Indefinite Morse 2-functions; broken fibrations and generalizations

A Morse 2-function is a generic smooth map from a smooth manifold to a surface. In the absence of definite folds (in which case we say that the Morse 2-function is indefinite), these are natural generalizations of broken (Lefschetz) fibrations. We prove existence and uniqueness results for indefinite Morse 2-functions mapping to arbitrary compact, oriented surfaces. "Uniqueness" means there is a set of moves which are sufficient to go between two homotopic indefinite Morse 2-functions while remaining indefinite throughout. We extend the existence and uniqueness results to indefinite, Morse 2-functions with connected fibers.Comment: 74 pages, 41 figures; further errors corrected, some exposition added, other exposition improved, following referee's comment

A CONDUCTING COMPOSITE OF POLYPYRROLE .1. SYNTHESIS AND CHARACTERIZATION

A conducting composite of polypyrrole was prepared via electrochemical methods. A polyamide was used as the insulating matrix polymer. The characterization of the composite was done by FT-IR, SEM, TGA, DSC and pyrolysis studies. Conductivity and solubility studies together with spectroscopic methods reveal that H bonding exists between the two polymers and a possible grafting to a certain extent

Exotic Smoothness and Quantum Gravity

Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. Thus, the negative result of Duston (arXiv:0911.4068) was a surprise. A closer look into the semi-classical approach uncovered the implicit assumption of a close connection between geometry and smoothness structure. But both structures, geometry and smoothness, are independent of each other. In this paper we calculate the "smoothness structure" part of the path integral in quantum gravity assuming that the "sum over geometries" is already given. For that purpose we use the knot surgery of Fintushel and Stern applied to the class E(n) of elliptic surfaces. We mainly focus our attention to the K3 surfaces E(2). Then we assume that every exotic smoothness structure of the K3 surface can be generated by knot or link surgery a la Fintushel and Stern. The results are applied to the calculation of expectation values. Here we discuss the two observables, volume and Wilson loop, for the construction of an exotic 4-manifold using the knot $5_{2}$ and the Whitehead link $Wh$. By using Mostow rigidity, we obtain a topological contribution to the expectation value of the volume. Furthermore we obtain a justification of area quantization.Comment: 16 pages, 1 Figure, 1 Table subm. Class. Quant. Grav

A study of the Czernik 2 and NGC 7654 open clusters using CCD UBV photometric and Gaia EDR3 data

We analysed the open clusters Czernik 2 and NGC 7654 using CCD UBV photometric and Gaia Early Data Release 3 (EDR3) photometric and astrometric data. Structural parameters of the two clusters were derived, including the physical sizes of Czernik 2 being r=5 and NGC 7654 as 8 min. We calculated membership probabilities of stars based on their proper motion components as released in the Gaia EDR3. To identify member stars of the clusters, we used these membership probabilities taking into account location and the impact of binarity on main-sequence stars. We used membership probabilities higher than $P=0.5$ to identify 28 member stars for Czernik 2 and 369 for NGC 7654. We estimated colour-excesses and metallicities separately using two-colour diagrams to derive homogeneously determined parameters. The derived $E(B-V)$ colour excess is 0.46(0.02) mag for Czernik 2 and 0.57(0.04) mag for NGC 7654. Metallicities were obtained for the first time for both clusters, -0.08(0.02) dex for Czernik 2 and -0.05(0.01) dex for NGC 7654. Keeping the reddening and metallicity as constant quantities, we fitted PARSEC models using colour-magnitude diagrams, resulting in estimated distance moduli and ages of the two clusters. We obtained the distance modulus for Czernik 2 as 12.80(0.07) mag and for NGC 7654 as 13.20(0.16) mag, which coincide with ages of 1.2(0.2) Gyr and 120(20) Myr, respectively. The distances to the clusters were calculated using the Gaia EDR3 trigonometric parallaxes and compared with the literature. We found good agreement between the distances obtained in this study and the literature. Present day mass function slopes for both clusters are comparable with the value of Salpeter (1955), being X=-1.37(0.24) for Czernik 2 and X=-1.39(0.19) for NGC 7654.Comment: 22 pages, 13 figures and 9 tables, accepted for publication in Astrophysics and Space Scienc

