Tímea Szabó

Reconstructing the transport history of pebbles on Mars

The discovery of remarkably rounded pebbles by the rover Curiosity, within an exhumed alluvial fan complex in Gale Crater, presents some of the most compelling evidence yet for sustained fluvial activity on Mars. While rounding is known to result from abrasion by inter-particle collisions, geologic interpretations of sediment shape have been qualitative. Here we show how quantitative information on the transport distance of river pebbles can be extracted from their shape alone, using a combination of theory, laboratory experiments and terrestrial field data. We determine that the Martian basalt pebbles have been carried tens of kilometres from their source, by bed-load transport on an alluvial fan. In contrast, angular clasts strewn about the surface of the Curiosity traverse are indicative of later emplacement by rock fragmentation processes. The proposed method for decoding transport history from particle shape provides a new tool for terrestrial and planetary sedimentology.

Quantifying the Significance of Abrasion and Selective Transport for Downstream Fluvial Grain Size Evolution

It is well known that pebble diameter systematically decreases downstream in rivers. The contribution of abrasion is uncertain, in part because (1) diameter is insufficient to characterize pebble mass loss due to abrasion and (2) abrasion rates measured in laboratory experiments cannot be easily extrapolated to the field. A recent geometric theory describes abrasion as a curvature-dependent process that produces a two-phase evolution: in Phase I, initially blocky pebbles round to smooth, convex shapes with little reduction in axis dimensions; then, in Phase II, smooth, convex pebbles slowly reduce their axis dimensions. Here we provide strong evidence that two-phase abrasion occurs in a natural setting, by examining downstream evolution of shape and size of thousands of pebbles over ~10 km in a tropical montane stream. The geometric theory is verified in this river system using a variety of manual and image-based shape parameters, providing a generalizable method for quantifying the significance of abrasion. Phase I occurs over ~1 km, in upstream bedrock reaches where abrasion is dominant and sediment storage is limited. In downstream alluvial reaches, where Phase II occurs, we observe the expected exponential decline in pebble diameter. Using a discretized abrasion model (the so-called “box equations”) with deposition, we deduce that abrasion removes more than one third of the mass of a pebble but that size-selective sorting dominates downstream changes in pebble diameter. Overall, abrasion is the dominant process in the downstream diminution of pebble mass (but not diameter) in the studied river, with important implications for pebble mobility and the production of fine sediments.

Universality of fragment shapes

The shape of fragments generated by the breakup of solids is central to a wide variety of problems ranging from the geomorphic evolution of boulders to the accumulation of space debris orbiting Earth. Although the statistics of the mass of fragments has been found to show a universal scaling behavior, the comprehensive characterization of fragment shapes still remained a fundamental challenge. We performed a thorough experimental study of the problem fragmenting various types of materials by slowly proceeding weathering and by rapid breakup due to explosion and hammering. We demonstrate that the shape of fragments obeys an astonishing universality having the same generic evolution with the fragment size irrespective of materials details and loading conditions. There exists a cutoff size below which fragments have an isotropic shape, however, as the size increases an exponential convergence is obtained to a unique elongated form. We show that a discrete stochastic model of fragmentation reproduces both the size and shape of fragments tuning only a single parameter which strengthens the general validity of the scaling laws. The dependence of the probability of the crack plan orientation on the linear extension of fragments proved to be essential for the shape selection mechanism.

On the equilibria of finely discretized curves and surfaces

Our goal is to identify the type and number of static equilibrium points of solids arising from fine, equidistant n-discretizations of smooth, convex surfaces. We assume uniform gravity and a frictionless, horizontal, planar support. We show that as n approaches infinity these numbers fluctuate around specific values which we call the imaginary equilibrium indices associated with the approximated smooth surface. We derive simple formulae for these numbers in terms of the principal curvatures and the radial distances of the equilibrium points of the solid from its center of gravity. Our results are illustrated on a discretized ellipsoid and match well the observations on natural pebble surfaces.

Generating spherical multiquadrangulations by restricted vertex splittings and the reducibility of equilibrium classes

We study the combinatorial properties associated with an earlier published, geometric algorithm capable of generating convex bodies in any primary equilibrium class (i.e. bodies with arbitrary numbers of equilibrium points) from a single ancestor. Primary equilibrium classes contain several topological secondary classes based on the arrangement of the equilibrium points. Here we show that the associated graph expansion algorithm is incomplete in the sense that using the same ancestor, not all secondary classes can be generated and we point out the nontrivial set of ancestors necessary to generate all secondary classes.