arXiv subjects

András A. Sipos

Publications and source records attributed to András A. Sipos.

3 recordsLinked to original sources

arXiv2025

Diverse patterns of pebbles on sand on Mars and Earth

On Mars, fields of sand dunes contrast with the general cratered, rocky terrain commonly seen from orbit. Near the equator, in Gale Crater, images from the rover, Curiosity, also reveal order on smaller scales: ripples on dunes, and ground patterns in scattered sites. The patterns include relatively inconspicuous forms: evenly spaced pebble-size rocks (termed clasts) on meter-scale domains of wind-blown sand. Here, we examine quantitatively several such domains on both Mars and Earth. The domains are significantly more orderly than expected by chance. Moreover, many are hyperuniform, a self-organized state recently recognized in diverse active materials and biological systems but that appears novel for planetary surfaces. We use numerical simulations to examine how diverse clast distributions, ranging from random and hyperuniform dispersions to distinct alignments, can emerge spontaneously from clast displacements induced by gravity, combined with the wind-driven evolution of the surface, sand transport, and ripple migration. This paper highlights easily overlooked self-organized patterns beyond distinct geometric patterns on at least two planets, and the simulations help understand the information coded in clast domains. Moreover, our methods and findings potentially have quantitatively implications for studies of issues of global significance on Earth, including dust emission from vast areas into the atmosphere.

physics.geo-ph↗

arXiv2018

Tracking critical points on evolving curves and surfaces

In recent years it became apparent that geophysical abrasion can be well characterized by the time evolution $N(t)$ of the number $N$ of static balance points of the abrading particle. Static balance points correspond to the critical points of the particle's surface represented as a scalar distance function $r$, measured from the center of mass, so their time evolution can be expressed as $N(r(t))$. The mathematical model of the particle can be constructed on two scales: on the macro scale the particle may be viewed as a smooth, convex manifold described by the smooth distance function $r$ with $N=N(r)$ equilibria, while on the micro scale the particle's natural model is a finely discretized, convex polyhedral approximation $r^Δ$ of $r$, with $N^Δ=N(r^Δ)$ equilibria. There is strong intuitive evidence suggesting that under some particular evolution models $N(t)$ and $N^Δ(t)$ primarily evolve in the opposite manner. Here we create the mathematical framework necessary to understand these phenomenon more broadly, regardless of the particular evolution equation. We study micro and macro events in one-parameter families of curves and surfaces, corresponding to bifurcations triggering the jumps in $N(t)$ and $N^Δ(t)$. We show that the intuitive picture developed for curvature-driven flows is not only correct, it has universal validity, as long as the evolving surface $r$ is smooth. In this case, bifurcations associated with $r$ and $r^Δ$ are coupled to some extent: resonance-like phenomena in $N^Δ(t)$ can be used to forecast downward jumps in $N(t)$ (but not upward jumps). Beyond proving rigorous results for the $Δ\to 0$ limit on the nontrivial interplay between singularities in the discrete and continuum approximations we also show that our mathematical model is structurally stable, i.e. it may be verified by computer simulations.

math.DS↗

arXiv2017

Explaining the elongated shape of 'Oumuamua by the Eikonal abrasion model

The photometry of the minor body with extrasolar origin (1I/2017 U1) 'Oumuamua revealed an unprecedented shape: Meech et al. (2017) reported a shape elongation b/a close to 1/10, which calls for theoretical explanation. Here we show that the abrasion of a primordial asteroid by a huge number of tiny particles ultimately leads to such elongated shape. The model (called the Eikonal equation) predicting this outcome was already suggested in Domokos et al. (2009) to play an important role in the evolution of asteroid shapes.

astro-ph.EP↗