An implicit free surface algorithm for geodynamical simulations

Identifying the dominant controls on Earth’s surface topography is of critical importance to understanding both the short- and long-term evolution of geological processes and past- and present-day dynamics of Earth’s coupled mantle–lithosphere system. The ability to simulate a stress free — or a so-called ‘free surface’ — boundary condition is required to examine such processes via numerical models. However, at present, geodynamical models incorporating a free surface are limited, as most underlying free surface algorithms place severe restrictions on the computational timestep. Consequently, the simulations are often intractable. In this study, we introduce a new approach for incorporating a free surface within geodynamical models: an algorithm, in which free surface elevation is treated as an independent variable and is solved for in conjunction with the momentum and continuity equation, using implicit time integration. We demonstrate that the method is straightforward to implement in existing models and, using a series of analytical and benchmark comparisons, we show that it does not suffer from the timestep constraints of previous schemes. Furthermore, the scheme can be made second order accurate in time, at no additional cost. The method therefore dramatically improves the computational efficiency of geodynamical simulations including a free surface, whilst maintaining solution accuracy

Thermal modeling of subduction zones with prescribed and evolving 2D and 3D slab geometries

The determination of the temperature in and above the slab in subduction zones, using models where the top of the slab is precisely known, is important to test hypotheses regarding the causes of arc volcanism and intermediate-depth seismicity. While 2D and 3D models can predict the thermal structure with high precision for fixed slab geometries, a number of regions are characterized by relatively large geometrical changes. Examples include the flat slab segments in South America that evolved from more steeply dipping geometries to the present day flat slab geometry. We devise, implement, and test a numerical approach to model the thermal evolution of a subduction zone with prescribed changes in slab geometry over time. Our numerical model approximates the subduction zone geometry by employing time dependent deformation of a B\'ezier spline which is used as the slab interface in a finite element discretization of the Stokes and heat equations. We implement the numerical model using the FEniCS open source finite element suite and describe the means by which we compute approximations of the subduction zone velocity, temperature, and pressure fields. We compute and compare the 3D time evolving numerical model with its 2D analogy at cross-sections for slabs that evolve to the present-day structure of a flat segment of the subducting Nazca plate

A divergence free C0C^0-RIPG stream function formulation of the incompressible Stokes system with variable viscosity

Pointwise divergence free velocity field approximations of the Stokes system are gaining popularity due to their necessity in precise modelling of physical flow phenomena. Several methods have been designed to satisfy this requirement; however, these typically come at a greater cost when compared with standard conforming methods, for example, because of the complex implementation and development of specialized finite element bases. Motivated by the desire to mitigate these issues for 2D simulations, we present a $C^0$-interior penalty Galerkin (IPG) discretization of the Stokes system in the stream function formulation. In order to preserve a spatially varying viscosity this approach does not yield the standard and well known biharmonic problem. We further employ the so-called robust interior penalty Galerkin (RIPG) method; stability and convergence analysis of the proposed scheme is undertaken. The former, which involves deriving a bound on the interior penalty parameter is particularly useful to address the $\mathcal{O}(h^{-4})$ growth in the condition number of the discretized operator. Numerical experiments confirming the optimal convergence of the proposed method are undertaken. Comparisons with thermally driven buoyancy mantle convection model benchmarks are presented

The mantle wedge's transient 3-D flow regime and thermal structure

Arc volcanism, volatile cycling, mineralization, and continental crust formation are likely regu-lated by the mantle wedge’s flow regime and thermal structure. Wedge flow is often assumed to follow a regular corner-flow pattern. However, studies that incorporate a hydrated rheology and thermal buoyancy predict internal small-scale-convection (SSC). Here, we systematically explore mantle-wedge dynamics in 3- D simulations. We find that longitudinal ‘‘Richter-rolls’’ of SSC (with trench-perpendicular axes) commonly occur if wedge hydration reduces viscosities to ≤1 ∙ 10^19 Pa s, although transient transverse rolls (with trench-parallel axes) can dominate at viscosities of ~5 ∙ 10^18 - 1 ∙ 10^19 Pa s. Rolls below the arc and back arc differ. Subarc rolls have similar trench-parallel and trench-perpendicular dimensions of 100–150 km and evolve on a 1–5 Myr time-scale. Subback-arc instabilities, on the other hand, coalesce into elongated sheets, usually with a preferential trench-perpendicular alignment, display a wavelength of 150–400 km and vary on a 5–10 Myr time scale. The modulating influence of subback-arc ridges on the subarc system increases with stronger wedge hydration, higher subduction velocity, and thicker upper plates. We find that trench-parallel averages of wedge velocities and temperature are consistent with those predicted in 2-D models. However, lithospheric thinning through SSC is somewhat enhanced in 3-D, thus expanding hydrous melting regions and shifting dehydration boundaries. Subarc Richter-rolls generate time-dependent trench-parallel temperature variations of up to ~150 K, which exceed the transient 50–100 K variations predicted in 2-D and may contribute to arc-volcano spacing and the variable seismic velocity structures imaged beneath some arcs

Interaction of subducted slabs with the mantle transition-zone: A regime diagram from 2-D thermo-mechanical models with a mobile trench and an overriding plate

