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首页> 外文期刊>Earth Surface Processes and Landforms: The journal of the British Geomorphological Research Group >The shape of patterns to come: from initial formation to long-term evolution
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The shape of patterns to come: from initial formation to long-term evolution

机译：模式的形状：从最初的形成到长期的演变

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Many studies focus on the emergence and development of rhythmic landscape patterns. In this contribution we explore the different behaviors found as patterns evolve; the trajectories that patterns exhibit as they transit from infinitesimal-amplitude perturbation to a statistically steady state (or in some cases to continued statistical evolution). The variety of behaviors observed, either through field and laboratory experiments or numerical modeling, can be reduced to four classes: (a) simple stabilization where predictions based on the initial growth of small perturbations corresponds with the characteristics of patterns observed in nature; (b) significant pattern coarsening en route to saturated wavelength, where non-linear interactions between finite-amplitude pattern elements change the geometric properties of a pattern as it approaches steady-state; (c) perpetual coarsening where the wavelength associated with the emerging pattern continues to grow over time and is only limited by physical boundaries or external constrains; (d) slow evolution toward a different attractor, a novel behavior observed in numerical modeling that involves profound temporal changes in pattern characteristics. Within these classes we also observe generalizable non-linear behaviors: dependence on initial conditions, the emergence of pattern-scale variables such as pattern defects, and the presence ofmultiple stable states. Predicting the shape of patterns to come remains a challenge - one that we suggest requires a range of modeling approaches to address both initial instabilities and the emergent properties of evolving patterns, which involve disparate forms of non-linear interactions. Consideration of generic system behaviors at the pattern scale could enhance future pattern formation studies, facilitating appropriate pairings of analysis approaches and pattern-evolution modes.
机译：许多研究关注有节奏的景观格局的出现和发展。在这一贡献中，我们探索了随着模式发展而发现的不同行为。模式从无穷小幅值扰动过渡到统计稳定状态（或在某些情况下到持续的统计演变）时显示的轨迹。通过现场和实验室实验或数值模型观察到的各种行为可以归为四类：（a）简单稳定，其中基于小扰动初始增长的预测与自然界中观察到的模式特征相对应; （b）在到达饱和波长的过程中会出现明显的图案粗化现象，其中，有限振幅图案元素之间的非线性相互作用会随着图案接近稳态而改变其几何特性; （c）永久性粗化，其中与出现的图案相关的波长会随着时间而持续增长，并且仅受物理边界或外部约束的限制; （d）向不同吸引子的缓慢发展，这是一种在数值建模中观察到的新颖行为，涉及模式特征的深刻时间变化。在这些类别中，我们还观察到可概括的非线性行为：对初始条件的依赖，图案尺寸变量（例如图案缺陷）的出现以及多个稳定状态的存在。预测即将到来的模式的形状仍然是一个挑战-我们建议人们需要一系列建模方法来解决初始不稳定性和正在演变的模式的新兴特性，这些模式涉及不同形式的非线性相互作用。在模式规模上考虑通用系统行为可能会增强未来的模式形成研究，从而促进分析方法和模式演化模式的适当组合。

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