Spectroscopic Tracking of Molecular Transport Junctions Generated by Using Click Chemistry

Click to fill the gap : The in situ modular fabrication of molecular transport junctions in nanogaps generated by on‐wire lithography is achieved by using click chemistry (see picture). The formation of molecular junctions proceeds in high yields and can be used to test different molecules; the triazole group also maintains conjugation in the molecular wires. Raman spectroscopy is used to characterize the molecular assembly processes.

     

Corrector estimates in homogenization of a nonlinear transmission problem for diffusion equations in connected domains

This paper is devoted to the homogenization of a nonlinear transmission problem stated in a two-phase domain. We consider a system of linear diffusion equations defined in a periodic domain consisting of two disjoint phases that are both connected sets separated by a thin interface. Depending on the field variables, at the interface, nonlinear conditions are imposed to describe interface reactions. In the variational setting of the problem, we prove the homogenization theorem and a bidomain averaged model. The periodic unfolding technique is used to obtain the residual error estimate with a first-order corrector.     

MCD-finite Domains and Ascent of IDF Property in Polynomial Extensions

An integral domain is said to have the IDF property when every non-zero element of it has only a finite number of non-associate irreducible divisors. A counterexample has already been found showing that the IDF property does not necessarily ascend in polynomial extensions. In this paper, we introduce a new class of integral domains, called MCD-finite domains, and show that for any domain D, D[X] is an IDF domain if and only if D is both IDF and MCD-finite. This result entails all the previously known sufficient conditions for the ascent of the IDF property. Our new characterization of polynomial domains with the IDF property enables us to use a different construction and build another counterexample which strengthen the previously known result on this matter.     

A synthesis of the marine antibiotic (-)-malyngolide from D-glucose

(-)_Malyngolide, an antibiotic from the marine blue-green alga Lyngbya majuscula, was synthesized in about 30% yield from ethyl 4,6-0-benzylidene-2-deoxy-α-D-erythro-hexopyranosid-3-ulose, a chiral synthon easily derived from commercially available methyl α-D-glucopyranoside.     

Efficient, “one-pot” synthesis of silylene–acetylene and disilylene–acetylene preceramic polymers from trichloroethylene

An extremely efficient process has been developed for the synthesis of linear silylene-acetylene and disilylene-acetylene polymers. Trichloroethylene is quantitatively converted by n-butyllithium to dilithioacetylene. Quenching with dialkyl-or diaryldichlorosilanes affords high yields of the polymers, $ \rlap{--} [{\rm SiR}_{\rm 2} \hbox{---} {\rm C} \equiv {\rm C\rlap{--} ]}_n ,{\rm and }\rlap{--} [{\rm SiMe}_{\rm 2} {\rm SiMe}_{\rm 2} - {\rm C} \equiv {\rm C\rlap{--} ]}_n $ if ClMe₂SiSiMe₂Cl is employed. Molecular weights are much higher with this route than when acetylene is used as the dilithio- or dimagnesium acetylide precursor. Some of these polymers can be pulled into continuous fibers, and all can be cast into coherent films and thermally converted into silicon carbide.     

Approximate analysis and design of rectangular-lattice photonic crystals

We present a theoretical analysis of wave propagation in rectangular- and square-lattice photonic crystals by approximating the arbitrary refractive-index function with a staircase profile. This profile has a number of tunable parameters that allow one to fit the band structures of the staircase and the desired structure over a large frequency range. The staircase profile is such that its corresponding two-dimensional wave equation decomposes into two one-dimensional equations by means of a constant decoupling parameter. We show that basic features of the band structure and Bloch waves in photonic crystals can be analyzed theoretically through this simple approximation.     

On the calibration of the Chaboche hardening model and a modified hardening rule for uniaxial ratcheting prediction

A systematic mathematical approach is developed in the context of uniaxial cyclic ratcheting for the parameter determination of the decomposed Chaboche hardening rule. This is achieved by deriving the relation between the evolution of the backstress and the plastic strain accumulation. Unlike current calibration techniques where a trial–error approach is employed to fit the simulation results to experimental data, the proposed method determines the parameters directly from uniaxial ratcheting experiments. Numerical results indicate that Chaboche’s hardening model is much more efficient than what has been demonstrated before. Finally, as an improvement to the decomposed model, a modification is made to one of the backstress components. This improved component enables the model to predict uniaxial ratcheting with more accuracy.     

Microbundles, manifolds and metrisability

The notion of a microbundle was introduced in the 1960s but the theory came to an abrupt halt when it was shown that for a metrisable manifold, microbundles are equivalent to fibre bundles. In this paper we consider microbundles over non-metrisable manifolds. In some cases microbundles are equivalent to fibre bundles but in others they are not. In particular, we show that a manifold is metrisable if and only if its tangent microbundle is equivalent to a fibre bundle. We also illustrate that for some non-metrisable manifolds every trivial microbundle contains a trivial fibre bundle whereas other manifolds may support a trivial microbundle not containing a trivial fibre bundle.