On: “Proposed Attenuation‐Dispersion Pair for Seismic Waves” by J. E. White and D. J. Walsh (GEOPHYSICS, June 1972, p. 456–461)

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 423-425 ◽  
Author(s):  
Ellis Strick
Keyword(s):  
Power Law ◽  
Seismic Waves ◽  
Low Frequency ◽  
Dispersion Relations ◽  
Minimum Phase ◽  
Power Law Model ◽  
Phase Property ◽  
Propagation Function ◽  
Complex Propagation ◽  
Frequency Behavior

In their paper, White and Walsh claim dispersion relations based upon an assumed minimum‐phase property of rock lead to such drastic low‐frequency behavior that any complex propagation function based upon dispersion relations is unacceptable. Since my power‐law model (Strick, 1967, 1970a) was placed in such a category, my response is as follows.

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals Unsteady thermal Maxwell power law nanofluid flow subject to forced thermal Marangoni Convection

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Jawad ◽  
Anwar Saeed ◽  
Taza Gul ◽  
Zahir Shah ◽  
Poom Kumam
Keyword(s):  
Relaxation Time ◽  
Power Law ◽  
Marangoni Convection ◽  
Power Law Model ◽  
Analysis Method ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Welan Gum ◽  
Homotopy Analysis ◽  
Power Law Nanofluid

AbstractIn the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

scholarly journals X-ray Properties of 3C 111: Separation of Primary Nuclear Emission and Jet Continuum

Universe ◽  
2020 ◽  
Vol 6 (11) ◽  
pp. 219
Author(s):  
Elena Fedorova ◽  
B.I. Hnatyk ◽  
V.I. Zhdanov ◽  
A. Del Popolo
Keyword(s):  
Accretion Disk ◽  
Power Law ◽  
Line Emission ◽  
High Energy ◽  
Power Law Model ◽  
X Ray ◽  
Additional Information ◽  
Observational Dataset ◽  
Simple Power ◽  
Photon Index

3C111 is BLRG with signatures of both FSRQ and Sy1 in X-ray spectrum. The significant X-ray observational dataset was collected for it by INTEGRAL, XMM-Newton, SWIFT, Suzaku and others. The overall X-ray spectrum of 3C 111 shows signs of a peculiarity with the large value of the high-energy cut-off typical rather for RQ AGN, probably due to the jet contamination. Separating the jet counterpart in the X-ray spectrum of 3C 111 from the primary nuclear counterpart can answer the question is this nucleus truly peculiar or this is a fake “peculiarity” due to a significant jet contribution. In view of this question, our aim is to estimate separately the accretion disk/corona and non-thermal jet emission in the 3C 111 X-ray spectra within different observational periods. To separate the disk/corona and jet contributions in total continuum, we use the idea that radio and X-ray spectra of jet emission can be described by a simple power-law model with the same photon index. This additional information allows us to derive rather accurate values of these contributions. In order to test these results, we also consider relations between the nuclear continuum and the line emission.

Magnetic Permeability and Relaxation Frequency in High Frequency Magnetic Materials.

2001 ◽  
Vol 674 ◽  
Author(s):  
M.I. Rosales ◽  
H. Montiel ◽  
R. Valenzuela
Keyword(s):  
High Frequency ◽  
Domain Walls ◽  
Magnetocrystalline Anisotropy ◽  
Low Frequency ◽  
Frequency Dispersion ◽  
Anisotropy Constant ◽  
Relaxation Frequency ◽  
Resonance Relaxation ◽  
Frequency Behavior

ABSTRACTAn investigation of the frequency behavior of polycrystalline ferrites is presented. It is shown that the low frequency dispersion (f < 10 MHz) of permeability is associated with the bulging of pinned domain walls, and has a mixed resonance-relaxation character, closer to the latter. It is also shown that there is a linear relationship between the magnetocrystalline anisotropy constant, K1, and the relaxation frequency. The slope of this correlation depends on the grain size. Such a relationship could allow the determination of this basic parameter from polycrystalline samples.

Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface

1978 ◽  
Vol 45 (1) ◽  
pp. 19-24 ◽  
Author(s):  
V. Narayanamurthy ◽  
P. K. Sarma
Keyword(s):  
Liquid Film ◽  
Power Law ◽  
Mathematical Formulation ◽  
Liquid Films ◽  
Interfacial Shear ◽  
Newtonian Liquid ◽  
Power Law Model ◽  
Falling Liquid Film ◽  
Falling Liquid Films ◽  
Special Case

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.

Erratum: Low‐frequency behavior of coupled Josephson junctions near phase locking [Appl. Phys. Lett. 41, 566 (1982)]

1983 ◽  
Vol 42 (3) ◽  
pp. 305-305 ◽  
Author(s):  
A. K. Jain ◽  
K. K. Likharev ◽  
J. E. Lukens ◽  
J. E. Sauvageau
Keyword(s):  
Josephson Junctions ◽  
Phase Locking ◽  
Low Frequency ◽  
Frequency Behavior
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