scholarly journals Rigorous time domain responses of polarizable media II

1998 ◽  
Vol 41 (3) ◽  
Author(s):  
M. Caputo ◽  
W. Plastino
Keyword(s):  
Exact Solution ◽  
Laplace Transform ◽  
Time Domain ◽  
Input Data ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Discharge Data ◽  
Time Domain Data ◽  
Previous Note ◽  
The Laplace Transform

We present and test in detail with synthetic data a method which may be used to retrieve the parameters describing the induced polarization properties of media which fit the generally accepted frequency dependent formula of Cole and Cole (1941) (CC model). We use time domain data and rigorous formulae obtained from the exact solution of the problem found in a previous note (Caputo, 1996). The observed data considered here are the theoretical responses of the medium to box inputs of given duration in media defined with different parameters; however, as is usually done, only the discharge data are used (Patella >F2<et al.>F1<, 1987). The curve at the beginning of the discharge is studied in some detail. The method is successful in identifying the parameters when the data fit the CC model; if the medium is not exactly of the CC type the method may also help identify how the medium departs from the CC model. The Laplace Transform of the discharge for a box type input data is also given.

Simple interpretation of time‐domain electromagnetic sounding using similarities between wave and diffusion propagation

Geophysics ◽  
1997 ◽  
Vol 62 (3) ◽  
pp. 763-774 ◽  
Author(s):  
Mier Gershenson
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Synthetic Data ◽  
Time Base ◽  
Time Interval ◽  
Exponential Time ◽  
The Laplace Transform ◽  
Image Function ◽  
The Time Domain ◽  
Conductive Media

By using similarities between EM sounding in dielectric and conductive media, it is shown that one can transform between solutions in one type of propagation to the other. The method is based on the similarities of the Laplace transform between diffusive and nondiffusive cases. In the diffusive case, the equation involves the Laplace variable s in the first power, while for the nondiffusive cases, similar equations occur with [Formula: see text]. Three alternative implementations are developed, and their use is demonstrated. The first implementation is based on substituting [Formula: see text] for the Laplace transform variable s using forward and inverse numerical Laplace transforms. The second implementation is based on expanding the diffusive time response on an exponential time base and replacing it with its image function in the wave case, namely, a sinusoidal function. The third implementation is based on direct transformation in the time domain using exponential time interval sampling. The performance of the techniques on synthetic data is demonstrated. Besides the advantage of simple implementation of these techniques, other advantages and limitations of the method and each of the implementations are discussed. A case history is presented. The application of common techniques used in the processing of seismic and radar for processing and EM sounding in conductive media is discussed. The use of the Poynting vector as a means of determining distance and direction is demonstrated.

scholarly journals The Mathematical Models of Lattice Functions in Modelling of Control System

2021 ◽  
Vol 2096 (1) ◽  
pp. 012149
Author(s):  
V Kramar
Keyword(s):  
Mathematical Model ◽  
Laplace Transform ◽  
Mathematical Models ◽  
Control Systems ◽  
Time Domain ◽  
Discrete Control ◽  
Automatic Control Systems ◽  
The Laplace Transform ◽  
Lattice Function ◽  
The Time Domain

Abstract The paper proposes an approach to constructing a mathematical model of lattice functions, which are mainly used in the study of discrete control systems in the time and domain of the Laplace transform. The proposed approach is based on the assumption of the physical absence of an impulse element. An alternative to the classical approach to the description of discrete data acquisition - the process of quantization in time, is considered. As a result, models of the lattice function in the time domain and the domain of the discrete Laplace transform are obtained. Based on the obtained mathematical models of lattice functions, a mathematical model of the time quantization element of the system is obtained. This will allow in the future to proceed to the construction of mathematical models of various discrete control systems, incl. expanding the proposed approaches to the construction of mathematical models of multi-cycle continuous-discrete automatic control systems

scholarly journals Discrete dipole approximation in time domain through the Laplace transform

2013 ◽  
Vol 88 (6) ◽  
Author(s):  
Patrick C. Chaumet ◽  
Ting Zhang ◽  
Adel Rahmani ◽  
Boris Gralak ◽  
Kamal Belkebir
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Dipole Approximation ◽  
Discrete Dipole Approximation ◽  
The Laplace Transform

A generalization of the Laplace transform

1967 ◽  
Vol 63 (1) ◽  
pp. 155-160 ◽  
Author(s):  
H. S. Dunn
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Finite Interval ◽  
Integral Transformation ◽  
System Response ◽  
Simple Scheme ◽  
Exponential Order ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Determine System

AbstractAn integral transformation is denned over a finite interval of the time domain. When the Laplace transform exists, the finite transform yields identical results. However, the finite transform is found to be considerably more general than the Laplace transform. It permits consideration of functions which are not of exponential order, leads to a simple scheme to determine system response, and is applicable to boundary-value problems.

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