arXiv subjects

Gabor Domokos

Publications and source records attributed to Gabor Domokos.

9 recordsLinked to original sources

arXiv2025

Recovering the polyhedral geometry of fragments

Not only is the geometry of rock fragments often well approximated by ideal convex polyhedra having few faces and vertices, but these numbers carry vital geophysical information on the fragmentation process. Despite their significance, the identification of the ideal polyhedron has so far been carried out through visual inspection. Here, we present an algorithm capable of performing this task in a reliable manner. The input is a 3D scan of the fragment which is essentially a triangulated polyhedron, which however has often large number of faces and vertices. Our algorithm performs a systematic simplification using the following steps: - Gaussian smoothing is performed on the spherical histogram of the 3D scans faces to identify the most important face orientations. - Planes carrying the faces of the ideal polyhedron are identified as maxima of the smoothed histogram - Polygon is reconstructed using the identified planes - Small faces are removed in a systematic manner We present two versions of the algorithm that we benchmarked the algorithm against a dataset of human measurements on 132 fragments. Beyond identifying the ideal polyhedral approximation for fragments, our method is also capable of tracing backward the shape evolution of rounded pebbles to their origins.

physics.geo-ph↗

arXiv2021

How curvature flows: scaling laws and global geometry of impact induced attrition processes

Impact induced attrition processes are, beyond being essential models of industrial ore processing, broadly regarded as the key to decipher the provenance of sedimentary particles. A detailed understanding of single impact phenomena of solid bodies has been obtained in physics and engineering, however, the description of gradual mass reduction and shape evolution in impact sequences relies on approximate mathematical models of mean field type, formulated as curvature-driven partial differential equations. Here we establish the first link between microscopic, particle-based material models and the mean field theory for these processes. Based on realistic computer simulations of particle-wall collision sequences, we first identify the well-known damage and fragmentation energy phases, then we show that the former is split into the abrasion phase with infinite sample lifetime, analogous to Sternberg's Law, at finite asymptotic mass and the cleavage phase with finite sample lifetime, decreasing as a power law of the impact velocity, analogous to Basquin's Law. We demonstrate that only in the abrasion phase does shape evolution emerging in microscopic material models reproduce with startling accuracy the spatio-temporal patterns predicted by macroscopic mean field approaches. Our results substantially extend the phase diagram of impact phenomena and set the boundaries of the applicability of geometric mean field theories for geological shape evolution. Additionally, the scaling laws obtained can be exploited for quantitative predictions of evolution histories.

cond-mat.dis-nn↗

arXiv2018

The evolution of geophysical shape descriptors under distance-driven flows

We investigate the evolution of axis ratios, roundness (isoperimetric ratio) and the number of static balance points under distance-driven flows. The latter have already been proposed by Aristotle as models of particle shape evolution and recent studies indicate that they may serve as models for frictional abrasion. We show exact conditions under which Aristotle's original claims are true. For several geophysical shape descriptors we prove monotonic or quasiconcave time evolution and compare these results with results from the literature on curvature-driven flows as models of collisional abrasion.

math.MG↗

arXiv2017

On the smallest parallel quadrangulation with minimum degree 3

The identity of the smallest quadrangulation with minimum degree 3 also containing parallel edges is unknown. However, it has already been determined that its order (the number of vertices) is between 11 and 14. This paper narrows this domain by showing that the order is at least 12.

math.CO↗

arXiv2014

On global equilibria of finely discretized curves and surfaces

In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant $n$-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on two scales: the local scale corresponds to the discretization, the global scale to the original, smooth surface. In that paper we showed that as $n$ approaches infinity, the number of local equilibria fluctuate around specific values which we call the imaginary equilibrium indices associated with the approximated smooth surface. Here we show how the number of global equilibria can be interpreted, defined and computed on such discretizations. Our results are relevant from the point of view of natural pebble surfaces, they admit a comparison between field data based on hand measurements and laboratory data based on 3D scans.

math.DG↗

arXiv2013

Nonsmooth geometry and collapse of flexible structures under smooth loads

While static equilibria of flexible strings subject to various load types (gravity, hydrostatic pressure, Newtonian wind) is well understood textbook material, the combinations of the very same loads can give rise to complex spatial behaviour at the core of which is the unilateral material constraint prohibiting compressive loads. While the effects of such constraints have been explored in optimisation problems involving straight cables, the geometric complexity of physical configurations has not yet been addressed. Here we show that flexible strings subject to combined smooth loads may not have smooth solutions in certain ranges of the load ratios. This non-smooth phenomenon is closely related to the collapse geometry of inflated tents. After proving the nonexistence of smooth solutions for a broad family of loadings we identify two alternative, critical geometries immediately preceding the collapse. We verify these analytical results by dynamical simulation of flexible chains as well as with simple table-top experiments with an inflated membrane.

math-ph↗

arXiv2011

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 $n$-discretrizations 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.

math.DG↗

arXiv2011

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.

physics.geo-ph↗

arXiv2004

trans-GZK Cosmic Rays: Strings, Black Holes, Neutrinos, or All Three?

We review the scenario in which ``strongly interacting neutrinos'' are responsible for inducing airshowers with inferred energies $E > 8\times10^{19}$ eV. This possibility arises naturally in string excitation models having a unification scale effectively decoupled from the Planck scale. We then show that phenomenological quantum gravity considerations reveal an equivalency of ``mini-black hole'' and strongly interacting neutrino pictures for explaining trans-GZK events. This equivalence can be exploited to predict single particle inclusive distributions. The resulting observable consequences in airshower development are studied using the Adaptive Longitudinal Profile Shower (ALPS) simulation.

hep-ph↗