Biomedical subjects

Karl Saunders

Publications and source records attributed to Karl Saunders.

3 recordsLinked to original sources

PubMed2006

Hydrodynamics of polar liquid crystals.

Starting from a microscopic definition of an alignment vector proportional to the polarization, we discuss the hydrodynamics of polar liquid crystals with local C infinity v symmetry. The free energy for polar liquid crystals differs from that of nematic liquid crystals (D infinity h) in that it contains terms violating the n --> -n symmetry. First we show that these Z2-odd terms induce a general splay instability of a uniform polarized state in a range of parameters. Next we use the general Poisson-bracket formalism to derive the hydrodynamic equations of the system in the polarized state. The structure of the linear hydrodynamic modes confirms the existence of the splay instability.

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PubMed2006

Pattern stabilization through parameter alternation in a nonlinear optical system.

We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are used for both numerical simulations and a weakly nonlinear analysis of the patterned states. The simulations show excellent agreement with the experiment. The nonlinear analysis provides an explanation of the patterning under alternation and accurately predicts both the observed dependence of the patterning on the frequency of alternation and the measured spatial frequencies of the patterns.

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PubMed2003

Driven depinning of strongly disordered media and anisotropic mean-field limits.

Extended systems driven through strong disorder are modeled generically using coarse-grained degrees of freedom that interact elastically in the directions parallel to the drive and slip along at least one of the directions transverse to the motion. In the limit of infinite-range elastic and viscous coupling this model has a tricritical point separating a region where the depinning is continuous, in the universality class of elastic depinning, from a region where depinning is hysteretic. Many of the collective transport models discussed in the literature are special cases of the generic model.

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