Exceptional Components

For a wild acyclic quiver Q, Kerner introduced the notion of exceptional components for the Auslander–Reiten quiver of Q over an algebraically closed field k. He then defined two invariants for these exceptional components and asked whether these invariants coincide for each exceptional component. He showed that for each exceptional component there is a related hereditary factor algebra B of the path algebra kQ. He then proved that B is tame or representation finite and asked whether the representation finite case does occur, at all. We will answer both of Kerner's questions.     

Bifurcation of critical points for continuous families of C 2 functionals of Fredholm type

Given a continuous family of C ² functionals of Fredholm type, we show that the nonvanishing of the spectral flow for the family of Hessians along a known (trivial) branch of critical points not only entails bifurcation of nontrivial critical points but also allows to estimate the number of bifurcation points along the branch. We use this result for several parameter bifurcation, estimating the number of connected components of the complement of the set of bifurcation points in the parameter space and apply our results to bifurcation of periodic orbits of Hamiltonian systems. By means of a comparison principle for the spectral flow, we obtain lower bounds for the number of bifurcation points of periodic orbits on a given interval in terms of the coefficients of the linearization.     

Fluctuations in the quark-meson model for QCD with isospin chemical potential

We study the two-flavor quark-meson (QM) model with the functional renormalization group (FRG) to describe the effects of collective mesonic fluctuations on the phase diagram of QCD at finite baryon and   isospin chemical potentials, _μB${\mu }_B$ and _μI${\mu }_I$. With only isospin chemical potential there is a precise equivalence between the competing dynamics of chiral versus pion condensation and that of collective mesonic and baryonic fluctuations in the quark-meson-diquark model for two-color QCD at finite baryon chemical potential. Here, finite _μB=3μ${\mu }_B=3\mu$ introduces an additional dimension to the phase diagram as compared to two-color QCD, however. At zero temperature, the (_μI,μ${\mu }_I,\mu$) plane of this phase diagram is strongly constrained by the “Silver Blaze problem.” In particular, the onset of pion condensation must occur at _μI=_mπ/2${\mu }_I=m_{\pi }/2$, independent of μ   as long as μ+_μI$\mu +{\mu }_I$ stays below the constituent quark mass of the QM model or the liquid-gas transition line of nuclear matter in QCD. In order to maintain this relation beyond mean field it is crucial to compute the pion mass from its timelike correlator with the FRG in a consistent way.     

Alternating Sign Multibump Solutions of Nonlinear Elliptic Equations in Expanding Tubular Domains

Let Γ denote a smooth simple curve in ? ^N , N ≥ 2, possibly with boundary. Let Ω _R be the open normal tubular neighborhood of radius 1 of the expanded curve RΓ: = {Rx | x ∈ Γ??Γ}. Consider the superlinear problem ? Δu + λu = f(u) on the domains Ω _R , as R → ∞, with homogeneous Dirichlet boundary condition. We prove the existence of multibump solutions with bumps lined up along RΓ with alternating signs. The function f is superlinear at 0 and at ∞, but it is not assumed to be odd. If the boundary of the curve is nonempty our results give examples of contractible domains in which the problem has multiple sign changing solutions.     

Divalent Sialylated Precision Glycooligomers Binding to Polyomaviruses and the Effect of Different Linkers

Divalent precision glycooligomers terminating in N‐acetylneuraminic acid (Neu5Ac) or 3′‐sialyllactose (3′‐SL) with varying linkers between scaffold and the glycan portions are synthesized via solid phase synthesis for co‐crystallization studies with the sialic acid‐binding major capsid protein VP1 of human Trichodysplasia spinulosa‐associated Polyomavirus. High‐resolution crystal structures of complexes demonstrate that the compounds bind to VP1 depending on the favorable combination of carbohydrate ligand and linker. It is found that artificial linkers can replace portions of natural carbohydrate linkers as long as they meet certain requirements such as size or flexibility to optimize contact area between ligand and receptor binding sites. The obtained results will influence the design of future high affinity ligands based on the structures presented here, and they can serve as a blueprint to develop multivalent glycooligomers as inhibitors of viral adhesion.     

Correlation Between Foam Flow Structure in Porous Media and Surfactant Formulation Properties

Transport in Porous Media - The optimization of foam injection in porous media for enhanced oil recovery or soil remediation requires a large screening of surfactant formulations. Tests of foam...     

Perylene polyphenylmethylsiloxanes for optoelectronic applications

The incorporation of fluorescent organic dyes in an encapsulating matrix represents a route to generate stable and processable materials for optoelectronic devices. Here, we present a method to embed perylene dyes into a high refractive index (HRI) polysiloxane matrix applying an allyl functionalized perylene dye and hydrosilylation chemistry. In a first approach, the dye molecules were covalently integrated into the backbone of linear polyphenylmethylsiloxane chains. The fluorescent and liquid polymers were synthesized with molecular weights from 5660 up to 8400 g mol^?1. In a second approach, the dye itself was used as a cross‐linking agent between linear polyphenylmethylsiloxane chains. These preformed fluorescent batch polymers are liquids with dye concentrations between 0.025 and 8 wt %. The applied synthetic methods incorporated the dye covalently into the polymer structure and avoided the crystallization of the dye molecules and thus the formation of excimers, which would reduce the optical emission. The resulting products can be easily incorporated into curable commercially available HRI polyphenylmethylsiloxane resins. The formed materials are ideal LED encapsulants with a solid and flexible consistency, a uniform dispersion of the dyes, and adjustable mechanical properties, realized by changing the amount of perylene polymers. Further properties of the obtained materials are thermal stabilities up to 478 °C, quantum yields larger than 0.97, and high photostabilities. Thus, the covalent integration of dyes into polyphenylsiloxane structures represents a possible route for the stabilization of the organic dyes against the extreme irradiance and thermal conditions in LED applications. © 2019 The Authors. Journal of Polymer Science Part B: Polymer Physics published by Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1062–1073