فهرس المقالات Pattern Formation

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  1 - ناپایداری تورینگ و نقش های فضایی در مدل های کنش-انتشار
  علی عطابیگی
  نقش ها همه جا در طبیعت وجود دارند و تحقیقات پنجاه سال اخیر فهم ما را نسبت به مکانیسم های تشکیل آنها تا حد زیادی افزایش داده اند. هدف از این مقاله مطالعه سیستم هایی است که در آنها نقش های فضایی پایدار بطور موقتی شکل می گیرند. بطور خاص، تأکید ویژه بر ناپایداری های تورینگ أکثر

  نقش ها همه جا در طبیعت وجود دارند و تحقیقات پنجاه سال اخیر فهم ما را نسبت به مکانیسم های تشکیل آنها تا حد زیادی افزایش داده اند. هدف از این مقاله مطالعه سیستم هایی است که در آنها نقش های فضایی پایدار بطور موقتی شکل می گیرند. بطور خاص، تأکید ویژه بر ناپایداری های تورینگ بعنوان متداول ترین مکانیسم تشکیل نقش ها خواهد بود. مدل گیرر-ماینهارت یکی از نمونه های اولیه سیستم های کنش انتشار است که پدیده تشکیل نقش را در فرایندهای طبیعی توصیف میکند. آنالیز انشعاب، بصورت تئوری و عددی، روی این مدل انجام میشود و اثر انتشار بر پایداری حالت تعادل آن بررسی میشود. نشان داده میشود که تحت شرایط خاصی، ناپایداری ناشی از انشعاب یا ناپایداری تورینگ در حالت تعادلی که در غیاب انتشار پایدار است، اتفاق می افتد. تفاصيل المقالة
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  2 - GAME OF COORDINATION FOR BACTERIAL PATTERN FORMATION: A FINITE AUTOMATA MODELLING
  Sudeepto Bhattacharya Gaurav Srivastava
  In this paper, we use game theory to describe the emergence of self-organization and consequent pattern formation through communicative cooperation inBacillus subtiliscolonies. The emergence of cooperative regime is modelled as an n-player Assurance game, with the bacte أکثر

  In this paper, we use game theory to describe the emergence of self-organization and consequent pattern formation through communicative cooperation inBacillus subtiliscolonies. The emergence of cooperative regime is modelled as an n-player Assurance game, with the bacterial colonies as individual players. The game is played iteratively through cooperative communication, and mediated by exchange of information about the local environment between the different bacterial colonies comprising the system. The iteration causes the interactive system to grow and produce beautiful complex spatial patterns signaling the emergence of self-organization. In laboratory, we have the bacterial growth environment mimicked in Petri dish, where chemical stress is introduced in a three- fold manner: through modification of nutrition and substrate amounts and introducing an antibiotic in the system. In our model, bacteria colonies, treated asindividual players, interact within the environment and grow according to a set of rules. The rules capture the biotic processes that allow bacteria to grow in the hostile environment, and cope with the stress. We find the effects of sophisticated communications and information-sharing between bacterial colonies to be a vital determinant for bacterial growth, which is manifested in the Petri dish as complex spatial patterns, often at fractal scales. As a formal description of the above game, we model the emergence of this cooperative behaviour as finite deterministic automata, whose transition function is informed by the Assurance game pay-off. Consequently, the exercise allows us to derive a grammar that provides the rules for describing the bacterial interactions leading to the emergence of the spatial structures. تفاصيل المقالة
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  3 - SPOT PATTERNS IN GRAY SCOTT MODEL WITH APPLICATION TO EPIDEMIC CONTROL
  Muhammad Abdullahi Yau M. U. Adehi Muktari Garba
  In this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables أکثر

  In this work, we analyse a pair of two-dimensional coupled reaction-diusion equations known as the Gray-Scott model, in which spot patterns have been observed. We focus on stationary patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. A complete bifurcation study of these solutions is presented. The main mathematical techniques employed in this analysis of the stationary patterns is the Turing instability theory. This paper addresses the question of how popula-tion diusion aects the formation of the spatial patterns in the Gray-Scott model by Turing mechanisms. In particular, we present a theoretical analysis of results of the numerical simulations in two dimensions. Moreover, there is a critical value for the system within the linear regime. Below the critical value the spatial patterns are impermanent, whereas above it stationary spot patterns can exist over time. We have observed the formation of spatial patterns during the evolution, which are sparsely isolated ordered spot patterns that emerge in thespace. In this research we focuse on three areas: rst, the biology; second, the mathematics and third, the application. We use these spatial patterns to understand the nature of disease spread and that means to understand the mechanism of interaction of the populations. There remains uncertainty in the mechanisms surrounding the genesis of how epidemics spread in their spatial enveronment. The role of mathematical modelling in understanding the spreadand control of epidemics can never be over emphised. تفاصيل المقالة