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Full-Text Articles in Physical Sciences and Mathematics
Mathematical Modelling Of Nematicons And Their Interactions, Prof. Tim Marchant
Mathematical Modelling Of Nematicons And Their Interactions, Prof. Tim Marchant
Tim Marchant
The mathematical modelling of guided wave (nematicon) propagation in liquid crystals is considered. Model equations are derived based on suitable trial functions in an averaged Lagrangian. These equations are used to model nematicon interactions.
Collisionless Shock Resolution In Nematic Liquid Crystals, Tim Marchant
Collisionless Shock Resolution In Nematic Liquid Crystals, Tim Marchant
Tim Marchant
The diffractive resolution on a collisionless shock formed along the spatial profile of a beam in a nematic liquid crystal is considered, this material being an example of a self-focusing, nonlocal medium. It is found that the shock is resolved through the formation of an undular bore structure which persists for experimentally relevant propagation distances due to nonlocality delaying the onset of modulational instability. Both 1+1 and 2+1 dimensional bores with circular symmetry are considered (termed line and circular bores, respectively). A semianalytical solution is developed for the line undular bore, approximating it as a train of uniform solitary waves. …
Nonlocal Validity Of An Asymptotic One-Dimensional Nematicon Solution, Tim Marchant
Nonlocal Validity Of An Asymptotic One-Dimensional Nematicon Solution, Tim Marchant
Tim Marchant
The propagation of coherent, polarized light in a nematic liquid crystal, governed by the nematicon equations, is considered. It is found that in the special case of 1 + 1 dimensions and the highly nonlocal limit, the nematicon equations have an asymptotic bulk solitary wave solution, termed a nematicon, which is given in terms of Bessel functions. This asymptotic solution gives both the ground state and the symmetric and antisymmetric excited states, which have multiple peaks. Numerical simulations of nematicon evolution, for parameters corresponding to experimental scenarios, are presented. It is found, for experimentally reasonable parameter choices, that the validity …
Dipole Soliton Formation In A Nematic Liquid Crystal In The Non-Local Limit, Tim Marchant
Dipole Soliton Formation In A Nematic Liquid Crystal In The Non-Local Limit, Tim Marchant
Tim Marchant
The interaction of two symmetric solitary waves, termed nematicons, in a liquid crystal is considered in the limit of nonlocal response of the liquid crystal. This nonlocal limit is the applicable limit for most experimentally available liquid crystals. In this nonlocal limit, two separate cases for the initial separation of the nematicons are considered, these being large and small separation. Both spinning and nonspinning nematicons are considered. It is found that in the case of large initial separation, the nematicons can form a spinning or nonspinning bound state with a finite steady separation, this being called a nematicon dipole, when …