Related papers: Modeling of reaction-diffusion transport into a co…
A system of degenerate drift-diffusion equations for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a three-dimensional bounded domain with mixed…
Malignant membranes cluster nutrient transporters within glycan-rich domains, sustaining metabolism through redundant intake routes. A theoretical framework links interfacial chemistry to transport suppression and energetic or redox…
Macroscopic elastic core-shell systems can be generated as toy models to be deformed and haptically studied by hand. On the mesoscale, colloidal core-shell particles and microgels are fabricated and investigated by different types of…
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…
Many processes in cell biology involve diffusion in a domain $\Omega$ that contains a target $\calU$ whose boundary $\partial \calU$ is a chemically reactive surface. Such a target could represent a single reactive molecule, an…
Metasurfaces composed of subwavelength unit cells usually require a large number of unit cells which leads to complicated design and optimization. Aggressive discretization in a metasurface can significantly reduce the number of unit cells…
Using computer simulations and scaling ideas, we study one-dimensional models of diffusion, aggregation and detachment of particles from islands in the post-deposition regime, i. e. without flux. The diffusion of isolated particles takes…
We study diffusion-reaction processes on periodic square planar lattices and simple cubic (sc) lattices. Considered first is a single diffusing reactant undergoing an irreversible reaction upon first encounter with a stationary co-reactant…
We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…
Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e. avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual based…
The tumour microenvironment plays a fundamental role in understanding the development and progression of cancer. This paper proposes a novel spatial point process model that accounts for inhomogeneity and interaction to flexibly model a…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
In this work, we study a system of degenerate parabolic equations modeling the dynamics of multiple cell populations in intestinal crypts. The model describes cell division, differentiation, and migration through a strongly coupled system…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
In this paper we consider the diffusion of nanoparticles taken up by a semi-permeable spherical cell placed in the path of a diffusive particle field generated by an external planar source. The cell interior and exterior are characterized…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We present a theoretical study of the phase diagram and the structure of a fluid adsorbed in high-porosity aerogels by means of an integral-equation approach combined with the replica formalism. To simulate a realistic gel environment, we…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
We study energy transport in the paradigmatic Hamiltonian mean-field (HMF) model and other related long-range interacting models using molecular dynamics simulations. We show that energy diffusion in the HMF model is subdiffusive in nature,…
We present an efficient point-particle approach to simulate reaction-diffusion processes of spherical absorbing particles in the diffusion-limited regime, as simple models of cellular uptake. The exact solution for a single absorber is used…