Related papers: Instabilities and geometry of growing tissues
Strain-based theory on elastic instabilities is being widely employed for studying onset of plasticity, phase transition or melting in crystals. And size effects, observed in nano-materials or solids under dynamic loadings, needs to account…
Living biological tissue is a complex system, constantly growing and changing in response to external and internal stimuli. These processes lead to remarkable and intricate changes in shape. Modeling and understanding both natural and…
We analyse the asymptotic behaviour of a nonlinear mathematical model of cellular proliferation which describes the production of blood cells in the bone marrow. This model takes the form of a system of two maturity structured partial…
The remarkable range of biological forms in and around us, such as the undulating shape of a leaf or flower in the garden, the coils in our gut, or the folds in our brain, raise a number of questions at the interface of biology, physics and…
Plastic deformation in microscale differs from the macroscopic plasticity in two respects: (i) the flow stress of small samples depends on their size (ii) the scatter of plasticity increases significantly. In this work we focus on the…
We numerically study a one-dimensional conserved growth equation with competing linear (Ehrlich-Schwoebel) and nonlinear instabilities. As a control parameter is varied, this model exhibits a non-equilibrium phase transition between two…
Representational similarity analysis and related methods have become standard tools for comparing the internal geometries of neural networks and biological systems. These methods measure what is represented, the alignment between two…
Inelastic surface growth associated with continuous creation of incompatibility on the boundary of an evolving body is behind a variety of natural and technological processes, including embryonic development and 3D printing. In this paper…
Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…
We investigate the curvature-dependence of the visco-elastic Taylor-Couette instability. The radius of curvature is changed over almost a decade and the critical Weissenberg numbers of the first linear instability are determined.…
When a block made of an elastomer is subjected to large shear, its surface remains flat. When a block of biological soft tissue is subjected to large shear, it is likely that its surface in the plane of shear will buckle (apparition of…
We consider a class of biologically-motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final…
As an extension to strain-gradient models of size-dependent plastic behaviour, this work proposes a model for a stress-gradient theory. The model is distinguished from earlier works on the topic by its being embedded in a thermodynamically…
We provide a simple physical picture which suggests that the asymptotic dynamics of inelastic gases in one dimension is independent of the degree of inelasticity. Statistical characteristics, including velocity fluctuations and the velocity…
We consider a macroscopic model for the growth of living tissues incorporating pressure-driven dispersal and pressure-modulated proliferation. Assuming a power-law relation between the mechanical pressure and the cell density, the model can…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity…
We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small…
In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or…
We consider a model to describe stable configurations in epitaxial growth of crystals in the two dimensional case, and in the regime of linearized elasticity. The novelty is that the model also takes into consideration the adatom density on…