Related papers: A Physical Model for Self-Similar Seashells
In this review, we present a symmetry-guided strategy that utilizes exact as well as partial symmetries for enabling a deeper understanding of and advancing ab initio studies for determining the microscopic structure of atomic nuclei. These…
We consider a new nonlocal and nonlinear one-dimensional evolution model arising in the study of oceanic flows in equatorial regions, recently derived in [A. Constantin and L. Molinet, Global Existence and Finite-Time Blow-Up for a…
In this work, shells are mathematically constructed by applying the cut and paste procedure to D-dimensional spherically symmetric geometries. The weak energy condition for the matter on the shells is briefly analyzed. The dynamical…
Understanding the rules underlying organismal development is a major unsolved problem in biology. Each cell in a developing organism responds to signals in its local environment by dividing, excreting, consuming, or reorganizing, yet how…
Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…
During growth, tissue expands and deforms. Given its elastic properties, stresses emerge in an expanding and deforming tissue. Cell rearrangements can dissipate these stresses and numerous experiments confirm the viscoelastic properties of…
Cell growth in size is a complex process coordinated by intrinsic and environmental signals. In a recent work [Tzur et al., Science, 2009, 325:167-171], size distributions in an exponentially growing population of mammalian cells were used…
A model of the thin shell expanding into a uniform ambient medium is developed. Density perturbations are described using equations with linear and quadratic terms, and the linear and the nonlinear solutions are compared. We follow the time…
Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are…
We consider an Individual-Based Model for self-rotating particles interacting through local alignment and investigate its macroscopic limit. This model describes self-propelled particles moving in the plane and trying to synchronize their…
A self-similar growth-fragmentation describes the evolution of particles that grow and split as time passes. Its genealogy yields a self-similar continuum tree endowed with an intrinsic measure. Extending results of Haas for pure…
We propose a model for describing the growth on an untreated tumor, which is characterized in a simple way by a minimal number of parameters with a well-defined physical interpretation. The model is motivated by invoking the Master Equation…
The material structure of bodies undergoing growth is considered. In the geometric framework of a general differential manifold modeling the physical space and a fiber bundle modeling spacetime, body points may be defined for any extensive…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
In this work, a new model for macroscopic plant tissue growth based on dynamical Riemannian geometry is presented. We treat 1D and 2D tissues as continuous, deformable, growing geometries for sizes larger than 1mm. The dynamics of the…
We examine the island size distribution function and spatial correlation function of a model for island growth in the submonolayer regime in both 1 and 2 dimensions. In our model the islands do not grow in shape, and a fixed number of…
This study presents an internalized morphogenesis model for autonomous systems, such as swarm robotics and micro-nanomachines, that eliminates the need for external spatial computation. Traditional self-organizing models often require…
We formalise a systematic method of constructing forward self-similar solutions to the Navier-Stokes equations in order to characterise the late stage of decaying process of turbulent flows. (i) In view of critical scale-invariance of type…
This paper presents a stochastic differential equation model for describing the process of fish schooling. The model equation always possesses a unique local solution, but global existence can be shown only in some particular cases. Some…
From flocking birds to schooling fish, organisms interact to form collective dynamics across the natural world. Self-organization is present at smaller scales as well: cells interact and move during development to produce patterns in fish…