Frenkel springs

The essential properties of incommensurate modulated structures can be studied within a simple one-dimensional model, the well-known Frenkel-Kontorova model . The competing interactions between the substrate potential and the lateral adatom interactions are modeled by a chain of adatoms, coupled with harmonic springs of force constant K, placed in a cosine substrate potential of amplitude V and periodicity b (see Fig. 27). The microscopic energy of this model is ... 

Frenkel N, Spaete RR, Vlazny DA, Deiss LP, Locker H (1982) The herpes simplex virus amplicon—a novel animal-virus cloning vector. hr Eucaryodc Viral Vectors (Gluzman Y, ed), pp 205—209. New York Cold Spring Harbor Laboratory. 

Figure 7. Schematic representation of the one dimensional Frenkel Kontorova Tomlinson model, a and b denote the lattice constant of the upper sohd and the substrate, respectively. The substrate is considered rigid, and its center of mass is kept fixed. In the shder, each atom is coupled with a spring of lateral stiffness to its ideal lattice site and with a spring of stiffness 2 to its neighbor. The PT model is obtained for 2 0, while the Frenkel Kontorova model corresponds to k = 0. We will drop the subscripts for these two cases since a single spring is relevant.

Applications The HMM has been applied to the study of friction between two-dimensional atomically flat crystal surfaces, dislocation dynamics in the Frenkel-Kontorova model (i.e., considering a one-dimensional chain of atoms in a periodic potential, coupled by linear springs ), and crack propagation in an inhomogeneous medium. ... 

Levine, A. J., van der Vliet, P. C., Rosenwirth, B., Rabek, J., Frenkel, G., and Ensinger, M., 1975, Adenovirus-infected cell-specific DNA binding proteins. Cold Spring Harbor Symp. Quant. Biol. 39 559. 

Most theories of structural superlubricity are based on the Prandtl-Tomlinson model or the more advanced Frenkel-Kontorova model [1043, 1044], in which the single atom/tip is replaced by a chain of atoms coupled by springs. However, Friedel and de Gennes [1045] noted recently that correct description of relative sliding of crystalline surfaces should include the motion and interaction of dislocations at the surfaces. This concept was taken up by Merkle and Marks [1045] and generalized using the well-established coincident site lattice theory and dislocation drag from solid-state physics. 

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