Related papers: Cellular automata model for elastic solid material
A three-dimensional (3-D) adaptive mesh refinement (AMR) cellular automata (CA) model is developed to simulate the equiaxed dendritic growth of pure substance. In order to reduce the mesh induced anisotropy by CA capture rules, a limited…
In line with the stability theory of continuous dynamical systems, Lyapunov exponents of cellular automata (CAs) have been conceived two decades ago to quantify to what extent their dynamics changes following a perturbation of their initial…
The stochastic discrete space-time model of an immune response on tumor spreading in a two-dimensional square lattice has been developed. The immunity-tumor interactions are described at the cellular level and then transferred into the…
To respect physics and nature, cellular automata (CA) models of self-organisation, emergence, computation and logical universality should be isotropic, having equivalent dynamics in all directions. We present a novel paradigm, the iso-rule,…
We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
Precipitation of fine particles into the base material of a metal is a potent strengthening mechanism. This is numerically analyzed within a continuum framework based on a higher order strain gradient plasticity theory and by use of an…
Cellular automata (CA) models are widely used to simulate complex systems with emergent behaviors, but identifying hidden parameters that govern their dynamics remains a significant challenge. This study explores the use of Convolutional…
Solid-state nanofoaming experiments are conducted on two PMMA grades of markedly different molecular weight using CO$_2$ as the blowing agent. The sensitivity of porosity to foaming time and foaming temperature is measured. Also, the…
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 propose a new variable cell-shape molecular dynamics algorithm where the dynamical variables associated with the cell are the six independent dot products between the vectors defining the cell instead of the nine cartesian components of…
Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
Simulation of human soft tissues in contact with their environment is essential in many fields, including visual effects and apparel design. Biological tissues are nearly incompressible. However, standard methods employ compressible…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
Matrix tablets are drug delivery devices designed to release a drug in a controlled manner over an extended period of time. We develop a cellular automaton (CA) model for the dissolution and release of a water-soluble drug and excipient…
Models of areas of physics in terms of cellular automata have become increasingly popular. Cellular automata (CAs) support the modeling of systems with discrete state component values and enforce the comprehensive specification of the…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
We focus on a family of one-dimensional probabilistic cellular automata with memory two: the dynamics is such that the value of a given cell at time $t+1$ is drawn according to a distribution which is a function of the states of its two…
Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell-cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to…
The paper presents a systematic approach for stiffness modeling of manipulators with complex and hybrid structures using matrix structural analysis. In contrast to previous results, it is suitable for mixed architectures containing…