The role of the shear mach number in earthquake source dynamics

1976 ◽  
Vol 66 (6) ◽  
pp. 1787-1799
Author(s):  
Ari Ben-Menahem
Keyword(s):  
Mach Number ◽  
Particle Motion ◽  
Surrounding Medium ◽  
Earthquake Source ◽  
Physical Parameters ◽  
Moving Force ◽  
Functional Relations ◽  
Shallow Earthquakes ◽  
Klein Gordon ◽  
The Time Domain

abstract The effect of the rupture velocity upon the spatial and temporal dependence of earthquake source functions is investigated. To this end a model is suggested in which the fault zone is realized as a flexible membrane under the action of a moving force with additional stiffness forces provided by the surrounding medium. The motion of each particle of the membrane is impeded by a displacement-dependent friction and radiation damping. The particle motion along the fault is found to obey an inhomogeneous Klein-Gordon equation whose solutions are derived in closed form. In the time domain, the solutions yield a particle-motion function that has frequently been derived by analysis of earthquake seismograms. The physical parameters in the theoretical source function are found to depend strongly on the Mach number, as already predicted by the theoretical directivity function. The theory excludes the possibility of supersonic rupture and asserts a transonic rupture for major shallow earthquakes and subsonic rupture for seismic events with low and intermediate magnitudes. It predicts new functional relations between the initial particle velocity at the fault's tip, D˙0, the Mach number, M = ν/β, the rise time τ, the stress drop σ∞ and the fault length L.

Numerical Simulation by CGM for Moving Force Identification

2012 ◽  
Vol 238 ◽  
pp. 826-829
Author(s):  
Zhen Chen ◽  
Jun Ling Han
Keyword(s):  
Numerical Simulation ◽  
Time Domain ◽  
Bending Moment ◽  
Identification Accuracy ◽  
Time Varying ◽  
Acceptable Solution ◽  
Moving Force ◽  
Ill Posed ◽  
Simulation Results ◽  
The Time Domain

The conjugate gradient method (CGM) is compared with the time domain method (TDM) in the paper. The numerical simulation results show that the CGM have higher identification accuracy and robust noise immunity as well as producing an acceptable solution to ill-posed problems to some extent when they are used to identify the moving force. When the bending moment responses are used to identify the time-varying loads, the identification accuracy is more obviously improved than the TDM, which is more suitable for the time-varying loads identification.

Sound-Induced Motion of a Nanoscale Fiber

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
R. N. Miles ◽  
J. Zhou
Keyword(s):  
Particle Motion ◽  
Surrounding Medium ◽  
System Response ◽  
Acoustic Excitation ◽  
Mechanical Motion ◽  
Thin Fiber ◽  
Reasonable Approximation ◽  
Wide Range ◽  
Resonant Behavior ◽  
Induced Motion

An analysis is presented of the motion of a thin fiber, supported on each end, due to a sound wave that propagates in the direction perpendicular to its long axis. Predicted and measured results indicate that when fibers or hairs having a diameter measurably less than 1 μm are subjected to air-borne acoustic excitation, their motion can be a very reasonable approximation to that of the acoustic particle motion at frequencies spanning the audible range. For much of the audible range of frequencies resonant behavior due to reflections from the supports tends to be heavily damped so that the details of the boundary conditions do not play a significant role in determining the overall system response. Thin fibers are thus constrained to simply move with the surrounding medium. These results suggest that if the diameter or radius is chosen to be sufficiently small, incorporating a suitable transduction scheme to convert its mechanical motion into an electronic signal could lead to a sound sensor that very closely depicts the acoustic particle motion over a wide range of frequencies.

Alternative solution to the gamma bench for the dielectric characterization of materials

2020 ◽  
Author(s):  
Imen boughanmi ◽  
Cyrille Fauchard ◽  
Nabil Benjelloun ◽  
Zouheir Riah
Keyword(s):  
Relative Permittivity ◽  
Wide Band ◽  
Cylindrical Sample ◽  
Cost Ratio ◽  
Physical Parameters ◽  
Dielectric Characterization ◽  
Density Control ◽  
Technical Specifications ◽  
Characterization Of Materials ◽  
The Time Domain

