Adjoint-based h–p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations

In this paper, we investigate and present an adaptive Discontinuous Galerkin algorithm driven by an adjoint-based error estimation technique for the inviscid compressible Euler equations. This approach requires the numerical approximations for the flow (i.e. primal) problem and the adjoint (i.e. dual) problem which corresponds to a particular simulation objective output of interest. The convergence of these two problems is accelerated by an hp-multigrid solver which makes use of an element Gauss–Seidel smoother on each level of the multigrid sequence. The error estimation of the output functional results in a spatial error distribution, which is used to drive an adaptive refinement strategy, which may include local mesh subdivision (h-refinement), local modification of discretization orders (p-enrichment) and the combination of both approaches known as hp-refinement. The selection between h- and p-refinement in the hp-adaptation approach is made based on a smoothness indicator applied to the most recently available flow solution values. Numerical results for the inviscid compressible flow over an idealized four-element airfoil geometry demonstrate that both pure h-refinement and pure p-enrichment algorithms achieve equivalent error reductions at each adaptation cycle compared to a uniform refinement approach, but requiring fewer degrees of freedom. The proposed hp-adaptive refinement strategy is capable of obtaining exponential error convergence in terms of degrees of freedom, and results in significant savings in computational cost. A high-speed flow test case is used to demonstrate the ability of the hp-refinement approach for capturing strong shocks or discontinuities while improving functional accuracy.     

On locally spherical polytopes of type {5, 3, 5}

There are only finitely many locally projective regular polytopes of type {5, 3, 5}. They are covered by a locally spherical polytope whose automorphism group is J₁×J₁×L₂(19), where J₁ is the first Janko group, of order 175560, and L₂(19) is the projective special linear group of order 3420. This polytope is minimal, in the sense that any other polytope that covers all locally projective polytopes of type {5, 3, 5} must in turn cover this one.     

Borohydride, azide, and chloride anions as terminal ligands on Fe/Mo/S clusters. Synthesis, structure and characterization of [(Cl4-cat)(PPr3) MoFe3S4(X)2]2(Bu4N)4 and [(Cl4-cat)(PPr3)MoFe3S4 (PPr3)(X)]2(Bu4N)2 (X = N3-, BH4-, Cl-) double-fused cubanes. NMR reactivity studies of [(Cl4-cat)(PPr3) MoFe3S4(BH4)2]2(Bu4N)4

Our explorations of the reactivity of Fe/Mo/S clusters of some relevance to the FeMoco nitrogenase have led to new double-fused cubane clusters with the Mo2Fe6S8 core as derivatives of the known (Cl4-cat)2Mo2Fe6S8(PPr3)6 (I) fused double cubane. The new clusters have been obtained by substitution reactions of the PPr3 ligands with Cl-, BH4-, and N3-. By careful control of the conditions of these reactions, the clusters [(Cl4-cat)(PPr3)MoFe3S4(BH4)2]2(Bu4N)4 (II), [(Cl4-cat)(PPr3)MoFe3S4(PPr3)(BH4)]2(Bu4N)2 (III), [(Cl4-cat)(PPr3)MoFe3S4(N3)2]2(Bu4N)4 (IV), [(Cl4-cat)(PPr3)MoFe3S4(PPr3)(N3)]2(Bu4N)2 (V), and [(Cl4-cat)(PPr3)MoFe3S4Cl2]2(Et4N)4 (VI) have been obtained and structurally characterized. A study of their electrochemistry shows that the reduction potentials for the derivatives of I are shifted to more positive values than those of I, suggesting a stabilization of the reduced clusters by the anionic ligands BH4- and N3-. Using 1H NMR spectroscopy, we have explored the lability of the BH4- ligand in II in coordinating solvents and its hydridic character, which is apparent in its reactivity toward proton sources such as MeOH or PhOH.     

Structure-function correlations in Iron(II) tris(pyrazolyl)borate spin-state crossover complexes

Iron(II) poly(pyrazolyl)borate complexes have been investigated to determine the impact of substituent effects, intramolecular ligand distortions, and intermolecular supramolecular structures on the spin-state crossover (SCO) behavior. The molecular structure of Fe[HB(3,4,5-Me3pz)3]2 (pz = pyrazolyl ring), a complex known to remain high spin when the temperature is lowered, reveals that this complex has an intramolecular ring-twist distortion that is not observed in analogous complexes that do exhibit a SCO at low temperatures, thus indicating that this distortion greatly influences the properties of these complexes. The structure of Fe[B(3-(cy)Prpz)4]2.(CH3OH) ((cy)Pr = cyclopropyl ring) at 294 K has two independent molecules in the unit cell, both of which are high spin; only one of these high-spin iron(II) sites, the site with the lesser ring-twist distortion, is observed to be low-spin iron(II) in the 90 K structure. A careful evaluation of the supramolecular structures of these complexes and several similar complexes reported previously revealed no strong correlation between the supramolecular packing forces and their SCO behavior. Magnetic and M?ssbauer spectral measurements on Fe[B(3-(cy)Prpz)4]2 and Fe[HB(3-(cy)Prpz)3]2 indicate that both complexes exhibit a partial SCO from fully high-spin iron(II) at higher temperatures, respectively, to a 50:50 high-spin/low-spin mixture of iron(II) below 100 K. These results may be understood, in the former case, by the differences in ring-twisting and, in the latter case, by a phase transition; in all complexes in which a phase transition is observed, this change dominates the SCO behavior. A comparison of the M?ssbauer spectral properties of these two complexes and of Fe[HB(3-Mepz)3]2 with that of other complexes reveals correlations between the M?ssbauer-effect isomer shift and the average Fe-N bond distance and between the quadrupole splitting and the average FeN-NB intraligand dihedral torsion angles and the distortion of the average N-Fe-N intraligand bond angles.     

