scholarly journals The Fourier analysis technique and epsilon-pseudo-eigenvalues

1993 ◽  
Author(s):  
J.M. Donato
Keyword(s):  
Fourier Analysis ◽  
Analysis Technique ◽  
Fourier Analysis Technique

Motion at an Explosive Source as Deduced From Surface Waves

1960 ◽  
Vol 31 (1-2) ◽  
pp. 5-17
Author(s):  
Carl Kisslinger
Keyword(s):  
Fourier Analysis ◽  
Vertical Acceleration ◽  
Analysis Method ◽  
Phase Velocities ◽  
The Earth ◽  
Analysis Technique ◽  
Explosive Source ◽  
History Of ◽  
Frequency Components ◽  
Fourier Analysis Technique

Abstract The history of events occurring near the source following a small explosion has been deduced from the Rayleigh waves recorded at two distances. The Fourier analysis method developed by Sato, and Lamb’s solution for the displacement on a half-space have been employed in two distinct approaches to this problem. The displacement history from the first approach shows an essentially rectilinear vibration of the earth partiele, following the initial compression. The second technique yields the vertical point force equivalent to the explosion. The vertical acceleration at the source from the first method agrees fairly well in general form with the force found in the second. Information about the phase velocities and the initial phases of the constituent frequency components is a valuable by product of the Fourier analysis technique.

Improvements to the molecular beam Fourier analysis technique

1984 ◽  
Vol 17 (4) ◽  
pp. 485-496 ◽  
Author(s):  
E.A. Kurz ◽  
J.B. Hudson
Keyword(s):  
Fourier Analysis ◽  
Molecular Beam ◽  
Analysis Technique ◽  
Fourier Analysis Technique

An In Situ XRD Technique For Annealing Investigations

1994 ◽  
Vol 38 ◽  
pp. 757-762
Author(s):  
D.E. Koylman ◽  
S.C. Axtel ◽  
B.W. Robertson
Keyword(s):  
Activation Energy ◽  
High Temperature ◽  
Copper Powder ◽  
Diffraction Data ◽  
Particle Growth ◽  
Annealing Behavior ◽  
In Situ Xrd ◽  
Analysis Technique ◽  
Fourier Analysis Technique

Abstract An in situ XRD technique employing a diffractometer equipped with a high temperature camera was used to investigate the annealing behavior of nanoerystalline copper powder produced by mechanical milling. Specimens were annealed isothermally for 12 h at temperatures between 480 and 770 K. The diffraction data was analyzed using a single-profile Fourier analysis technique. The activation energy for diffracting particle growth was determined to be 0.45 eV/atom.

scholarly journals Error Estimates for Solutions of the Semilinear Parabolic Equation in Whole Space

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaomei Hu
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Error Estimates ◽  
Three Dimensional ◽  
Semilinear Parabolic Equation ◽  
Energy Methods ◽  
Analysis Technique ◽  
Whole Space ◽  
Fourier Analysis Technique ◽  
Semilinear Parabolic

This paper is focused on the error estimates for solutions of the three-dimensional semilinear parabolic equation with initial datau0∈L2(ℝ3). Employing the energy methods and Fourier analysis technique, it is proved that the error between the solution of the semilinear parabolic equation and that of linear heat equation has the behavior asO((1+t)−3/8).

Influences of an Initial Micro Gap on Wave Transmission

2010 ◽  
Vol 29-32 ◽  
pp. 2662-2667
Author(s):  
Xiao Yun Chen ◽  
Gui Lan Yu
Keyword(s):  
Elastic Waves ◽  
Frictional Contact ◽  
Superposition Method ◽  
Energy Partition ◽  
Non Destructive Evaluation ◽  
Analysis Technique ◽  
Fourier Analysis Technique ◽  
Propagation Of Elastic Waves ◽  
Non Destructive ◽  
Gap Width

The propagation of elastic waves through a micro gap considering frictional contact is investigated in the present paper. Using the Fourier analysis technique and corrective solution superposition method, the problem is solved analytically. Special examples for identical materials are discussed in detail. The results show that the initial gap width has significant influences on the harmonics and energy partition and their relations may be effective on non-destructive evaluation of a pre-existing gap.

scholarly journals AlgebraicL2Decay for Weak Solutions of the Nonlinear Heat Equations in Whole SpaceR3

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Yuexing Yang
Keyword(s):  
Weak Solutions ◽  
Nonlinear Term ◽  
Heat Equations ◽  
Energy Methods ◽  
Time Decay ◽  
Analysis Technique ◽  
Nonlinear Heat Equations ◽  
Whole Space ◽  
Fourier Analysis Technique ◽  
Time Decay Rate

We obtained the algebraicL2time decay rate for weak solutions of the nonlinear heat equations with the nonlinear term∇u2uin whole spaceR3. The methods are based on energy methods and Fourier analysis technique.

Energy Partition of Harmonic Waves through a Micro Gap

2011 ◽  
Vol 66-68 ◽  
pp. 1428-1433
Author(s):  
Xiao Yun Chen ◽  
Gui Lan Yu
Keyword(s):  
Incident Angle ◽  
Superposition Method ◽  
Harmonic Waves ◽  
Algebraic Equations ◽  
Energy Partition ◽  
Analysis Technique ◽  
Nonlinear Boundary Problem ◽  
Fourier Analysis Technique ◽  
Incident Waves ◽  
Gap Width

Energy partition of harmonic waves through a micro gap considering frictional contact was investigated. The incident waves were assumed to be strong enough to make the two solids come into contact. Using the Fourier analysis technique and corrective solution superposition method, the nonlinear boundary problem was reduced to a set of algebraic equations. Special examples for identical materials were discussed in detail. The locations and extents of the separation, slip and stick zones and the energy partition are displayed. Moreover, the effects of gap width, coefficients of friction and incident angle are discussed. These relations are quite effective on seismology and civil engineering.

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