S U M M A R YWe develop and validate a systematic approach to infer plate boundary strength and rheological parameters in models of mantle flow from surface velocity observations. Based on a realistic rheological model that includes yielding and strain rate weakening from dislocation creep, we formulate the inverse problem in a Bayesian inference framework. To study the distribution of parameters that are consistent with the observations, we compute the maximum a posteriori (MAP) point, Gaussian approximations of the parameter distribution around that MAP point, and employ Markov Chain Monte Carlo (MCMC) sampling methods. The computation of the MAP point and the Gaussian approximation require first and second derivatives of an objective function subject to non-linear Stokes equations; these derivatives are computed efficiently using adjoint Stokes equations. We set up 2-D numerical experiments with many of the elements expected in a global geophysical inversion. This setup incorporates three subduction zones with slab and weak zone (interplate fault) geometry consistent with average seismic characteristics. With these experiments, we demonstrate that when the temperature field is known, we can recover the strength of plate boundaries, the yield stress and strain rate exponent in the upper mantle. When the number of uncertain parameters increases, there are trade-offs between the inferred parameters. These trade-offs depend on how well the observational data represents the surface velocities, and on the weakness of plate boundaries. As the plate boundary coupling drops below a threshold, the uncertainty of the inferred parameters increases due to insensitivity of plate motion to plate coupling. Comparing the trade-offs between inferred rheological parameters found from the Gaussian approximation of the parameter distribution and from MCMC sampling, we conclude that the Gaussian approximation-which is significantly cheaper to compute-is often a good approximation, in particular locally around the MAP point. Thus, the method can be applied to the global problem of inferring non-linear constitutive parameters and plate coupling factors for each subduction zone in a global geophysical inversion with known slab structure.

The density relaxation phenomenon is modeled using both Monte Carlo and discrete element simulations to investigate the effects of regular taps applied to a vessel having a planar floor filled with monodisperse spheres. Results suggest the existence of a critical tap intensity which produces a maximum bulk solids fraction. We find that the mechanism responsible for the relaxation phenomenon is an evolving ordered packing structure propagating upwards from the plane floor.

The dynamics of a vertical stack of particles subject to gravity and a sequence of small, periodically applied taps is considered. First, the motion of the particles, assumed to be identical, is modeled as a system of ordinary differential equations, which is analyzed with an eye to observing connections with finite-dimensional Hamiltonian systems. Then, two approaches to obtaining approximate continuum models for large numbers of particles are described: the long-wave approximation that yields partial differential equations and the BSR method that employs integro-partial differential models. These approximate continuum models, which comprise infinite-dimensional dynamical systems, are studied with a focus on nonlinear wave type behavior, which naturally leads to investigating links to infinitedimensional Hamiltonian systems. Several examples are solved numerically to show similarities among the solution properties of the finite-dimensional (lattice-dynamics), and the approximate long-wave and BSR continuum models. Extensions to higher dimensions and more general dynamically driven particle configurations are also sketched.

We report our findings on the evolution of solids fraction in a tapped system of inelastic, frictional spheres as a function of the applied acceleration obtained via discrete element simulations. Animations of the simulation data reveal the propagation of a wave initiated from the base that causes local rearrangements of the particles ultimately leading to the development of a dense microstructure. We also describe the analysis of dynamical models capable of predicting the simulated behavior, and advanced visualization techniques for revealing the dynamics. Mathematics Subject Classification 35C07 · 35Q51 · 37N15Electronic supplementary material The online version of this article (

The density relaxation phenomenon is modeled using both Monte Carlo and discrete element simulations to investigate the effects of regular taps applied to a vessel having a planar floor filled with monodisperse spheres. Results suggest the existence of a critical tap intensity which produces a maximum bulk solids fraction. We find that the mechanism responsible for the relaxation phenomenon is an evolving quasi-ordered packing structure propagating upwards from the plane floor.