḡn(p) to a given function f̄(p) of the Laplace transform operator p. These approximations are best in the sense that analytic inversion of ḡn(p) gives a function gn(t) of the time variable t, which approximates the (generally unknown) inverse f(t) of f̄(p in a minimum least-squares manner. Only f̄(p) but not f(t) is required to be known in order to carry out this process. n is the “order” of the approximation, and it can be shown that as n tends to infinity gn(t) tends to f(t) in the mean. Under suitable conditions on f(t) the convergence is extremely rapid, and quite low values of n (four or five, say) are sufficient to give high accuracy for all t ≧ 0. For seismological applications, we use geometrical optics to subtract out of f(t) its discontinuities, and bring it to a form in which the above inversion method is very rapidly convergent. This modification is of course carried out (suitably transformed) on f̄(p), and the discontinuities are restored to f(t) after the inversion. An application is given to an example previously treated by the first author by a different method, and it is a certain vindication of the present method that an error in the previously given solution is brought to light. The paper also presents a new analytical method for handling the Bessel function integrals that occur in theoretical seismic problems related to layered media.

scholarly journals The duality principle and new forms of the inverse Laplace transform for the analysis of signal propagation in inhomogeneous media with dispersion

2019 ◽  
Vol 489 (6) ◽  
pp. 558-563
Author(s):  
A. G. Pavelyev ◽  
A. A. Pavelyev
Keyword(s):  
Laplace Transform ◽  
Impulse Response ◽  
Angular Spectrum ◽  
Signal Propagation ◽  
Inhomogeneous Media ◽  
Inverse Laplace Transform ◽  
Duality Principle ◽  
Causality Principle ◽  
Speed Of Light ◽  
Laplace Transform Inversion

New equations for Laplace transform inversion are obtained. The equations satisfy the causality principle. The impulse response of a channel is determined in order to analyze dispersion distortions in inhomogeneous media. The impulse response excludes the possibility that the signal exceeds the speed of light in the medium. The transmission bandwidth, the angular spectrum, and the Doppler shift in the ionosphere are computed.

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