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The radiation (reaction, Robin) boundary condition for the continuum diffusion equation is widely used in chemical and biological applications to express reactive boundaries. The underlying trajectories of the diffusing particles are…
Spheroids are aggregates of cells that can mimic the cellular organization often found in tissues. They are typically formed through the self-assembly of cells in a culture where there is a promotion of interactions and cell-to-cell…
Turing patterns are stationary, wave-like structures that emerge from the nonequilibrium assembly of reactive and diffusive components. While they are foundational in biophysics, their classical formulation relies on a single characteristic…
Diffusive molecular communication (DMC) is one of the most promising approaches for realizing nano-scale communications in biological environments for healthcare applications. In this paper, a DMC system in biological cylindrical…
We consider a nonlinear reaction--diffusion equation in a domain consisting of two bulk regions connected via small channels periodically distributed within a thin layer. The height and the thickness of the channels are of order $\epsilon$,…
We show how the nonlinear interaction effects `volume filling' and `adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with…
We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance…
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…
We study the appearance of a boundary condition along an interface between two regions, one with constant diffusivity $1$ and the other with diffusivity $\eps>0$, when $\eps\to0$. In particular, we take Fick's diffusion law in a context of…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
While the diffusion of hydrogen on silicon surfaces has been relatively well characterised both experimentally and theoretically, the diffusion around corners between surfaces, as will be found on nanowires and nanostructures, has not been…
In the presence of a chemically active particle, a nearby chemically inert particle can respond to a concentration gradient and move by diffusiophoresis. The nature of the motion is studied for two cases: first, a fixed reactive sphere and…
We investigate the large time behavior of solutions of reaction-diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
Image generation techniques, particularly latent diffusion models, have exploded in popularity in recent years. Many techniques have been developed to manipulate and clarify the semantic concepts these large-scale models learn, offering…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
The effects of a boundary on reaction systems are examined in the framework of the general single-species reaction/coalescence process. The boundary naturally represents the reactants' container, but is applicable to exciton dynamics in a…
Densely packed systems of thermal particles in curved geometries are frequently encountered in biological and microfluidic systems. In 2D systems, at sufficiently high surface coverage, diffusive motion is widely known to be strongly…
Experiments on carrier recombination in two-dimensional organic structures are often interpreted in the frame of the Langevin model with taking into account only the drift of the charge carriers in their mutual electric field. While this…
We study fluctuations of particle absorption by a three-dimensional domain with multiple absorbing patches. The domain is in contact with a gas of interacting diffusing particles. This problem is motivated by living cell sensing via…