Related papers: Differences in boundary behavior in the 3D vertex …
We derive a course grained, continuum model of the 2D vertex model, applicable for different underlying geometries, and allowing for analytical analysis of an otherwise numerical model. Using a geometric approach and out--of--equilibrium…
Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to…
In biological tissues, it is now well-understood that mechanical cues are a powerful mechanism for pattern regulation. While much work has focused on interactions between cells and external substrates, recent experiments suggest that cell…
Voronoi diagrams are a fundamental geometric data structure for obtaining proximity relations. We consider collections of axis-aligned orthogonal polyhedra in two and three-dimensional space under the max-norm, which is a particularly…
In multicellular organisms, relations among parts and between parts and the whole are contextual and interdependent. These organisms and their cells are ontogenetically linked: an organism starts as a cell that divides producing…
We theoretically explore fluidization of epithelial tissues by active T1 neighbor exchanges. We show that the geometry of cell-cell junctions encodes important information about the local features of the energy landscape, which we support…
Many physical systems are composed of polyhedral cells of varying sizes and shapes. These structures are simple in the sense that no more than three faces meet at an edge and no more than four edges meet at a vertex. This means that…
In this article the dynamics of pedestrian streams in four different scenarios are compared empirically to investigate the influence of boundary conditions on it. The Voronoi method, which allows high resolution and small fluctuations of…
The alignment of fibers and cells in living tissues affect their mechanical properties and functionality. In this context, one can draw an analogy between tissues and nematic liquid crystal elastomers. We explore this analogy by growing…
Cells of Voronoi diagrams in two dimensions are usually considered as having edges of zero width. However, this is not the case in several experimental situations in which the thickness of the edges of the cells is relatively large. In this…
To insight the relationships between the self-organizing structures of cells, such as the cell clusters, and the properties of biotissues is helpful in revealing the function and designing biomaterial. Traditional random foam model neglects…
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.…
Recent work on particle-based models of tissues has suggested that any finite rate of cell division and cell death is sufficient to fluidize an epithelial tissue. At the same time, experimental evidence has indicated the existence of glassy…
Every real algebraic variety determines a Voronoi decomposition of its ambient Euclidean space. Each Voronoi cell is a convex semialgebraic set in the normal space of the variety at a point. We compute the algebraic boundaries of these…
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the…
Hyperuniform materials, characterized by their suppressed density fluctuations and vanishing structure factors as the wave number approaches zero, represent a unique state of matter that straddles the boundary between order and randomness.…
Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics determine macroscopic materials properties. The process of formation of various statistical…
Two-dimensional (2D) mechanical models of confluent tissues have related the mechanical state of a monolayer of cells to the average perimeter length of the cell cross sections, predicting floppiness or rigidity of the material. For the…
Structural cellular materials in nature, such as wood, trabecular bone, corals, and dentin combine complex biological functions with structural roles, such as skeletal support and impact protection1,2. They feature complex structural…