Spiral Waves and Target Patterns
螺旋波和目标模式
基本信息
- 批准号:2106566
- 负责人:
- 金额:$ 35万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2021
- 资助国家:美国
- 起止时间:2021-07-01 至 2024-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Many biological, chemical, and physical processes exhibit spiral waves and target patterns. Spiral waves occur, for instance, in autocatalytic chemical reactions, during cellular signaling of amoebae, and in cardiac tissue where they are often the cause of cardiac arrhythmias and the precursor to ventricular fibrillation and cardiac arrest. Similarly, target patterns appear prominently in autocatalytic reactions and are also often found in systems with small spatial inhomogeneities. This project focuses on understanding when spiral waves and target patterns arise, under which conditions they can be observed, and what mechanisms cause them to change their shape or disappear. The investigator will develop analytical, computational, and geometric tools to answer these questions and apply the findings to models of autocatalytic chemical reactions and wave propagation in cardiac tissue. Graduate and undergraduate students will be engaged in these research activities.This project focuses on understanding existence, multiplicity, stability, and bifurcations of spiral waves and target patterns through the development of spatial-dynamics methodologies that can be applied to a broad range of reaction-diffusion systems. The investigator will establish multiplicity results for one-dimensional spiral waves and target patterns in reaction-diffusion systems using spatial dynamics and apply these results to the Brusselator model. The second project centers on transverse instabilities of spiral waves and target patterns. Transverse instabilities do not contribute to the spectra of planar structures, though they do cause linear instabilities. The aim is to investigate how these instabilities manifest themselves on large bounded disks. The third project focuses on making the numerical computation of spiral spectra more robust by developing preconditioners that rely on appropriate exponential weights to reduce the norm of the resolvent independently of the size of the domain. In the last project, singular perturbation methods will be developed to understand the limits of profiles and spectra of planar spiral waves and target patterns when some of the diffusion coefficients in the model approach zero.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.
许多生物、化学和物理过程都表现出螺旋波和目标模式。例如,螺旋波发生在自催化化学反应中,在变形虫的细胞信号传导期间,以及在心脏组织中,它们通常是心律失常的原因以及心室颤动和心脏骤停的前兆。类似地,目标模式在自催化反应中表现突出,并且也经常在具有小空间不均匀性的系统中发现。该项目的重点是了解螺旋波和目标图案何时出现,在何种条件下可以观察到它们,以及是什么机制导致它们改变形状或消失。研究人员将开发分析,计算和几何工具来回答这些问题,并将研究结果应用于心脏组织中自催化化学反应和波传播的模型。研究生和本科生将从事这些研究活动。本项目的重点是通过开发可应用于广泛反应扩散系统的空间动力学方法来理解螺旋波和目标模式的存在性,多重性,稳定性和分叉。研究人员将建立多重性结果的一维螺旋波和目标模式的反应扩散系统中使用空间动力学和应用这些结果的selector模型。第二个项目集中在螺旋波和目标图案的横向不稳定性。横向不稳定性对平面结构的光谱没有贡献,尽管它们确实引起线性不稳定性。其目的是研究这些不稳定性如何表现在大的有界磁盘。第三个项目的重点是使螺旋谱的数值计算更强大的开发预条件,依赖于适当的指数权重,以减少独立的域的大小的预解的范数。在最后一个项目中,奇异摄动方法将被开发出来,以了解当模型中的一些扩散系数接近零时,平面螺旋波和目标模式的轮廓和光谱的限制。该奖项反映了NSF的法定使命,并被认为是值得支持的,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。
项目成果
期刊论文数量(8)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
SCOTv2: Single-Cell Multiomic Alignment with Disproportionate Cell-Type Representation
- DOI:10.1089/cmb.2022.0270
- 发表时间:2022-10
- 期刊:
- 影响因子:0
- 作者:Pinar Demetci;Rebecca Santorella;Manav Chakravarthy;Bjorn Sandstede;Ritambhara Singh
- 通讯作者:Pinar Demetci;Rebecca Santorella;Manav Chakravarthy;Bjorn Sandstede;Ritambhara Singh
