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Network theory is used to formulate an atomistic material network. Spectral sparsification is applied to the network as a method for approximating the interatomic forces. Local molecu- lar forces and the total force balance is quantified when the inter- nal forces are approximated. In particular, we compare spectral sparsification to conventional thresholding (radial cut-off dis- tance) of molecular forces for a Lennard–Jones potential and a Coulomb potential. The spectral sparsification for the Lennard– Jones potential yields comparable results while spectral sparsi- fication of the Coulomb potential outperforms the thresholding approach. The results show promising opportunities which may accelerate molecular simulations containing long-range electri- cal interactions which are relevant to many multifunctional ma- terials.
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This content will become publicly available on May 1, 2026
Analytical sphere-thin rod interaction potential
A compact analytical form is derived through an integration approach for the interaction between a sphere and a thin rod of finite and infinite lengths, with each object treated as a continuous medium of material points interacting by the Lennard-Jones 12-6 potential and the total interaction potential as a summation of the pairwise potential between material points on the two objects. Expressions for the resultant force and torque are obtained. Various asymptotic limits of the analytical sphere–rod potential are discussed. The integrated potential is applied to investigate the adhesion between a sphere and a thin rod. When the rod is sufficiently long and the sphere sufficiently large, the equilibrium separation between the two (defined as the distance from the center of the sphere to the axis of the rod) is found to be well approximated as a + 0.787σ, where a is the radius of the sphere and σ is the unit of length of the Lennard–Jones potential. Furthermore, the adhesion between the two is found to scale with √a.
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- Award ID(s):
- 1944887
- PAR ID:
- 10581720
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- The European Physical Journal E
- Volume:
- 48
- Issue:
- 4-5
- ISSN:
- 1292-8941
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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