Related papers: Collective Invasion: When does domain curvature ma…
Variation in genotypes may be responsible for differences in dispersal rates, directional biases, and growth rates of individuals. These traits may favor certain genotypes and enhance their spatio-temporal spreading into areas occupied by…
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is…
For a two-species reaction-diffusion-competition system on a domain that translates at constant speed and/or whose boundary varies periodically with time, we prove sufficient conditions such that one species can, and cannot, invade an…
We consider the non-local Fisher-KPP equation modeling a population with individuals competing with each other for resources with a strength related to their distance, and obtain the asymptotics for the position of the invasion front…
We evaluate the Community ocean Vertical Mixing (CVMix) project version of the K-profile parameterization (KPP). For this purpose, one-dimensional KPP simulations are compared across a suite of oceanographically relevant regimes against…
Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion…
We develop a general theory of transport-limited aggregation phenomena occurring on curved surfaces, based on stochastic iterated conformal maps and conformal projections to the complex plane. To illustrate the theory, we use stereographic…
We consider here a model of accelerating fronts, introduced in [2], consisting of one equation with nonlocal diffusion on a line, coupled via the boundary condition with a reaction-diffusion equation of the Fisher-KPP type in the upper…
Diffusive transport is a universal phenomenon, throughout both biological and physical sciences, and models of diffusion are routinely used to interrogate diffusion-driven processes. However, most models neglect to take into account the…
The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to a bulk diffusion equation with a non-linear boundary condition. Cell…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be…
A classical particle under spatial constraints is strictly confined to live on a specific space manifold or path, but this assumption is incompatible with the zero-point fluctuations of a quantum particle. One way to describe quantum…
These notes are based on the lectures given in a mini-course at VIASM (Vietnam Institute for Advanced Study in Mathematics) 2025 Summer School. They give a brief account of the theory (with detailed proofs) for propagation governed by a…
In Part II of this series of papers, we consider an initial-boundary value problem for the Kolmogorov--Petrovskii--Piscounov (KPP) type equation with a discontinuous cut-off in the reaction function at concentration $u=u_c$. For fixed…
We present multiscale models of cancer tumor invasion with components at the molecular, cellular, and tissue levels. We provide biological justifications for the model components, present computational results from the model, and discuss…
In these Notes, a comprehensive description of the universal fractal geometry of conformally-invariant scaling curves or interfaces, in the plane or half-plane, is given. The present approach focuses on deriving critical exponents…
Reaction--diffusion mechanism are a robust paradigm that can be used to represent many biological and physical phenomena over multiple spatial scales. Applications include intracellular dynamics, the migration of cells and the patterns…
We present the first direct computation of spatially averaged dynamical quantities in the local Universe, employing the Cosmicflows-4++ reconstruction and a covariant scalar averaging formalism. We extract the domain-averaged density,…
We discuss fattening phenomenon for the evolution of planar curves according to their nonlocal curvature. More precisely, we consider a class of generalized curvatures which correspond to the first variation of suitable nonlocal perimeter…
In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval…