The Elastodynamic Green’s Function for a Torsional Ring Source

1998 ◽  
Vol 65 (3) ◽  
pp. 566-568 ◽  
Author(s):  
Yichi Lu
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Legendre Function ◽  
Logarithmic Singularity ◽  
Hankel Transform ◽  
Linear Elastic ◽  
Half Degree ◽  
Homogeneous Linear ◽  
Ring Source

The elastodynamic Green’s fimction for a torsional ring source in a homogeneous, linear elastic medium is derived using the Fourier-Hankel transform. The Green’s function is found to possess the same logarithmic singularity as the Legendre function of half-degree of the second kind.

ON VOLTERRA'S DISLOCATIONS IN A SEMI-INFINITE ELASTIC MEDIUM

1958 ◽  
Vol 36 (2) ◽  
pp. 192-205 ◽  
Author(s):  
J. A. Steketee
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Displacement Field ◽  
General Problem ◽  
Function Method ◽  
Green’S Functions ◽  
Boundary Surface ◽  
Green’S Function Method ◽  
Plane Parallel

In this paper a Green's function method is developed to deal with the problem of a Volterra dislocation in a semi-infinite elastic medium in such a way that the boundary surface of the medium remains free from stresses. (A Volterra dislocation is here defined as a surface across which the displacement components show a discontinuity of the type Δu = U + Ω ×r, where U and Ω are constant vectors.) It is found that the general problem requires the construction of six sets of Green's functions. The method for the construction is outlined and applied to one of the six sets, which is of the type of two double forces with moments in a plane parallel with the boundary. The displacement field thus generated is computed. Several of the results obtained are believed to be of geophysical interest, but a more detailed discussion of these applications is postponed to a further communication which is being prepared.

On estimating the impulse response between receivers in a controlled ultrasonic experiment

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI79-SI84 ◽  
Author(s):  
K. van Wijk
Keyword(s):  
Data Processing ◽  
Laboratory Experiment ◽  
Green’S Function ◽  
Detailed Analysis ◽  
Elastic Medium ◽  
Impulse Response ◽  
Green's Function ◽  
Geophysical Data ◽  
Seismic Interferometry ◽  
Band Limited

A controlled ultrasonic laboratory experiment provides a detailed analysis of retrieving a band-limited estimate of the Green's function between receivers in an elastic medium. Instead of producing a formal derivation, this paper appeals to a series of intuitive operations, common to geophysical data processing, to understand the practicality of seismic interferometry. Whereas the retrieval of the full Green's function is based on the crosscorrelation of receivers in the presence of equipartitioned signal, an estimate of the impulse response is recovered successfully with 40 sources in a line covering six wavelengths at the surface.

Green’s function for the scattered field near the surface of a dissipative elastic medium.

2010 ◽  
Vol 127 (3) ◽  
pp. 2012-2012 ◽  
Author(s):  
Evgenia A. Zabolotskaya ◽  
Yurii A. Ilinskii ◽  
Mark F. Hamilton
Keyword(s):  
Green’S Function ◽  
Elastic Medium ◽  
Green's Function ◽  
Scattered Field

Near Field Representations of the Acoustic Green's Function in a Shallow Ocean with Fluid-Like Seabed

2007 ◽  
Vol 14 (1) ◽  
pp. 109-123
Author(s):  
Robert Gilbert ◽  
Miao-Jung Ou
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Near Field ◽  
Sound Field ◽  
Hankel Transform ◽  
Field Approximation ◽  
Construction Scheme ◽  
Stratified Ocean ◽  
Asymptotic Representations ◽  
Layer Waveguide

Abstract In this paper, the near-field approximation of the acoustic Green's function in a two-layer waveguide is constructed by using a variation of the method of Ahluwalia and Keller [Exact and asymptotic representations of the sound field in a stratified ocean, Springer, 1977]. The relation between the constructed multiple-scattering representation (suitable for near-field) and the Hankel transform representation (suitable for mid-range) is also discussed in this paper. The construction scheme presented in this paper can be generalized for an N-layer waveguide.

Unique and Explicit Formulas for Green's Function in Three-Dimensional Anisotropic Linear Elasticity

2013 ◽  
Vol 80 (5) ◽  
Author(s):  
Federico C. Buroni ◽  
Andrés Sáez
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Three Dimensional ◽  
Position Vector ◽  
Mixed Complex ◽  
Elastic Solids ◽  
Explicit Formulas ◽  
Linear Elastic ◽  
Derivatives Of ◽  
Appl Math

Unique, explicit, and exact expressions for the first- and second-order derivatives of the three-dimensional Green's function for general anisotropic materials are presented in this paper. The derived expressions are based on a mixed complex-variable method and are obtained from the solution proposed by Ting and Lee (Ting and Lee, 1997,“The Three-Dimensional Elastostatic Green's Function for General Anisotropic Linear Elastic Solids,” Q. J. Mech. Appl. Math. 50, pp. 407–426) which has three valuable features. First, it is explicit in terms of Stroh's eigenvalues pα (α=1,2,3) on the oblique plane with normal coincident with the position vector; second, it remains well-defined when some Stroh's eigenvalues are equal (mathematical degeneracy) or nearly equal (quasi-mathematical degeneracy); and third, they are exact. Therefore, both new proposed solutions inherit these appealing features, being explicit in terms of Stroh's eigenvalues, simpler, unique, exact and valid independently of the kind of degeneracy involved, as opposed to previous approaches. A study of all possible degenerate cases validate the proposed scheme.

scholarly journals Green’s Function of the Linearized Logarithmic Keller–Segel–Fisher/KPP System

2018 ◽  
Vol 23 (4) ◽  
pp. 56 ◽  
Author(s):  
Jean Rugamba ◽  
Yanni Zeng
Keyword(s):  
Nonlinear System ◽  
Green’S Function ◽  
Green's Function ◽  
Linear Problem ◽  
Logarithmic Singularity ◽  
Complete Solution ◽  
Logistic Growth ◽  
Chemotaxis Model ◽  
Logarithmic Sensitivity ◽  
Shed Light

We consider a Keller–Segel type chemotaxis model with logarithmic sensitivity and logistic growth. The logarithmic singularity in the system is removed via the inverse Hopf–Cole transformation. We then linearize the system around a constant equilibrium state, and obtain a detailed, pointwise description of the Green’s function. The result provides a complete solution picture for the linear problem. It also helps to shed light on small solutions of the nonlinear system.

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