RUI - Pattern forming dynamical systems in theory and experiment

昆虫、鱼类、鸟类和其他生物的生物群影响着生态和进化动力学，是自主车辆算法开发的原型，是模式的丰富来源。蜂群的形成是内生社会力量和外生环境力量相互作用的结果。描述社会力量的核心是群体模型的关键要素。为了提高对这些模型的数学理解，阐明外源和内源力量如何相互作用影响聚集模式和形态，并为研究蚜虫和蝗虫提供生物学上的见解，我们开展了三个项目。(1)分析和模拟了一个广泛适用的基于微分方程的模型，该模型描述了生物在内力和外力作用下的运动。我们将群体模式的性质与这两种力的性质联系起来。(2)在实验中，我们测量了豌豆蚜虫在群内的运动轨迹。利用(1)中的模型，我们对社会核进行了量化。(3)通过引入一个动态演化的核来模拟沙漠蝗虫的社会和反社会行为阶段，我们推广了(1)中的研究。这项工作将提出种群控制策略，以最大限度地减少聚集，从而改善蝗虫种群的一些负面经济和人道主义影响。图腾模式源于不同化学、生物和物理系统中反应和扩散之间的竞争。为了有助于对强迫模式的数学和化学理解，我们在二氧化氯-碘-丙二酸(CDIMA)图灵系统上进行了实验。具体地说，我们用时间周期光源强制图灵图案，并测量产生的图案抑制如何随强制参数的变化而变化。这些项目包括通过12名本科生研究人员的研究参与教育，包括女性、其他代表性不足的少数族裔，以及准备进行研究生学习的学士学位后学生。为了在实验和理论之间建立联系，一些学生将进行实验工作，所有学生都将在PI的实验/理论实验室进行培训。学生们将与其他大学和本科学院的理论家和实验者互动。实验室和课程的改进将提供超出资助期的好处。

Biological swarms of insects, fish, birds, and other organisms influence ecological and evolutionary dynamics, serve as prototypes for algorithm development of autonomous vehicles, and are rich sources of patterns. Swarms are shaped by an interaction of endogenous social forces with exogenous environmental ones. A kernel describing the social forces is a key element of swarm models. To improve the mathematical understanding of these models, to clarify how exogenous and endogenous forces interact to influence aggregation pattern and morphology, and to provide biological insight into aphids and locusts, we carry out three projects. (1) We analyze and simulate a broadly applicable differential equation based model describing organisms whose movement is due to endogenous and exogenous forces. We connect properties of swarm patterns to properties of the two forces. (2) In experiment, we measure trajectories of pea aphids moving within a group. Using the model from (1), we quantify the social kernel. (3) We generalize the study from (1) by incorporating a dynamically evolving kernel that models social and antisocial behavioral phases in desert locusts. This work will suggest swarm control strategies to minimize aggregation and hence ameliorate some of the negative economic and humanitarian impacts of locust swarms.Turing patterns arise from a competition between reaction and diffusion in diverse chemical, biological, and physical systems. To contribute to the mathematical and chemical understanding of forced patterns, we perform experiments on the chlorine dioxide - iodine - malonic acid (CDIMA) Turing system. Specifically, we force Turing patterns with a time-periodic light source and measure how the resulting pattern suppression scales with forcing parameters.These projects incorporate education through research involvement of twelve undergraduate student researchers, including women, other underrepresented minorities, and post-baccalaureate students bound for graduate study. To forge links between experiment and theory, some students will perform experimental work and all will train within the PI's experimental/theoretical lab. Students will interact with theorists and experimentalists at other universities and undergraduate colleges. Lab and curricular enhancements will provide benefits beyond the term of the grant.