<p>In the field of civil engineering, and more particularly in the road building, it is necessary to control some physical parameters with standard methods. These controls ensure the implementation is performed according to the technical specifications. They also allow to optimize the structure dimensions  with the best safety/cost ratio and an optimal lifetime. Compactness related to density and therefore indicative of mechanical strength necessary to support traffic solicitations is a key parameter to control. Currently, density control in the laboratory is done using bench with nuclear sources on pavement cores, based on the emission and reception of gamma rays. Its replacement has now become a major issue since this method generates increasingly high costs and constraints (use, storage, transport and exposure to ionizing radiation). The objective of this work is to find an alternative non-nuclear solution to control the pavement compactness with an accuracy equivalent to the gamma-bench method . The proposed solution is an electromagnetic bench (EM), allowing cores tomography to measure permittivity. The density will then be evaluated by means of mixing rules. The EM bench consists of a vector network analyzer (Agilent E8362B) and two Ultra-Wide Band antennas [1.4-15 GHz] which are developed in this project in order to have the best performances (accuracy, dimensions…).</p><p>The antennas are placed facing each other, separated by a distance D.  A cylindrical sample (core) extracted from stratified road medium of diameter d to be tested is placed in the middle of the system and both antennas move with a given step (ranging from a few mm to 1 cm) along the sample to measure by stratification the core EM properties. The entire EM bench is motorized and driven by software developed in the laboratory. At each step, a measurement of S<sub>21</sub> -parameter is recorded. Then signals are processed in the time domain to evaluate the relative permittivity.</p><p>The first results of modeling and measurements on laboratory asphalt samples show that the system makes it possible to evaluate the relative permittivity of different stratified materials. Accuracy, resolution and perspectives will be discussed.</p><p>key words : density, asphalt concrete, radar, electromagnetic bench</p>

scholarly journals Waves and null congruences in a draining bathtub

2016 ◽  
Vol 25 (09) ◽  
pp. 1641004 ◽  
Author(s):  
David Dempsey ◽  
Sam R. Dolan
Keyword(s):  
Light Cone ◽  
Null Geodesic ◽  
Method Of Lines ◽  
Eikonal Approximation ◽  
Lorentzian Geometry ◽  
Circular Orbits ◽  
Kerr Spacetime ◽  
Frame Dragging ◽  
Klein Gordon ◽  
The Time Domain

We study wave propagation in a draining bathtub: a black hole analogue in fluid mechanics whose perturbations are governed by a Klein–Gordon equation on an effective Lorentzian geometry. Like the Kerr spacetime, the draining bathtub geometry possesses an (effective) horizon, an ergosphere and null circular orbits. We propose here that a ‘pulse’ disturbance may be used to map out the light-cone of the effective geometry. First, we apply the eikonal approximation to elucidate the link between wavefronts, null geodesic congruences and the Raychaudhuri equation. Next, we solve the wave equation numerically in the time domain using the method of lines. Starting with Gaussian initial data, we demonstrate that a pulse will propagate along a null congruence and thus trace out the light-cone of the effective geometry. Our new results reveal features, such as wavefront intersections, frame-dragging, winding and interference effects, that are closely associated with the presence of null circular orbits and the ergosphere.

scholarly journals Wave dispersion derived from the square-root Klein–Gordon–Poisson system

2013 ◽  
Vol 79 (4) ◽  
pp. 371-376 ◽  
Author(s):  
F. HAAS
Keyword(s):  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Fundamental Aspect ◽  
Physical Parameters ◽  
Linear Wave ◽  
Relativistic Energy ◽  
Square Root ◽  
Maxwell System ◽  
Poisson System ◽  
Klein Gordon

AbstractRecently, there has been great interest around quantum relativistic models for plasmas. In particular, striking advances have been obtained by means of the Klein–Gordon–Maxwell system, which provides a first-order approach to the relativistic regimes of quantum plasmas. The Klein–Gordon–Maxwell system provides a reliable model as long as the plasma spin dynamics is not a fundamental aspect, to be addressed using more refined (and heavier) models involving the Pauli–Schrödinger or Dirac equations. In this work, a further simplification is considered, tracing back to the early days of relativistic quantum theory. Namely, we revisit the square-root Klein–Gordon–Poisson system, where the positive branch of the relativistic energy–momentum relation is mapped to a quantum wave equation. The associated linear wave propagation is analyzed and compared with the results in the literature. We determine physical parameters where the simultaneous quantum and relativistic effects can be noticeable in weakly coupled electrostatic plasmas.

scholarly journals Numerical investigation of particle motion at the steel—slag interface in continuous casting using VOF method and dynamic overset grids

2022 ◽  
Author(s):  
Xiaomeng Zhang ◽  
Stefan Pirker ◽  
Mahdi Saeedipour
Keyword(s):  
Particle Motion ◽  
Particle System ◽  
Particle Density ◽  
Steel Slag ◽  
Physical Parameters ◽  
Slag Particle ◽  
Dynamic Overset Grids ◽  
Capillary Interactions ◽  
Speed Up ◽  
A Minor

