In this paper, we investigate the dynamics of inextensible flow of adjoint curves in Euclidean 3-space. We construct a new method for inextensible flows of adjoint curves in three-dimensional Euclidean 3-space. Using the Frenet frame of the given curve, we present partial differential equations. Furthermore, we give some new characterizations of curvatures in terms of the evolution equations in space. Next by mapping Ferromagnetic and Antiferromagnetic chain on the inextensible flow of curves in space.
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