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Phyllotactic patterns, i.e. regular arrangements of leaves or seeds around a plant stem, are fascinating examples of complex structures encountered in Nature. In botany, their symmetries develop when a new primordium periodically grows in…
Capturing the emergence of deformation waves in contractile living tissues is a challenge that has recently been tackled with models of actively deformable particles. Inspired by the anisotropic deformation of cardiomyocytes in cardiac…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…
Emergence of regular spatial patterns is a hallmark in living matter ranging from subcellular organelles to developing embryos and to ecosystems. Mechanisms for the formation of ordered spatial patterns in biology often require chemical…
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a…
This paper outlines our recent attempts to model the growth and form of microbialites from the perspective of the statistical physics of evolving surfaces. Microbialites arise from the environmental interactions of microbial communities…
Quantifying the outcomes of cells collisions is a crucial step in building the foundations of a kinetic theory of living matter. Here, we develop a mechanical theory of such collisions by first representing individual cells as extended…
Organogenesis is a tightly regulated process that has been studied experimentally for decades. We are developing mechanistic models for the morphogenesis of limbs, lungs, and kidneys with a view to integrate available knowledge and to…
The emergence of a body axis is a fundamental step in the development of multicellular organisms. In simple systems such as $\textit{Hydra}$, growing evidence suggests that mechanical forces generated by collective cellular activity play a…
We investigate possible shapes of the electric field, which oscillating dipoles in a certain region of biological tissue can produce in a neighboring region, or outside the tissue boundaries. We find that a wide range of shapes, including…
There is now growing evidence of the emergence and biological functionality of liquid crystal features, including nematic order and topological defects, in cellular tissues. However, how such features that intrinsically rely on particle…
Bacteria possess diverse mechanisms to regulate their motility in response to environmental and physiological signals, enabling them to navigate complex habitats and adapt their behavior. Among these mechanisms, interspecies recognition…
This paper proposes an agent-based model which reproduces different structures of animal groups. The shape and structure of the group is the effect of simple interaction rules among individuals: each animal deploys itself depending on the…
Mathematical models of biological growth commonly attempt to distinguish deformation due to growth from that due to mechanical stresses through a hypothesised multiplicative decomposition of the deformation gradient. Here we demonstrate…
We study the morphology of a fluid membrane in spherical confinement. When the area of the membrane is slightly larger than the area of the outer container, a single axisymmetric invagination is observed. For higher area, self-contact…
Cities are living organisms. They are out of equilibrium, open systems that never stop developing and sometimes die. The local geography can be compared to a shell constraining its development. In brief, a city's current layout is a step in…
The hydrodynamic theory of active nematics has been often used to describe the spatio-temporal dynamics of cell flows and motile topological defects within soft confluent tissues. Those theories, however, often rely on the assumption that…
In Part I of this article we have developed a novel mechanobiological model of a Tissue Engineering process that accounts for the mechanisms through which an isotropic or anisotropic adherence condition regulates the active functions of the…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
Results of experimental investigation are presented of evolutionary dynamics of several stochastic pattern formation and growth models designed by modifications of the famous mathematical Game of Life. The modifications are two-fold: Game…