scholarly journals Semi-analytical solution for consolidation of vertical drain to unsaturated soils considering well resistance and smear effect under time-varying loadings

2020 ◽  
Vol 198 ◽  
pp. 02033
Author(s):  
Aifang Qin ◽  
Lianghua Jiang ◽  
Linzhong Li ◽  
Xinhao Li
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Unsaturated Soils ◽  
Inverse Laplace Transform ◽  
Loading Frequency ◽  
Time Varying ◽  
Numerical Inverse Laplace Transform ◽  
Vertical Drain ◽  
Special Cases ◽  
The Time Domain

In this paper, based on equal-strain assumption a semi-analytical solution, considering well re-sistance, smear effect and time-varying loading, is deduced for radial consolidation aided by vertical drain (VD) to unsaturated soils. Firstly, by employing the general integration, Laplace transform, decoupling methods and numerical inverse Laplace transform, the semi-analytical solution in the time domain is ob-tained. Then, its validity is verified by the special cases of the proposed solution under instantaneous loading. Finally, the case analysis show that the dissipation of excess pore pressures is accelerated with the decrease of smear coefficients (αa or αw) or well resistance factors (Ga or Gw). In addition, when the well resistance factor is less than 1, the barrier of VD material to flow can be ignored. Furthermore, a smaller value of the loading frequency of cyclic loading, the bigger the amplitude, and the less fluctuation period in the dissipa-tion rates. Moreover, the current solution can analyse the consolidation characteristics of unsaturated soils with VDs under arbitrary time-varying loadings, including cyclic loadings.

scholarly journals Laplace Transform for Finite Element Analysis of Electromagnetic Interferences in Underground Metallic Structures

2022 ◽  
Vol 12 (2) ◽  
pp. 872
Author(s):  
Andrea Cristofolini ◽  
Arturo Popoli ◽  
Leonardo Sandrolini ◽  
Giacomo Pierotti ◽  
Mattia Simonazzi
Keyword(s):  
Finite Element ◽  
Laplace Transform ◽  
Electromagnetic Interference ◽  
Inverse Laplace Transform ◽  
Element Analysis ◽  
Metallic Structures ◽  
Numerical Inverse Laplace Transform ◽  
Transient Electromagnetic ◽  
The Time Domain ◽  
High Voltage Power Lines

A numerical methodology is proposed for the calculation of transient electromagnetic interference induced by overhead high-voltage power lines in metallic structures buried in soil—pipelines for oil or gas transportation. A series of 2D finite element simulations was employed to sample the harmonic response of a given geometry section. The numerical inverse Laplace transform of the results allowed obtaining the time domain evolution of the induced voltages and currents in the buried conductors, for any given condition of the power line.

Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. Toutain ◽  
J.-L. Battaglia ◽  
C. Pradere ◽  
J. Pailhes ◽  
A. Kusiak ◽  
...  
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Periodic Function ◽  
Thermal Characterization ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Time Resolved ◽  
Reliable Technique ◽  
Numerical Inverse Laplace Transform ◽  
Thermal Disturbance

The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.

Analytical solutions of citrate–phosphate coupled model of rice (Oryza sativa L.) roots

2020 ◽  
Vol 13 (07) ◽  
pp. 2050061
Author(s):  
Huiping Zhang ◽  
Shuyue Wang ◽  
Zhonghui Ou
Keyword(s):  
Oryza Sativa ◽  
Analytical Solution ◽  
Laplace Transform ◽  
Oryza Sativa L ◽  
Coupled Model ◽  
Inverse Laplace Transform ◽  
Citrate Solution ◽  
Separation Variable ◽  
The Laplace Transform ◽  
Citrate Phosphate

The citrate secreted by the rice (Oryza sativa L.) roots will promote the absorption of phosphate, and this process is described by the Kirk model. In our work, the Kirk model is divided into citrate sub-model and phosphate sub-model. In the citrate sub-model, we obtain the analytical solution of citrate with the Laplace transform, inverse Laplace transform and convolution theorem. The citrate solution is substituted into the phosphate sub-model, and the analytical solution of phosphate is obtained by the separation variable method. The existence of the solutions can be proved by the comparison test, the Weierstrass M-test and the Abel discriminating method.

scholarly journals Computer-Aided Numerical Inversion of Laplace Transform

2000 ◽  
Vol 22 (3) ◽  
pp. 189-213 ◽  
Author(s):  
Umesh Kumar
Keyword(s):  
Laplace Transform ◽  
Probability Density Functions ◽  
Numerical Inversion ◽  
Time Varying ◽  
Inversion Technique ◽  
Computer Aided ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Time Invariant ◽  
Exponential Probability

This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

scholarly journals A unified inverse Laplace transform formula involving the product of a general class of polynomials and the Fox $H$-function

2005 ◽  
Vol 36 (2) ◽  
pp. 87-92
Author(s):  
R. C. Soni ◽  
Deepika Singh
Keyword(s):  
Laplace Transform ◽  
General Class ◽  
Special Functions ◽  
Inverse Laplace Transform ◽  
General Class Of Polynomials ◽  
Special Cases ◽  
Main Formula

In the present paper we obtain the inverse Laplace transform of the product of a general class of polynomials and the Fox $H$-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in nature. Therefore, the inverse Laplace transform of the product of a large variety of polynomials and numerous simple special functions can be obtained as simple special cases of our main result. The results obtained by Gupta and Soni [2] and Srivastava [5] follow as special cases of our main result.

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