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首页> 外文期刊>Journal of Computational Physics >Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction-diffusion systems
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Spatially adaptive stochastic numerical methods for intrinsic fluctuations in reaction-diffusion systems

机译：反应扩散系统内在波动的空间自适应随机数值方法

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摘要

Stochastic partial differential equations are introduced for the continuum concentration fields of reaction-diffusion systems. The stochastic partial differential equations account for fluctuations arising from the finite number of molecules which diffusively migrate and react. Spatially adaptive stochastic numerical methods are developed for approximation of the stochastic partial differential equations. The methods allow for adaptive meshes with multiple levels of resolution, Neumann and Dirichlet boundary conditions, and domains having geometries with curved boundaries. A key issue addressed by the methods is the formulation of consistent discretizations for the stochastic driving fields at coarse-refined interfaces of the mesh and at boundaries. Methods are also introduced for the efficient generation of the required stochastic driving fields on such meshes. As a demonstration of the methods, investigations are made of the role of fluctuations in a biological model for microorganism direction sensing based on concentration gradients. Also investigated, a mechanism for spatial pattern formation induced by fluctuations. The discretization approaches introduced for SPDEs have the potential to be widely applicable in the development of numerical methods for the study of spatially extended stochastic systems.
机译：为反应扩散系统的连续浓度场引入了随机偏微分方程。随机偏微分方程解释了由于有限数量的分子扩散迁移和反应而引起的波动。开发了空间自适应随机数值方法，用于逼近随机偏微分方程。该方法允许具有多个级别的分辨率，Neumann和Dirichlet边界条件以及具有带有弯曲边界的几何形状的域的自适应网格。这些方法解决的一个关键问题是在网格的粗化界面和边界处为随机驱动场制定一致的离散化。还介绍了在此类网格上有效生成所需随机驱动场的方法。作为方法的证明，对基于浓度梯度的微生物方向传感生物学模型中波动的作用进行了研究。还研究了由波动引起的空间图案形成的机制。为SPDE引入的离散化方法具有潜在的潜力，可广泛应用于研究空间扩展随机系统的数值方法。

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