Laser-Induced Heating of a Multilayered Medium Resting on a Half-Space: Part I—Stationary Source

1988 ◽  
Vol 55 (1) ◽  
pp. 93-97 ◽  
Author(s):  
R. Kant
Keyword(s):  
Laplace Transform ◽  
Half Space ◽  
Hankel Transform ◽  
Optical Recording ◽  
Time Intervals ◽  
Homogeneous Half Space ◽  
Multilayered Medium ◽  
Rule Application ◽  
The Laplace Transform ◽  
The Time Domain

Laser induced heating of a multilayered medium resting on a homogeneous half-space is considered. The transient heat transfer equation is solved by employing the Laplace transform in the time domain and the Hankel transform in the space domain (r direction). Numerical inversion of the Laplace transform is obtained by using a technique developed by Crump. For the time intervals of interest, inversion of the Hankel transform is obtained by the Simpson rule. Application to magneto-optical recording is discussed.

Laser-Induced Heating of a Multilayered Medium Resting on a Half-Space: Part II—Moving Source

1991 ◽  
Vol 113 (1) ◽  
pp. 12-20 ◽  
Author(s):  
R. Kant ◽  
K. L. Deckert
Keyword(s):  
Fourier Transform ◽  
Laplace Transform ◽  
Half Space ◽  
Disk Surface ◽  
Optical Recording ◽  
Direct Access ◽  
Laser Source ◽  
Magnetic Medium ◽  
Multilayered Medium ◽  
The Laplace Transform

Direct access storage devices (DASDs) are widely used in the computer industry to store and manage data. In conventional magnetic recording, an induction head flying very close to the disk surface alters the polarization of the magnetic field of the disk surface to erase and/or write the information on the disk. However, a new technology known as magneto-optical recording or optical recording has considerable promise to increase data densities and reliability of data storage. In magneto-optical storage, magnetic fields are altered by a laser source, which heats the magnetic medium beyond its Curie point, a temperature at which the magnetic medium loses its magnetization. This domain with zero magnetization is subsequently reversed by using an induction magnet. All these processes take place when the disk is rotating at a very high speed with respect to the laser source. An optical disk is a multilayered medium consisting of a thick glass disk on which many layers of different materials are sputtered, only one layer of which serves as a magnetic medium. Therefore, in this paper, a problem of laser-induced heating of a multilayered medium resting on a half-space is considered when the laser is translating with respect to it. The transient heat conduction equation is solved by employing the Laplace transform in the time domain and the Fourier Transform in the x, y dimensions. The resulting ordinary differential equation is solved and the inversion of the Laplace transform is obtained by a technique developed by Crump. The Fourier inversion is obtained by using a Fast Fourier Transform. The technique developed here is then applied to calculate domain size for recorded bits for a given disk, laser power, source characteristics, and rotational velocity.

scholarly journals A Relation between Laplace and Hankel Transforms

1962 ◽  
Vol 5 (3) ◽  
pp. 114-115 ◽  
Author(s):  
B. R. Bhonsle
Keyword(s):  
Laplace Transform ◽  
Hankel Transform ◽  
Laplace And Hankel Transforms ◽  
Hankel Transforms ◽  
The Laplace Transform ◽  
Image Position

The Laplace transform of a function f(t) ∈ L(0, ∞) is defined by the equationand its Hankel transform of order v is defined by the equationThe object of this note is to obtain a relation between the Laplace transform of tμf(t) and the Hankel transform of f(t), when ℛ(μ) > − 1. The result is stated in the form of a theorem which is then illustrated by an example.

Computation of Green’s tensor integrals for three‐dimensional electromagnetic problems using fast Hankel transforms

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1754-1759 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Hankel Transform ◽  
Electromagnetic Modeling ◽  
Electromagnetic Problems ◽  
Hankel Transforms ◽  
Homogeneous Half Space ◽  
Green's Tensor ◽  
Green’S Tensor ◽  
The Many

