Related papers: Cell shape analysis of random tessellations based …
Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness.…
Spatially homogeneous random tessellations that are stable under iteration (nesting) in the 3-dimensional Euclidean space are considered, so-called STIT tessellations. They arise as outcome of a spatio-temporal process of subsequent cell…
We apply Minkowski functionals and various derived measures to decipher the morphological properties of large-scale structure seen in simulations of gravitational evolution. Minkowski functionals of isodensity contours serve as tools to…
In this paper we consider a random partition of the plane into cells, the partition being based on the nodes and links of a {\it random planar geometric graph}. The resulting structure generalises the \emph{random \tes}\ hitherto studied in…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
In this paper, a two-scale approach for elastic shape optimization of fine-scale structures in additive manufacturing is investigated. To this end, a free material optimization is performed on the macro-scale using elasticity tensors in a…
Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…
Most granular packings possess shear moduli ($G$) that increase with the applied external pressure, and bulk moduli ($B$) that increase or remain constant with pressure. This paper presents "tessellated" granular metamaterials for which…
Using a popular vertex-based model to describe a spatially disordered planar epithelial monolayer, we examine the relationship between cell shape and mechanical stress at the cell and tissue level. Deriving expressions for stress tensors…
Many closed-cell foams exhibit an elongated cell shape in the foam rise direction, resulting in anisotropic compressive properties. Nevertheless, the underlying deformation mechanisms and how cell shape anisotropy induces this mechanical…
Entangled materials offer attractive structural features including tensile strength and large deformations, combined with infinite assembly and disassembly capabilities. How the geometry of individual particles governs entanglement, and in…
For material modeling of microstructured media, an accurate characterization of the underlying microstructure is indispensable. Mathematically speaking, the overall goal of microstructure characterization is to find simple functionals which…
Morphogenetic dynamics of tissue sheets require coordinated cell shape changes regulated by global patterning of mechanical forces. Inspired by such biological phenomena, we propose a minimal mechanochemical model based on the notion that…
Intra-tumor heterogeneity driving disease progression is characterized by distinct growth and spatial proliferation patterns of cells and their nuclei within tumor and non-tumor tissues. A widely accepted hypothesis is that these spatial…
Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering and life sciences. In this work, we investigate the statistical properties of…
Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
Recent advances in local models for point processes have highlighted the need for flexible methodologies to account for the spatial heterogeneity of external covariates influencing process intensity. In this work, we introduce tessellated…
Molecular self-assembly plays a very important role in various aspects of technology as well as in biological systems. Governed by the covalent, hydrogen or van der Waals interactions - self-assembly of alike molecules results in a large…
100 years after Smoluchowski introduces his approach to stochastic processes, they are now at the basis of mathematical and physical modeling in cellular biology: they are used for example to analyse and to extract features from large…