Related papers: Parameter degeneracy in the vertex model for tissu…
Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are…
One of the mechanisms that ensure cancer robustness is tumor heterogeneity, and its effects on tumor cells dynamics have to be taken into account when studying cancer progression. There is no unifying theoretical framework in mathematical…
The size and shape of a large variety of polymeric particles, including biological cells, star polymers, dendrimes, and microgels, depend on the applied stresses as the particles are extremely soft. In high-density suspensions these…
When analyzing parametric statistical models, a useful approach consists in modeling geometrically the parameter space. However, even for very simple and commonly used hierarchical models like statistical mixtures or stochastic deep neural…
We deal with a degenerate model in divergence form describing the dynamics of a population depending on time, on age and on space. We assume that the degeneracy occurs in the interior of the spatial domain and we focus on null…
Tissue dynamics and collective cell motion are crucial biological processes. Their biological machinery is mostly known, and simulation models such as the "active vertex model" (AVM) exist and yield reasonable agreement with experimental…
Tissue homeostasis, the biological process of maintaining a steady state in tissue via control of cell proliferation, death, and metabolic function, is essential for the development, growth, maintenance, and proper function of living…
The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…
The paper focuses on the stiffness modeling of parallel manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones. In these manipulators, there usually exist essential internal…
A continuum description is built to characterize the stationary and transient deformations of confluent tissues subject to heterogeneous activities. By defining a coarse-grained texture matrix field to represent the shape and size of cells,…
In this work we use cosmography to alleviate the degeneracy among cosmological models, proposing a way to parameterize matter and dark energy in terms of cosmokinematics quantities. The recipe of using cosmography allows to expand…
We introduce a new method which resolves the problem of regularity and compactness of entropy solutions for nonlinear degenerate parabolic equations under non-degeneracy conditions on the sphere. In particular, we address a problem of…
Computer simulation models are widely used to study complex physical systems. A related fundamental topic is the inverse problem, also called calibration, which aims at learning about the values of parameters in the model based on…
In this paper homogenization of a mathematical model for plant tissue biomechanics is presented. The microscopic model constitutes a strongly coupled system of reaction-diffusion-convection equations for chemical processes in plant cells,…
We are interested in evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a…
A widely employed method for estimating the mass of stellar systems with apparent spherical symmetry is dynamical modelling using the spherically symmetric Jeans equation. Unfortunately this approach suffers from a degeneracy between the…
In a previous work [J. Chem. Phys. 155, 244111 (2021)], we found counterexamples to the fundamental Hohenberg-Kohn theorem from density-functional theory in finite-lattice systems represented by graphs. Here, we demonstrate that this only…
The vertex model is a popular framework for modelling tightly packed biological cells, such as confluent epithelia. Cells are described by convex polygons tiling the plane and their equilibrium is found by minimizing a global mechanical…
General relativity (GR) has been well tested up to solar system scales, but it is much less certain that standard gravity remains an accurate description on the largest, that is, cosmological, scales. Many extensions to GR have been studied…
The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…