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A stochastic model is used to assess the effect of external parameters on the development of submerged biofilms on smooth and rough surfaces. The model includes basic cellular mechanisms, such as division and spreading, together with an…
This paper provides a unified mathematical analysis of a family of non-local diffuse interface models for tumor growth describing evolutions driven by long-range interactions. These integro-partial differential equations model cell-to-cell…
The microscopic structure of a plant cell wall is given by cellulose microfibrils embedded in a cell wall matrix. In this paper we consider a microscopic model for interactions between viscoelastic deformations of a plant cell wall and…
A simulation approach to the stochastic growth of bacterial towers is presented, in which a non-uniform and finite nutrient supply essentially determines the emerging structure through elementary chemotaxis. The method is based on cellular…
Hydride Vapor Phase Epitaxy (HVPE) is a promising technology that can aid in the cost reduction of III-V materials and devices manufacturing, particularly high-efficiency solar cells for space and terrestrial applications. However, recent…
In this paper we present a derivation and multiscale analysis of a mathematical model for plant cell wall biomechanics that takes into account both the microscopic structure of a cell wall coming from the cellulose microfibrils and the…
Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an…
In this manuscript, we study a nonlinear model of tumor growth, described by a coupled hyperbolic-elliptic system of partial differential equations. In this model, the compressible flow of tumor cells is modeled by a transport equation for…
A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modelled as an elastic curve, subject to an internal pressure force. Net…
We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the…
Plant morphogenesis relies on dynamic growth deformations at the cell and tissue scales driven by osmotic fluxes. A mechanistic understanding of this phenomenon demands a physical framework that integrates cell imbibition, tissue mechanics,…
We present new algorithm for growth of non-clustered planar graphs by aggregation of cells with given distribution of size and constraint of connectivity k=3 per node. The emergent graph structures are controlled by two parameters--chemical…
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…
The motility of eukaryotic cells is strongly influenced by their environment, with confined cells often developing qualitatively different motility patterns from those migrating on simple two-dimensional substrates. Recent experiments,…
We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface diffusion and…
We investigate morphologies of proliferating cellular tissues using a newly developed numerical simulation model for mechanical cell division and migration in 2D. The model is applied to a bimodal mixture consisting of stiff cells with a…
Morphological trends in growing colonies of living cells are at the core of physiological and evolutionary processes. Using active gel equations, which include cell division, we show that shape changes during the growth can be regulated by…
We investigate a class of Young diagrams growing via the addition of unit cells and satisfying the constraint that the height difference between adjacent columns $\geq r$. In the long time limit, appropriately re-scaled Young diagrams…
We introduce a kinetic model for the growth of epitaxial graphene on 6H-SiC. The model applies to vicinal surfaces composed of half-unit-cell height steps where experiment shows that step flow sublimation of SiC promotes the formation and…
The principles underlying plant development are extended to allow a more molecular mechanism to elaborate the schema by which ground cells differentiate into vascular cells. Biophysical considerations dictate that linear dynamics are not…