New analytical laws and applications of interaction potentials with a focus on van der Waals attraction

IF 4.4 2区工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY

Applied Mathematical Modelling Pub Date : 2025-03-24 DOI:10.1016/j.apm.2025.116100

A. Borković , M.H. Gfrerer , R.A. Sauer

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引用次数: 0

Abstract

The paper aims to improve the efficiency of modeling interactions between slender deformable bodies that resemble the shape of fibers. Interaction potentials are modeled as inverse-power laws with respect to the point-pair distance, and the complete body-body potential is obtained by pairwise summation (integration). To speed-up integration, we consider the analytical pre-integration of potentials between specific geometries such as disks, cylinders, rectangles, and rectangular prisms. Several exact new interaction laws are obtained, such as disk-infinite half-space and (in-plane) rectangle-rectangle for an arbitrary exponent, and disk-disk and rectangle-rectangle for van der Waals attraction. To balance efficiency and accuracy, approximate laws are proposed for disk-disk, point-cylinder, and disk-cylinder interactions. Additionally, we have developed a novel formulation for the interaction between a spatial beam and an infinite half-space. The application of the pre-integrated interaction potentials within the finite element method is illustrated via two examples.

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相互作用势的新分析定律和应用，重点是范德华引力

本文旨在提高类似纤维形状的细长可变形体之间相互作用的建模效率。相互作用势以关于点对距离的逆幂律建模，并通过成对求和（积分）得到完整的体-体势。为了加速积分，我们考虑了特定几何形状（如圆盘、圆柱体、矩形和矩形棱镜）之间势的解析预积分。得到了一些精确的新相互作用定律，如圆盘-无限半空间和（平面内）矩形-矩形对任意指数，圆盘-圆盘和矩形-矩形对范德华引力。为了平衡效率和精度，提出了磁盘-磁盘、点-圆柱体和磁盘-圆柱体相互作用的近似定律。此外，我们还开发了空间光束与无限半空间之间相互作用的新公式。通过两个算例说明了预积分相互作用势在有限元法中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematical Modelling 数学-工程：综合

CiteScore

9.80

自引率

8.00%

发文量

508

审稿时长

43 days

期刊介绍： Applied Mathematical Modelling focuses on research related to the mathematical modelling of engineering and environmental processes, manufacturing, and industrial systems. A significant emerging area of research activity involves multiphysics processes, and contributions in this area are particularly encouraged. This influential publication covers a wide spectrum of subjects including heat transfer, fluid mechanics, CFD, and transport phenomena; solid mechanics and mechanics of metals; electromagnets and MHD; reliability modelling and system optimization; finite volume, finite element, and boundary element procedures; modelling of inventory, industrial, manufacturing and logistics systems for viable decision making; civil engineering systems and structures; mineral and energy resources; relevant software engineering issues associated with CAD and CAE; and materials and metallurgical engineering. Applied Mathematical Modelling is primarily interested in papers developing increased insights into real-world problems through novel mathematical modelling, novel applications or a combination of these. Papers employing existing numerical techniques must demonstrate sufficient novelty in the solution of practical problems. Papers on fuzzy logic in decision-making or purely financial mathematics are normally not considered. Research on fractional differential equations, bifurcation, and numerical methods needs to include practical examples. Population dynamics must solve realistic scenarios. Papers in the area of logistics and business modelling should demonstrate meaningful managerial insight. Submissions with no real-world application will not be considered.