Anomalous Elasticity of Polymer Cholesterics

We show that polymer cholesterics have much longer pitches than comparable short molecule cholesterics, due to their anomalous elasticity. The pitch $P$ of a chiral mixture with concentration $c$ near the racemic (non-chiral) concentration $c^*$ diverges like $\vert c-c^*\vert^{-\nu}$ with $\nu=1.43 \pm 0.04$ (for short molecule cholesterics $\nu=1$). The short molecule law is recovered for polymers of finite molecular length $\ell$ once the pitch is longer than a length that diverges like $\ell^\gamma$ with $\gamma=0.67 \pm 0.01$. Our predictions could be tested by measurements of the pitch in DNA.Comment: 12 pages, Plain TeX, (1 postscript figure, compressed, uuencoded and appended to paper), minor corrections, IASSNS-HEP-94/4

A New Phase of Tethered Membranes: Tubules

We show that fluctuating tethered membranes with {\it any} intrinsic anisotropy unavoidably exhibit a new phase between the previously predicted ``flat'' and ``crumpled'' phases, in high spatial dimensions $d$ where the crumpled phase exists. In this new "tubule" phase, the membrane is crumpled in one direction but extended nearly straight in the other. Its average thickness is $R_G\sim L^{\nu_t}$ with $L$ the intrinsic size of the membrane. This phase is more likely to persist down to $d=3$ than the crumpled phase. In Flory theory, the universal exponent $\nu_t=3/4$, which we conjecture is an exact result. We study the elasticity and fluctuations of the tubule state, and the transitions into it.Comment: 4 pages, self-unpacking uuencoded compressed postscript file with figures already inside text; unpacking instructions are at the top of file. To appear in Phys. Rev. Lett. November (1995

Minimal model for active nematics: quasi-long-range order and giant fluctuations

We propose a minimal microscopic model for active nematic particles similar in spirit to the Vicsek model for self-propelled polar particles. In two dimensions, we show that this model exhibits a Kosterlitz-Thouless-like transition to quasi-long-range orientational order and that in this non-equilibrium context, the ordered phase is characterized by giant density fluctuations, in agreement with the predictions of Ramaswamy {\it et al.} [Europhys. Lett. {\bf 62}, 196 (2003)].Comment: Submitted to Phys. Rev. Lett. 4 pages, 4 figure

Sliding Columnar Phase of DNA-Lipid Complexes

We introduce a simple model for DNA-cationic-lipid complexes in which galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices that couple orientationally and positionally to lattices in neighboring galleries. We identify a new equilibrium phase in which there are long-range orientational but not positional correlations between DNA lattices. We discuss properties of this new phase such as its X-ray structure factor S(r), which exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane separation r.Comment: This file contains 4 pages of double column text and one postscript figure. This version includes interactions between dislocations in a given gallery and presents an improved estimate of the decoupling temperature. It is the published versio

Ground state properties of solid-on-solid models with disordered substrates

We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow algorithm. Results for the height-height correlation function are compared with analytical and numerical predictions. The domain wall energy of a boundary induced step grows logarithmically with system size, indicating the marginal stability of the ground state, and the fractal dimension of the step is estimated. The sensibility of the ground state with respect to infinitesimal variations of the quenched disorder is analyzed.Comment: 4 pages RevTeX, 3 eps-figures include

A variational study of the random-field XY model

A disorder-dependent Gaussian variational approach is applied to the $d$-dimensional ferromagnetic XY model in a random field. The randomness yields a non extensive contribution to the variational free energy, implying a random mass term in correlation functions. The Imry-Ma low temperature result, concerning the existence ($d>4$) or absence ($d < 4$) of long-range order is obtained in a transparent way. The physical picture which emerges below $d=4$ is that of a marginally stable mixture of domains. We also calculate within this variational scheme, disorder dependent correlation functions, as well as the probability distribution of the Imry-Ma domain size.Comment: 14 pages, latex fil

Live Soap: Order, Fluctuations and Instabilities in Active Smectics

We construct a hydrodynamic theory of noisy, apolar active smectics, in bulk suspension or on a substrate. Our predictions include: quasi-long-ranged smectic order in dimension d = 2, and long- ranged in d = 3, extending previously published results to all dynamical regimes; Kosterlitz-Thouless melting to an active nematic at high and low concentrations in d = 2; nonzero second-sound speed parallel to the layers; the suppression of giant number fluctuations by smectic elasticity; instability to spontaneous undulation and flow in bulk contractile smectics; a layer spacing instability, possibly oscillatory, for large enough extensile active stresses.Comment: 5 pages, 1 figure, submitted to Phys Rev Let

Non-Ergodic Dynamics of the 2D Random-phase Sine-Gordon Model: Applications to Vortex-Glass Arrays and Disordered-Substrate Surfaces

The dynamics of the random-phase sine-Gordon model, which describes 2D vortex-glass arrays and crystalline surfaces on disordered substrates, is investigated using the self-consistent Hartree approximation. The fluctuation-dissipation theorem is violated below the critical temperature T_c for large time t>t* where t* diverges in the thermodynamic limit. While above T_c the averaged autocorrelation function diverges as Tln(t), for T<T_c it approaches a finite value q* proportional to 1/(T_c-T) as q(t) = q* - c(t/t*)^{-\nu} (for t --> t*) where \nu is a temperature-dependent exponent. On larger time scales t > t* the dynamics becomes non-ergodic. The static correlations behave as Tln{x} for T>T_c and for T<T_c when x < \xi* with \xi* proportional to exp{A/(T_c-T)}. For scales x > \xi*, they behave as (T/m)ln{x} where m is approximately T/T_c near T_c, in general agreement with the variational replica-symmetry breaking approach and with recent simulations of the disordered-substrate surface. For strong- coupling the transition becomes first-order.Comment: 12 pages in LaTeX, Figures available upon request, NSF-ITP 94-10