Longitudinal Impact of a Semi-Infinite, Cylindrical, Viscoelastic Shell

1965 ◽  
Vol 32 (4) ◽  
pp. 813-820 ◽  
Author(s):  
R. B. Testa ◽  
H. H. Bleich
Keyword(s):  
Laplace Transform ◽  
Error Estimates ◽  
Asymptotic Methods ◽  
Elastic Shell ◽  
Longitudinal Impact ◽  
Viscoelastic Shell ◽  
Viscous Effects ◽  
The Laplace Transform ◽  
Oscillatory Character ◽  
Cylindrical Viscoelastic Shell

The response of a semi-infinite, cylindrical, viscoelastic shell to longitudinal impact is studied using the Laplace transform. The evaluation by asymptotic methods for large values of time also gives error estimates defining the range of applicability. It is found that, at sufficiently large distances from the point of impact, the oscillatory character of the response of an elastic shell to longitudinal impact is suppressed by viscous effects, resulting in nearly identical solutions for a viscoelastic shell and for an infinitely thin viscoelastic rod of the same material. In addition, it is shown that the solutions for shell and rod, with limitations, are also nearly identical for smaller values of time, where nonasymptotic solutions for the rod apply.

scholarly journals On Maxima and Ladder Processes for a Dense Class of Lévy Process

2006 ◽  
Vol 43 (01) ◽  
pp. 208-220 ◽  
Author(s):  
Martijn Pistorius
Keyword(s):  
Laplace Transform ◽  
Error Estimates ◽  
Lévy Process ◽  
Iterative Procedure ◽  
Levy Process ◽  
Distribution Of The Maximum ◽  
Phase Type ◽  
The Laplace Transform ◽  
The Law ◽  
Dense Class

In this paper, we present an iterative procedure to calculate explicitly the Laplace transform of the distribution of the maximum for a Lévy process with positive jumps of phase type. We derive error estimates showing that this iteration converges geometrically fast. Subsequently, we determine the Laplace transform of the law of the upcrossing ladder process and give an explicit pathwise construction of this process.

scholarly journals On Maxima and Ladder Processes for a Dense Class of Lévy Process

2006 ◽  
Vol 43 (1) ◽  
pp. 208-220 ◽  
Author(s):  
Martijn Pistorius
Keyword(s):  
Laplace Transform ◽  
Error Estimates ◽  
Lévy Process ◽  
Iterative Procedure ◽  
Levy Process ◽  
Distribution Of The Maximum ◽  
Phase Type ◽  
The Laplace Transform ◽  
The Law ◽  
Dense Class

In this paper, we present an iterative procedure to calculate explicitly the Laplace transform of the distribution of the maximum for a Lévy process with positive jumps of phase type. We derive error estimates showing that this iteration converges geometrically fast. Subsequently, we determine the Laplace transform of the law of the upcrossing ladder process and give an explicit pathwise construction of this process.

The Vibrations of an Infinite Orthotropic Layered Cylindrical Viscoelastic Shell in an Acoustic Medium

1976 ◽  
Vol 43 (4) ◽  
pp. 668-670 ◽  
Author(s):  
B. S. Berger
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Solution ◽  
Finite Difference Scheme ◽  
Elastic Shell ◽  
Numerical Results ◽  
Acoustic Medium ◽  
Viscoelastic Shell ◽  
Cylindrical Viscoelastic Shell ◽  
Acoustic Fluid

In the following a numerical solution is given for the vibration of an orthotropic layered cylindrical viscoelastic shell in an acoustic medium. The acoustic fluid is modeled through a finite-difference scheme. Numerical results for the elastic shell in an acoustic medium agree with previous solutions.

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

scholarly journals Algebraic inversion of the Laplace transform

2005 ◽  
Vol 50 (1-2) ◽  
pp. 179-185 ◽  
Author(s):  
P.G. Massouros ◽  
G.M. Genin
Keyword(s):  
Laplace Transform ◽  
The Laplace Transform
Sign in / Sign up

Export Citation Format

Share Document