scholarly journals Multiscale Asymptotic Analysis and Parallel Algorithm of Parabolic Equation in Composite Materials

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Xin Wang ◽  
Xi-liang Duan ◽  
Yang Gao
Keyword(s):  
Fourier Transform ◽  
Parabolic Equation ◽  
Asymptotic Analysis ◽  
Frequency Domain ◽  
Expansion Method ◽  
Convergence Result ◽  
Oscillating Coefficients ◽  
Multiscale Fem ◽  
Periodic Configuration ◽  
The Fourier Transform

An efficient parallel multiscale numerical algorithm is proposed for a parabolic equation with rapidly oscillating coefficients representing heat conduction in composite material with periodic configuration. Instead of following the classical multiscale asymptotic expansion method, the Fourier transform in time is first applied to obtain a set of complex-valued elliptic problems in frequency domain. The multiscale asymptotic analysis is presented and multiscale asymptotic solutions are obtained in frequency domain which can be solved in parallel essentially without data communications. The inverse Fourier transform will then recover the approximate solution in time domain. Convergence result is established. Finally, a novel parallel multiscale FEM algorithm is proposed and some numerical examples are reported.

A PUBLIC MESH WATERMARKING ALGORITHM BASED ON ADDITION PROPERTY OF FOURIER TRANSFORM

2006 ◽  
Vol 06 (01) ◽  
pp. 35-43 ◽  
Author(s):  
LI LI ◽  
ZHIGENG PAN ◽  
DAVID ZHANG
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Spatial Domain ◽  
Experimental Results ◽  
Original Image ◽  
The Fourier Transform

This paper presents a public mesh watermarking algorithm whereby the resultant watermarked image minus the original image is the watermark information. According to the addition property of the Fourier transform, a change of spatial domain will cause a change in the frequency domain. The watermark information is then scaled down and embedded in one part of the x-coordinate of the original mesh. Finally, the x-coordinate of the test mesh is amplified before extraction. Experimental results prove that our algorithm is resistant to a variety of attacks without the need for any preprocessing.

THEORETICAL TRANSFORMS OF THE GRAVITY ANOMALIES OF TWO IDEALIZED BODIES

Geophysics ◽  
1978 ◽  
Vol 43 (3) ◽  
pp. 631-633 ◽  
Author(s):  
Robert D. Regan ◽  
William J. Hinze
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Three Dimensional ◽  
Gravity Anomalies ◽  
Vertical Line ◽  
The Fourier Transform ◽  
Line Elements ◽  
Distribution Of Magnetization

Odegard and Berg (1965) have shown that the interpretational process can be simplified for several idealized bodies by utilizing the Fourier transform of the resultant theoretical gravity anomalies. Additional studies relating similar conclusions for other idealized bodies have been reported by Gladkii (1963), Roy (1967), Sharma et al (1970), Davis (1971), Eby (1972), and Saha (1975), and a summary of the spatial and frequency domain equations is given in Regan and Hinze (1976, Table 1); however, the transforms of the three‐dimensional prism and vertical line elements, often utilized in interpretation, have not been previously examined in this manner. Although Bhattacharyya and Chen (1977) have developed and utilized the transform of the 3-D prism in their method for determining the distribution of magnetization in a localized region, it is still of value to present the interpretive advantages of the transform equation itself.

The Remaining Cases Where m = 2 and B = 3 or B = 4

2016 ◽  
Author(s):  
Isroil A. Ikromov ◽  
Detlef Müller
Keyword(s):  
Fourier Transform ◽  
Domain Decomposition ◽  
Frequency Domain ◽  
Fourier Integral ◽  
Basic Approach ◽  
Small Letter ◽  
The Fourier Transform ◽  
Frequency Domain Decomposition

