Related papers: On study of cell proliferation and diffusion using…
Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose…
In this work, we consider a diffuse interface model for tumour growth in the presence of a nutrient which is consumed by the tumour. The system of equations consists of a Cahn--Hilliard equation with source terms for the tumour cells and a…
Diffusion Models represent a significant advancement in generative modeling, employing a dual-phase process that first degrades domain-specific information via Gaussian noise and restores it through a trainable model. This framework enables…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion…
We prove the existence of solutions to a non-linear, non-local, degenerate equation which was previously derived as the formal hydrodynamic limit of an active Brownian particle system, where the particles are endowed with a position and an…
We propose a new semiparametric approach for modelling nonlinear univariate diffusions, where the observed process is a nonparametric transformation of an underlying parametric diffusion (UPD). This modelling strategy yields a general class…
Nearly all thermal radiation phenomena involving materials with linear response can be accurately described via semi-classical theories of light. Here, we go beyond these traditional paradigms to study a nonlinear system which, as we show,…
A variety of researchers have successfully obtained the parameters of low dimensional diffusion models using the data that comes out of atomistic simulations. This naturally raises a variety of questions about efficient estimation,…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
We study a system of $n$ differential equations, each in dimension $d$. Only the first equation is forced by a Brownian motion and the dependence structure is such that, under a local weak H\"ormander condition, the noise propagates to the…
In many biological processes heterogeneity within cell populations is an important issue. In this work we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations.…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…
It has been argued that there is biological and modeling evidence that a non-linear diffusion coefficient of the type D(b) = D_0 b^{k} underlies the formation of a number of growth patterns of bacterial colonies. We study a…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
This paper proposes a model for the growth two interacting populations of cells that do not mix. The dynamics is driven by pressure and cohesion forces on the one hand and proliferation on the other hand. Following earlier works on the…
The function of biomolecules such as proteins depends on their ability to interconvert between a wide range of structures or "conformations." Researchers have endeavored for decades to develop computational methods to predict the…
The paper treats a reaction-diffusion equation with hysteretic nonlinearity on a one-dimensional lattice. It arises as a result of the spatial discretization of the corresponding continuous model with so-called nontransverse initial data…
We study a mathematical model of cell populations dynamics proposed by M. Rotenberg and investigated by M. Boulanouar. Here, a cell is characterized by her maturity and speed of maturation. The growth of cell populations is described by a…