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With the development of network science, Turing pattern has been proven to be formed in discrete media such as complex networks, opening up the possibility of exploring it as a generation mechanism in the context of biology, chemistry, and…
We propose two toy-models to describe, predict, and interpret the wrinkles appearing on the surface of skin when it is sheared. With the first model, we account for the lines of greatest tension present in human skin by subjecting a layer…
The coupling of electric fields to the mechanics of lipid membranes gives rise to intriguing electromechanical behavior, as, for example, evidenced by the deformation of lipid vesicles in external electric fields. Electromechanical effects…
Fluid-structure interaction models involve parameters that describe the solid and the fluid behavior. In simulations, there often is a need to vary these parameters to examine the behavior of a fluid-structure interaction model for…
Patterns generated by a colloidal suspension of nanospheres drying on a frictional substrate are studied by experiments and computer simulations. The obtained two-dimensional self-assembled structures are commonly used for nanosphere…
Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock like salt, gypsum or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the…
The assembly of banana-shaped rodlike proteins on membranes, and the associated membrane shape transformations, are investigated by analytical theory and coarse-grained simulations. The membrane-mediated interactions between two…
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
Alan Turing's pioneering work on computability, and his ideas on morphological computing support Andrew Hodges' view of Turing as a natural philosopher. Turing's natural philosophy differs importantly from Galileo's view that the book of…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…
A central problem of geometry is the tiling of space with simple structures. The classical solutions, such as triangles, squares, and hexagons in the plane and cubes and other polyhedra in three-dimensional space are built with sharp…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
A theory for wetting of structured solid surfaces is developed, based on the delta-comb periodic potential. It possesses two matching parameters: the effective line tension and the friction coefficient on the three-phase contact line at the…
This work presents a new procedure to extract features of grey-level texture images based on the discrete Schroedinger transform. This is a non-linear transform where the image is mapped as the initial probability distribution of a wave…
Morphological development into evolutionary patterns under structural instability is ubiquitous in living systems and often of vital importance for engineering structures. Here we propose a data-driven approach to understand and predict…
The structural analysis of shape boundaries leads to the characterization of objects as well as to the understanding of shape properties. The literature on graphs and networks have contributed to the structural characterization of shapes…
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
As zebrafish develop, black and gold stripes form across their skin due to the interactions of brightly colored pigment cells. These characteristic patterns emerge on the growing fish body, as well as on the anal and caudal fins. While…