Shapes of semiflexible polymer rings

The shape of semiflexible polymer rings is studied over their whole range of flexibility. Investigating the joint distribution of asphericity and the nature of asphericity as well as their respective averages, we find two distinct shape regimes depending on the flexibility of the polymer. For a small perimeter to persistence length the fluctuating rings exhibit only planar, elliptical configurations. At higher flexibilities three-dimensional, crumpled structures arise. Analytic calculations confirm the qualitative behavior of the averaged shape parameters and the elliptical shape in the stiff regime.     

Fluctuating semiflexible polymer ribbon constrained to a ring

Twist stiffness and an asymmetric bending stiffness of a polymer or a polymer bundle is captured by the elastic ribbon model. We investigate the effects a ring geometry induces to a thermally fluctuating ribbon, finding bend-bend coupling in addition to twist-bend coupling. Furthermore, due to the geometric constraint the polymer's effective bending stiffness increases. A new parameter for experimental investigations of polymer bundles is proposed: the mean square diameter of a ribbonlike ring, which is determined analytically in the semiflexible limit. Monte Carlo simulations are performed which affirm the model's prediction up to high flexibility.     

The Morse and Maslov indices for Schrödinger operators

We study the spectrum of Schrödinger operators with matrixvalued potentials, utilizing tools from infinite-dimensional symplectic geometry. Using the spaces of abstract boundary values, we derive relations between the Morse and Maslov indices for a family of operators on a Hilbert space obtained by perturbing a given self-adjoint operator by a smooth family of bounded self-adjoint operators. The abstract results are applied to the Schrödinger operators with θ-periodic, Dirichlet, and Neumann boundary conditions. In particular, we derive an analogue of the Morse-Smale Index Theorem for multi-dimensional Schrödinger operators with periodic potentials. For quasi-convex domains in Rⁿ, we recast the results, connecting the Morse and Maslov indices using the Dirichlet and Neumann traces on the boundary of the domain.     

Analysis of the AC electrical data in the Davidson-Cole dielectric representation

The representation of the AC electrical data in the complex plane reveal two major classifications of the relaxation processes known as ideal (Debye) and non-ideal (non-Debye) types. The non-Debye relaxation has been empirically observed via Cole-Cole (C-C), Davidson-Cole (D-C), and Havriliak-Negami (H-N) responses. Each of these non-Debye relaxations is visualized with an equivalent circuit similar to the ideal relaxation. Both ideal and C-C relaxations reveal semicircular behavior in the complex plane while D-C and H-N relaxations deviate from the usual semicircular loci known as skewed behavior. The extracted equivalent circuit elements are essentially non-Debye for both D-C and H-N relaxations possessing complexity in the relaxation time. The analytical method of extracting these elements in conjunction with the empirical parameters of the D-C relaxation is described using conventional (real) domain and complex domain. The curve fitting procedure provided extremely small error for the complex domain analysis. The behavior of the D-C relaxation function and the depression parameter β are also discussed using ωτ=1 and ωτ≠1 corresponding to the maximum of the imaginary part of the impedance (Z^*) or permittivity (ε^*).     

Airy Equation for the Topological String Partition Function in a Scaling Limit

We use the polynomial formulation of the holomorphic anomaly equations governing perturbative topological string theory to derive the free energies in a scaling limit to all orders in perturbation theory for any Calabi–Yau threefold. The partition function in this limit satisfies an Airy differential equation in a rescaled topological string coupling. One of the two solutions of this equation gives the perturbative expansion and the other solution provides geometric hints of the non-perturbative structure of topological string theory. Both solutions can be expanded naturally around strong coupling.     

Two new "onium" fluorosilicates, the products of interaction of fluorosilicic acid with 12-membered macrocycles: structures and spectroscopic properties

Two novel compounds, (L(1)H)(2)[SiF(6)] x 2H(2)O (1) and (L(2)H)(2)[SiF(5)(H(2)O)](2) x 3H(2)O (2), resulting from the reactions of H(2)SiF(6) with 4'-aminobenzo-12-crown-4 (L(1)) and monoaza-12-crown-4 (L(2)), respectively, were studied by X-ray diffraction and characterised by IR and (19)F NMR spectroscopic methods. Both complexes have ionic structures due to the proton transfer from the fluorosilicic acid to the primary amine group in L(1) and secondary amine group incorporated into the macrocycle L(2). The structure of 1 is composed of [SiF(6)](2-) centrosymmetric anions, N-protonated cations (L(1)H)(+), and two water molecules, all components being bound in the layer through a system of NH[...]F, NH[...]O and OH[...]F hydrogen bonds. The [SiF(6)](2-) anions and water molecules are assembled into inorganic negatively-charged layers via OH[dot dot dot]F hydrogen bonds. The structure of 2 is a rare example of stabilisation of the complex anion [SiF(5)(H(2)O)](-), the labile product of hydrolytic transformations of the [SiF(6)](2-) anion in an aqueous solution. The components of 2, i.e., [SiF(5)(H(2)O)](-), (L(2)H)(+), and water molecules, are linked by a system of NH[...]F, NH[...]O, OH[...]F, OH[dot dot dot]O hydrogen bonds. In a way similar to 1, the [SiF(5)(H(2)O)](-) anions and water molecules in 2 are combined into an inorganic negatively-charged layer through OH[...]F and OH[...]O interactions.     

Photocatalytic properties of Ta-doped TiO2

Ionics - This work reports the effect of tantalum (0.1–1 at.% Ta) on the photocatalytic performance of TiO2 annealed at 1373 and 1673 K in air. It was shown that addition of...