Parasites and Pattern Formation

1999 ◽  
Vol 54 (2) ◽  
pp. 146-152 ◽  
Author(s):  
J. Ackermann ◽  
T. Kirner
Keyword(s):  
Pattern Formation ◽  
Flow Reactor ◽  
Spiral Waves ◽  
Cooperative Interaction ◽  
Biological Information ◽  
Parameter Region ◽  
Parasitic Species ◽  
Model Complex ◽  
Complex Patterns ◽  
The Stability

Abstract Biological information is coded in replicating molecules. To maintain a given amount of in-formation a cooperative interaction between these molecules is essential. The main problem for the stability of a system of prebiotic replicators are emerging parasites. Stabilization against such parasites is possible if space is introduced in the model. Complex patterns like spiral waves and self-replicating spot patterns have been shown to stabilize such systems. Stability of replicating systems, however, occurs only in parameter regions were such complex patterns occur. We show that parasites are able to push such systems into a parameter region were life is possible. To demonstrate this influence of parasites on such systems, we introduce a parasitic species in the Gray-Scott model. The growing concentration of parasites will kill the system, and the cooperative Gray-Scott system will be diluted out in a well mixed flow reactor. While considering space, in the model stabilizing pattern formation in a narrow parameter region is possible. We demonstrate that the concentration of the parasitic species is able to push the system into a region were stabilizing patterns emerge.

Optimization of the Robust Stability Limit for Multi-Cutter Turning Processes

2015 ◽  
Author(s):  
Marta J. Reith ◽  
Daniel Bachrathy ◽  
Gabor Stepan
Keyword(s):  
Robust Stability ◽  
Optimal Parameter ◽  
Stability Limit ◽  
Boundary Function ◽  
Lower Envelope ◽  
Computation Method ◽  
Parameter Region ◽  
Dynamical Parameters ◽  
The Stability ◽  
Machining Parameter

Multi-cutter turning systems bear huge potential in increasing cutting performance. In this study we show that the stable parameter region can be extended by the optimal tuning of system parameters. The optimal parameter regions can be identified by means of stability charts. Since the stability boundaries are highly sensitive to the dynamical parameters of the machine tool, the reliable exploitation of the so-called stability pockets is limited. Still, the lower envelope of the stability lobes is an appropriate upper boundary function for optimization purposes with an objective function taken for maximal material removal rates. This lower envelope is computed by the Robust Stability Computation method presented in the paper. It is shown in this study, that according to theoretical results obtained for optimally tuned cutters, the safe stable machining parameter region can significantly be extended, which has also been validated by machining tests.

The Stability of Spiral Waves

2009 ◽  
Author(s):  
Faridon Amdjadi ◽  
Robert Wallace ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Spiral Waves ◽  
The Stability

scholarly journals Traveling and standing waves mediate pattern formation in cellular protrusions

2020 ◽  
Vol 6 (32) ◽  
pp. eaay7682
Author(s):  
Sayak Bhattacharya ◽  
Tatsat Banerjee ◽  
Yuchuan Miao ◽  
Huiwang Zhan ◽  
Peter N. Devreotes ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Traveling Waves ◽  
Standing Waves ◽  
Cell Cortex ◽  
Theoretical Studies ◽  
Direct Transformation ◽  
Diffusion Parameters ◽  
Excitable Systems ◽  
Mutant Strains ◽  
The Stability

The mechanisms regulating protrusions during amoeboid migration exhibit excitability. Theoretical studies have suggested the possible coexistence of traveling and standing waves in excitable systems. Here, we demonstrate the direct transformation of a traveling into a standing wave and establish conditions for the stability of this conversion. This theory combines excitable wave stopping and the emergence of a family of standing waves at zero velocity, without altering diffusion parameters. Experimentally, we show the existence of this phenomenon on the cell cortex of some Dictyostelium and mammalian mutant strains. We further predict a template that encompasses a spectrum of protrusive phenotypes, including pseudopodia and filopodia, through transitions between traveling and standing waves, allowing the cell to switch between excitability and bistability. Overall, this suggests that a previously-unidentified method of pattern formation, in which traveling waves spread, stop, and turn into standing waves that rearrange to form stable patterns, governs cell motility.

scholarly journals Pattern Formation in Predator-Prey Model with Delay and Cross Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Xinze Lian ◽  
Shuling Yan ◽  
Hailing Wang
Keyword(s):  
Time Delay ◽  
Pattern Formation ◽  
Turing Instability ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model ◽  
Diffusion Controlled ◽  
The Stability ◽  
Self Replication

We consider the effect of time delay and cross diffusion on the dynamics of a modified Leslie-Gower predator-prey model incorporating a prey refuge. Based on the stability analysis, we demonstrate that delayed feedback may generate Hopf and Turing instability under some conditions, resulting in spatial patterns. One of the most interesting findings is that the model exhibits complex pattern replication: the model dynamics exhibits a delay and diffusion controlled formation growth not only to spots, stripes, and holes, but also to spiral pattern self-replication. The results indicate that time delay and cross diffusion play important roles in pattern formation.

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.

