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This Communication reports a geometrical factor that is necessary in the diffusion boundary condition across surface steps. Specifically, this factor relates adatom concentration to its spatial gradient at a surface step, and it describes…
Various molecules exclusively accumulate at the front or back of migrating eukaryotic cells in response to a shallow gradient of extracellular signals. Directional sensing and signal amplification highlight the essential properties in the…
We consider an epidemic model with nonlocal diffusion and free boundaries, which describes the evolution of an infectious agents with nonlocal diffusion and the infected humans without diffusion, where humans get infected by the agents, and…
The lateral diffusion and trapping of neurotransmitter receptors within the postsynaptic membrane of a neuron plays a key role in determining synaptic strength and plasticity. Trapping is mediated by the reversible binding of receptors to…
A reaction-diffusion-advection model is proposed and investigated to understand the invasive dynamics of Aedes aegypti mosquitoes. The free boundary is introduced to model the expanding front of the invasive mosquitoes in a heterogenous…
We discuss velocity-jump models for chemotaxis of bacteria with an internal state that allows the velocity jump rate to depend on the memory of the chemoattractant concentration along their path of motion. Using probabilistic techniques, we…
We propose and analyze a one-dimensional multi-species cross-diffusion system with non-zero-flux boundary conditions on a moving domain, motivated by the mod- eling of a Physical Vapor Deposition process. Using the boundedness by entropy…
At the continuous level, we consider two types of tumor growth models: the cell density model, which is based on the fluid mechanical construction, is more favorable for scientific interpretation and numerical simulations; and the free…
The focus of this article is studying an optimal control problem for branching diffusion processes. Initially, we introduce the problem in its strong formulation and expand it to include linearly growing drifts. Then, we present a relaxed…
In this paper, we first propose a diffusive pathogen infection model with general incidence rate which incorporates cell-to-cell transmission. By applying the theory of monotone dynamical systems, we prove that the model admits the global…
Molecular communication (MC), one of the emerging techniques in the field of communication, is entering a new phase following several decades of foundational research. Recently, attention has shifted toward MC in liquid media, particularly…
In the absence of environmental cues, a migrating cell performs an isotropic random motion. Recently, the breaking of this isotropy has been observed when cells move in the presence of asymmetric adhesive patterns. However, up to now the…
The time dependency of the diffusion coefficient of particles in porous media is an efficient probe of their geometry. The analysis of this quantity, measured e.g. by nuclear magnetic resonance (PGSE-NMR), can provide rich information…
The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular…
We study a driven many particle system comprising of two identical lanes of finite lengths. On one lane, particles hop diffusively with a bias in a specific direction. On the other lane, particles hop in a specific direction obeying mutual…
We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of…
Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent…
We present a collision model for phase-resolved Direct Numerical Simulations of sediment transport that couple the fluid and particles by the Immersed Boundary Method. Typically, a contact model for these types of simulations comprises a…
The search to understand how the HIV virus spreads inside the human body and how the immune response works to control it has motivated studies related to Mathematical Immunology. Actually, researches include the idea of mathematical models…
Problems involving the capture of a moving entity by a trap occur in a variety of physical situations, the moving entity being an electron, an excitation, an atom, a molecule, a biological object such as a receptor cluster, a cell, or even…