A knife-edge measurement of the beam profile of STXM 5.3.2.2 using a focussed ion beam milled metallic glass

We present a simple knife-edge measurement of the STXM 5.3.2.2 synchrotron X-ray beam width. The knife edge was constructed by ion beam milling a metallic glass alloy consisting of 60% gold, 20% nickel and 20% hafnium and was determined to be well-defined to within 2 nm by TEM. An asymmetric beam profile of 120 nm FWHM in the vertical direction and 150 nm FWHM in the horizontal direction was determined and was observed to depart from the expected Airy function profile.     

On the thermo-acoustic Fant equation

A ‘reduced complexity’ equation is derived to investigate combustion instabilities of a Rijke burner. The equation is nonlinear and furnishes limit cycle solutions for finite amplitude burner modes. It is a generalisation to combustion flows of the Fant equation used to investigate the production of voiced speech by unsteady throttling of flow by the vocal folds [G. Fant, Acoustic Theory of Speech Production. Mouton, The Hague, 1960]. In the thermo-acoustic problem the throttling occurs at the flame holder. The Fant equation governs the unsteady volume flow past the flame holder which, in turn, determines the acoustics of the entire system. The equation includes a fully determinate part that depends on the geometry of the flame holder and the thermo-acoustic system, and terms defined by integrals involving thermo-aerodynamic sources, such as a flame and vortex sound sources. These integrals provide a clear indication of what must be known about the flow to obtain a proper understanding of the dynamics of the thermo-acoustic system. Illustrative numerical results are presented for the linearised equation. This governs the growth rates of the natural acoustic modes, determined by system geometry, boundary conditions and mean temperature distribution, which are excited into instability by unsteady heat release from the flame and damped by large scale vorticity production and radiation losses into the environment. In addition, the equation supplies information about the ‘combustion modes’ excited by the local time-delay feedback dynamics of the flame.     

Model-free control of Lorenz chaos using an approximate optimal control strategy

In this paper, we are concerned with model-free control of the Lorenz chaotic system, where only the online input and output are available while the mathematic model of the system is unknown. The problem is formulated from an optimal control perspective and solved using an iterative method. The convergence of the iteration and the stability of the control law are proven in theory. Simulations validate theoretical conclusions and demonstrate the effectiveness of the proposed method.     

Dynamic scaling in a simple one-dimensional model of dislocation activity

We examine a simple one-dimensional (1D) model of dislocation activity, including a stress-activated source and mutually interacting dislocations. We demonstrate, through numerical and analytical steps, that the dislocations emitted from a 1D stress-activated source evolve towards a distribution which is self-similar in time, and we derive the power-law forms and distribution function. We show that the asymptotic distribution is a step function, and the dislocation front moves out linearly in time. The spacing between dislocations in the asymptotic distribution is uniform and increases logarithmically in time. The number of dislocations increases as t/ln(t), and the strain increases as t ²/ln(t).     

Kinetic Resolution of 2-Substituted Indolines by N-Sulfonylation using an Atropisomeric 4-DMAP-N-oxide Organocatalyst

The first catalytic kinetic resolution by N-sulfonylation is described. 2-Substituted indolines are resolved (s=2.6–19) using an atropisomeric 4-dimethylaminopyridine-N-oxide (4-DMAP-N-oxide) organocatalyst. Use of 2-isopropyl-4-nitrophenylsulfonyl chloride is critical to the stereodiscrimination and enables facile deprotection of the sulfonamide products with thioglycolic acid. A qualitative model that accounts for the stereodiscrimination is proposed.     

Synthesis of α-Alkoxylidene Lactones

The α-formylation of α-lactones and the high yield conversion into their respective α-alkoxylidene lactones are described