A note on spectral velocity approximation at shorter intermediate periods

2021 ◽  
Vol 141 ◽  
pp. 106422
Author(s):  
Ashish Pal ◽  
Vinay K. Gupta
Keyword(s):  
Spectral Velocity ◽  
Velocity Approximation

Strong Ground Motion Prediction Model for PGV and Spectral Velocity for the Chilean Subduction Zone

2021 ◽  
Author(s):  
Gonzalo A. Montalva ◽  
Nicolás Bastías ◽  
Felipe Leyton
Keyword(s):  
Subduction Zone ◽  
Ground Motion ◽  
Fundamental Frequency ◽  
Spectral Response ◽  
Motion Prediction ◽  
Slight Reduction ◽  
Ground Motion Prediction ◽  
Proposed Model ◽  
Strong Ground Motion Prediction ◽  
Spectral Velocity

ABSTRACT Ground-motion prediction models (GMPMs) are a critical tool in performing seismic hazard analyses; in turn, these studies condition structural designs. Consequently, new research has appeared not only with a regionalization focus but has also explored the prediction of intensities other than acceleration. We present a GMPM for peak ground velocity (PGV) and spectral velocity (Sv) for the Chilean subduction zone. Because of the limitations of VS30 as site proxy, the proposed model adds the site’s fundamental frequency (f0) as an explanatory variable for the site term in the GMPM. We developed the model for PGV and spectral response periods between 0.06 and 10 s. The total error (σ) of the model shows a slight reduction with the inclusion of the fundamental frequency (f0) compared with a similar model for the pseudoacceleration response spectrum in the same zone. We used the proposed model to predict structural damage during the 2010 Mw 8.8 Maule earthquake, showing a good fit with the geographical distribution of damage, and this creates an opportunity to characterize the seismic behavior of soil deposits, including basins, for urban planning.

scholarly journals Two basic systems of maxwell’s equations in a rotating frame: application in theory of ring laser gyro

2020 ◽  
pp. 64-73
Author(s):  
Evgen Bondarenko
Keyword(s):  
Ring Laser ◽  
Electromagnetic Waves ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Plane Waves ◽  
Rotating Frame ◽  
Cylindrical Coordinates ◽  
Laser Gyro ◽  
Component Form ◽  
Velocity Approximation

In the paper, using a linear in angular velocity approximation, two basic well-known systems of Maxwell’s equations in a uniformly rotating frame of reference are considered. The first system of equations was first obtained in the work [L. I. Schiff, Proc. Natl. Acad. Sci. USA 25, 391 (1939)] on the base of use of the formalism of the theory of general relativity, and the second one – in the work [W. M. Irvine, Physica 30, 1160 (1964)] on the base of use of the method of orthonormal tetrad in this theory. In the paper, in the approximation of plane waves, these two vectorial systems of Maxwell’s equations are simplified and rewritten in cylindrical coordinates in scalar component form in order to find the lows of propagation of transversal components of electromagnetic waves in a circular resonator of ring laser gyro in the case of its rotation about sensitivity axis. On the base of these two simplified systems of Maxwell’s equations, the well-known wave equation and its analytical solutions for the named transversal components are obtained. As a result of substitution of these solutions into the first and second simplified systems of Maxwell’s equations, it is revealed that they satisfy only the second one.  On this basis, the conclusion is made that the second system of Maxwell’s equations is more suitable for application in the theory of ring laser gyro than the first one.

scholarly journals Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow

2020 ◽  
Vol 30 (05) ◽  
pp. 847-865
Author(s):  
Gabriel Barrenechea ◽  
Erik Burman ◽  
Johnny Guzmán
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Inviscid Flow ◽  
Element Approximation ◽  
Well Posedness ◽  
Hodge Laplacian ◽  
Conforming Finite Element ◽  
Velocity Approximation

We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth domains. The model problem is then discretised using [Formula: see text](div)-conforming finite element methods, for which we prove error estimates for the velocity approximation in the [Formula: see text]-norm of order [Formula: see text]. We also prove error estimates for the pressure error in the [Formula: see text]-norm.

scholarly journals Evaluation of a Substitute Structure Method to Estimate Seismic Displacement Demand in Piers and Wharves

2018 ◽  
Vol 34 (2) ◽  
pp. 759-772 ◽  
Author(s):  
Rakesh K. Goel
Keyword(s):  
Spectral Acceleration ◽  
Design Spectrum ◽  
Seismic Displacement ◽  
Long Period ◽  
History Analysis ◽  
Short Period ◽  
Response History Analysis ◽  
Nonlinear Response History Analysis ◽  
Displacement Demand ◽  
Spectral Velocity

This paper compares seismic displacement from the MOTEMS and the ASCE/COPRI 61-14 substitute structure method (SSM) with results from the nonlinear response history analysis (NLRHA). It is found that the SSM is biased toward overpredicting displacement demand for short-period systems and under-predicting displacement demand for long-period systems. The overprediction was found to be excessive for very-short period systems (i.e., systems with periods shorter than the period at which the design spectrum transitions from linearly increasing spectral acceleration to constant spectral acceleration). It is recommended that the SSM not be used for such systems. It is also recommended that the SSM not be used for long-period systems (i.e., systems with periods longer than the period at which the design spectrum transitions from constant spectral acceleration to constant spectral velocity), where it underpredicts displacement demand and may lead to unconservative design. The SSM provides reasonable results (within 20% of results from NLRHA) for systems with periods in the constant spectral acceleration region of the design spectrum.

scholarly journals Laguerre–Hermite pseudo-spectral velocity formulation of gyrokinetics

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
N. R. Mandell ◽  
W. Dorland ◽  
M. Landreman
Keyword(s):  
Three Dimensional ◽  
Collision Operator ◽  
Zonal Flow ◽  
Phase Mixing ◽  
Final Model ◽  
Nonlinear Phase ◽  
Wide Range ◽  
H Theorem ◽  
Spectral Velocity ◽  
Pseudo Spectral

First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution three-dimensional (3-D) gyrofluid representation and the conventional but more expensive 5-D gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Laguerre–Hermite velocity-space basis. We discuss issues related to collisions, closures and entropy. While any collision operator can be used in the formulation, we highlight a model operator that has a particularly sparse Laguerre–Hermite representation, while satisfying conservation laws and the H theorem. Free streaming, magnetic drifts and nonlinear phase mixing each give rise to closure problems, which we discuss in relation to the instabilities of interest and to free energy conservation. We show that the model is capable of reproducing gyrokinetic results for linear instabilities and zonal flow dynamics. Thus the final model is appropriate for the study of instabilities, turbulence and transport in a wide range of geometries, including tokamaks and stellarators.

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