Related papers: A Physical Model for Self-Similar Seashells
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…
The self-assembly of polyhedral shells, each constructed from 60 trapezoidal particles, is simulated using molecular dynamics. The spatial organization of the component particles in this shell is similar to the capsomer proteins forming the…
Sigmoid growth models are often used to study population dynamics. The size of a population at equilibrium commonly depends explicitly on the availability of resources, such as an energy or nutrient source, which is not explicit in standard…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow…
Self-propelling organisms locomote via generation of patterns of self-deformation. Despite the diversity of body plans, internal actuation schemes and environments in limbless vertebrates and invertebrates, such organisms often use similar…
We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…
Results from molecular dynamics simulations of simple, structured particles capable of self-assembling into polyhedral shells are described. The analysis focuses on the growth histories of individual shells in the presence of an explicit…
The dynamical system constituted by two spherically symmetric thin shells and their own gravitational field is studied. The shells can be distinguished from each other, and they can intersect. At each intersection, they exchange energy on…
Morphoelasticity represents a foundational theory for tracing back growth, remodelling, and morphogenesis, yet crucial challenges persist. A unified growth law -- independent of a priori assumptions about constitutive relations or specified…
Quantitative assessment of the growth of biological organisms has produced many mathematical equations. Many efforts have been given on statistical identification of the correct growth model from experimental data. Every growth equation is…
In this paper we linearise the recently introduced geometrically nonlinear constrained Cosserat-shell model. In the framework of the linear constrained Cosserat-shell model, we provide a comparison of our linear models with the classical…
We analyze the morphological stability against azimuthal, axial, and general helical perturbations for epitaxial core-shell nanowires in the growth regimes limited by either surface diffusion or evaporation-condensation surface kinetics.…
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…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
The present view of biological phenomena is based on a biochemical paradigm that development of living organisms is defined by information stored in a molecular form as some genetic code. However, new discoveries indicate that biological…
Using $\Gamma$-convergence arguments, we construct a nonlinear membrane-like Cosserat shell model on a curvy reference configuration starting from a geometrically nonlinear, physically linear three-dimensional isotropic Cosserat model. Even…
The aim of this study is three-fold: (i) to present a general higher-order shell theory to analyze large deformations of thin or thick shell structures made of general compressible hyperelastic materials; (ii) to utilize the orthonormal or…