Transition zone slab deformation influences Earth's thermal, chemical, and tectonic evolution. However, the mechanisms responsible for the wide range of imaged slab morphologies remain debated. Here we use 2-D thermo-mechanical models with a mobile trench, an overriding plate, a temperature and stress-dependent rheology, and a 10, 30, or 100-fold increase in lower mantle viscosity, to investigate the effect of initial subducting and overriding-plate ages on slab-transition zone interaction. Four subduction styles emerge: (i) a "vertical folding" mode, with a quasi-stationary trench, near-vertical subduction, and buckling/folding at depth (VF); (ii) slabs that induce mild trench retreat, which are flattened/"horizontally deflected" and stagnate at the upper-lower mantle interface (HD); (iii) inclined slabs, which result from rapid sinking and strong trench retreat (ISR); (iv) a two-stage mode, displaying backward-bent and subsequently inclined slabs, with late trench retreat (BIR). Transitions from regime (i) to (iii) occur with increasing subducting plate age (i.e., buoyancy and strength). Regime (iv) develops for old (strong) subducting and overriding plates. We find that the interplay between trench motion and slab deformation at depth dictates the subduction style, both being controlled by slab strength, which is consistent with predictions from previous compositional subduction models. However, due to feedbacks between deformation, sinking rate, temperature, and slab strength, the subducting plate buoyancy, overriding plate strength, and upper-lower mantle viscosity jump are also important controls in thermo-mechanical subduction. For intermediate upper-lower mantle viscosity jumps (×30), our regimes reproduce the diverse range of seismically imaged slab morphologies

Reconciling mantle wedge thermal structure with arc lava thermobarometric determinations in oceanic subduction zones

Subduction zone mantle wedge temperatures impact plate interaction, melt generation, and chemical recycling. However, it has been challenging to reconcile geophysical and geochemical constraints on wedge thermal structure. Here we chemically determine the equilibration pressures and temperatures of primitive arc lavas from worldwide intraoceanic subduction zones and compare them to kinematically driven thermal wedge models. We find that equilibration pressures are typically located in the lithosphere, starting just below the Moho, and spanning a wide depth range of ∼25 km. Equilibration temperatures are high for these depths, averaging ∼1300°C. We test for correlations with subduction parameters and find that equilibration pressures correlate with upper plate age, indicating overriding lithosphere thickness plays a role in magma equilibration. We suggest that most, if not all, thermobarometric pressure and temperature conditions reflect magmatic reequilibration at a mechanical boundary, rather than reflecting the conditions of major melt generation. The magma reequilibration conditions are difficult to reconcile, to a first order, with any of the conditions predicted by our dynamic models, with the exception of subduction zones with very young, thin upper plates. For most zones, a mechanism for substantially thinning the overriding plate is required. Most likely thinning is localized below the arc, as kinematic thinning above the wedge corner would lead to a hot fore arc, incompatible with fore-arc surface heat flow and seismic properties. Localized subarc thermal erosion is consistent with seismic imaging and exhumed arc structures. Furthermore, such thermal erosion can serve as a weakness zone and affect subsequent plate evolutio

Opposite-side flavour tagging of B mesons at the LHCb experiment

The calibration and performance of the oppositeside flavour tagging algorithms used for the measurements of time-dependent asymmetries at the LHCb experiment are described. The algorithms have been developed using simulated events and optimized and calibrated with B + →J/ψK +, B0 →J/ψK ∗0 and B0 →D ∗− μ + νμ decay modes with 0.37 fb−1 of data collected in pp collisions at √ s = 7 TeV during the 2011 physics run. The oppositeside tagging power is determined in the B + → J/ψK + channel to be (2.10 ± 0.08 ± 0.24) %, where the first uncertainty is statistical and the second is systematic

Search for CP violation in D+→K−K+π+D^{+} \to K^{-}K^{+}\pi^{+} decays

A model-independent search for direct CP violation in the Cabibbo suppressed decay $D^+ \to K^- K^+\pi^+$ in a sample of approximately 370,000 decays is carried out. The data were collected by the LHCb experiment in 2010 and correspond to an integrated luminosity of 35 pb$^{-1}$. The normalized Dalitz plot distributions for $D^+$ and $D^-$ are compared using four different binning schemes that are sensitive to different manifestations of CP violation. No evidence for CP asymmetry is found.Comment: 13 pages, 8 figures, submitted to Phys. Rev.

Measurement of the ratio of branching fractions BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma)

The ratio of branching fractions of the radiative B decays B0 -> K*0 gamma and Bs0 -> phi gamma has been measured using 0.37 fb-1 of pp collisions at a centre of mass energy of sqrt(s) = 7 TeV, collected by the LHCb experiment. The value obtained is BR(B0 -> K*0 gamma)/BR(Bs0 -> phi gamma) = 1.12 +/- 0.08 ^{+0.06}_{-0.04} ^{+0.09}_{-0.08}, where the first uncertainty is statistical, the second systematic and the third is associated to the ratio of fragmentation fractions fs/fd. Using the world average for BR(B0 -> K*0 gamma) = (4.33 +/- 0.15) x 10^{-5}, the branching fraction BR(Bs0 -> phi gamma) is measured to be (3.9 +/- 0.5) x 10^{-5}, which is the most precise measurement to date.Comment: 15 pages, 1 figure, 2 table

Differential branching fraction and angular analysis of the decay B0→K∗0μ+μ−

The angular distribution and differential branching fraction of the decay B 0→ K ∗0 μ + μ − are studied using a data sample, collected by the LHCb experiment in pp collisions at s√=7 TeV, corresponding to an integrated luminosity of 1.0 fb−1. Several angular observables are measured in bins of the dimuon invariant mass squared, q 2. A first measurement of the zero-crossing point of the forward-backward asymmetry of the dimuon system is also presented. The zero-crossing point is measured to be q20=4.9±0.9GeV2/c4 , where the uncertainty is the sum of statistical and systematic uncertainties. The results are consistent with the Standard Model predictions