scholarly journals Envelope broadening of spherically outgoing waves in three-dimensional random media having power law spectra

2002 ◽  
Vol 107 (B5) ◽  
Author(s):  
Tatsuhiko Saito
Keyword(s):  
Power Law ◽  
Random Media ◽  
Three Dimensional

scholarly journals Inversion of flow Measurements for Stress and Rheological Parameters in a Valley Glacier

1973 ◽  
Vol 12 (64) ◽  
pp. 19-44
Author(s):  
Charles F. Raymond
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Measurement Errors ◽  
Effective Viscosity ◽  
Three Dimensional ◽  
Rheological Parameters ◽  
Mean Stress ◽  
Flow Measurements ◽  
Anomalous Zone ◽  
Flow Law

AbstractMethods are developed for determining the distributions of stress and effective viscosity in a glacier, under the assumptions: the ice is quasi-viscous, the flow is time independent, and acceleration forces are negligible. Measurements of the three-dimensional distribution of velocity are needed for their application. The differential equations of mechanical equilibrium, expressed in terms of viscosity, strain-rate components, mean stress, and their gradients, are viewed as equations to be solved for viscosity and mean stress subject to boundary conditions at the free upper surface. For certain rectilinear flow patterns, unique distributions of stress and effective viscosity can always be derived. For more complicated flow this is not necessarily so. However, it is still possible to choose the best values of rheological parameters in any trial flow law based on the requirement that the residuals to the equations of equilibrium be minimized in a mean-square sense. The techniques are applied to measurements of internal deformation made in nine bore holes on the Athabasca Glacier. At the center line the magnitude of the surface-parallel shear stress increases with depth more slowly than would be expected from a standard shape factor correction or the theoretical distribution of Nye. Correspondingly the lateral distribution of lateral shear stress shows the opposite relationships. In the lower one- to two-thirds of the depth corresponding to a range in effective stress from about 0.5 to 1.2 bars, the gross rheology of the ice is not distinguishably different from the experimentally determined flow law of Glen (n = 4.2, T = 0.02° C) as generalized by Nye. The results do not support the conclusion that the effective viscosity is higher than would be expected from Glen’s experiments as indicated by the more limited measurements of Paterson and Savage. Power-law parameters derived for the different bore holes considered separately show a spread, which suggests some rheological inhomogeneity. However, no definite conclusions can be drawn, because of direct measurement errors at the bore holes and less definable uncertainty in the interpolated distribution of velocity between the holes. The upper one- to two-thirds of the glacier constitutes an anomalous zone in which there is either a strong effect from a complex distribution of stress arising from longitudinal stress gradients or more complicated rheology than in a homogeneous power-law material.

scholarly journals Critical flow and dissipation in a quasi–one-dimensional superfluid

2015 ◽  
Vol 1 (4) ◽  
pp. e1400222 ◽  
Author(s):  
Pierre-François Duc ◽  
Michel Savard ◽  
Matei Petrescu ◽  
Bernd Rosenow ◽  
Adrian Del Maestro ◽  
...  
Keyword(s):  
Power Law ◽  
Capillary Flow ◽  
Three Dimensional ◽  
Universality Class ◽  
Superfluid State ◽  
One Dimensional ◽  
Flow Experiment ◽  
20 Nm ◽  
Bulk Behavior ◽  
Superfluid Velocity

In one of the most celebrated examples of the theory of universal critical phenomena, the phase transition to the superfluid state of 4He belongs to the same three-dimensional (3D) O(2) universality class as the onset of ferromagnetism in a lattice of classical spins with XY symmetry. Below the transition, the superfluid density ρs and superfluid velocity vs increase as a power law of temperature described by a universal critical exponent that is constrained to be identical by scale invariance. As the dimensionality is reduced toward 1D, it is expected that enhanced thermal and quantum fluctuations preclude long-range order, thereby inhibiting superfluidity. We have measured the flow rate of liquid helium and deduced its superfluid velocity in a capillary flow experiment occurring in single 30-nm-long nanopores with radii ranging down from 20 to 3 nm. As the pore size is reduced toward the 1D limit, we observe the following: (i) a suppression of the pressure dependence of the superfluid velocity; (ii) a temperature dependence of vs that surprisingly can be well-fitted by a power law with a single exponent over a broad range of temperatures; and (iii) decreasing critical velocities as a function of decreasing radius for channel sizes below R ≃ 20 nm, in stark contrast with what is observed in micrometer-sized channels. We interpret these deviations from bulk behavior as signaling the crossover to a quasi-1D state, whereby the size of a critical topological defect is cut off by the channel radius.

