Three-dimensional cavity fields

If the guest molecule is assumed to be confined, in the thermodynamic sense, within a particular cavity, if the internal vibrational and rotational states of the molecule are unaltered by occlusion, and if the potential field within a cavity is sufficiently uniform so that the movement of the molecule within the cavity can be represented as three-dimensional translation within the free volume of the cavity (), then the appropriate expression for the ratio of partition functions becomes simply... 

The formation of RES and their evolution into post-solitons have been observed in three-dimensional simulations as well [14], The EM structure of the three-dimensional soliton is such that the electric field is poloidal and the magnetic field is toroidal. Therefore it is named a TM-soliton. The soliton core is characterized by an overall positive charge, resulting in its Coulomb explosion and in the acceleration of the ion. On the long time-scale, the quasi-neutral plasma cavity is subject to a slow continuous radial expansion, while the soliton amplitude decreases and the ion temperature increases. 

Now let us proceed to the three-dimensional case. For definiteness we choose a rectangular cavity with dimensions Lx,Ly,Lz (briefly designated by symbol L ). If these dimensions do not depend on time, each field mode is determined by three integers m, n, l, responsible for the eigenfrequency... 

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