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Monte Carlo simulations are employed to investigate the surface growth generated by deposition of particles of different sizes on a substrate, in one and two dimensions. The particles have a linear form, and occupy an integer number of…
We present a geometric framework to study the growth-division dynamics of cells and protocells, and demonstrate that self-reproduction emerges only when a system's growth dynamics and division strategy are mutually compatible. Using several…
We investigate the growth of needles from a flat substrate. We focus on the situation when needles suddenly begin to grow from the seeds randomly distributed on the line. The width of needles is ignored and we additionally assume that (i)…
We describe a numerical model of faceted crystal growth using a cellular automata method that incorporates admolecule diffusion on faceted surfaces in addition to bulk diffusion in the medium surrounding the crystal. The model was developed…
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary conditions. Using the theory of semigroups of positive…
We present a minimal driven lattice gas model which generates the morphological characteristics associated with single colony mycelium arising from the growth and branching process of fungal hyphae, which is fed by a single source of…
In this paper, we study the dynamical connection between the surface growth scheme and the conformal field theory with $T\bar{T}$ deformation. By utilizing the extended one-shot entanglement distillation tensor network, we find that the…
In the natural world, there are many insect species whose individual members have a life history that takes them through two stages, immature and mature. Moreover, the rates of survival, development, and reproduction almost always depend on…
The ubiquitous existence of microbial communities marks the importance of understanding how species interact within the community to coexist and their spatial organization. We study a two-species mutualistic cross-feeding model through a…
We study pattern formation in a reaction-diffusion system for a benthic bacteria-nutrient model in a marine sediment, which originally contains some spatially varying coefficients and with these shows some layering of patterns. Using the…
We consider a general growth mechanism, which acts at cellular level and above (organs, systems and whole organisms). Using its mathematical representation, the growth equation, we study the growth and division mechanisms of amoeba and…
We present a two-dimensional continuum model of tumor growth, which treats the tissue as a composition of six distinct fluid phases; their dynamics are governed by the equations of mass and momentum conservation. Our model divides the…
We employ the framework of multitype Galton-Watson processes to model a population of dividing cells. The cellular type is represented by its biological age, defined as the count of harmful proteins hosted by the cell. The stochastic…
Variational problems of splitting-type with mixed linear-superlinear growth conditions are considered. In the twodimensional case the minimizing problem is given by \[ J [w] = \int_{\Omega} \Big[f_1\big(\partial_1 w\big) +…
For one-dimensional growth processes we consider the distribution of the height above a given point of the substrate and study its scale invariance in the limit of large times. We argue that for self-similar growth from a single seed the…
We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
Many mathematical models in different disciplines involve the formulation of free boundary problems, where the domain boundaries are not predefined. These models present unique challenges, notably the nonlinear coupling between the solution…
In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model…
The displacement of a fluid by another less viscous one in a quasi-two dimensional geometry typically leads to complex fingering patterns. In an isotropic system, dense-branching growth arises, which is characterized by repeated…