A new study on Ooid growth

Shape evolution of ooids: a geometric model
András A. Sipos, Gábor Domokos, Douglas J. Jerolmack

Abstract: 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.

New paper on granular systems published

Frustrated packing in a granular system under geometrical confinement
Sára Lévay, David Fischer, Ralf Stannarius, Balázs Szabó, Tamás Börzsönyi and János Török

Abstract: Optimal packings of uniform spheres are solved problems in two and three dimensions. The main difference between them is that the two-dimensional ground state can be easily achieved by simple dynamical processes while in three dimensions, this is impossible due to the difference in the local and global optimal packings. In this paper we show experimentally and numerically that in 2 + ε dimensions, realized by a container which is in one dimension slightly wider than the spheres, the particles organize themselves in a triangular lattice, while touching either the front or rear side of the container. If these positions are denoted by up and down the packing problem can be mapped to a 1/2 spin system. At first it looks frustrated with spin-glass like configurations, but the system has a well defined ground state built up from isosceles triangles. When the system is agitated, it evolves very slowly towards the potential energy minimum through metastable states. We show that the dynamics is local and is driven by the optimization of the volumes of 7-particle configurations and by the vertical interaction between touching spheres.

Guest lecturer: Rocky Taylor

Morphodynamics of sea ice: exploring morphological evolution of ice rubble and ridges during the seasonal life cycle of deformed first-year sea ice

Rocky S. Taylor, Memorial University of Newfoundland, Canada

November 13, 2017

Abstract: Sea ice features in nature can take on many different forms. For marine and offshore engineering applications, ice loads during interactions with ice rubble and ice ridges are an important design consideration. Morphodynamic aspects of sea ice deformation and degradation processes are of interest in understanding the seasonal evolution of these features, since such methods may provide opportunities to simplify modelling of these highly complex processes. During deformation of a level ice sheet, it is of interest to understand how resultant distributions of block sizes and shapes are linked to the parent ice thickness and other environmental conditions. Similarly, for existing ice rubble and ridges, it is of interest how block shape evolution occurs during freezing/thawing cycles and how this influences the internal buoyancy forces on submerged ice blocks within a ridge. Such processes in turn influence rubble pile stability, since evolution of the shapes and associated centres of buoyancy for each block will change the distribution of stresses on the bonds between them. This can influence the degradation of strength of ice ridges, ultimately contributing to the breakdown of these features during spring thaw. These processes are of interest to help identify the key deterioration mechanisms for ridges, since it is not clear if this process would result in local progressive failure of a ridge (e.g. blocks shed away gradually from the outside with the failure front moving inward over time until the whole ridge is gone) or if there is sufficient reserve strength in the bonds so that the change in buoyancy results in a build-up of stresses due to these shifting buoyance forces that ultimately results in a sudden, global collapse of the whole ridge. Understanding these processes is important in developing new mathematical models, not only for modelling strength of deteriorated ridges during ice-structure interactions, but also for improving deterioration models that may be incorporated into larger-scale thermodynamic ice environmental models.


Dr. Rocky Taylor is an Assistant Professor in Mechanical Engineering at Memorial University of Newfoundland in St. John’s, Canada, where he is also the Centre for Arctic Resource Development (CARD) Chair in Ice Mechanics. In this role he leads a team of researchers and graduate students working on Ice Compressive Failure Mechanics, Ice Rubble Mechanics, Ice Environmental Characterization and Ice-Structure Interaction Modelling. He has carried out field work in the Labrador Sea, Northern Newfoundland, the North Humberland Strait, the Caspian Sea, and the Barents Sea. He has more than 50 peer reviewed publications, has worked on many industry and academic projects and is currently a member of the ISO 19906 Canadian Review Committee.

New pre-print available

A shape evolution model under affine transformations
Gábor Domokos, Zsolt Lángi, Márk Mezei

Abstract: In this note we describe a discrete dynamical system acting on the similarity classes of a plane convex body within the affine class of the body. We find invariant elements in all affine classes, and describe the orbits of bodies in some special classes. We point out applications with abrasion processes of pebble shapes.

Guest lecturer: László Székelyhidi

Rigid surfaces and how Nash bent them

László Székelyhidi
Universität Leipzig

October 2, 2017

Abstract: A compact surface in R3 is called rigid if the only length-preserving transformations of it are congruencies of the ambient space – in simple terms rigid surfaces are unbendable. Rigidity is a topic which is already found in Euclid’s Elements. Euler conjectured in 1766 that every smooth compact surface is rigid. The young Cauchy found a proof in 1813 for convex polyhedra, but it took another 100 years until a proof for smooth convex surfaces appeared. Whilst it seems clear that convexity, and more generally curvature plays an important role for rigidity, it came as a shock to the world of geometry when J. Nash showed in 1954 that every surface can be bent in an essentially arbitrary, albeit non-convex manner. The proof of Nash involves a highly intricate fractal-like construction, that has in recent years found applications in many different branches of applied mathematics, such as elasticity and fluid mechanics. The talk will provide an overview of this fascinating subject and the most recent developments.