Related papers: Nonlocal adhesion models for two cancer cell pheno…
Existing nonlocal diffusion models are predominantly classified into two categories: bond-based models, which involve a single-fold integral and usually simulate isotropic diffusion, and state-based models, which contain a double-fold…
Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To understand better this impact, we propose a mathematical model…
Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories…
We present a systematic theory connecting the nonlocal response kernel of a homogeneous medium to its effective surface susceptibilities for an arbitrary curved interface. Starting from the most general tensorial nonlocal constitutive…
For some spatially nonlocal diffusion models with a finite range of nonlocal interactions measured by a positive parameter $\delta$, we review their formulation defined on a bounded domain subject to various conditions that correspond to…
The employment of nonlocal PDE models to describe biological aggregation and other phenomena has gained considerable traction in recent years. For cell populations, these methods grant a means of accommodating essential elements such as…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
A continuum description of unstructured meshes in two dimensions, both for planar and curved surface domains, is proposed. The meshes described are those which, in the limit of an increasingly finer mesh (smaller cells), and away from…
A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net…
In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua…
In this paper, we consider a nonlocal advection model for two populations on a bounded domain. The first part of the paper is devoted to the existence and uniqueness of solutions and the associated semi-flow properties. Here we use the…
We review theoretical results for the adhesion-induced phase behavior of biomembranes. The focus is on models in which the membranes are represented as discretized elastic sheets with embedded adhesion molecules. We present several…
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…
The Voronoi-based cellular model is highly successful in describing the motion of two-dimensional confluent cell tissues. In the homogeneous version of this model, the energy of each cell is determined solely by its geometric shape and…
This work deals with a parabolic chemotaxis model with nonlinear diffusion and nonlocal reaction source. The problem is formulated on the whole space and, depending on a specific interplay between the coefficients associated to such…
Based on the development in dealing with nonlocal boundary conditions, we propose a seamless local-nonlocal coupling diffusion model in this paper. In our model, a finite constant interaction horizon is equipped in the nonlocal part and…
We developed a new self-adjoint, consistent, and stable coupling strategy for nonlocal diffusion models, inspired by the quasinonlocal atomistic-to-continuum method for crystalline solids. The proposed coupling model is coercive with…
We consider a model for the dynamics of active cells interacting with their quiescent counterparts under the influence of acidity characterized by proton concentration. The active cells perform nonlinear diffusion and infer proliferation or…
The behaviour and fate of tissue cells is controlled by the rigidity and geometry of their adhesive environment, possibly through forces localized to sites of adhesion. We introduce a mechanical model that predicts cellular force…
We study the (generalized) one-dimensional population model developed by Anguige \& Schmeiser [1], which reflects cell-cell adhesion and volume filling under no-flux boundary condition. In this generalized model, depending on the adhesion…