Related papers: Roundness of grains in cellular microstructures

We calculate the physical structure of protoplanetary disks by evaluating the gas density and temperature self-consistently and solving separately for the dust temperature. The effect of grain growth is taken into account by assuming a…

Amorphous materials lack long-range order but short-range order can still persist through the recurrence of similar local packing motifs. While the short-range order in bulk amorphous phases has been well studied and identified as an…

The growth pattern of an invasive cell-to-cell propagation (called the successive coronas) on the square grid is a tilted square. On the triangular and hexagonal grids, it is an hexagon. It is remarkable that, on the aperiodic structure of…

In this paper, we have investigated, using finite element calculations, the effect of initial texture on the formation of multiple necking patterns in ductile metallic rings subjected to rapid radial expansion. The mechanical behavior of…

In order to characterize the early growth of fine-grained dust rims (FGRs) that commonly surround chondrules, we perform numerical simulations of dust accretion onto chondrule surfaces. We employ a Monte Carlo algorithm to simulate the…

We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. We give formulas for their dimension and vertex degree. In the…

Every realistic instance of a percolation problem is faced with some degree of polydispersity, e.g., the pore-size distribution of an inhomogeneous medium, the size distribution of filler particles in composite materials, or the vertex…

This paper studies groups of symplectomorphisms of ruled surfaces for symplectic forms with varying cohomology class. This class is characterized by the ratio R of the size of the base to that of the fiber. By considering appropriate spaces…

We investigate the local- and long-range structure of four different space-filling cellular patterns: bubbles in a quasi-2d foam plus Voronoi constructions made around points that are uncorrelated (Poisson patterns), low discrepancy (Halton…

We study Voronoi cells in the statistical setting by considering preimages of the maximum likelihood estimator that tessellate an open probability simplex. In general, logarithmic Voronoi cells are convex sets. However, for certain…

We develop primal and mixed variational formulations of transport phenomena on cell complexes with simple polytope connectivity. This framework addresses materials with internal structures comprising components of different topological…

Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two- and three dimensional…

The self-assembly of hard polyhedral particles confined to a flat interface is studied using Monte Carlo simulations. The particles are pinned to the interface by restricting their movement in the direction perpendicular to it while…

Stagnation of grain growth is often attributed to impurity segregation. Yttria-stabilized cubic zirconia does not evidence any segregation-induced slowdown, as its grain growth obeys the parabolic law when the grain size increases by more…

A progress report on two recent theoretical approaches proposed to understand the physics of irreversible fractal aggregates showing up a structural transition from a rather dense to a more multibranched growth is presented. In the first…

The study of grain boundary phase transitions is an emerging field until recently dominated by experiments. The major bottleneck in exploration of this phenomenon with atomistic modeling has been the lack of a robust computational tool that…

A recurring motif in the organization of biological tissues are networks of long, fibrillar protein strands effectively confined to cylindrical surfaces. Often, the fibers in such curved, quasi-2D geometries adopt a characteristic order:…

We study a class of mechanisms known as Kokotsakis polyhedra with a quadrangular base. These are $3\times3$ quadrilateral meshes whose faces are rigid bodies and joined by hinges at the common edges. In contrast to existing work, the…

Understanding and controlling the properties and dynamics of topological defects is a lasting challenge in the study of two-dimensional materials, and is crucial to achieve high-quality films required for technological applications. Here…

Grain growth fundamentally shapes the microstructure of crystalline materials upon annealing, affecting their overall mechanical and functional properties. Recently, it has been rationalized that grain growth in polycrystals does not result…