Related papers: Modeling of reaction-diffusion transport into a co…
The study of the interactions of living adherent cells with mechanically stable (visco)elastic materials enables understanding and exploiting physiological phenomena mediated by cell-extracellular communication. However, insight on the…
The exact solution of a diffusion$-$reaction model for the trapping and annihilation of positrons in small extended spherical defects (clusters, voids, small precipitates) with competitive rate-limited trapping in vacancy-type point defects…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…
Intercellular exchange networks are essential for the adaptive capabilities of populations of cells. While diffusional exchanges have traditionally been difficult to map, recent advances in nanotechnology enable precise probing of exchange…
Design and characterisation of capsules is not an easy task owing to the multiple involved preparation factors and parameters. Here, a novel method to characterise capsule membrane permeability to solute molecules by an inverse approach is…
A nutrient-limited model for avascular cancer growth including cell proliferation, motility and death is presented. The model qualitatively reproduces commonly observed morphologies for primary tumors, and the simulated patterns are…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…
We study the Schloegl model in a vesicle with semi-permeable membrane. The diffusion constant takes a smaller value in the membrane region, which prevents the outflow of self-catalytic product. A nonequilibrium state is stably maintained…
Diffusion to capture is an ubiquitous phenomenon in many fields in biology and physical chemistry, with implications as diverse as ligand-receptor binding on eukaryotic and bacterial cells, nutrient uptake by colonies of unicellular…
In this paper, a distributed optimal control problem is studied for a diffuse interface model of tumor growth which was proposed in [A. Hawkins-Daruud, K.G. van der Zee, J.T. Oden, Numerical simulation of a thermodynamically consistent…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
We present a mathematical study for the development of multiple sclerosis based on a reaction-diffusion system. The model describes interactions among different populations of human cells, motion of immune cells stimulated by cytokines,…
We investigate reversible diffusion-influenced reactions of an isolated pair in two dimensions. To this end, we employ convolution relations that permit deriving the survival probability of the reversible reaction directly in terms of the…
Many cellular and subcellular biological processes can be described in terms of diffusing and chemically reacting species (e.g. enzymes). Such reaction-diffusion processes can be mathematically modelled using either deterministic…
We study a reaction-diffusion process that involves two species of atoms, immobile and diffusing. We assume that initially only immobile atoms, uniformly distributed throughout the entire space, are present. Diffusing atoms are injected at…
A three-dimensional cell culture called a spheroid serves as a foundational entity in a wide variety of modern tissue engineering applications, including 3D-bioprinting and preclinical drug testing. Lack of oxygen within tissue spheroids…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
The reversible reactions like A+B <-> C in the many-component diffusive system affect the diffusive properties of the constituents. The effective conjugation of irreversible processes of different dimensionality takes place due to the…