Related papers: A macroscopic approach for stress driven anisotrop…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
A macroscopic theory for describing cellular states during steady-growth is presented, which is based on the consistency between cellular growth and molecular replication, as well as the robustness of phenotypes against perturbations.…
Morphoelastic rods are thin bodies which can grow and can change their intrinsic curvature and torsion. We deduce a system of equations ruling accretion and remodeling in a morphoelastic rod by combining balance laws involving non-standard…
Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel…
The mechanical response of static, unconfined, overcompressed face centred cubic, granular arrays is studied using large-scale, discrete element method simulations. Specifically, the stress response due to the application of a localised…
We analyze the representation of viscous stresses in the one-fluid formulation of the two-phase Navier-Stokes equations, the model on which all computational approaches making use of a fixed mesh to discretize the flow field are grounded.…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
Within developing embryos, tissues flow and reorganize dramatically on timescales as short as minutes. This includes epithelial tissues, which often narrow and elongate in convergent extension movements due to anisotropies in external…
Some existing models of the atherosclerosis development are discussed and a new improved mathematical model, which takes into account new experimental results about diverse roles of macrophages in atherosclerosis, is proposed. Using technic…
In contrast with ordinary materials, living matter drives its own motion by generating active, out-of-equilibrium internal stresses. These stresses typically originate from localized active elements embedded in an elastic medium, such as…
Embryonic tissues deform across broad spatial and temporal scales and relax stress through active rearrangements. A quantitative link between cell-scale activity, spatial forcing, and emergent tissue-scale mechanics remains incomplete.…
In this paper we present a new general framework for anisotropic elastoplasticity at large strains. The new framework presents the following characteristics: (1) It is valid for non-moderate large strains, (2) it is valid for both elastic…
We study the nonlinear elastic response of a two-dimensional material to a localized boundary force, with the particular goal of understanding the differences observed between isotropic granular materials and those with hexagonal…
The evolution of various competing cell types in tissues, and the resulting persistent tissue population, is studied numerically and analytically in a particle-based model of active tissues. Mutations change the properties of cells in…
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an…
We consider an immersed elastic body that is actively driven through a structured fluid by a motor or an external force. The behavior of such a system generally cannot be solved analytically, necessitating the use of numerical methods.…
Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…
There has been increasing experimental evidence of non-affine elastic deformation mechanisms in biological soft tissues. These observations call for novel constitutive models which are able to describe the dominant underlying…
We formulate and prove a shape theorem for a continuous-time continuous-space stochastic growth model under certain general conditions. Similarly to the classical lattice growth models the proof makes use of the subadditive ergodic theorem.…
We study a one-dimensional equation arising in the multiscale modeling of some non-Newtonian fluids. At a given shear rate, the equation provides the instantaneous mesoscopic response of the fluid, allowing to compute the corresponding…