Optical transmission matrix as a probe of the photonic interaction strength

We demonstrate that optical transmission matrices (TM) of disordered complex media provide a powerful tool to extract the photonic interaction strength, independent of surface effects. We measure TM of strongly scattering GaP nanowires and plot the singular value density of the measured matrices and a random matrix model. By varying the free parameters of the model, the transport mean free path and effective refractive index, we retrieve the photonic interaction strength. From numerical simulations we conclude that TM statistics is hardly sensitive to surface effects, in contrast to enhanced backscattering or total transmission based methods

Optical transmission matrix as a probe of the photonic strength

We demonstrate that optical transmission matrices (TM) of disordered complex media provide a powerful tool to extract the photonic interaction strength, independent of surface effects. We measure TM of strongly scattering GaP nanowires and plot the singular value density of the measured matrices and a random matrix model. By varying the free parameters of the model, the transport mean free path and effective refractive index, we retrieve the photonic interaction strength. From numerical simulations we conclude that TM statistics is hardly sensitive to surface effects, in contrast to enhanced backscattering or total transmission based methods.We acknowledge support from ERC grant 27948, NWOVici, STW, the Royal Society, and EPSRC through fellowship EP/J016918/1

Fake R^4's, Einstein Spaces and Seiberg-Witten Monopole Equations

We discuss the possible relevance of some recent mathematical results and techniques on four-manifolds to physics. We first suggest that the existence of uncountably many R^4's with non-equivalent smooth structures, a mathematical phenomenon unique to four dimensions, may be responsible for the observed four-dimensionality of spacetime. We then point out the remarkable fact that self-dual gauge fields and Weyl spinors can live on a manifold of Euclidean signature without affecting the metric. As a specific example, we consider solutions of the Seiberg-Witten Monopole Equations in which the U(1) fields are covariantly constant, the monopole Weyl spinor has only a single constant component, and the 4-manifold M_4 is a product of two Riemann surfaces Sigma_{p_1} and Sigma_{p_2}. There are p_{1}-1(p_{2}-1) magnetic(electric) vortices on \Sigma_{p_1}(\Sigma_{p_2}), with p_1 + p_2 \geq 2 (p_1=p_2= 1 being excluded). When the two genuses are equal, the electromagnetic fields are self-dual and one obtains the Einstein space \Sigma_p x \Sigma_p, the monopole condensate serving as the cosmological constant.Comment: 9 pages, Talk at the Second Gursey Memorial Conference, June 2000, Istanbu

Quantum D-branes and exotic smooth R^4

In this paper, we present the idea that the formalism of string theory is connected with the dimension 4 in a new way, not covered by phenomenological or model-building approaches. The main connection is given by structures induced by small exotic smooth R^4's having intrinsic meaning for physics in dimension 4. We extend the notion of stable quantum D-branes in a separable noncommutative C* algebras over convolution algebras corresponding to the codimension-1 foliations of S^3 which are mainly connected to small exotic R^4. The tools of topological K-homology and K-theory as well KK-theory describe stable quantum branes in the C* algebras when naturally extended to algebras. In case of convolution algebras, small exotic smooth R^4's embedded in exotic R^4 correspond to a generalized quantum branes on the algebras. These results extend the correspondence between exotic R^4 and classical D and NS branes from our previous work.Comment: 16 pages, no figure, see arXiv/1101.3169 for Part 1 This is part 2 of the work based on the talk "Small exotic smooth $\mathbb{R}^{4}$ and string theory" given at the International Congress of Mathematicians, ICM2010, 19-28.08.2010, Hyderabad, Indi