Gravity and the Newtonian limit in the Randall-Sundrum model

We point out that the gravitational evolution equations in the Randall-Sundrum model appear in a different form than hitherto assumed. As a consequence, the model yields a correct Newtonian limit in a novel manner.Comment: 9 pages, LaTeX, sign changed and references added. We have also appended a remark on the compatibility of the 4D Poincare invariant metric of Randall and Sundrum with the boundary equation

Smectic Order in Double-Twist Cylinders

I propose a double-twist texture with local smectic order, which may have been seen in recent experiments. As in the Renn-Lubensky TGB phase, the smectic order is broken only through a lattice of screw dislocations. A melted lattice of screw dislocations can produce a double-twist texture as can an unmelted lattice. In the latter case I show that geometry only allows for certain angles between smectic regions. I discuss the possibility of connecting these double-twist tubes together to form a smectic blue phase.Comment: 12 pages, plain TeX (macros included), 5 postscript figures (included). Revised version has some more text and a new figure. To appear in J. Phys. II France (1997

Flory Exponents from a Self-Consistent Renormalization Group

The wandering exponent $\nu$ for an isotropic polymer is predicted remarkably well by a simple argument due to Flory. By considering oriented polymers living in a one-parameter family of background tangent fields, we are able to relate the wandering exponent to the exponent in the background field through an $\epsilon$-expansion. We then choose the background field to have the same correlations as the individual polymer, thus self-consistently solving for $\nu$. We find $\nu=3/(d+2)$ for $d<4$ and $\nu=1/2$ for $d\ge 4$, which is exactly the Flory result.Comment: 11 pages, Plain Tex (macros included), IASSNS-HEP-93/1

Liquids with Chiral Bond Order

I describe new phases of a chiral liquid crystal with nematic and hexatic order. I find a conical phase, similar to that of a cholesteric in an applied magnetic field for Frank elastic constants $K_2>K_3$. I discuss the role of fluctuations in the context of this phase and the possibility of satisfying the inequality for sufficiently long polymers. In addition I discuss the topological constraint relating defects in the bond order field to textures of the nematic and elucidate its physical meaning. Finally I discuss the analogy between smectic liquid crystals and chiral hexatics and propose a defect-riddled ground state, akin to the Renn-Lubensky twist grain boundary phase of chiral smectics.Comment: plain TeX, 19 Pages, four figures, uufiled and included. Minor correction and clarificatio