Topological modular forms and conformal nets

We describe the role conformal nets, a mathematical model for conformal field theory, could play in a geometric definition of the generalized cohomology theory TMF of topological modular forms. Inspired by work of Segal and Stolz-Teichner, we speculate that bundles of boundary conditions for the net of free fermions will be the basic underlying objects representing TMF-cohomology classes. String structures, which are the fundamental orientations for TMF-cohomology, can be encoded by defects between free fermions, and we construct the bundle of fermionic boundary conditions for the TMF-Euler class of a string vector bundle. We conjecture that the free fermion net exhibits an algebraic periodicity corresponding to the 576-fold cohomological periodicity of TMF; using a homotopy-theoretic invariant of invertible conformal nets, we establish a lower bound of 24 on this periodicity of the free fermions

Micromechanisms of thermomechanical fatigue: A comparison with isothermal fatigue

Thermomechanical Fatigue (TMF) experiments were conducted on Mar-M 200, B-1900, and PWA-1480 (single crystals) over temperature ranges representative of gas turbine airfoil environments. The results were examined from both a phenomenological basis and a micromechanical basis. Depending on constituents present in the superalloy system, certain micromechanisms dominated the crack initiation process and significantly influenced the TMF lives as well as sensitivity of the material to the type TMF cycle imposed. For instance, high temperature cracking around grain boundary carbides in Mar-M 200 resulted in short in-phase TMF lives compared to either out-of-phase or isothermal lives. In single crystal PWA-1480, the type of coating applied was seen to be the controlling factor in determining sensitivity to the type of TMF cycle imposed. Micromechanisms of deformation were observed over the temperature range of interest to the TMF cycles, and provided some insight as to the differences between TMF damage mechanisms and isothermal damage mechanisms. Finally, the applicability of various life prediction models to TMF results was reviewed. Current life prediction models based on isothermal data must be modified before being generally applied to TMF

Preliminary study of thermomechanical fatigue of polycrystalline MAR-M 200

Thermomechanical fatigue (TMF) experiments were conducted on polycrystalline MAR-M 200 over a cyclic temperature range of 500 to 1000 C. Inelastic strain ranges of 0.03 to 0.2 percent were imposed on the specimens. The TMF lives were found to be significantly shorter than isothermal low-cycle-fatigue (LCF) life at the maximum cycle temperature, and in-phase cycling was more damaging than out-of-phase cycling. Extensive crack tip oxidation appeared to play a role in promoting the severity of in-phase cycling. Carbide particle - matrix interface cracking was also observed after in-phase TMF cycling. The applicability of various life prediction models to the TMF results obtained was assessed. It was concluded that current life prediction models based on isothermal data as input must be modified to be applicable to the TMF results

Simultaneous Kummer congruences and E∞\mathbb{E}_\infty-orientations of KO and tmf

Building on results of M. Ando, M.J. Hopkins and C. Rezk, we show the existence of uncountably many $\mathbb{E}_\infty$-String orientations of real K-theory KO and of topological modular forms tmf, generalizing the $\hat{A}$- (resp. the Witten) genus. Furthermore, the obstruction to lifting an $\mathbb{E}_\infty$-String orientations from KO to tmf is identified with a classical Iwasawa-theoretic condition. The common key to all these results is a precise understanding of the classical Kummer congruences, imposed for all primes simultaneously. This result is of independent arithmetic interest.Comment: final versio