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We consider a generalization of the classical logistic growth model introducing more than one inflection point. The growth, called multi-sigmoidal, is firstly analyzed from a deterministic point of view in order to obtain the main…
The evolution of autocatalytic sets (ACS) is a widespread process in biological, chemical and ecological systems which is of great significance in many applications, such as the evolution of new species or complex chemical organizations. In…
$\beta$-$\mathrm{Ga}_{2}\mathrm{O}_{3}$ has gained intensive interests of research and application as an ultrawide bandgap semiconductor. Epitaxial growth technique of the $\beta$-$\mathrm{Ga}_{2}\mathrm{O}_{3}$ thin film possesses a…
Hydrodynamics is known to have strong effects on the kinetics of phase separation. There exist open questions on how such effects manifest in systems under confinement. Here, we have undertaken extensive studies of the kinetics of phase…
In this paper a macroscopic model of tumor cord growth is developed, relying on the mathematical theory of deformable porous media. Tumor is modeled as a saturated mixture of proliferating cells, extracellular fluid and extracellular…
A growth mechanism for a perfect one-dimensional (1D) quasiperiodic structure is presented with a local covering rule. We use rectangular tiles with two different types of string decorations. The string position in a tile is allowed to move…
Studying shape changing thick surfaces induced by differential growth helps us understand morphogenesis in biology and offers opportunities for device design. While ideal 2D differential growth maps have been well studied for both isotropic…
Bacterial colonies can form a wide variety of shapes and structures based on ambient and internal conditions. To help understand the mechanisms that determine the structure of and the diversity within these colonies, various numerical…
Cell invasion and spatial pattern formation are two distinct manifestations of cellular self-organisation in development, regeneration, and disease. Here, we develop and analyse a unified theoretical framework that links these two seemingly…
The surface directed spinodal decomposition of a binary liquid confined inside cylindrical pore is investigated using molecular dynamics simulation. One component of the liquid wets the pore surface while the other remains neutral. A…
We study the kinetics of two-temperature induced phase separation (2-TIPS) in dilute binary mixtures of active ("hot") and passive ("cold") particles using molecular dynamics simulations and a coarse-grained hydrodynamic model. Following a…
We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
We investigate the dynamic behavior of finite-size systems close to a first-order transition (FOT). We develop a dynamic finite-size scaling (DFSS) theory for the dynamic behavior in the coexistence region where different phases coexist. It…
The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll…
Cancer development is a multistep process often starting with a single cell in which a number of epigenetic and genetic alterations have accumulated thus transforming it into a tumor cell. The progeny of such a single benign tumor cell…
An Euclidean first-passage percolation (FPP) model describing the competing growth between $k$ different types of infection is considered. We focus on the long time behavior of this multi-type growth process and we derive multi-type shape…
A tropical expansion is a degeneration of a toroidal embedding, induced by a polyhedral subdivision of its tropicalisation. Each irreducible component of a tropical expansion admits a collapsing map down to a stratum of the original…
This paper introduces a continuous model for Multi-cellular Developmental Design. The cells are fixed on a 2D grid and exchange "chemicals" with their neighbors during the growth process. The quantity of chemicals that a cell produces, as…
We consider a partial differential equation model for the growth of heterogeneous cell populations subdivided into multiple distinct discrete phenotypes. In this model, cells preferentially move towards regions where they feel less…