Pseudospectral Methods in Applied Mathematics
应用数学中的伪谱方法
基本信息
- 批准号:RGPIN-2017-03913
- 负责人:
- 金额:$ 1.02万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2020
- 资助国家:加拿大
- 起止时间:2020-01-01 至 2021-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
( ) Refs in CCV; [ ] Research Refs.
This proposal emphasizes the use of pseudospectral methods based on nonclassical quadrature grids [1] applied to the solution of important problems in statistical mechanics (4,9-11), quantum chemistry (1,7) and physics (6), mathematical biology and image reconstruction. A pseudospectral method refers to a numerical solution of PDEs and Integral eqs. (IE) on a grid [1]. The popular choices are the uniform Fourier grid or the nonuniform Chebyshev quadrature. The disadvantage of a Fourier grid is the Gibbs phenomena which is the non-spectral convergence of the Fourier series for functions at jump discontinuties. The Gibbs phenomenon contaminates images in all forms of tomography. A major ongoing objective is to develop a method of identifying the "edges" where the oscillations occur and to employ the previous Gibbs resolution techniques [23,24] to resolve the images. Likewise, the interpolation of data on a uniform grid leads to large oscillations at the ends of the interval; the Runge phenomenon (RP). The RP can be resolved with nonuniform nonclassical quadratures with spectral accuracy.
The topics in mathematical biology include the advance of a gene in a population modeled with Fishers equation and spiral waves in cardiac tissue studied with the Fitzhugh-Nagumo equation. The approach to equilibrium for nonequilibrium systems are studied with solutions of the Fokker Planck equation (FPE) (4) and the Boltzmann equation (BE) (1,11). The BE is also used to model the the high altitude regions of the atmospheres of Earth and Mars in comparison with available satellite data from enhanced Polar Outflow Probe (ePOP) and MAVEN. The resolution of images for tomography and magnetic resonance images is considered based on previous work for the resolution of the Gibbs phenomenon, the nonspectral convergence of a Fourier series of piecewise smooth functions. The basis for the modeling these different phenomena are multidimensional partial differential (PDE) and integral (IE) equations. Fishers reaction-diffusion equation [27], which models the advance of a gene, has localized traveling waves and solutions that are difficult to resolve. Spiral waves in cardiac tissue that are suspected to give rise to cardiac arrhythmias [28] are studied with the two-dimensional Fitzhugh-Nagumo equation with different ionic membrane models. For plasmas and globular clusters, the BE is approximated with a FPE which with particular diffusion coefficients yields a steady Kappa distribution used extensively in space science. A Poisson solver [15] is required to define the drift and diffusion coefficients in the FPE for plasmas. Ffficient Poisson solvers for Poisson's equation are required in fluid dynamics, plasma physics and cosmology. Efficient and accurate numerical methods are required to solve the Schroedinger equation (SE) (6) to describe many chemical and physical phenomenon.
()CCV中的参考文献; [ ]研究参考文献。
该建议强调使用基于非经典正交网格[1]的伪谱方法,用于解决统计力学(4,9 -11),量子化学(1,7)和物理学(6),数学生物学和图像重建中的重要问题。伪谱方法是指偏微分方程和积分方程的数值解。(IE)在一个网格上[1]。流行的选择是均匀傅里叶网格或非均匀切比雪夫求积。 傅立叶网格的缺点是吉布斯现象,这是傅立叶级数在跳跃不连续处的非谱收敛。 吉布斯现象污染了所有形式的断层扫描图像。一个正在进行的主要目标是开发一种识别振荡发生的“边缘”的方法,并采用以前的吉布斯分辨率技术[23,24]来解析图像。 同样,在均匀网格上插值数据会导致间隔两端的大振荡;龙格现象(RP)。RP可以解决与非均匀非经典求积谱精度。
数学生物学的主题包括用Fishers方程模拟的群体中基因的进展和用Fitzhugh-Nagumo方程研究的心脏组织中的螺旋波。本文用福克-普朗克方程(FPE)(4)和玻尔兹曼方程(BE)(1,11)的解研究了非平衡系统的平衡态逼近。 BE还用于对地球和火星大气的高海拔区域进行建模,并与增强型极地外流探测器(ePOP)和MAVEN的可用卫星数据进行比较。断层扫描和磁共振图像的分辨率被认为是基于以前的工作的分辨率的吉布斯现象,分段光滑函数的傅立叶级数的非谱收敛。这些不同现象的建模基础是多维偏微分(PDE)和积分(IE)方程。费舍尔反应扩散方程[27]模拟了基因的进展,具有难以解决的局部行波和解。用二维Fitzhugh-Nagumo方程和不同的离子膜模型研究了被怀疑引起心律失常的心脏组织中的螺旋波[28]。对于等离子体和球状星团,BE近似与FPE与特定的扩散系数产生一个稳定的Kappa分布广泛用于空间科学。需要泊松求解器[15]来定义等离子体FPE中的漂移和扩散系数。 在流体动力学、等离子体物理和宇宙学等领域中,需要有足够的泊松方程求解器。需要有效和精确的数值方法来求解薛定谔方程(SE)(6)以描述许多化学和物理现象。