AbstractThe capillary interactions are prominent for a micro-sized particle at the steel—slag interface. In this study, the dynamics of a spherical particle interacting with the steel—slag interface is numerically investigated using the volume of fluid method in combination with the overset grid technique to account for particle motion. The simulations have shown the particle’s separation process at the interface and successfully captured the formation and continuous evolution of a meniscus in the course of particle motion. A sensitivity analysis on the effect of different physical parameters in the steel—slag—particle system is also conducted. The result indicates that the wettability of particle with the slag phase is the main factor affecting particle separation behavior (trapped at the interface or fully separated into slag). Higher interfacial tension of fluid interface and smaller particle size can speed up the particle motion but have less effect on the equilibrium position for particle staying at the interface. In comparison, particle density shows a minor influence when the motion is dominated by the capillary effect. By taking account of the effect of meniscus and capillary forces on a particle, this study provides a more accurate simulation of particle motion in the vicinity of the steel—slag interface and enables further investigation of more complex situations.

CONVERGENCE ORDER OF ONE REGULARIZATION METHOD

2003 ◽  
Vol 8 (1) ◽  
pp. 25-32
Author(s):  
S. Guseinov
Keyword(s):  
Differential Equations ◽  
Linear Theory ◽  
Regularization Method ◽  
Convergence Order ◽  
Physical Parameters ◽  
Two Phase ◽  
Small Oscillations ◽  
Harmonic Wavelets ◽  
Connection Coefficients ◽  
Klein Gordon

The multiscale solution of the Klein‐Gordon equations in the linear theory of (two‐phase) materials with microstructure is defined by using a family of wavelets based on the harmonic wavelets. The connection coefficients are explicitly computed and characterized by a set of differential equations. Thus the propagation is considered as a superposition of wavelets at different scale of approximation, depending both on the physical parameters and on the connection coefficients of each scale. The coarse level concerns with the basic harmonic trend while the small details, arising at more refined levels, describe small oscillations around the harmonic zero‐scale approximation.

Regional bias in estimates of earthquake MS due to surface-wave path effects

1994 ◽  
Vol 84 (2) ◽  
pp. 377-382
Author(s):  
Rachel E. Abercrombie
Keyword(s):  
Surface Wave ◽  
Tectonic Setting ◽  
High Surface ◽  
Earthquake Source ◽  
Plate Boundaries ◽  
Source Type ◽  
Shallow Earthquakes ◽  
Seismic Strain Rate ◽  
Seismic Strain ◽  
Wave Path

Abstract Continental earthquakes have long been known to have anomalously high surface-wave magnitudes relative to their seismic moments. A recent global study of shallow earthquakes by Ekström and Dziewonski (1988) confirmed this and found other regional, systematic anomalies in the MS-M0 relationship. It is important to determine the source of these anomalies in order to understand the controls on earthquake-source radiation and to obtain accurate estimates of historical seismic strain rates. In this study the magnitudes of 82 earthquakes from eight different tectonic regions are recalculated using a simple surface-wave path correction to determine whether path effects are responsible for the observed anomalies. The magnitudes of continental earthquakes are reduced by an average of 0.2 magnitude units, an improvement in fit to the global average significant at the 98% level. Surface-wave path effects are clearly responsible for the high MS observed in continental areas. There is a small decrease in scatter in the other areas, but lateral refraction of the surface waves at plate boundaries prevents the simple correction from having a significant effect. There is no evidence in the observed anomalies, however, for any dependence of earthquake-source type on tectonic setting. It is clear that to obtain reliable, unbiased estimates of regional seismic strain rate and hazard, a local moment-magnitude relationship should be preferred to a global one.

Relativistic oscillators in new type of the extended uncertainty principle

2019 ◽  
Vol 34 (32) ◽  
pp. 1950218 ◽  
Author(s):  
A. Merad ◽  
M. Aouachria ◽  
M. Merad ◽  
T. Birkandan
Keyword(s):  
Uncertainty Principle ◽  
Laguerre Polynomials ◽  
Operator Method ◽  
Wave Functions ◽  
Uniform Electric Field ◽  
Physical Parameters ◽  
Eigenvalues And Eigenfunctions ◽  
Klein Gordon ◽  
New Type ◽  
Extended Uncertainty

We present the exact solutions of one-dimensional Klein–Gordon and Dirac oscillators subject to the uniform electric field in the context of the new type of the extended uncertainty principle using the displacement operator method. The energy eigenvalues and eigenfunctions are determined for both cases. For the Klein–Gordon oscillator case, the wave functions are expressed in terms of the associated Laguerre polynomials and for the Dirac oscillator case, the wave functions are obtained in terms of the confluent Heun functions. The limiting cases are also studied using the special values of the physical parameters.

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