Helicity vector field theory

The electric and magnetic fields are dual to one another and have the same properties in Maxwell theory in empty space. Given the divergenceless vector field B, we have defined the magnetic helicity as... 

The static theory discussed in the previous section describes the equilibrium situation in chiral nematics very well - in general, theory and experiment are in good accord. The dynamic situation is less clear. On the molecular scale, the chiral nematic and nematic phases are identical the question then becomes, how does the macroscopic twist or helicity modify the vector stress tensor of the achiral nematic phase defined by the so-called [109] Leslie friction coefficients a -a T Experimentally, viscosity coefficients that are then related to the Leslie coefficients are measured in a way that depends specifically on the experiment being used to determine them. The starting point for discussion of dynamic properties is to use classical mechanics to describe the time dependencies of the director field n (r, t), the velocity field v (r, t), and their interdependency. Excellent reviews of this, for achiral nematics, are to be found in [59,109,... 

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