A new method is presented that rapidly evaluates the many Green’s tensor integrals encountered in three‐dimensional electromagnetic modeling using an integral equation. Application of a fast Hankel transform (FHT) algorithm (Anderson, 1982) is the basis for the new solution, where efficient and accurate computation of Hankel transforms are obtained by related and lagged convolutions (linear digital filtering). The FHT algorithm is briefly reviewed and compared to earlier convolution algorithms written by the author. The homogeneous and layered half‐space cases for the Green’s tensor integrals are presented in a form so that the FHT can be easily applied in practice. Computer timing runs comparing the FHT to conventional direct convolution methods are discussed, where the FHT’s performance was about 6 times faster for a homogeneous half‐space, and about 108 times faster for a five‐layer half‐space. Subsequent interpolation after the FHT is called is required to compute specific values of the tensor integrals at selected transform arguments; however, due to the relatively small lagged convolution interval used (same as the digital filter’s), a simple and fast interpolation is sufficient (e.g., by cubic splines).

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 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 Analytical Solution for the Sound Radiation Field of a Viscoelastically Supported Beam Traversed by a Moving Load

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Rezgar Shakeri ◽  
Davood Younesian
Keyword(s):  
Laplace Transform ◽  
Acoustic Pressure ◽  
Moving Load ◽  
Sound Radiation ◽  
Dynamic Responses ◽  
Integral Approach ◽  
Design Parameters ◽  
Transform Method ◽  
The Laplace Transform ◽  
The Time Domain

Sound radiation from a beam resting on a viscoelastic foundation is analytically studied when it is subjected to a moving load. The topic could cover a range of applications such as submerged floating tunnels, buried pipelines, and railway tracks. Galerkin’s method is employed to obtain the transverse vibration of the beam. Based on the Rayleigh integral approach, acoustic pressure distribution around the beam is obtained in the time domain. In the second part of this paper, corresponding displacement and acoustic pressure are obtained by the use of the Rayleigh-Ritz approach in conjunction with the Laplace transform method and by the use of the Fourier transform, respectively. Durbin’s numerical Laplace transform inversion scheme is eventually employed to obtain dynamic responses. A parametric study is then carried out and influences of the design parameters as well as the loading conditions on the acoustic pressure field are investigated.

scholarly journals On the integral of geometric Brownian motion

2003 ◽  
Vol 35 (1) ◽  
pp. 159-183 ◽  
Author(s):  
Michael Schröder
Keyword(s):  
Brownian Motion ◽  
Integral Representation ◽  
Laplace Transform ◽  
Finite Time ◽  
Integral Representations ◽  
Geometric Brownian Motion ◽  
Bessel Processes ◽  
Time Intervals ◽  
The Laplace Transform ◽  
The Law

This paper studies the law of any real powers of the integral of geometric Brownian motion over finite time intervals. As its main results, an apparently new integral representation is derived and its interrelations with the integral representations for these laws originating by Yor and by Dufresne are established. In fact, our representation is found to furnish what seems to be a natural bridge between these other two representations. Our results are obtained by enhancing the Hartman-Watson Ansatz of Yor, based on Bessel processes and the Laplace transform, by complex analytic techniques. Systematizing this idea in order to overcome the limits of Yor's theory seems to be the main methodological contribution of the paper.

Transient Response of an Elastic Homogeneous Half-Space to Suddenly Applied Rectangular Loading

1994 ◽  
Vol 61 (2) ◽  
pp. 256-263 ◽  
Author(s):  
F. Guan ◽  
M. Novak
Keyword(s):  
Laplace Transform ◽  
Half Space ◽  
Transient Response ◽  
Integral Kernel ◽  
Closed Form Solution ◽  
Contact Problems ◽  
Form Solution ◽  
Inverse Laplace Transform ◽  
Line Load ◽  
Homogeneous Half Space

A closed-form solution of transient response to suddenly applied loading distributed over a rectangular area on the surface of an elastic homogeneous half-space is developed for special purposes such as analysis of dynamic soil-structure interaction or contact problems. The solution is obtained using Laplace transform with respect to time and Fourier transform with respect to space. Inverse Laplace transform is implemented analytically. As extreme cases of rectangular loading, the solutions for a point force or finite line load can also be obtained. The advantages of this solution over most other solutions by numerical analyses are that the multiple integrations are reduced by one order, the singularity is removed from the integral kernel, and no additional discretization in the vicinity of the region of interest is required.

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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