The static and time-dependent signature of ocean–continent and ocean–ocean subduction: the case studies of Sumatra and Mariana complexes

SUMMARY The anomalous density structure at subduction zones, both in the wedge and in the upper mantle, is analysed to shed light on the processes that are responsible for the characteristic gravity fingerprints of two types of subduction: ocean–continent and ocean–ocean. Our modelling is then performed within the frame of the EIGEN-6C4 gravitational disturbance pattern of two subductions representative of the above two types, the Sumatra and Mariana complexes, finally enabling the different characteristics of the two patterns to be observed and understood on a physical basis, including some small-scale details. A 2-D viscous modelling perpendicular to the trench accounts for the effects on the gravity pattern caused by a wide range of parameters in terms of convergence velocity, subduction dip angle and lateral variability of the crustal thickness of the overriding plate, as well as compositional differentiation, phase changes and hydration of the mantle. Plate coupling, modelled within a new scheme where the relative velocity at the plate contact results self-consistently from the thermomechanical evolution of the system, is shown to have an important impact on the gravity signature. Beyond the already understood general bipolar fingerprint of subduction, perpendicular to the trench, we obtain the density and gravity signatures of the processes occurring within the wedge and mantle that are responsible for the two different gravity patterns. To be compliant with the geodetic EIGEN-6C4 gravitational disturbance and to compare our predictions with the gravity at Sumatra and Mariana, we define a model normal Earth. Although the peak-to-peak gravitational disturbance is comparable for the two types of subductions, approximately 250 mGal, from both observations and modelling, encompassing the highest positive maximum on the overriding plates and the negative minimum on the trench, the trough is wider for the ocean–ocean subduction: approximately 300 km compared to approximately 180 km for the ocean–continent subduction. Furthermore, the gravitational disturbance pattern is more symmetric for the ocean–ocean subduction compared to the ocean–continent subduction in terms of the amplitudes of the two positive maxima over the overriding and subducting plates. Their difference is, for the ocean–ocean type, approximately one half of the ocean–continent one. These different characteristics of the two types of subductions are exploited herein in terms of the different crustal thicknesses of the overriding plate and of the different dynamics in the wedge and in the mantle for the two types of subduction, in close agreement with the gravity data.

Stepper Motor Driven Four-Bar: Dynamic Modeling and Synthesis

This paper presents the dynamic modeling and synthesis of a four-bar mechanism that is driven by a four-phase, variable-reluctance stepper motor. Dynamic models of both the mechanism and the motor are derived and subsequently combined in order to numerically determine the system dynamic response. In the stepper motor model, full circuit equations are derived for each of 8 stator poles, with full expressions for armature self- and mutual-inductances, as well as developed motor torque. The stepper motor model admits arbitrary input pulse trains, and includes both coil resistance and inductance. A set of five, simultaneous, nonlinear, second-order ordinary differential equations is analytically derived and numerically solved to determine stepper response. In the four-bar mechanism model, three dynamical properties (primary effective inertia, secondary effective inertia, and gravitational disturbance torque) are derived using a Lagrangian approach, and utilized to determine the dynamic suitability of candidate four-bars for three-position, rigid body guidance. Three candidate four-bar mechanisms are synthesized, and their dynamic response (when coupled to the variable-reluctance stepper motor) is compared. It is shown that an engineering trade-off exists between parallelogram and crank-rocker four-bars, in which the former may possess lower primary effective inertia, but the latter may possess lower gravitational disturbance torque.

Changement de phase dans un champ de gravitation: Possibilité de détection interférentielle

We calculate the phase shift of a quantum mechanics wave function and of an electromagnetic wave produced by any gravitational disturbance using the eikonal approximation. We examine the best conditions for detection of gravitational waves. In particular, we establish that any resonant effect has a linear time dependance.