S U M M A R YTemperature is one of the most important factors that controls the extent and location of the seismogenic coupled and transition, partially coupled segments of the subduction interplate fault. The width of the coupled fault inferred from the continuous GPS observations for the steady interseismic period and the transient width of the last slow aseismic slip event (M w ∼ 7.5) that occurred in the Guerrero subduction zone in 2001-2002 extends up to 180-220 km from the trench. Previous thermal models do not consider this extremely wide coupled interface in Guerrero subduction zone that is characterized by shallow subhorizontal plate contact. In this study, a finite element model is applied to examine the temperature constraints on the width of the coupled area. The numerical scheme solves a system of 2-D Stokes equation and 2-D steady-state heat transfer equations.The updip limit of the coupling zone is taken between 100 and 150 • C, while the downdip limit is accepted at 450 • C as the transition from partial coupling to stable sliding. From the entire coupled zone, the seismogenic zone extends only up to ∼82 km from the trench (inferred from the rupture width of large subduction thrust earthquakes), corresponding to the 250 • C isotherm. Only a small amount of frictional heating is needed to fit the intersection of the 450 • C isotherm and the subducting plate surface at 180-205 km from the trench.The calculated geotherms in the subducting slab and the phase diagram for MORB are used to estimate the metamorphic sequences within the oceanic subducting crust. A certain correlation exists between the metamorphic sequences and the variation of the coupling along the interplate fault.

Considerable geochemical and petrographic evidence suggests that magma mixing phenomena are important in producing the chemical heterogeneity commonly observed in plutonic and volcanic rocks on a variety of scales in both space and time. Simulations of time‐dependent, variable viscosity, double‐diffusive convection have been carried out to quantitatively investigate the mixing dynamics of magma in melt‐dominated magma bodies. Two distinct measures of the “goodness of mixing” are used to quantify magma mixing: (1) the linear scale of segregation (L) which corresponds to the length scale of a typical compositional anomaly; and, (2) the intensity of segregation (I) which is a measure of the deviation of compositional anomalies from the mean. Nondimensionalization of the governing conservation equations shows that the style and time scale of mixing depend on the flux Rayleigh number (Rq = αgqd4/kκνm), the buoyancy ratio (Rr = βΔCk/αqd), the Lewis number (Le = κ/D), the silicic to mafic melt viscosity ratio (νr = νS/νm), and the aspect ratio (A = w/d) of the chamber. Simulations of magma mixing were carried out by solving the conservation equations for parameter ranges 105 < Rq < 3 × 105, 0 < Rr < 1.1, 100 < Le < 600, 1 < νr < 20, 0.3 < A < 3 by a Galerkin finite element method over a two‐dimensional domain with various geologically relevant boundary conditions. The mixing time (tmix) is defined as the time required for the intensity of segregation to decay to a certain value. Magma mixing occurs by complex time‐dependent flows with numerous flow reversals associated with local unmixing events superimposed on a larger time scale process in which the intensity of segregation decays to zero. For parameters within the ranges investigated, tmix is roughly proportional to νr1/2Le1/2Rr2Rq−1 for the heating from below scenario. For values of νr, Le, Rr, and Rq appropriate to natural systems, this relationship gives a range of mixing times from about one tenth to 10 times d2/κ, implying that both well‐mixed and heterogeneous magmas will be commonly observed in nature. Mixing times are at a minimum for equant bodies, while for silllike bodies, mixing is inhibited by the formation of multiple cells of different composition in the horizontal. Assimilation and fractional crystallization geochemical models that assume “well‐mixed” magma bodies may be grossly misleading. A viscous (i.e., crystal laden), large (d∼5 km) magma body heated weakly from below and initially strongly chemically stratified will remain unmixed for several Ma. A large‐volume, thermally well‐connected basaltic body will mix rapidly (103–104 years). Because flow reversals may occur in dynamic mixing (Rr>0), crystal distributions within convecting magma bodies will be different from those predicted assuming steady state velocity fields. Flow reversals cause significant temporal variation in the heat supplied to the roof of the chamber; these may be important in explaining episodic phases of hydrothermal alteration. In sill‐like magma bodies (A>2), multiple cells...

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The error-field penetration process of the dynamic ergodic divertor (DED) on the TEXTOR tokamak has been investigated analytically in terms of a single fluid MHD model with a finite plasma resistivity and viscosity in a cylindrical geometry. The linear model produces a localization of the induced current at the resonance surface and predicts a vortex structure of the velocity field near the resonance layer. Moreover, effects of the Alfvén resonance for the error-field penetration are identified by two peaks in the radial profiles of the perturbed toroidal current and the perturbed magnetic flux when the relative rotation velocity between the DED and the rotating tokamak plasma is set to large. Fine structures of the vorticity induced by the DED in the vicinity of the rational surface disappear by introducing a finite plasma perpendicular viscosity. In addition, it is shown that the two peaks of the perturbed toroidal current overlap by an anomalous plasma perpendicular viscosity. Likewise, a bifurcation of the penetration process from the suppressed to the excited state is obtained by a quasi-linear approach taking into account modifications of the radial profiles of the equilibrium current and the plasma rotation due to the DED. A comparison with real experimental results of the DED on the TEXTOR tokamak is shown.

Generic conditions are established for producing a non-Fraunhofer response of the critical supercurrent subject to an external magnetic field in ferromagnetic Josephson junctions. Employing the quasiclassical KeldyshUsadel method, we demonstrate theoretically that an inhomogeneity in the magnitude of the energy scales in the system, including Thouless energy, exchange field and temperature gradient normal to the transport direction, influences drastically the standard Fraunhofer pattern. The exotic non-Fraunhofer response, similar to that observed in recent experiments, is described in terms of an intricate interplay between multiple '0-π'-states and is related to the appearance of proximity vortices.

We study the numerical solutions for an integro-differential parabolic problem modeling a process with jumps and stochastic volatility in financial mathematics. We present two general algorithms to calculate numerical solutions. The algorithms are implemented in PDE2D, a general-purpose, partial differential equation solver.

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