Nonlocal Variational Problems from Physical and Biological Models
物理和生物模型的非局部变分问题
基本信息
- 批准号:2306962
- 负责人:
- 金额:$ 20.21万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2023
- 资助国家:美国
- 起止时间:2023-08-01 至 2026-07-31
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Nonlocal models are used to describe a wide array of physical phenomena in material science, quantum mechanics, mathematical physics, and biology. The pertinence of these models is that they introduce scales used to investigate microstructures in macroscopic domains, as in the case of the nonlocal variational models characterizing the collective behavior in biological systems. This project involves the mathematical analysis of nonlocal attractive-repulsive interaction energies that are directly connected to aggregations models for biological and robotic swarming, granular media, and self-assembly of nanoparticles. The emphasis is on understanding the competing effects of interactions on the physical systems considered. This will yield insight into the general phenomenology of nonlocality and ultimately provide predictions of collective behavior in these systems and guide the design of improved devices. Training of undergraduate and graduate students will be integrated in the research project, which will lead to the discovery of new results through student research projects. The project has three main mathematical aims: (1) Develop new tools to study symmetry of optimizers of a model describing the distribution of oppositely charged phases; (2) study the effect of regularization via an interfacial free energy in swarming models described by attractive-repulsive nonlocal energies; and, finally, (3) introduce an extension of Gamow’s liquid drop model to investigate the effect of neutrons in determining the shape of the nucleus of an atom and the threshold of nuclear fission. To pursue these goals, techniques varying from nonlinear to geometric analysis, optimization and partial differential equations will be implemented. These techniques will be combined with computer-based experimentation. The common aim of all three directions is understanding structures of optimizers in a variety of physical systems of practical interest.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
非定域模型用于描述材料科学、量子力学、数学物理和生物学中的各种物理现象。这些模型的相关性在于,它们引入了用于研究宏观领域中微观结构的尺度,例如在表征生物系统中集体行为的非局部变分模型的情况下。该项目涉及非局部吸引-排斥相互作用能的数学分析,这些相互作用能直接与生物和机器人群集,颗粒介质和纳米颗粒自组装的聚集模型有关。重点是理解相互作用对所考虑的物理系统的竞争效应。这将使我们深入了解非定域性的一般现象,并最终提供这些系统中集体行为的预测,并指导改进设备的设计。本科生和研究生的培训将被整合到研究项目中,这将导致通过学生研究项目发现新的成果。 该项目有三个主要数学目标:(1)开发新工具来研究描述相反电荷相分布的模型的优化器的对称性;(2)研究通过吸引-排斥非局部能量描述的蜂拥模型中的界面自由能进行正则化的效果;(3)推广伽莫夫的液滴模型,研究中子对原子核形状和核裂变阈值的影响。为了追求这些目标,将实施从非线性到几何分析、优化和偏微分方程的技术。这些技术将与基于计算机的实验相结合。这三个方向的共同目标是理解各种实际感兴趣的物理系统中的优化器结构。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Ihsan Topaloglu其他文献
Explainable attention ResNet18-based model for asthma detection using stethoscope lung sounds
基于 ResNet18 的可解释注意力模型,使用听诊器肺音检测哮喘
- DOI:
10.1016/j.engappai.2023.106887 - 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Ihsan Topaloglu;P. Barua;Arif Metehan Yıldız;Tuğçe Keleş;S. Dogan;M. Baygin;Huseyin Fatih Gul;T. Tuncer;Ruyan Tan;Usha R. Acharya - 通讯作者:
Usha R. Acharya
Videolaryngoscopy is associated with a lower rate of double-lumen endotracheal tube malposition in thoracic surgery procedures, retrospective single-center study
- DOI:
10.1186/s13019-024-03239-z - 发表时间:
2025-01-04 - 期刊:
- 影响因子:1.500
- 作者:
Soner Kına;Güntuğ Batıhan;Ihsan Topaloglu;Huseyin Turkan - 通讯作者:
Huseyin Turkan
Singular perturbation of an elastic energy with a singular weight
具有奇异重量的弹性能量的奇异扰动
- DOI:
10.1016/j.physd.2020.132422 - 发表时间:
2019 - 期刊:
- 影响因子:0
- 作者:
Oleksandr Misiats;Ihsan Topaloglu;D. Vasiliu - 通讯作者:
D. Vasiliu
Standing waves for a generalized Davey-Stewartson system: Revisited
广义 Davey-Stewartson 系统的驻波:重新审视
- DOI:
10.1016/j.aml.2007.04.003 - 发表时间:
2008 - 期刊:
- 影响因子:3.7
- 作者:
A. Eden;A. Eden;Ihsan Topaloglu - 通讯作者:
Ihsan Topaloglu
Ihsan Topaloglu的其他文献
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