András Árpád Sipos

How river rocks round: resolving the shape-size paradox.

River-bed sediments display two universal downstream trends: fining, in which particle size decreases; and rounding, where pebble shapes evolve toward ellipsoids. Rounding is known to result from transport-induced abrasion; however many researchers argue that the contribution of abrasion to downstream fining is negligible. This presents a paradox: downstream shape change indicates substantial abrasion, while size change apparently rules it out. Here we use laboratory experiments and numerical modeling to show quantitatively that pebble abrasion is a curvature-driven flow problem. As a consequence, abrasion occurs in two well-separated phases: first, pebble edges rapidly round without any change in axis dimensions until the shape becomes entirely convex; and second, axis dimensions are then slowly reduced while the particle remains convex. Explicit study of pebble shape evolution helps resolve the shape-size paradox by reconciling discrepancies between laboratory and field studies, and enhances our ability to decipher the transport history of a river rock.

Formation of Sharp Edges and Planar Areas of Asteroids by Polyhedral Abrasion

While the number of asteroids with known shapes has drastically increased over the past few years, little is known on the time-evolution of shapes and the underlying physical processes. Here we propose an averaged abrasion model based on micro-collisions, accounting for asteroids not necessarily evolving toward regular spheroids, rather (depending on the fall-back rate of ejecta) following an alternative path, thus confirming photometry-derived features, e.g., existence of large, relatively flat areas separated by edges. We show that our model is realistic, since the bulk of the collisions falls into this category.

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.

A Discrete Random Model Describing Bedrock Profile Abrasion

We use a simple, collision-based, discrete, random abrasion model to compute the profiles for the stoss faces in a bedrock abrasion process. The model is the discrete equivalent of the generalized version of a classical, collision based model of abrasion. Three control parameters (which describe the average size of the colliding objects, the expected direction of the impacts and the average volume removed from the body due to one collision) are sufficient for realistic predictions.Our computations show the robust emergence of steady state shapes, both the geometry and the time evolution of which shows good quantitative agreement with laboratory experiments.

Applying the improved saleve framework for modeling abrasion of pebbles

Saleve is a generic framework for making the development of Parameter Study tasks easy for scientists and engineers not familiar with distributed technologies In this paper we present our lightweight authentication procedure for Saleve to delegate user credentials towards the grid Then we present a detailed statistics of abrasion of pebbles gained with Saleve Finally we make remarks on the makespan of the application and look for ways to reduce it.

Shape evolution of ooids: a geometric model

Striking shapes in nature have been documented to result from chemical precipitation — such as terraced hot springs and stromatolites — which often proceeds via surface-normal growth. Another studied class of objects is those whose shape evolves by physical abrasion — the primary example being river and beach pebbles — which results in shape-dependent surface erosion. While shapes may evolve in a self-similar manner, in neither growth nor erosion can a surface remain invariant. Here we investigate a rare and beautiful geophysical problem that combines both of these processes; the shape evolution of carbonate particles known as ooids. We hypothesize that mineral precipitation, and erosion due to wave-current transport, compete to give rise to novel and invariant geometric forms. We show that a planar (2D) mathematical model built on this premise predicts time-invariant (equilibrium) shapes that result from a balance between precipitation and abrasion. These model results produce nontrivial shapes that are consistent with mature ooids found in nature.

Analysing current density in the solder joints of chip-size Surface Mounted resistors

The paper discusses a numerical modelling research, where different sized Surface Mounted Device (SMD) chip-size resistors and their solder joints are analysed from the aspect of current density. The solder joint structure and the connecting traces to the Printed Circuit Board (PCB) solder pads define the route of the current in the structure, where corners may form areas with higher current density, increasing the possibility of electromigration. In our research, we used 0201, 0402 and 0603 jumper resistors for the highest applicable current load. The paper presents the process of 3D modelling, where the shape of the solder joint is calculated with Surface Evolver. The current routes and the possible regions with high current stresses are calculated with Finite Element Method (FEM). The results highlight the critical configuration of solder joint shape, connecting trace direction and current load on the given components.

Circular, Stationary Profiles Emerging in Unidirectional Abrasion

Models of moving interfaces, especially those with stable soliton-like behavior, are of central importance in many areas of physics, for example, surface growth models, chemical waves, and more. Here described for the first time in a realistic geophysical context is a partial differential equation model of bedrock abrasion by unidirectional impacts generalizing earlier pioneering work on pebble shapes by Bloore who treated isotropic impacts (Bloore in Math. Geol. 9:113–122, 1977). The result is a simple geometrical partial differential equation exhibiting circular arcs as solitary wave profiles. The latter seem to be the first known analytic solutions on Bloore-type models. Solitonic behavior, although familiar in many areas of physics, appears not to have been encountered in the geophysical literature. Not only are the existence and stability of these stationary, traveling shapes demonstrated here by numerical experiments based on finite difference approximations, but it is also shown that the results received here are consistent with recent laboratory experiments. The simulations within show that, depending on initial profile shape and other parameters, these circular profiles may evolve via long transients, which in a geological setting, may appear as noncircular stationary profiles.

Reconstruction of early phase deformations by integrated magnetic and mesotectonic data evaluation

Abstract Markers of brittle faulting are widely used for recovering past deformation phases. Rocks often have oriented magnetic fabrics, which can be interpreted as connected to ductile deformation before cementation of the sediment. This paper reports a novel statistical procedure for simultaneous evaluation of AMS (Anisotropy of Magnetic Susceptibility) and fault-slip data. The new method analyzes the AMS data, without linearization techniques, so that weak AMS lineation and rotational AMS can be assessed that are beyond the scope of classical methods. This idea is extended to the evaluation of fault-slip data. While the traditional assumptions of stress inversion are not rejected, the method recovers the stress field via statistical hypothesis testing. In addition it provides statistical information needed for the combined evaluation of the AMS and the mesotectonic (0.1 to 10 m) data. In the combined evaluation a statistical test is carried out that helps to decide if the AMS lineation and the mesotectonic markers (in case of repeated deformation of the oldest set of markers) were formed in the same or different deformation phases. If this condition is met, the combined evaluation can improve the precision of the reconstruction. When the two data sets do not have a common solution for the direction of the extension, the deformational origin of the AMS is questionable. In this case the orientation of the stress field responsible for the AMS lineation might be different from that which caused the brittle deformation. Although most of the examples demonstrate the reconstruction of weak deformations in sediments, the new method is readily applicable to investigate the ductile-brittle transition of any rock formation as long as AMS and fault-slip data are available.

Author Correction: Shape evolution of ooids: a geometric model

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.