Self-organization of polybases neutralized with mesogenic wedge-shaped sulfonic acid molecules: an approach toward supramolecular cylinders

Complexes consisting of poly(4-vinylpyridine) and mesogenic wedge-shaped ligands 4'-[3",4",5"-tris(dodecyloxy)benzoyloxy]azobenzene-4-sulfonic acid and 4'-[3",4",5"-tris(octyloxy)benzoyloxy]azobenzene-4-sulfonic acid have been prepared with different monomer/ligand ratios. Upon protonation of the poly(4-vinylpyridine) chains by the wedge-shaped sulfonic acid molecules a hypsochromic and hyperchromic effect was observed with the pi-pi* transition of the azo-chromophor, allowing us to monitor the neutralization process by means of UV-vis spectroscopy in solution. The changes of the absorption characteristics implied a conformational change of the polymer backbone. In the bulk the interaction between pyridine and sulfonic acid moieties was proved by FT-IR spectroscopy. Polarizing optical microscopy, differential scanning calorimetry, and X-ray diffraction measurements were used to study the bulk structure of the complexes. The complexes formed a liquid crystalline lamellar phase at low degrees of substitution, while a hexagonal columnar mesophase was observed at degrees of neutralization of 80% and higher.     

Sliding in a piecewise-smooth dynamical system with a hold-on effect

In this paper, we study a piecewise-smooth dynamical system of a Filippov type that has a specific discontinuity in the form of a hold-on term. The system resembles a driven dry-friction oscillator with the difference that the magnitude of the friction depends on the value of a local maximum of the oscillator displacement. Due to the hold-on term, the definition of the sliding region is not trivial. Along with a sliding region that is found analytically and is valid for any orbits, there exists a sliding region that we name ‘virtual’ because it is specific for each particular orbit. The existence of the virtual sliding region is explained by the specific discontinuity — the hold-on term — and the behavior associated with the sliding region and its boundaries can be considered as a new type of sliding-associated behavior.     

2-μm high-power multiple-frequency single-mode Q-switched Ho:YLF laser for DIAL application

We report on the development and the demonstration of a two-wavelength single-frequency laser oscillator based on Ho:YLF crystal. This laser is especially suitable for application as a transmitter in differential absorption lidar (DIAL)/integrated path differential absorption (IPDA) measurements of atmospheric carbon dioxide (CO₂) using the R30 CO₂ absorption line at 2,050.967 nm. The oscillator consists in a fiber-coupled and free-space solid-state hybrid system and can be used in high-energy middle-rate or moderate-energy high-rate configurations. The latter produced On and Off sequentially single-frequency laser pulses with 13 mJ of energy at a repetition rate of 2 kHz and pulse duration of 42 ns. The pulse energy and frequency stabilities are specially documented in free-running, single-frequency and two-frequency seeding single-mode operations. Standard deviation is 7.7 % for pulse energy and 2 MHz for frequency stability for the two-wavelength seeding operation. Allan variance plot shows that frequency fluctuations are reduced below 70 kHz for 10 s of averaging which is suitable for accurate CO₂ DIAL or IPDA measurements.     

The Groupoidal Analogue \widetilde{{\Theta}} to Joyal’s Category Θ is a Test Category

We introduce the groupoidal analogue $\widetilde{\Theta}$ to Joyal’s cell category Θ and we prove that $\widetilde{\Theta}$ is a strict test category in the sense of Grothendieck. This implies that presheaves on $\widetilde{\Theta}$ model homotopy types in a canonical way. We also prove that the canonical functor from Θ to $\widetilde{\Theta}$ is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on $\widetilde{\Theta}$ to weak equivalences of presheaves on Θ. Our proofs apply to other categories analogous to Θ.     

Efficacy of End-Only-Functionalized Oligo(arylene-ethynylene)s in Killing Bacterial Biofilms

Cationic end-only-functionalized oligo(arylene-ethynylene)s (EO-OPEs) have recently been found to be broad-spectrum and effective antimicrobial agents because of their unique structure and optical properties. In this study, we investigated their potential use for preventing and reducing Escherichia coli (E. coli) biofilms. The Calgary biofilm device (CBD) was used to form bacterial biofilms of E. coli; in these studies, the minimum inhibitory concentration (MIC) and the minimum biofilm eradication concentration (MBEC) were determined. E. coli biofilms uniformly grow on pegs of the CBD device lid. The MIC values determined for EO-OPEs are comparable to those found for standard antibiotics such as kanamycin (MIC = 11.2 μg/mL). About 10-30 times the concentration of EO-OPEs was required to eradicate E. coli biofilms and prevent regrowth in the dark. Near-UV irradiation of EO-OPEs enhanced their efficacy in killing biofilms.