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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Shizgal, Bernard其他文献
Shizgal, Bernard的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Shizgal, Bernard', 18)}}的其他基金
Pseudospectral Methods in Applied Mathematics
应用数学中的伪谱方法
- 批准号:
RGPIN-2017-03913 - 财政年份:2021
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Pseudospectral Methods in Applied Mathematics
应用数学中的伪谱方法
- 批准号:
RGPIN-2017-03913 - 财政年份:2019
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Pseudospectral Methods in Applied Mathematics
应用数学中的伪谱方法
- 批准号:
RGPIN-2017-03913 - 财政年份:2018
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Pseudospectral Methods in Applied Mathematics
应用数学中的伪谱方法
- 批准号:
RGPIN-2017-03913 - 财政年份:2017
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Statistical mechanics of nonequilibrium processes
非平衡过程的统计力学
- 批准号:
6424-2009 - 财政年份:2009
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Theoretical modelling of nonequilibrium processes
非平衡过程的理论建模
- 批准号:
6424-2004 - 财政年份:2008
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Theoretical modelling of nonequilibrium processes
非平衡过程的理论建模
- 批准号:
6424-2004 - 财政年份:2007
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Theoretical modelling of nonequilibrium processes
非平衡过程的理论建模
- 批准号:
6424-2004 - 财政年份:2006
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Theoretical modelling of nonequilibrium processes
非平衡过程的理论建模
- 批准号:
6424-2004 - 财政年份:2005
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Theoretical modelling of nonequilibrium processes
非平衡过程的理论建模
- 批准号:
6424-2004 - 财政年份:2004
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
相似国自然基金
Computational Methods for Analyzing Toponome Data
- 批准号:60601030
- 批准年份:2006
- 资助金额:17.0 万元
- 项目类别:青年科学基金项目
相似海外基金
Can audit and feedback be applied to target healthcare professionals recruitment and retention behaviour in RCTs? A mixed methods exploration
审计和反馈是否可以应用于随机对照试验中目标医疗保健专业人员的招聘和保留行为?
- 批准号:
2889285 - 财政年份:2023
- 资助金额:
$ 1.02万 - 项目类别:
Studentship
Computational models, algorithms and methods for comparative genomics, applied to pathogens and anopheles mosquitoes genomes
应用于病原体和按蚊基因组的比较基因组学计算模型、算法和方法
- 批准号:
RGPIN-2017-03986 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Uncertainty quantification methods applied to wind energy systems
应用于风能系统的不确定性量化方法
- 批准号:
RGPIN-2020-04511 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Optimization models, methods and algorithms applied to hydropower operations planning
水电调度优化模型、方法和算法
- 批准号:
RGPIN-2018-06331 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Comprehensive research on "Shoen-ezu" survey and analysis methods and applied research on general-purpose historical geographic information
“正圆江津”调查分析方法综合研究及通用历史地理信息应用研究
- 批准号:
22H00016 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Grant-in-Aid for Scientific Research (A)
Development of new, integrated computer modelling and inversion methods for applied geophysics and for joint geology-geophysics Earth modelling
开发新的集成计算机建模和反演方法,用于应用地球物理学和地质-地球物理学联合地球建模
- 批准号:
RGPIN-2018-06626 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Numerical methods for incompressible multiphase flows applied to magnetohydrodynamics
应用于磁流体动力学的不可压缩多相流数值方法
- 批准号:
2208046 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Standard Grant
Resource exploration for a net-zero emission future with electromagnetic methods in applied geophysics
应用地球物理学中电磁方法的资源勘探,实现净零排放的未来
- 批准号:
RGPAS-2021-00026 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Accelerator Supplements
Resource exploration for a net-zero emission future with electromagnetic methods in applied geophysics
应用地球物理学中电磁方法的资源勘探,实现净零排放的未来
- 批准号:
RGPIN-2021-02528 - 财政年份:2022
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual
Optimization models, methods and algorithms applied to hydropower operations planning
水电调度优化模型、方法和算法
- 批准号:
RGPIN-2018-06331 - 财政年份:2021
- 资助金额:
$ 1.02万 - 项目类别:
Discovery Grants Program - Individual