Numerical simulations of the effects of retinoids on pattern formation in a hydroid

1986 ◽  
Vol 195 (2) ◽  
pp. 128-132 ◽  
Author(s):  
Wolf Kemmner
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations

SINGLE-ELECTRON CIRCUITS PERFORMING DENDRITIC PATTERN FORMATION WITH NATURE-INSPIRED CELLULAR AUTOMATA

2007 ◽  
Vol 17 (10) ◽  
pp. 3651-3655 ◽  
Author(s):  
TAKAHIDE OYA ◽  
IKUKO N. MOTOIKE ◽  
TETSUYA ASAI
Keyword(s):  
Pattern Formation ◽  
Cellular Automata ◽  
Physical Properties ◽  
Cellular Automaton ◽  
Numerical Simulations ◽  
Thermal Effects ◽  
Semiconductor Device ◽  
Single Electron ◽  
Dendritic Trees ◽  
Single Electron Devices

We propose a novel semiconductor device in which electronic-analogue dendritic trees grow on multilayer single-electron circuits. A simple cellular-automaton circuit was designed for generating dendritic patterns by utilizing the physical properties of single-electron devices, i.e. quantum and thermal effects in tunneling junctions. We demonstrate typical operations of the proposed circuit through extensive numerical simulations.

Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response

2017 ◽  
Vol 10 (05) ◽  
pp. 1750073 ◽  
Author(s):  
Peng Feng
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Spatial Pattern ◽  
Numerical Simulations ◽  
Functional Response ◽  
Allee Effect ◽  
Turing Instability ◽  
Spatial Pattern Formation ◽  
The Stability ◽  
Steady State Solutions

In this paper, we study the dynamics of a diffusive modified Leslie–Gower model with the multiplicative Allee effect and Bazykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

scholarly journals Global dynamics and spatio-temporal patterns of predator–prey systems with density-dependent motion

2020 ◽  
pp. 1-31
Author(s):  
HAI-YANG JIN ◽  
ZHI-AN WANG
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
Prey Density ◽  
Temporal Patterns ◽  
Steady States ◽  
Global Dynamics ◽  
Predator Prey ◽  
Density Dependent ◽  
Spatially Homogeneous ◽  
Spatio Temporal

In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator–prey systems with density-dependent prey-taxis in a two-dimensional bounded domain with Neumann boundary conditions, where the coefficients of motility (diffusiq‘dfdon) and mobility (prey-taxis) of the predator are correlated through a prey density-dependent motility function. We establish the existence of classical solutions with uniform-in time bound and the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on parameters by constructing Lyapunov functionals. With numerical simulations, we further demonstrate that spatially homogeneous time-periodic patterns, stationary spatially inhomogeneous patterns and chaotic spatio-temporal patterns are all possible for the parameters outside the stability regime. We also find from numerical simulations that the temporal dynamics between linearised system and nonlinear systems are quite different, and the prey density-dependent motility function can trigger the pattern formation.

scholarly journals Pattern formation in clouds via Turing instabilities

2020 ◽  
Vol 6 (1) ◽  
pp. 75-96
Author(s):  
Juliane Rosemeier ◽  
Peter Spichtinger
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
General Class ◽  
Cloud Model ◽  
Generic Model ◽  
Weakly Nonlinear ◽  
Cloud Models ◽  
Special Cases ◽  
Turing Instabilities ◽  
Cloud Patterns

Abstract Pattern formation in clouds is a well-known feature, which can be observed almost every day. However, the guiding processes for structure formation are mostly unknown, and also theoretical investigations of cloud patterns are quite rare. From many scientific disciplines the occurrence of patterns in non-equilibrium systems due to Turing instabilities is known, i.e. unstable modes grow and form spatial structures. In this study we investigate a generic cloud model for the possibility of Turing instabilities. For this purpose, the model is extended by diffusion terms. We can show that for some cloud models, i.e special cases of the generic model, no Turing instabilities are possible. However, we also present a general class of cloud models, where Turing instabilities can occur. A key requisite is the occurrence of (weakly) nonlinear terms for accretion. Using numerical simulations for a special case of the general class of cloud models, we show spatial patterns of clouds in one and two spatial dimensions. From the numerical simulations we can see that the competition between collision terms and sedimentation is an important issue for the existence of pattern formation.

Enslaved Phase-Separation Fronts and Liesegang Pattern Formation

2011 ◽  
Vol 9 (5) ◽  
pp. 1081-1093 ◽  
Author(s):  
E. M. Foard ◽  
A. J. Wagner
Keyword(s):  
Phase Separation ◽  
Pattern Formation ◽  
Numerical Simulations ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Critical Value ◽  
Exact Form ◽  
Analytical Derivation ◽  
Boltzmann Method

AbstractWe show that an enslaved phase-separation front moving with diffusive speeds can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. To our knowledge this is the first fully analytical derivation of the Liesegang laws. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.

SPATIAL PATTERNS INDUCED BY RANDOM SWITCHING

2002 ◽  
Vol 02 (01) ◽  
pp. L21-L29 ◽  
Author(s):  
J. BUCETA ◽  
KATJA LINDENBERG ◽  
J. M. R. PARRONDO
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
Spatial Patterns ◽  
Reaction Diffusion ◽  
Homogeneous State ◽  
Ordered Structures ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Random Switching ◽  
Random Alternation

We propose a mechanism whereby a random alternation of two dynamics each leading to a different homogeneous state can lead to complex ordered structures. The proposed general formalism, based on the ideas of so-called paradoxical games, is illustrated via numerical simulations of particular examples. The relevance of the present study to other situations that lead to pattern formation, such as reaction-diffusion systems, is noted.

scholarly journals Transition of Liesegang Precipitation Systems: Simulations with an Adaptive Grid PDE Method

2011 ◽  
Vol 10 (4) ◽  
pp. 867-881 ◽  
Author(s):  
Paul A. Zegeling ◽  
István Lagzi ◽  
Ferenc Izsák
Keyword(s):  
Pattern Formation ◽  
Numerical Simulations ◽  
Initial Conditions ◽  
Qualitative Change ◽  
Adaptive Grid ◽  
Time Behavior ◽  
Centrally Symmetric ◽  
Type Pattern ◽  
Long Time ◽  
Pde Method

AbstractThe dynamics of the Liesegang type pattern formation is investigated in a centrally symmetric two-dimensional setup. According to the observations in real experiments, the qualitative change of the dynamics is exhibited for slightly different initial conditions. Two kinds of chemical mechanisms are studied; in both cases the pattern formation is described using a phase separation model including the Cahn-Hilliard equations. For the numerical simulations we make use of an adaptive grid PDE method, which successfully deals with the computationally critical cases such as steep gradients in the concentration distribution and investigation of long time behavior. The numerical simulations show a good agreement with the real experiments.

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