Exact form of the exponential correlation function in the glassy super-rough phase

Acoustic impedance is modeled as a special type of Markov chain, one which is constrained to have a purely exponential correlation function. The stochastic model is parsimoniously described by M parameters, where M is the number of states or rocks composing an impedance well log. The probability mass function of the states provides M-1 parameters, and the “blockiness” of the log determines the remaining degree of freedom. Synthetic impedance and reflectivity logs constructed using the Markov model mimic the blockiness of the original logs. Both synthetic impedance and reflectivity are shown to be Bussgang, i.e., if the sequence is input into an instantaneous nonlinear device, then the correlation of input and output is proportional to the autocorrelation of the input. The final part of the paper uses the stochastic model in formulating an algorithm that transforms a deconvolved seismogram into acoustic impedance. The resulting function is blocky and free of random walks or sags. Low‐frequency information, as provided by moveout velocities, can be easily incorporated into the algorithm.

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Effects of a Fluctuating Carrying Capacity on the Generalized Malthus-Verhulst Model

Advances in Mathematical Physics ◽

10.1155/2014/597012 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

Author(s):

Héctor Calisto ◽

Kristopher J. Chandía ◽

Mauro Bologna

Keyword(s):

Correlation Function ◽

Population Growth ◽

Carrying Capacity ◽

Analytical Expression ◽

Constant Quantity ◽

Verhulst Model ◽

Exponential Correlation Function ◽

Number Of Individuals

We consider a generalized Malthus-Verhulst model with a fluctuating carrying capacity and we study its effects on population growth. The carrying capacity fluctuations are described by a Poissonian process with an exponential correlation function. We will find an analytical expression for the average of a number of individuals and show that even in presence of a fluctuating carrying capacity the average tends asymptotically to a constant quantity.

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Band-Limited Exponential Correlation Function for Rough-Surface Scattering

IEEE Transactions on Geoscience and Remote Sensing ◽

10.1109/tgrs.2007.893817 ◽

2007 ◽

Vol 45 (5) ◽

pp. 1198-1206 ◽

Cited By ~ 14

Author(s):

Alongkorn Darawankul ◽

Joel T. Johnson

Keyword(s):

Correlation Function ◽

Rough Surface ◽

Surface Scattering ◽

Rough Surface Scattering ◽

Band Limited ◽

Exponential Correlation Function

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From Quantum Affine Groups to the Exact Dynamical Correlation Function of the Heisenberg Model

International Journal of Modern Physics B ◽

10.1142/s0217979297000125 ◽

1997 ◽

Vol 11 (01n02) ◽

pp. 103-107

Author(s):

A. H. Bougourzi ◽

M. Couture ◽

M. Kacir

Keyword(s):

Correlation Function ◽

Form Factors ◽

Exact Formula ◽

Exact Form ◽

Zero Temperature ◽

Dynamical Correlation ◽

Xxz Model ◽

Affine Groups ◽

Affine Symmetry ◽

Xxx Model

The exact form factors of the Heisenberg models XXX and XXZ have been recently computed through the quantum affine symmetry of XXZ model in the thermodynamic limit. We use them to derive an exact formula for the contribution of two spinons to the dynamical correlation function of XXX model at zero temperature.

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Wavelength Dependence of the Zodiacal Light

International Astronomical Union Colloquium ◽

10.1017/s0252921100084736 ◽

1985 ◽

Vol 85 ◽

pp. 249-253

Author(s):

R. Schiffer ◽

K.O. Thielheim

Keyword(s):

Surface Roughness ◽

Correlation Function ◽

Angular Dependence ◽

Cross Section ◽

Wavelength Dependence ◽

Scattering Cross Section ◽

Zodiacal Light ◽

Scattering Cross ◽

Exponential Correlation Function

AbstractWe calculated the scattering cross section of an ensemble of large, convex, randomly oriented particles with a slight surface roughness. If the roughness structure is described by an exponential correlation function, the degree and angular dependence of the zodiacal light reddening are well reproduced by our model.

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Algebraic approximations of a polyhedron correlation function stemming from its chord-length distribution

Acta Crystallographica Section A Foundations and Advances ◽

10.1107/s2053273320014229 ◽

2021 ◽

Vol 77 (1) ◽

pp. 75-80

Author(s):

Salvino Ciccariello

Keyword(s):

Fourier Transform ◽

Correlation Function ◽

Full Range ◽

Length Distribution ◽

Chord Length ◽

Exact Form ◽

Chord Length Distribution ◽

Algebraic Approximation ◽

Left And Right ◽

The Common

An algebraic approximation, of order K, of a polyhedron correlation function (CF) can be obtained from γ′′(r), its chord-length distribution (CLD), considering first, within the subinterval [D i−1, D i ] of the full range of distances, a polynomial in the two variables (r − D i−1)1/2 and (D i − r)1/2 such that its expansions around r = D i−1 and r = D i simultaneously coincide with the left and right expansions of γ′′(r) around D i−1 and D i up to the terms O(r − D i−1) K/2 and O(D i − r) K/2, respectively. Then, for each i, one integrates twice the polynomial and determines the integration constants matching the resulting integrals at the common end-points. The 3D Fourier transform of the resulting algebraic CF approximation correctly reproduces, at large q's, the asymptotic behaviour of the exact form factor up to the term O[q −(K/2+4)]. For illustration, the procedure is applied to the cube, the tetrahedron and the octahedron.

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Consolute Critical Phenomena in Dilute Silica Gel

MRS Proceedings ◽

10.1557/proc-290-59 ◽

1992 ◽

Vol 290 ◽

Author(s):

B. J. Frisken ◽

Fabio Ferri ◽

David S. Cannell

Keyword(s):

Correlation Function ◽

Critical Phenomena ◽

Liquid Mixtures ◽

Phase Region ◽

Silica Network ◽

Exponential Form ◽

Pure System ◽

Consolute Point ◽

Exponential Correlation Function ◽

The One

AbstractThe effect of even dilute silica networks on the critical phenomena of binary liquid mixtures is profound. The network preferentially adsorbs one component, preventing a portion of the mixture from participating in critical fluctuations. Fluctuations in the remaining mixture are found to decay with a non-exponential correlation function near the consolute point. A correlation function consisting of the sum of an exponential decay and a non-exponential term of either an activated or stretched exponential form fits the data well. In the presence of the silica network, the mixtures are observed to phase separate near the critical temperature of the pure system, but while still in the one-phase region of the pure system.

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