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We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary…
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
Biofilms are antibiotic-resistant bacterial aggregates that grow on moist surfaces and can trigger hospital-acquired infections. They provide a classical example in biology where the dynamics of cellular communities may be observed and…
We develop a Fokker-Planck theory of tissue growth with three types of cells (symmetrically dividing, asymmetrically dividing and non-dividing) as main agents to study the growth dynamics of human cerebral organoids. Fitting the theory to…
A "fat slit" is a compact domain in the upper half plane bounded by a curve with endpoints on the real axis and a segment of the real axis between them. We consider conformal maps of the upper half plane to the exterior of a fat slit…
We consider the problem of the long time dynamics for a diffuse interface model for tumor growth. The model describes the growth of a tumor surrounded by host tissues in the presence of a nutrient and consists in a Cahn-Hilliard-type…
In a recent paper, a novel surface growth approach for reconstructing bulk geometry and matter fields was proposed, it was shown that this picture can be explicitly realized by the one-shot entanglement distillation tensor network and the…
In solving real world systems for higher-codimension bifurcation problems, one often faces the difficulty in computing the normal form or the focus values associated with generalized Hopf bifurcation, and the normal form with unfolding for…
The rate at which individual bacterial cells grow depends on the concentrations of cellular components such as ribosomes and proteins. These concentrations continuously fluctuate over time and are inherited from mother to daughter cells,…
Under low concentrations of antibiotics causing DNA damage, \textit{Escherichia coli} bacteria can trigger stochastically a stress response known as the SOS response. While the expression of this stress response can make individual cells…
Epitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult.…
A one-dimensional continuum-mechanical model of axonal elongation due to assembly of tubulin dimers in the growth cone is presented. The conservation of mass leads to a coupled system of three differential equations. A partial differential…
This paper deals with the cellular biological network analysis of the tumor-growth model, consisting of multiple spaces and time scales. In this paper, we present a model in graph simulation using ABM for tumor growth. In particular, we…
Using three-dimensional numerical simulations, we demonstrate the growth saturation of an unstable thin liquid film on micropatterned hydrophilic-hydrophobic substrates. We consider different transverse-striped micropatterns, characterized…
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
The evolution of InAs quantum dots grown on InP substrates by metal-organic vapour phase epitaxy is studied as a function of InAs coverage. Under specific growth conditions, the onset of the two- to three-dimensional transition is seen to…
Here we extend the approach developed in \cite{adel_2} to study the thermodynamics of Taub-NUT-AdS and dyonic Taub-NUT-AdS solutions. Furthermore, we investigate in details the possible phase structures of the dyonic Taub-NUT-AdS solution.…
Elucidating the neurophysiological mechanisms underlying neural pattern formation remains an outstanding challenge in Computational Neuroscience. In this paper, we address the issue of understanding the emergence of neural patterns by…
In atom probe tomography (APT), accurate reconstruction of the spatial positions of field evaporated ions from measured detector patterns depends upon a correct understanding of the dynamic tip shape evolution and evaporation laws of…