Unzipping Vortices in Type-II Superconductors

The unzipping of vortex lines using magnetic-force microscopy from extended defects is studied theoretically. We study both the unzipping isolated vortex from common defects, such as columnar pins and twin-planes, and the unzipping of a vortex from a plane in the presence of other vortices. We show, using analytic and numerical methods, that the universal properties of the unzipping transition of a single vortex depend only on the dimensionality of the defect in the presence and absence of disorder. For the unzipping of a vortex from a plane populated with many vortices is shown to be very sensitive to the properties of the vortices in the two-dimensional plane. In particular such unzipping experiments can be used to measure the ``Luttinger liquid parameter'' of the vortices in the plane. In addition we suggest a method for measuring the line tension of the vortex directly using the experiments.Comment: 19 pages 15 figure

DNA unzipped under a constant force exhibits multiple metastable intermediates

Single molecule studies, at constant force, of the separation of double-stranded DNA into two separated single strands may provide information relevant to the dynamics of DNA replication. At constant applied force, theory predicts that the unzipped length as a function of time is characterized by jumps during which the strands separate rapidly, followed by long pauses where the number of separated base pairs remains constant. Here, we report previously uncharacterized observations of this striking behavior carried out on a number of identical single molecules simultaneously. When several single lphage molecules are subject to the same applied force, the pause positions are reproducible in each. This reproducibility shows that the positions and durations of the pauses in unzipping provide a sequence-dependent molecular fingerprint. For small forces, the DNA remains in a partially unzipped state for at least several hours. For larger forces, the separation is still characterized by jumps and pauses, but the double-stranded DNA will completely unzip in less than 30 min

Towards a Tetravalent Chemistry of Colloids

We propose coating spherical particles or droplets with anisotropic nano-sized objects to allow micron-scale colloids to link or functionalize with a four-fold valence, similar to the sp3 hybridized chemical bonds associated with, e.g., carbon, silicon and germanium. Candidates for such coatings include triblock copolymers, gemini lipids, metallic or semiconducting nanorods and conventional liquid crystal compounds. We estimate the size of the relevant nematic Frank constants, discuss how to obtain other valences and analyze the thermal distortions of ground state configurations of defects on the sphere.Comment: Replaced to improve figures. 4 figures Nano Letter

Sinai model in presence of dilute absorbers

We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space renormalization method. We compute the survival probability, the averaged diffusion front and return probability, the two particle meeting probability, the distribution of total distance traveled before absorption and the averaged Green's function of the associated Schrodinger operator. Our work confirms some recent results of Texier and Hagendorf obtained by Dyson-Schmidt methods, and extends them to other observables and in presence of a drift. In particular the power law density of states is found to hold in all cases. Irrespective of the drift, the asymptotic rescaled diffusion front of surviving particles is found to be a symmetric step distribution, uniform for $|x| < {1/2} \xi(t)$, where $\xi(t)$ is a new, survival length scale ($\xi(t)=T \ln t/\sqrt{\rho}$ in the absence of drift). Survival outside this sharp region is found to decay with a larger exponent, continuously varying with the rescaled distance $x/\xi(t)$. A simple physical picture based on a saddle point is given, and universality is discussed.Comment: 21 pages, 2 figure

Sequence Effects on DNA Entropic Elasticity

DNA stretching experiments are usually interpreted using the worm-like chain model; the persistence length A appearing in the model is then interpreted as the elastic stiffness of the double helix. In fact the persistence length obtained by this method is a combination of bend stiffness and intrinsic bend effects reflecting sequence information, just as at zero stretching force. This observation resolves the discrepancy between the value of A measured in these experiments and the larger ``dynamic persistence length'' measured by other means. On the other hand, the twist persistence length deduced from torsionally-constrained stretching experiments suffers no such correction. Our calculation is very simple and analytic; it applies to DNA and other polymers with weak intrinsic disorder.Comment: LaTeX; postscript available at http://dept.physics.upenn.edu/~nelson/index.shtm

Defects in Chiral Columnar Phases: Tilt Grain Boundaries and Iterated Moire Maps

Biomolecules are often very long with a definite chirality. DNA, xanthan and poly-gamma-benzyl-glutamate (PBLG) can all form columnar crystalline phases. The chirality, however, competes with the tendency for crystalline order. For chiral polymers, there are two sorts of chirality: the first describes the usual cholesteric-like twist of the local director around a pitch axis, while the second favors the rotation of the local bond-orientational order and leads to a braiding of the polymers along an average direction. In the former case chirality can be manifested in a tilt grain boundary phase (TGB) analogous to the Renn-Lubensky phase of smectic-A liquid crystals. In the latter case we are led to a new "moire" state with twisted bond order. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In the moire state polymers are simultaneously entangled, crystalline, and aligned, on average, in a common direction. In this case the polymer trajectories in the plane perpendicular to their average direction are described by iterated moire maps of remarkable complexity, reminiscent of dynamical systems.Comment: plain TeX, (33 pages), 17 figures, some uufiled and included, the remaining available at ftp://ftp.sns.ias.edu/pub/kamien/ or by request to [email protected]

