Related papers: A hybrid discrete-continuum approach to model Turi…
In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid-liquid phase separation and a further transition into a…
Morphogenesis is central to biology but remains largely unexplored in chemistry. Reaction-diffusion (RD) mechanisms are, however, essential to understand how shape emerges in the living world. While numerical methods confirm the incredible…
This work explores the differences between static and dynamically evolving physico-chemical models of pre-stellar cores. A 3D MHD model of a pre-stellar core embedded in a dynamic star-forming cloud is post-processed using sequentially dust…
Piecewise smooth hybrid systems, involving continuous and discrete variables, are suitable models for describing the multiscale regulatory machinery of the biological cells. In hybrid models, the discrete variables can switch on and off…
This paper deals with the derivation of a collective model of cell populations out of an individual-based description of the underlying physical particle system. By looking at the spatial distribution of cells in terms of time-evolving…
A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
Diffusion models have emerged as a leading framework in generative modeling, poised to transform the traditionally slow and costly process of drug discovery. This review provides a systematic comparison of their application in designing two…
Morphogenesis is the ensemble of processes that determines form, shape and patterns in organisms. Based on a reaction-diffusion theoretical setting and some prototype reaction schemes, we make a review of the models and experiments that…
Building upon the classical chemo-mechanical theory of Larch{\'e} and Cahn for equilibrium, numerous studies have investigated the transport of species in solids, with or without trapping phenomena. In most applications -- such as the…
It is widely recognized that reciprocal interactions between cells and their microenvironment, via mechanical forces and biochemical signaling pathways, regulate cell behaviors during normal development, homeostasis and disease progression…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
Self-organized pattern formation is vital for many biological processes. Reaction-diffusion models have advanced our understanding of how biological systems develop spatial structures, starting from homogeneity. However, biological…
Oncolytic virotherapy, utilizing genetically modified viruses to combat cancer and trigger anti-cancer immune responses, has garnered significant attention in recent years. In our previous work arXiv:2305.12386, we developed a stochastic…
The interactions between diffusing molecules and membrane-bound receptors drive numerous cellular processes. In this work, we develop a spatial model of molecular interactions with membrane receptors by homogenizing the cell membrane and…
In this article we apply a discrete action principle for the Vlasov--Maxwell equations in a structure-preserving particle-field discretization framework. In this framework the finite-dimensional electromagnetic potentials and fields are…
A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…
The self-organization of proteins into enriched compartments and the formation of complex patterns are crucial processes for life on the cellular level. Liquid-liquid phase separation is one mechanism for forming such enriched compartments.…
A coupled system of nonlinear mixed-type equations modeling early stages of angiogenesis is analyzed in a bounded domain. The system consists of stochastic differential equations describing the movement of the positions of the tip and stalk…