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Full-Text Articles in Physical Sciences and Mathematics
Cyclic Shifts Of The Van Der Corput Set, Dmitriy Bilyk
Cyclic Shifts Of The Van Der Corput Set, Dmitriy Bilyk
Faculty Publications
In 1980, K. Roth showed that the expected value of the L2 discrepancy of the cyclic shifts of the N-point van der Corput set is bounded by a constant multiple of √logN, thus guaranteeing the existence of a shift with asymptotically minimal L2 discrepancy. In the present paper, we construct a specific example of such a shift.
Dynamics And Rheology Of Biaxial Liquid Crystal Polymers, Sarthok K. Sircar
Dynamics And Rheology Of Biaxial Liquid Crystal Polymers, Sarthok K. Sircar
Theses and Dissertations
In this thesis we derive a hydrodynamical kinetic theory to study the orientational response of a mesoscopic system of nematic liquid crystals in the presence of an external flow field. Various problems have been attempted in this direction. First, we understand the steady-state behavior of uniaxial LCPs under an imposed elongational flow, electric and magnetic field respectively. We show that (1) the Smoluchowski equation can be cast into a generic form, (2) the external field is parallel to one of the eigenvectors of the second moment tensor, and (3) the steady state probability density function is of the Boltzmann type. …