Nonlinear Elasticity of the Sliding Columnar Phase

The sliding columnar phase is a new liquid-crystalline phase of matter composed of two-dimensional smectic lattices stacked one on top of the other. This phase is characterized by strong orientational but weak positional correlations between lattices in neighboring layers and a vanishing shear modulus for sliding lattices relative to each other. A simplified elasticity theory of the phase only allows intralayer fluctuations of the columns and has three important elastic constants: the compression, rotation, and bending moduli, $B$, $K_y$, and $K$. The rotationally invariant theory contains anharmonic terms that lead to long wavelength renormalizations of the elastic constants similar to the Grinstein-Pelcovits renormalization of the elastic constants in smectic liquid crystals. We calculate these renormalizations at the critical dimension $d=3$ and find that $K_y(q) \sim K^{1/2}(q) \sim B^{-1/3}(q) \sim (\ln(1/q))^{1/4}$, where $q$ is a wavenumber. The behavior of $B$, $K_y$, and $K$ in a model that includes fluctuations perpendicular to the layers is identical to that of the simple model with rigid layers. We use dimensional regularization rather than a hard-cutoff renormalization scheme because ambiguities arise in the one-loop integrals with a finite cutoff.Comment: This file contains 18 pages of double column text in REVTEX format and 6 postscript figure

Critical Fluctuations and Disorder at the Vortex Liquid to Crystal Transition in Type-II Superconductors

We present a functional renormalization group (FRG) analysis of a Landau-Ginzburg model of type-II superconductors (generalized to $n/2$ complex fields) in a magnetic field, both for a pure system, and in the presence of quenched random impurities. Our analysis is based on a previous FRG treatment of the pure case [E.Br\'ezin et. al., Phys. Rev. B, {\bf 31}, 7124 (1985)] which is an expansion in $\epsilon = 6-d$. If the coupling functions are restricted to the space of functions with non-zero support only at reciprocal lattice vectors corresponding to the Abrikosov lattice, we find a stable FRG fixed point in the presence of disorder for $1<n<4$, identical to that of the disordered $O(n)$ model in $d-2$ dimensions. The pure system has a stable fixed point only for $n>4$ and so the physical case ($n = 2$) is likely to have a first order transition. We speculate that the recent experimental findings that disorder removes the apparent first order transition are consistent with these calculations.Comment: 4 pages, no figures, typeset using revtex (v3.0

Single Molecule Statistics and the Polynucleotide Unzipping Transition

We present an extensive theoretical investigation of the mechanical unzipping of double-stranded DNA under the influence of an applied force. In the limit of long polymers, there is a thermodynamic unzipping transition at a critical force value of order 10 pN, with different critical behavior for homopolymers and for random heteropolymers. We extend results on the disorder-averaged behavior of DNA's with random sequences to the more experimentally accessible problem of unzipping a single DNA molecule. As the applied force approaches the critical value, the double-stranded DNA unravels in a series of discrete, sequence-dependent steps that allow it to reach successively deeper energy minima. Plots of extension versus force thus take the striking form of a series of plateaus separated by sharp jumps. Similar qualitative features should reappear in micromanipulation experiments on proteins and on folded RNA molecules. Despite their unusual form, the extension versus force curves for single molecules still reveal remnants of the disorder-averaged critical behavior. Above the transition, the dynamics of the unzipping fork is related to that of a particle diffusing in a random force field; anomalous, disorder-dominated behavior is expected until the applied force exceeds the critical value for unzipping by roughly 5 pN.Comment: 40 pages, 18 figure

Directed Polymers with Random Interaction : An Exactly Solvable Case -

We propose a model for two $(d+1)$-dimensional directed polymers subjected to a mutual $\delta$-function interaction with a random coupling constant, and present an exact renormalization group study for this system. The exact $\beta$-function, evaluated through an $\epsilon(=1-d)$ expansion for second and third moments of the partition function, exhibits the marginal relevance of the disorder at $d=1$, and the presence of a phase transition from a weak to strong disorder regime for $d>1$. The lengthscale exponent for the critical point is $\nu=1/2\mid\epsilon\mid$. We give details of the renormalization. We show that higher moments do not require any new interaction, and hence the $\beta$ function remains the same for all moments. The method is extended to multicritical systems involving an $m$ chain interaction. The corresponding disorder induced phase transition for $d>d_m=1/(m-1)$ has the critical exponent ${\nu}_m=[2d(m-1)-2]^{-1}$. For both the cases, an essential singularity appears for the lengthscale right at the upper critical dimension $d_m$. We also discuss the strange behavior of an annealed system with more than two chains with pairwise random interactions among each other.Comment: No of pages: 36, 7figures on request, Revtex3, Report No:IP/BBSR/929