Related papers: On Target Pattern Formation in the CHNS system
We present an anisotropic mesh adaptation procedure based on Riemannian metrics for the simulation of two-phase incompressible flows with non-matching densities. The system dynamics are governed by the Cahn-Hilliard Navier-Stokes (CHNS)…
Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…
Experiments on a thin layer of cohesive wet granular matter under vertical vibrations reveal kink separated domains that collide with the container at different phases. Due to the strong cohesion arising from the formation of liquid bridges…
The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector…
Spatial and temporal pattern formation in reaction-diffusion systems is typically studied with two or more equations, as scalar reaction-diffusion equations confined to convex domains do not admit stable inhomogeneous states in time or…
We derive a novel thermodynamically consistent Navier--Stokes--Cahn--Hilliard system with dynamic boundary conditions. This model describes the motion of viscous incompressible binary fluids with different densities. In contrast to previous…
We consider a model for a one-dimensional photonic crystal formed by a succession of Kerr-type equidistant spaceless interfaces immersed in a linear medium. We calculate the band structure and reflectance of this structure as a function of…
An easily implementable path solution algorithm for 2D spatial problems, based on excitable/programmable characteristics of a specific cellular nonlinear network (CNN) model is presented and numerically investigated. The network is a single…
We perform molecular dynamics simulations of ionic liquids confined between graphene walls under a large variety of conditions (pure ionic liquids, mixtures with water and alcohols, mixtures with lithium salts and defective graphene walls).…
In this paper we consider a multiscale phase-field model for capillarity-driven flows in porous media. The presented model constitutes a reduction of the conventional Navier-Stokes-Cahn-Hilliard phase-field model, valid in situations where…
Twisting and stacking two copies of a 2D crystal can produce a long-wavelength periodic interference pattern known as a moir\'e pattern. Performing the same procedure with an aperiodic structure instead generates a single moir\'e spot at…
Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…
We describe spatiotemporal patterns in a network of identical van der Pol oscillators coupled in a two-dimensional geometry. In this study, we show that the system under study demonstrates a plethora of different spatiotemporal structures…
A model of pattern formation in living systems is presented. The pattern is achieved by the sequential interaction of two signaling pathways. The coupling of the pattern to the (thick) epithelial sheet changes is given, when the Gauss…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
Based on a multi-agent model, we investigate how target waves emerge from a population dynamics with cyclical interactions among three species. We show that the periodically injecting source in a small central area can generate target waves…
While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…
We studied the effect of nearest pattern interaction on a globally pattern formation in a 2-dimensional space, where patterns are to grow initially from a noise in the presence of periodic supply of energy. Although our approach is general,…
This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…