<i>Mathematical Methods for Physicists, 4th ed</i>.

Arfken, George B.; Weber, H. J.; Spector, Donald

doi:10.1119/1.19217

Cited by 128 publications

(95 citation statements)

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“…22 The effect of simultaneous irradiation of length t p is to rotate the original wave function by ϭ ͱ (⍀ 10 2 ϩ⍀ 1Ϫ 2 )t p /2 about an axis in the y -z plane, rotated from the z-axis by an angle , where ϭtan Ϫ1 (⍀ 1Ϫ /⍀ 10 ). That is ͉⌿(t)͘ϭe ϪiH Q t/ប e i(cos I z ϩsin I y ) ͉⌿(0)͘, where we assume Ϫ a ϭ 0 a ϭ0 for the moment.…”

Section: Theorymentioning

confidence: 99%

Secondary echoes in three-frequency nuclear quadrupole resonance of spin-1 nuclei

Sauer

Suits

Garroway

et al. 2003

The Journal of Chemical Physics

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We demonstrate, theoretically and experimentally, that the irradiation of a powder sample containing spin-1 nuclei by two of the three characteristic nuclear quadrupole resonance ͑NQR͒ frequencies can result in several echo signals at the third NQR frequency. One of these echoes, the principal echo, has the same shape and time of occurrence as an echo produced after a pair of single-frequency excitations. The other echoes are not equivalent to any single-frequency echo. These secondary echoes are the focus of this paper. The time of occurrence and shape of the secondary echoes are determined by the correlation of the distribution in one transition frequency to the distribution in a second transition frequency. This correlation is in turn determined by the correlation between the distributions of the electric field gradient components, which is itself determined by the types and concentrations of crystalline defects present. We present the optimal conditions to observe such secondary echoes and compare theory with experiment using 14 N (Iϭ1) in powder samples of sodium nitrite and RDX.

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Section: Theorymentioning

confidence: 99%

Secondary echoes in three-frequency nuclear quadrupole resonance of spin-1 nuclei

Sauer

Suits

Garroway

et al. 2003

The Journal of Chemical Physics

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“…The Helmholtz decomposition of the fluid velocity vector separates u i into irrotational (curl-free) and solenoidal (divergence-free) components 23 and is written as…”

Section: Helmholtz Decompositionmentioning

confidence: 99%

Improved ALE mesh velocities for complex flows

Bakosi

Waltz

Morgan

2017

Numerical Methods in Fluids

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Summary A key choice in the development of arbitrary Lagrangian‐Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring‐force model. This approach allows distinct and separate control over rotational and translational modes. The utility of the new mesh motion algorithm is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.

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“…However, these approaches can generate two different types of errors: the local errors that affect some few pixels in the phase image and the global errors when a local error is propagated. For this reason, most of the proposed local approaches are based on the residue cut technique to avoid these kinds of ambiguous pixels [3], [26], [27]. Other local approaches for phase unwrapping (PU) are based on local frequency estimation [13] using the Fourier transform in a local given window to analyze the fringes of the interferogram [28], [29].…”

Section: Introductionmentioning

confidence: 99%

A Joint Markov Random Field Approach for SAR Interferogram Filtering and Unwrapping

Abdallah

Abdelfattah

2016

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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This paper presents a new integrated interferometric synthetic aperture radar (InSAR) phase filtering and unwrapping method based on a Markov random field (MRF) model. This approach aims to estimate a noiseless unwrapped phase from the observed noisy interferogram. The phase image is modeled using a joint MRF with a corresponding energy function related simultaneously to noise filtering and phase unwrapping (PU). This function contains two parts: the first is for interferogram filtering process and the second aims to unwrap this filtered phase. The filtered unwrapped phase image is estimated by minimizing the proposed energy function using the genetic algorithm (GA). The proposed approach is tested and validated on simulated and real interferograms acquired with the Radarsat-2, ERS-2, and Envisat satellites acquired over two distinct regions in Tunisia (Mahdia and Ben Guerden) with different geographical characteristics. The obtained results show a significant improvement with respect to other simultaneously filtering and unwrapping algorithms.Index Terms-Genetic algorithm (GA), InSAR phase filtering, Markov random field (MRF), phase unwrapping (PU).

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Mathematical Methods for Physicists, 4th ed.

Cited by 128 publications

References 0 publications

Secondary echoes in three-frequency nuclear quadrupole resonance of spin-1 nuclei

Secondary echoes in three-frequency nuclear quadrupole resonance of spin-1 nuclei

Improved ALE mesh velocities for complex flows

A Joint Markov Random Field Approach for SAR Interferogram Filtering and Unwrapping

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