Unsupervised Integration of Single-Cell Multi-omics Datasets with Disproportionate Cell-Type Representation
具有不成比例的细胞类型表示的单细胞多组学数据集的无监督整合
- DOI:10.1007/978-3-031-04749-7_1
- 发表时间:2022
- 期刊:
- 影响因子:0
- 作者:Demetçi, Pinar;Santorella, Rebecca;Sandstede, Bjorn;Singh, Ritambhara
- 通讯作者:Singh, Ritambhara
Behavior of Spiral Wave Spectra with a Rank-Deficient Diffusion Matrix
- DOI:10.1137/21m1455917
- 发表时间:2021-10
- 期刊:
- 影响因子:2
- 作者:S. Dodson;Bjorn Sandstede
- 通讯作者:S. Dodson;Bjorn Sandstede
Quantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish Patterns
- DOI:10.1137/22m1543082
- 发表时间:2023-01-01
- 期刊:
- 影响因子:2.1
- 作者:Cleveland,Electa;Zhu,Angela;Volkening,Alexandria
- 通讯作者:Volkening,Alexandria
Parameter Identifiability in PDE Models of Fluorescence Recovery After Photobleaching
- DOI:10.1007/s11538-024-01266-4
- 发表时间:2024-04-01
- 期刊:
- 影响因子:3.5
- 作者:Ciocanel,Maria-Veronica;Ding,Lee;Sandstede,Bjorn
- 通讯作者:Sandstede,Bjorn
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Bjorn Sandstede其他文献
Dynamics of Spiral Waves on Unbounded Domains Using Center-Manifold Reductions
使用中心流形约简的无界域上的螺旋波动力学
- DOI:
10.1006/jdeq.1997.3326 - 发表时间:
1997 - 期刊:
- 影响因子:2.4
- 作者:
Bjorn Sandstede;A. Scheel;C. Wulff - 通讯作者:
C. Wulff
Absolute instabilities of standing pulses
驻脉冲的绝对不稳定性
- DOI:
10.1088/0951-7715/18/1/017 - 发表时间:
2005 - 期刊:
- 影响因子:1.7
- 作者:
Bjorn Sandstede;A. Scheel - 通讯作者:
A. Scheel
Stability of N -fronts bifurcating from a twisted heteroclinic loop and an application to the FitzHugh-Nagumo equation
- DOI:
10.1137/s0036141096297388 - 发表时间:
1998 - 期刊:
- 影响因子:2
- 作者:
Bjorn Sandstede - 通讯作者:
Bjorn Sandstede
Viscous perturbations of marginally stable Euler flow and finite-time Melnikov theory
边际稳定欧拉流的粘性扰动和有限时间梅尔尼科夫理论
- DOI:
10.1088/0951-7715/18/2/001 - 发表时间:
2005 - 期刊:
- 影响因子:1.7
- 作者:
E. Grenier;C. Jones;F. Rousset;Bjorn Sandstede - 通讯作者:
Bjorn Sandstede
Determining stability of pulses for partial differential equations with time delays
确定具有时滞的偏微分方程的脉冲稳定性
- DOI:
10.1080/14689360500035693 - 发表时间:
2005 - 期刊:
- 影响因子:0
- 作者:
G. Samaey;Bjorn Sandstede - 通讯作者:
Bjorn Sandstede
Bjorn Sandstede的其他文献
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{{ truncateString('Bjorn Sandstede', 18)}}的其他基金
RTG: Mathematics of Information and Data with Applications to Science
RTG:信息和数据数学及其在科学中的应用
- 批准号:
2038039 - 财政年份:2021
- 资助金额:
$ 35万 - 项目类别:
Continuing Grant
TRIPODS+X: EDU: Collaborative Research: Investigations of Student Difficulties in Data Science Instruction
TRIPODS X:EDU:协作研究:学生在数据科学教学中遇到的困难的调查
- 批准号:
1839259 - 财政年份:2018
- 资助金额:
$ 35万 - 项目类别:
Standard Grant
Tripods+X:Res:Collaborative Research: Identification of Gene Regulatory Network Function from Data
Tripods X:Res:协作研究:从数据中识别基因调控网络功能
- 批准号:
1839262 - 财政年份:2018
- 资助金额:
$ 35万 - 项目类别:
Standard Grant
Dynamics and Stability of Spatially Extended Patterns
空间扩展模式的动力学和稳定性
- 批准号:
1714429 - 财政年份:2017
- 资助金额:
$ 35万 - 项目类别:
Standard Grant
Foundations of Model Driven Discovery from Massive Data
海量数据中模型驱动发现的基础
- 批准号:
1740741 - 财政年份:2017
- 资助金额:
$ 35万 - 项目类别:
Standard Grant
RTG: Integrating Dynamics and Stochastics (IDyaS)
RTG:动态和随机积分 (IDyaS)
- 批准号:
1148284 - 财政年份:2012
- 资助金额:
$ 35万 - 项目类别:
Continuing Grant
Conference on Geometric Methods in Infinite-dimensional Dynamical Systems
无限维动力系统几何方法会议
- 批准号:
1140723 - 财政年份:2011
- 资助金额:
$ 35万 - 项目类别:
Standard Grant
Collaborative Research: Absolute and essential instabilities in spatially extended systems
合作研究:空间扩展系统中的绝对和本质不稳定性
- 批准号:
0203854 - 财政年份:2002
- 资助金额:
$ 35万 - 项目类别:
Standard Grant
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