Rayleigh-Taylor instability for immiscible fluids of arbitrary viscosities: a magnetic levitation investigation and theoretical model

A magnetic field gradient was used to draw down a low density paramagnetic fluid below a more dense fluid in a Hele-Shaw cell. On turning off the field a Rayleigh-Taylor instability was observed in situ, and the growth of the most unstable wave vector was measured versus time. A theory for the instability that permits different viscosities for two immiscible fluids was developed, and good agreement was found with the experimental results. The technique of magnetic levitation promises to broaden significantly the accessible parameter space of gravitational interfacial instability experiments.     

Dynamics of prestressed semiflexible polymer chains as a model of cell rheology

We report on a model of a prestressed nonlinear semiflexible polymer chain that links thermally driven dynamics to the creep behavior of living cells. Numerical simulations show that the chain's creep follows a power law with an exponent that decreases with increasing prestress. This is related to the propagation of free energy through the chain in response to stretching, where the propagation speed is regulated by the prestress via the chain's nonlinear elasticity. These results indicate that the main aspects of cell rheology are consistent with the dynamics of single polymer chains under tension.     

Nematic-isotropic pretransitional behaviour in dimers with odd and even spacer lengths

Magnetic field induced optical birefringence measurements in the isotropic phase are reported for two members of a series of phenyl benzoate dimers: one having an odd number of methylene units in the spacer and one having an even number. The discontinuity at the nematic-isotropic transition, as determined by the difference between the first order phase transition temperature TNI and the supercooling limit of the isotropic phase T*, is approximately 8 ± 3 times larger for the even species than for the odd. In addition, the product of the Cotton-Mouton coefficient dΔn/dH² and T-T* is the same for both materials. In terms of both steric and molecular field theories, the results indicate that the orientations of the terminal mesogenic groups are essentially uncorrected in the isotropic phase.     

Ergodic and mixing random walks on locally compact groups

Mathematische Annalen -     

Nematic order in nanoscopic liquid crystal droplets

We have used atomistic molecular-dynamics simulations to model the detailed molecular configuration of 5CB (4-n-pentyl-4'-cyanobiphenyl) molecules in the form of a nanoscopic liquid crystal droplet in a vacuum microgravity environment. We find the equilibrium state of droplets consisting of as few as 26 or 50 molecules to exhibit significant nematic ordering. The shape of the droplets is also anisotropic, but there is little angular correlation between the nematic director and the long axis of the droplet. Some tendency to micelle formation is observed in droplets of 50 molecules.     

Remarks on ergodicity of stationary irreducible transient Markov chains

Summary Consider a stationary process {X _n(), – < n < . If the measure of the process is finite (the measure of the whole sample space finite), it is well known that ergodicity of the process {X _n(), - < n < and of each of the subprocesses {X _n(), 0 n < , {X _n(), – < n 0 are equivalent (see [3]). We shall show that this is generally not true for stationary processes with a sigma-finite measure, specifically for stationary irreducible transient Markov chains. An example of a stationary irreducible transient Markov chain {X _n(), - < n <} with {itX_n(), 0 n < < ergodic but {X _n(), < n 0 nonergodic is given. That this can be the case has already been implicitly indicated in the literature [4]. Another example of a stationary irreducible transient Markov chain with both {X _n(), 0 n < and {itX _n(),-< < n 0} ergodic but {X _n(), - < n < nonergodic is presented. In fact, it is shown that all stationary irreducible transient Markov chains {X _n(), - < n < < are nonergodic.This research was supported in part by the Office of Naval Research.John Simon Guggenheim Memorial Fellow.     

Characterizations of regular almost periodicity in compact minimal abelian flows

Regular almost periodicity in compact minimal abelian flows was characterized for the case of discrete acting group by W. Gottschalk and G. Hedlund and for the case of -dimensional phase space by W. Gottschalk a few decades ago. In 1995 J. Egawa gave characterizations for the case when the acting group is . We extend Egawa's results to the case of an arbitrary abelian acting group and a not necessarily metrizable phase space. We then show how our statements imply previously known characterizations in each of the three special cases and give various other applications (characterization of regularly almost periodic functions on arbitrary abelian topological groups, classification of uniformly regularly almost periodic compact minimal - and -flows, conditions equivalent with uniform regular almost periodicity, etc.).

     

Heterodyne schlieren system

A new heterodyne technique for the quantitative analysis of schlieren images is described. The technique is based on phase measurements of signals generated by a photodetector observing the variations in light intensity caused by a traveling grating of slits located at the knife-edge plane of a conventional schlieren system. The phase of the signal is proportional to the displacement of the slit image on the knife-edge plane as a result of the light deflection passing through a phase object. The displacement is proportional to the ray deflection angle and hence to the local gradient of the index of refraction. The technique, which is quantitatively precise and sensitive, is demonstrated by measurement of deflections caused by a lens with a focal length of f = 20 m. A displacement of 0.22 mm and a deflection of an angle of 5.2 x 10(-4) rad were detected.