Salt Effects on the Thermodynamics of a Frameshifting RNA Pseudoknot under Tension

Because of the potential link between -1 programmed ribosomal frameshifting and response of a pseudoknot (PK) RNA to force, a number of single molecule pulling experiments have been performed on PKs to decipher the mechanism of programmed ribosomal frameshifting. Motivated in part by these experiments, we performed simulations using a coarse-grained model of RNA to describe the response of a PK over a range of mechanical forces ($f$s) and monovalent salt concentrations ($C$s). The coarse-grained simulations quantitatively reproduce the multistep thermal melting observed in experiments, thus validating our model. The free energy changes obtained in simulations are in excellent agreement with experiments. By varying $f$ and $C$, we calculated the phase diagram that shows a sequence of structural transitions, populating distinct intermediate states. As $f$ and $C$ are changed, the stem-loop tertiary interactions rupture first, followed by unfolding of the $3^{\prime}$-end hairpin ($\textrm{I}\rightleftharpoons\textrm{F}$). Finally, the $5^{\prime}$-end hairpin unravels, producing an extended state ($\textrm{E}\rightleftharpoons\textrm{I}$). A theoretical analysis of the phase boundaries shows that the critical force for rupture scales as $\left(\log C_{\textrm{m}}\right)^{\alpha}$ with $\alpha=1\,(0.5)$ for $\textrm{E}\rightleftharpoons\textrm{I}$ ($\textrm{I}\rightleftharpoons\textrm{F}$) transition. This relation is used to obtain the preferential ion-RNA interaction coefficient, which can be quantitatively measured in single-molecule experiments, as done previously for DNA hairpins. A by-product of our work is the suggestion that the frameshift efficiency is likely determined by the stability of the $5^{\prime}$-end hairpin that the ribosome first encounters during translation.Comment: Final draft accepted in Journal of Molecular Biology, 16 pages including Supporting Informatio

D-branes in Topological Minimal Models: the Landau-Ginzburg Approach

We study D-branes in topologically twisted N=2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our results with the boundary state formalism, where possible, and find agreement.Comment: 29 pages, late

Non-compact Mirror Bundles and (0,2) Liouville Theories

We study (0,2) deformations of N=2 Liouville field theory and its mirror duality. A gauged linear sigma model construction of the ultraviolet theory connects (0,2) deformations of Liouville field theory and (0,2) deformations of N=2 SL(2,R)/U(1) coset model as a mirror duality. Our duality proposal from the gauged linear sigma model completely agrees with the exact CFT analysis. In the context of heterotic string compactifications, the deformation corresponds to the introduction of a non-trivial gauge bundle. This non-compact Landau-Ginzburg construction yields a novel way to study the gauge bundle moduli for non-compact Calabi-Yau manifolds.Comment: 34 page

D-brane Categories for Orientifolds -- The Landau-Ginzburg Case

We construct and classify categories of D-branes in orientifolds based on Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet parity action on the matrix factorizations plays the key role. This provides all the requisite data for an orientifold construction after embedding in string theory. One of our main results is a computation of topological field theory correlators on unoriented worldsheets, generalizing the formulas of Vafa and Kapustin-Li for oriented worldsheets, as well as the extension of these results to orbifolds. We also find a doubling of Knoerrer periodicity in the orientifold context.Comment: 45 pages, 6 figure

Statistical mechanics and large-scale velocity fluctuations of turbulence

Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed with experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.Comment: 7 pages, accepted by Physics of Fluids (see http://pof.aip.org/

Two-point velocity average of turbulence: statistics and their implications

For turbulence, although the two-point velocity difference u(x+r)-u(x) at each scale r has been studied in detail, the velocity average [u(x+r)+u(x)]/2 has not thus far. Theoretically or experimentally, we find interesting features of the velocity average. It satisfies an exact scale-by-scale energy budget equation. The flatness factor varies with the scale r in a universal manner. These features are not consistent with the existing assumption that the velocity average is independent of r and represents energy-containing large-scale motions alone. We accordingly propose that it represents motions over scales >= r as long as the velocity difference represents motions at the scale r.Comment: 8 pages, accepted by Physics of Fluids (see http://pof.aip.org/

A Bilocal Field Theory in Four Dimensions

A bilocal field theory having M\"{o}bius gauge invariance is proposed. In four dimensions there exists a zero momentum state of the first quantized model, which belongs to a non-trivial BRS cohomology class. A field theory lagrangian having a gauge invariance only in four dimensions is constructed.Comment: 13 pages, TEP-9R, LaTe

N=2 Liouville Theory with Boundary

We study N=2 Liouville theory with arbitrary central charge in the presence of boundaries. After reviewing the theory on the sphere and deriving some important structure constants, we investigate the boundary states of the theory from two approaches, one using the modular transformation property of annulus amplitudes and the other using the bootstrap of disc two-point functions containing degenerate bulk operators. The boundary interactions describing the boundary states are also proposed, based on which the precise correspondence between boundary states and boundary interactions is obtained. The open string spectrum between D-branes is studied from the modular bootstrap approach and also from the reflection relation of boundary operators, providing a consistency check for the proposal.Comment: 1+48 pages, no figure. typos corrected and references added. the version to appear in JHE

Monopole-vortex complex in a theta vacuum

We discuss aspects of the monopole-vortex complex soliton arising in a hierarchically broken gauge system, G to H to 1, in a theta vacuum of the underlying G theory. Here we focus our attention mainly on the simplest such system with G=SU(2) and H=U(1). A consistent picture of the effect of the theta parameter is found both in a macroscopic, dual picture and in a microscopic description of the monopole-vortex complex soliton.Comment: 18 pages 3 figure

Half-Twisted Correlators from the Coulomb Branch

We compute correlators of chiral operators in half-twisted (0,2) supersymmetric gauged linear sigma models. Our results give simple algebraic formulas for a (0,2) generalization of genus zero Gromov-Witten invariants of compact toric varieties. We derive compact expressions for deformed quantum cohomology relations and apply our general method to several examples.Comment: 21 pages, LaTex; typos corrected; some discussion adde