This chapter discusses the remaining cases for l = 1. With the same basic approach as in Chapter 5, the chapter again performs an additional dyadic frequency domain decomposition related to the distance to a certain Airy cone. This is needed in order to control the integration with respect to the variable x₁ in the Fourier integral defining the Fourier transform of the complex measures ν‎subscript Greek small letter delta superscript Greek small letter lamda. It first applies a suitable translation in the x₁-coordinate before performing a more refined analysis of the phase Φ‎superscript Music sharp sign. The chapter then treats the case where λ‎ρ‎(̃‎δ‎) ≲ 1 and hereafter deals with the case where λ‎ρ‎(̃‎δ‎) ≲ 1 and B = 4. Finally, the chapter turns to the case where B = 3.

scholarly journals Convergence results for compound Poisson distributions and applications to the standard Luria–Delbrück distribution

2005 ◽  
Vol 42 (03) ◽  
pp. 620-631
Author(s):  
M. Möhle
Keyword(s):  
Distribution Function ◽  
Fourier Transform ◽  
Probability Measure ◽  
Integral Representation ◽  
Convergence Result ◽  
Compound Poisson ◽  
Poisson Distributions ◽  
Convergence Results ◽  
The Fourier Transform ◽  
Related Paper

We provide a scaling for compound Poisson distributions that leads (under certain conditions on the Fourier transform) to a weak convergence result as the parameter of the distribution tends to infinity. We show that the limiting probability measure belongs to the class of stable Cauchy laws with Fourier transform t ↦ exp(−c|t|− iat log|t|). We apply this convergence result to the standard discrete Luria–Delbrück distribution and derive an integral representation for the corresponding limiting density, as an alternative to that found in a closely related paper of Kepler and Oprea. Moreover, we verify local convergence and we derive an integral representation for the distribution function of the limiting continuous Luria–Delbrück distribution.

Efficient 3D frequency response modeling with spectral accuracy by the rapid expansion method

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. T117-T123 ◽  
Author(s):  
Chunlei Chu ◽  
Paul L. Stoffa
Keyword(s):  
Fourier Transform ◽  
Frequency Response ◽  
Time Domain ◽  
Wave Equations ◽  
Time Integration ◽  
Expansion Method ◽  
Rapid Expansion ◽  
The Fourier Transform ◽  
The Time Domain ◽  
Response Modeling

Frequency responses of seismic wave propagation can be obtained either by directly solving the frequency domain wave equations or by transforming the time domain wavefields using the Fourier transform. The former approach requires solving systems of linear equations, which becomes progressively difficult to tackle for larger scale models and for higher frequency components. On the contrary, the latter approach can be efficiently implemented using explicit time integration methods in conjunction with running summations as the computation progresses. Commonly used explicit time integration methods correspond to the truncated Taylor series approximations that can cause significant errors for large time steps. The rapid expansion method (REM) uses the Chebyshev expansion and offers an optimal solution to the second-order-in-time wave equations. When applying the Fourier transform to the time domain wavefield solution computed by the REM, we can derive a frequency response modeling formula that has the same form as the original time domain REM equation but with different summation coefficients. In particular, the summation coefficients for the frequency response modeling formula corresponds to the Fourier transform of those for the time domain modeling equation. As a result, we can directly compute frequency responses from the Chebyshev expansion polynomials rather than the time domain wavefield snapshots as do other time domain frequency response modeling methods. When combined with the pseudospectral method in space, this new frequency response modeling method can produce spectrally accurate results with high efficiency.

Linear Dynamic System Identification in the Frequency Domain Using Fractional Derivatives

2010 ◽  
Vol 17 (2) ◽  
pp. 279-288 ◽  
Author(s):  
Tomasz Janiczek ◽  
Janusz Janiczek
Keyword(s):  
Fourier Transform ◽  
Dynamic System ◽  
Frequency Domain ◽  
Fractional Differential Equations ◽  
Fractional Derivatives ◽  
Linear Dynamic System ◽  
Transform Method ◽  
Linear Dynamic ◽  
Fractional Differential ◽  
The Fourier Transform

Linear Dynamic System Identification in the Frequency Domain Using Fractional DerivativesThis paper presents a study of the Fourier transform method for parameter identification of a linear dynamic system in the frequency domain using fractional differential equations. Fundamental definitions of fractional differential equations are briefly outlined. The Fourier transform method of identification and their algorithms are generalized so that they include fractional derivatives and integrals.

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