A new method for calculating three-particle interaction in the theory of modulus elasticity

Autor: O. V. Kukin, Yu. M. Gufan, A. Yu. Smolin
Rok vydání: 2011
Předmět:
Zdroj: Bulletin of the Russian Academy of Sciences: Physics. 75:1267-1273
ISSN: 1934-9432
1062-8738
DOI: 10.3103/s1062873811090103
Popis: We propose a new method for calculating the potential of multiparticle interaction. Our method considers the energy symmetry for clusters that contain N identical particles with respect to permutation of the number of atoms and free rotation in three-dimensional space. As an example, we calculate moduli of third-order rigidity for copper considering only the three-particle interaction. We analyze nine models of energy dependence on the polynomials that form the integral rational basis of invariants (IRBI) for the group G 3 = O(3) ⋇ P 3. In this work, we use only the simplest relation between energy and the invariants forming the IRBI: $$\varepsilon \left( {\left. {i,k,l} \right|j} \right) = \sum\nolimits_{i,k,l} {\left[ { - A_1 r_{ik}^{ - 6} + A_2 r_{ik}^{ - 12} + Q_j I_j^{ - n} } \right]}$$ , where I j is the invariant number j (j = 1, 2,..., 9). The results are in good agreement with the experimental values. The best agreement is observed at n = 2, j = 4: $$I_4 = \left( {\vec r_{ik} \vec r_{kl} } \right)\left( {\vec r_{kl} \vec r_{li} } \right) + \left( {\vec r_{kl} \vec r_{li} } \right)\left( {\vec r_{li} \vec r_{ik} } \right) + \left( {\vec r_{li} \vec r_{ik} } \right)\left( {\vec r_{ik} \vec r_{kl} } \right)$$ .
Databáze: OpenAIRE
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