Dynamic Simulation of Mixing-Limited Pattern Formation in Homogeneous Autocatalytic Reactions

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
Ankur Gupta ◽  
Saikat Chakraborty
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Three Dimensional ◽  
Diffusion Reaction ◽  
Dynamic Simulations ◽  
Transverse Mixing ◽  
Autocatalytic Reactions ◽  
Steady State Bifurcation ◽  
The Stability ◽  
Parametric Analyses

Interaction between transport and reaction generates a variety of complex spatio-temporal patterns in chemical reactors. These patterned states, which are typically initiated by autocatalytic effects and sustained by differences in diffusion/local mixing rates, often cause undesired effects in the reactor. In this work, we analyze the dynamic evolution of mixing-limited spatial pattern formation in fast, homogeneous autocatalytic reactions occurring in isothermal tubular reactors using two-dimensional (2-D) convection-diffusion-reaction (CDR) models that are obtained through rigorous spatial averaging of the three-dimensional (3-D) CDR model using Liapunov-Schmidt technique of bifurcation theory. We use the spatially-averaged 2-D CDR model (and its "regularized" form) to perform steady-state bifurcation analysis that captures the region of multiple solutions, and we analyze the stability of these multiple steady states to transverse perturbations using linear stability analysis. Parametric analyses of the steady-state bifurcation diagrams and stability boundaries show that when transverse mixing is significantly slower than the rate of autocatalytic reaction, mixing-limited patterns emerge from the unstable middle branch that connects the ignition and extinction points of an S-shaped bifurcation curve. Our dynamic simulations show the emergence of three different types of spatial patterns namely, Band, Anti-phase and Target, depending on the nature of transverse perturbation. The temporal evolution of these patterns consists of rapid intensification of the concentration-segregation process (especially when transverse mixing is much slower than reaction) followed by slow diffusion-mediated return to symmetry that occurs at time scales much larger than the reactor residence time. Our parametric analysis of the dynamics reveals that while larger Péclet numbers (both axial and transverse) increase the stability and decay time of the patterned states, larger Damköhler numbers lead to faster ignition resulting in the opposite effect.

scholarly journals Self-Organized Crystallization Patterns from Evaporating Droplets of Common Wheat Grain Leakages as a Potential Tool for Quality Analysis

2011 ◽  
Vol 11 ◽  
pp. 1712-1725 ◽  
Author(s):  
Maria Olga Kokornaczyk ◽  
Giovanni Dinelli ◽  
Ilaria Marotti ◽  
Stefano Benedettelli ◽  
Daniele Nani ◽  
...  
Keyword(s):  
Pattern Formation ◽  
Common Wheat ◽  
Seed Quality ◽  
Dark Field ◽  
Quality Analysis ◽  
Wheat Cultivars ◽  
Wheat Kernel ◽  
Self Organized ◽  
Complex Patterns ◽  
Pattern Forming

We studied the evaporation-induced pattern formation in droplets of common wheat kernel leakages prepared out of ancient and modern wheat cultivars as a possible tool for wheat quality analysis. The experiments showed that the substances which passed into the water during the soaking of the kernels created crystalline structures with different degrees of complexity while the droplets were evaporating. The forms ranged from spots and simple structures with single ramifications, through dendrites, up to highly organized hexagonal shapes and fractal-like structures. The patterns were observed and photographed using dark field microscopy in small magnifications. The evaluation of the patterns was performed both visually and by means of the fractal dimension analysis. From the results, it can be inferred that the wheat cultivars differed in their pattern-forming capacities. Two of the analyzed wheat cultivars showed poor pattern formation, whereas another two created well-formed and complex patterns. Additionally, the wheat cultivars were analyzed for their vigor by means of the germination test and measurement of the electrical conductivity of the grain leakages. The results showed that the more vigorous cultivars also created more complex patterns, whereas the weaker cultivars created predominantly poor forms. This observation suggests a correlation between the wheat seed quality and droplet evaporation patterns.

An Urban Pattern Dynamics with Capital and Knowledge Accumulation

1993 ◽  
Vol 25 (3) ◽  
pp. 357-370 ◽  
Author(s):  
W-B Zhang
Keyword(s):  
Pattern Formation ◽  
Capital Accumulation ◽  
Research Policy ◽  
Central Business District ◽  
Dynamic Interactions ◽  
Pattern Dynamics ◽  
Urban Patterns ◽  
Urban Pattern ◽  
The Stability ◽  
Business District

In this paper a dynamic model of urban pattern formation with endogenous knowledge and capital accumulation is proposed. The Alonso model is extended to include two of the most important dynamic forces for urban development—capital accumulatin and technological progress. The standard assumption of the existence of the central business district (CBD) is still accepted in this approach. It is assumed that two production sectors (industry and service) and one knowledge production sector (research institutions and university) are located at the CBD. First, a compact framework for analysing dynamic interactions of the three sectors and urban pattern formation is suggested. Then, the existence of stationary urban patterns is guaranteed and the stability conditions provided. Last, the effects of changes in government's research policy and some other parameters upon the system are examined.

Sign in / Sign up

Export Citation Format

Share Document