Joshua R. Davis

Determining vorticity axes from grain-scale dispersion of crystallographic orientations

Kinematic shear sense indicators are critical tools for tectonic interpretation of shear zones. The appropriate plane in which to interpret shear sense indicators is the vorticity normal surface, which is often inferred using fabric (foliation, lineation) orientation. Strain modeling, however, suggests that such fabrics can be unreliable for determining a kinematic framework. We demonstrate the application of a new quantitative method, crystallographic vorticity axis (CVA) analysis, that utilizes rotation statistics to calculate dispersion axes from crystallographic orientations at the grain scale. We apply CVA analysis to samples from three shear zones that exhibit distinct kinematics and deformation geometries. In all cases, the aggregate of calculated grain-scale dispersion axes yields a preferred axis of crystallographic vorticity at the specimen scale that is coincident with the independently determined bulk vorticity axis. This new method allows the position of vorticity axes to be evaluated independently of foliation and lineation information, and without assumptions about the kinematics of deformation.

Using field data to constrain a numerical kinematic model for ridge-transform deformation in the Troodos ophiolite, Cyprus

The Troodos ophiolite in Cyprus provides a unique opportunity to examine spatially varying patterns of deformation near a ridge-transform intersection. We focus on the paleo–inside corner defined by the E-W–striking, dextral Arakapas transform fault and the N-S–striking Solea graben. Rocks within the inside corner are primarily sheeted dikes and gabbros. The strikes of dikes vary with proximity to the Arakapas fault, changing from NW- to N- to E-striking with increasing proximity to the fault. We report new paleomagnetic results from 24 stations in the gabbroic rocks. When augmented with data from several previous studies, the combined paleomagnetic data set indicates that vertical-axis rotations increase from 5° to 90° with distance from the Solea graben. Rotations are also largest near the transform fault. We develop numerical kinematic models for deformation within the inside corner based on these field data. First, we fit an interpolation function to the two-dimensional field of vertical-axis rotations. This field is then used to undeform dikes, assuming that dikes were either part of rigid blocks or passive markers within a continuum. We find that dikes return to a consistent NW to NNW strike throughout much of the inside corner. This initial orientation is not ridge-parallel and therefore different from most common assumptions of dike behavior in Cyprus. However, the orientation is consistent with predictions from dynamic models of heterogeneous stress directions that develop near ridge-transform intersections.

Mediated Equilibria in Load-Balancing Games

Mediators are third parties to whom the players in a game can delegate the task of choosing a strategy; a mediator forms a mediated equilibrium if delegating is a best response for all players. Mediated equilibria have more power to achieve outcomes with high social welfare than Nash or correlated equilibria, but less power than a fully centralized authority. Here we begin the study of the power of mediation by using the mediation analogue of the price of stability--the ratio of the social cost of the best mediated equilibrium

Homogeneous steady deformation: A review of computational techniques

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Modern methods of analysis for three-dimensional orientational data

to that of the socially optimal outcome

Non-steady homogeneous deformations: Computational techniques using Lie theory, and application to ellipsoidal markers in naturally deformed rocks

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An inverse approach to constraining strain and vorticity using rigid clast shape preferred orientation data

. We focus on load-balancing games with social cost measured by weighted average latency. Even in this restricted class of games,

Equilibria and Efficiency Loss in Games on Networks

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The utility of statistical analysis in structural geology

can range from as good as

Mediated Equilibria in Load-Balanced Games.

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