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，是自动驾驶汽车算法开发的原型，也是模式的丰富来源。群体是由内生的社会力量与外生的环境力量相互作用而形成的。描述社会力量的核是群模型的关键元素。为了提高对这些模型的数学理解，阐明外源和内源力如何相互作用以影响聚集模式和形态，并提供对蚜虫和蝗虫的生物学见解，我们开展了三个项目。(1)我们分析和模拟一个广泛适用的微分方程为基础的模型描述生物体的运动是由于内源性和外源性的力量。我们连接属性的群体模式的属性的两种力量。(2)在实验中，我们测量了豌豆蚜虫在群体中的运动轨迹。使用（1）中的模型，我们量化了社会内核。(3)我们从（1）中概括了这项研究，并结合了一个动态演变的内核，模拟了沙漠蝗虫的社会和反社会行为阶段。这项工作将建议集群控制策略，以尽量减少聚集，从而减轻一些负面的经济和人道主义影响的蝗虫swarms.Turing模式产生的反应和扩散之间的竞争，在不同的化学，生物和物理系统。为了促进对强迫模式的数学和化学理解，我们对二氧化氯-碘-丙二酸（CDIMA）图灵系统进行了实验。具体来说，我们迫使图灵模式与时间周期性的光源和测量如何产生的模式抑制规模与forcing parameters.These项目纳入教育通过研究参与12名本科生研究人员，包括妇女，其他代表性不足的少数民族，和学士后的学生为研究生学习。为了建立实验和理论之间的联系，一些学生将进行实验工作，所有人都将在PI的实验/理论实验室内进行培训。学生将与其他大学和本科院校的理论家和实验家互动。实验室和课程的改进将提供超出补助金期限的好处。

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.