Collaborative Research: Numerical methods for high-dimensional sticky diffusions
合作研究:高维粘性扩散的数值方法
基本信息
- 批准号:2111163
- 负责人:
- 金额:$ 34.92万
- 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:2021-09-01 至 2024-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Numerical simulations can provide insight into many problems in science or engineering, for example by providing access to variables that are otherwise difficult or impossible to observe experimentally, or by allowing a user to optimize over variables more cheaply than though experiments. Yet, numerical simulations can be a challenge to implement, because computers cannot reproduce all scales from the quantum mechanical to the macroscopic scales of interest. A particularly challenging system to simulate are collections of interacting particles, which are studied in a wide variety of applications, from designing new materials such as impact-resistant or energy-efficient materials, to understanding how the interior of a cell works, to biomedical applications such as designing the lipid nanoparticles that carry the mRNA vaccines. This project will develop methods to simulate interacting particles which currently require the computer to take timesteps that are many times smaller than the timescales of interest. We will build upon a recent mathematical description of the effective interactions between such particles to allow a simulation to take significantly larger timesteps. This will allow for simulations over significantly longer times and of larger collections of particles, and hence will enable scientists to use computations to understand a richer collection of systems that arise in a variety of important applications. Students will be involved and trained in interdisciplinary applications. This project aims to develop numerical methods to simulate high-dimensional stochastic differential equations (SDEs) modeling systems of particles that can repeatedly form, break and re-form bonds due to stiff, short-ranged forces. Such particles are models for systems such as colloids, cross-linked polymers (gels), DNA nanotechnology, networks of actin filaments or other cytoskeletal components, chromatin in the cell, among many others. Because of the stiffness of the particle forces, current simulation methods require extremely small time steps and thus prohibitively long simulation times. The project will develop methods that allow significantly larger timesteps and thus can work for systems of hundreds to thousands of particles, and the approach is based on two key developments. The first is an analytic result which eliminates the stiff forces and replaces them with rigid bonds when particles are in contact, which can be achieved with the help of sticky boundary conditions. The resulting sticky diffusion allows particles to evolve stochastically subject to rigid distance constraints, but crucially, allows these constraints to change. The second is a discretization of SDEs in space and numerical PDE theory to discretize the infinitesimal generator of the sticky diffusion to be later used to simulate a Markov Jump Process. This approach allows one to handle sticky boundary conditions because one can choose discretization points directly on the boundary. The methods will be applied to study systems such as DNA-coated colloids and networks of actin filaments.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.
数值模拟可以为科学或工程中的许多问题提供见解,例如,通过提供对实验中难以或不可能观察到的变量的访问,或者通过允许用户比通过实验更便宜地对变量进行优化。然而,数值模拟可能是一个挑战,因为计算机不能重现从量子力学到宏观尺度的所有尺度。一个特别具有挑战性的模拟系统是相互作用粒子的集合,在各种各样的应用中进行研究,从设计新材料(如抗冲击或节能材料)到了解细胞内部如何工作,再到生物医学应用(如设计携带mRNA疫苗的脂质纳米颗粒)。该项目将开发模拟相互作用粒子的方法,目前需要计算机采取比感兴趣的时间尺度小许多倍的时间步长。我们将建立在最近对这些粒子之间有效相互作用的数学描述之上,以允许模拟采取更大的时间步长。这将允许模拟更长的时间和更大的粒子集合,因此将使科学家能够使用计算来理解在各种重要应用中出现的更丰富的系统集合。学生将参与并接受跨学科应用的培训。该项目旨在开发数值方法来模拟高维随机微分方程(SDEs)建模系统的粒子,这些粒子可以由于刚性、短程力而反复形成、断裂和重新形成键。这些粒子是胶体、交联聚合物(凝胶)、DNA纳米技术、肌动蛋白细丝网络或其他细胞骨架成分、细胞中的染色质等系统的模型。由于粒子力的刚度,目前的模拟方法需要极小的时间步长,因此模拟时间长得令人望而却步。该项目将开发允许更大时间步长的方法,从而可以适用于数百到数千个粒子的系统,该方法基于两个关键的发展。第一种是在粘性边界条件的帮助下,消除颗粒接触时的刚性力而代之以刚性键的解析结果。由此产生的粘性扩散允许粒子在严格的距离约束下随机演化,但关键的是,允许这些约束发生变化。其次是空间离散化sde和数值PDE理论,以离散黏扩散的无穷小发生器,稍后用于模拟马尔可夫跳变过程。这种方法允许处理粘性边界条件,因为可以直接在边界上选择离散点。该方法将应用于研究系统,如dna包被胶体和肌动蛋白丝网络。该奖项反映了美国国家科学基金会的法定使命,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(3)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Mass Changes the Diffusion Coefficient of Particles with Ligand-Receptor Contacts in the Overdamped Limit
- DOI:10.1103/physrevlett.129.048003
- 发表时间:2022-07-21
- 期刊:
- 影响因子:8.6
- 作者:Marbach,Sophie;Holmes-Cerfon,Miranda
- 通讯作者:Holmes-Cerfon,Miranda
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Miranda Holmes-Cerfon其他文献
Transverse rigidity is prestress stability
- DOI:
10.1016/j.dam.2022.07.019 - 发表时间:
2022-12-15 - 期刊:
- 影响因子:
- 作者:
Steven J. Gortler;Miranda Holmes-Cerfon;Louis Theran - 通讯作者:
Louis Theran
Miranda Holmes-Cerfon的其他文献
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{{ truncateString('Miranda Holmes-Cerfon', 18)}}的其他基金
FRG: Collaborative Research: Stability of Structures Large and Small
FRG:合作研究:大大小小的结构的稳定性
- 批准号:
1564487 - 财政年份:2016
- 资助金额:
$ 34.92万 - 项目类别:
Continuing Grant
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