Three-dimensional records of surface displacement on the Superstition Hills fault zone associated with the earthquakes of 24 November 1987

1989 ◽  
Vol 79 (2) ◽  
pp. 376-389
Author(s):  
Robert V. Sharp ◽  
John L. Saxton
Keyword(s):  
Fault Zone ◽  
Power Law ◽  
Main Shock ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Displacement Component ◽  
Observation Data ◽  
Fault Movement ◽  
Remarkable Agreement ◽  
Observation Period

Abstract Seven quadrilaterals, constructed at broadly distributed points on surface breaks within the Superstition Hills fault zone, were repeatedly remeasured after the pair of 24 November 1987 earthquakes to monitor the growing surface displacement. Changes in the dimensions of the quadrilaterals are recalculated to right-lateral and extensional components at millimeter resolution, and vertical components of change are resolved at 0.2 mm precision. The displacement component data for four of the seven quadrilaterals record the complete fault movement with respect to an October 1986 base. These data fit with remarkable agreement the power law U ( t ) = U f ( B t 1 + B t ) c , where U(t) is a displacement component at time t after the second main shock and Uf, B, and c are constants. This power law permits estimation of the final displacement, Uf, from the data obtained within the period of observation. Data from one quadrilateral, located near the epicenter of the second main shock and northeast-trending conjugate faults, allow that about 5 cm of right-lateral slip may have been associated with the first main shock there. Data from the other quadrilaterals confirm that the surface faulting on most of the Superstition Hills fault zone did initiate at the time of the second main shock of the 1987 earthquakes. The three-dimensional motion vectors all describe nearly linear trajectories throughout the observation period, and they indicate smooth shearing on their respective fault surfaces. The inclination of the shear surfaces is generally nearly vertical, except near the south end of the Superstition Hills fault zone where two strands dip northeastward at about 70°. Surface displacement on these strands is right reverse. Another kind of deformation, superimposed on the fault displacements, has been recorded at all quadrilateral sites. It consists of a northwest-southeast contraction or component of contraction that ranged from 0 to 0.1 per cent of the quadrilateral lengths between November 1987 and April 1988.

scholarly journals IDEAL-MODIFIED BOSONIC GAS TRAPPED IN AN ARBITRARY THREE-DIMENSIONAL POWER-LAW POTENTIAL

2012 ◽  
Vol 27 (31) ◽  
pp. 1250181 ◽  
Author(s):  
E. CASTELLANOS ◽  
C. LÄMMERZAHL
Keyword(s):  
Dispersion Relation ◽  
Power Law ◽  
Three Dimensional ◽  
Particle Dispersion ◽  
Einstein Condensate ◽  
Gravity Models ◽  
Condensation Temperature ◽  
Bose Einstein Condensate ◽  
Bose Einstein ◽  
Number Of Particles

We analyze the effects caused by an anomalous single-particle dispersion relation suggested in several quantum-gravity models, upon the thermodynamics of a Bose–Einstein condensate trapped in a generic three-dimensional power-law potential. We prove that the shift in the condensation temperature, caused by a deformed dispersion relation, described as a non-trivial function of the number of particles and the shape associated to the corresponding trap, could provide bounds for the parameters associated to such deformation. In addition, we calculate the fluctuations in the number of particles as a criterium of thermodynamic stability for these systems. We show that the apparent instability caused by the anomalous fluctuations in the thermodynamic limit can be suppressed considering the lowest energy associated to the system in question.

scholarly journals Three-dimensional universality class of the Ising model with power-law correlated critical disorder

2019 ◽  
Vol 100 (14) ◽  
Author(s):  
Wenlong Wang ◽  
Hannes Meier ◽  
Jack Lidmar ◽  
Mats Wallin
Keyword(s):  
Ising Model ◽  
Power Law ◽  
Three Dimensional ◽  
Universality Class
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