High-order ghost-point immersed boundary method for viscous compressible flows based on summation-by-parts operators

A high-order immersed boundary method is devised for the compressible Navier-Stokes equations by employing high-order summation-by-parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high-order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross-section of a human upper airway is simulated.     

Smooth Fréchet globalizations of Harish-Chandra modules

We give an alternative proof of the Casselman-Wallach globalization theorem. The approach is based on lower bounds for matrix coefficients on a reductive group.     

Self-seeded, position-controlled InAs nanowire growth on Si: A growth parameter study

In this work, the nucleation and growth of InAs nanowires on patterned SiO(2)/Si(111) substrates is studied. It is found that the nanowire yield is strongly dependent on the size of the etched holes in the SiO(2), where openings smaller than 180?nm lead to a substantial decrease in nucleation yield, while openings larger than ≈500nm promote nucleation of crystallites rather than nanowires. We propose that this is a result of indium particle formation prior to nanowire growth, where the size of the indium particles, under constant growth parameters, is strongly influenced by the size of the openings in the SiO(2) film. Nanowires overgrowing the etched holes, eventually leading to a merging of neighboring nanowires, shed light into the growth mechanism.     

Singular Hochschild cohomology via the singularity category

We show that the singular Hochschild cohomology (= Tate–Hochschild cohomology) of an algebra A is isomorphic, as a graded algebra, to the Hochschild cohomology of the differential graded enhancement of the singularity category of A. The existence of such an isomorphism is suggested by recent work by Zhengfang Wang.     

Fused Bis(hemi-indigo): Broad-Range Wavelength-Independent Photoswitches

Wavelength-independent conversion of organic photoswitches in the photostationary state is a rare phenomenon that opens up a way for many practical applications. In this work, three fused bis(hemi-indigo) derivatives with different substitution patterns were synthesized and their photoswitching was investigated by optical spectroscopy, real-time NMR spectroscopy and TD-DFT calculations. We disclosed that the Z-E photoisomerization of the meta-bis(hemi-indigo) derivative was remarkably independent of the irradiation wavelength from UV up to yellow light. The wavelength-independent forward photoswitching together with the inhibited backward photoisomerization, high thermal stability of the photoinduced isomers as well as significant overlap between the photoswitch absorption and the solar spectrum allows to suggest bis(hemi-indigo) derivatives as promising candidates for molecular solar thermal energy storage (MOST) systems.