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Flat sheets encoded with patterns of contraction/elongation morph into curved surfaces. If the surfaces bear Gauss curvature, the resulting actuation can be strong and powerful. We deploy the Gauss-Bonnet theorem to deduce the Gauss…
We present some results of Monte Carlo simulations for the deposition of particles of different sizes on a two-dimensional substrate. The particles are linear, height one, and can be deposited randomly only in the two, $x$ and $y$…
A general theory of thermodynamically consistent biomechanical--biochemical growth in a body, considering mass addition in the bulk and at an incoherent interface, is developed. The incoherency arises due to incompatibility of growth and…
Time series of cell size evolution in unicellular marine algae (division Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a system of linear stochastic differential equations of hierarchical structure. The data…
This paper is the first part of an axis symmetric description of a single crystal tube growth process by micro-pulling-down method.the description concerns the following aspects:the free surfaces equations and the pressure difference across…
In this study, we explore a mathematical model for tissue growth focusing on the interplay between multiple cell subpopulations with distinct phenotypic characteristics. The model addresses the dynamics of tissue growth influenced by…
Bacteria on surfaces exhibit collective behaviors, such as active turbulence and active stresses, which result from their motility, growth, and interactions with their local surroundings. However, interfacial deformations on soft surfaces…
This paper presents an interesting experimental example of voter-model statistics in biology. In recent work on mouse tail-skin, where proliferating cells are confined to a two-dimensional layer, we showed that cells proliferate and…
A random growth lattice filling model of percolation with touch and stop growth rule is developed and studied numerically on a two dimensional square lattice. Nucleation centers are continuously added one at a time to the empty sites and…
We study two competing growth models. Each of these models describes the spread of a finite number of infections on a graph. Each infection evolves like an (oriented or unoriented) first passage percolation process except that once a vertex…
This work presents some fundamental features of pyramidal site-controlled InGaAs Quantum Dots (QDs) grown by MetalOrganic Vapour Phase Epitaxy on patterned GaAs (111)B substrate. The dots self-form inside pyramidal recesses patterned on the…
We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption…
Herewith we discuss a network model of the ferroptosis avascular and vascular tumor growth based on our previous proposed framework. Chiefly, ferroptosis should be viewed as a first order phase transition characterized by a supercritical…
A class of Laplacian growth models in the channel geometry is studied using the formalism of tripolar Loewner evolutions, in which three points, namely, the channel corners and infinity, are kept fixed. Initially, the problem of fingered…
Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to…
We study the Cahn-Hilliard-Biot model with respect to its mathematical well-posedness. The system models flow through deformable porous media in which the solid material has two phases with distinct material properties. The two phases of…
Spiral surface growth is well understood in the limit where the step motion is controlled by the local supersaturation of adatoms near the spiral ridge. In epitaxial thin-film growth, however, spirals can form in a step-flow regime where…
Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate…
Investigating the emergence of a particular cell type is a recurring theme in models of growing cellular populations. The evolution of resistance to therapy is a classic example. Common questions are: when does the cell type first occur,…
This paper presents an experimental investigation on pattern formation and evolution in bilayered tubular organs using swelling deformation of polydimethylsiloxane (PDMS) and aims at supplying a thorough comparison with theoretical and…