Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid-structure interaction

Fluid-structure interaction (FSI) simulations are used extensively to calculate the vibration of structures subjected to an internal or external flow. In the case of partitioned FSI simulations, separate flow and structure solvers are used, which requires some kind of coupling between both. The time step in both solvers is typically taken the same, but this unnecessarily leads to long calculation times when the time step is small due to stability reasons in one of the two solvers. Subcycling, the procedure where the time step of one solver is chosen smaller than the time step used in the other solver, may reduce the computational cost of the FSI simulation. The subcycling procedure can be either explicit or implicit, the latter implying the use of coupling iterations in each time step. Contrary to explicit subcycling, no stability analyses of implicit subcycling schemes are found in the literature. In this paper, the temporal stability of the implicit subcycling procedure is investigated. The one-dimensional flow in an elastic cylindrical tube is studied analytically. The results of this analysis are subsequently compared to a partitioned two-dimensional axisymmetric FSI calculation with implicit coupling between the flow and structure solvers.     

Sodium Bicyclo[1.1.1]pentanesulfinate: A Bench-Stable Precursor for Bicyclo[1.1.1]pentylsulfones and Bicyclo- [1.1.1]pentanesulfonamides

Herein, we present the synthesis of the bench-stable sodium bicyclo[1.1.1]pentanesulfinate (BCP-SO₂Na) and its application in the synthesis of bicyclo[1.1.1]pentyl (BCP) sulfones and sulfonamides. The salt can be obtained in a four-step procedure from commercially available precursors in multigram scale without the need for column chromatography or crystallization. Sulfinates are known to be useful precursors in radical and nucleophilic reactions and are widely used in medicinal chemistry. This building block enables access to BCP sulfones and sulfonamides avoiding the volatile [1.1.1]propellane which is favorable for the extension of SAR studies. Further, BCP-SO₂Na enables the synthesis of products that were not available with previous methods. A chlorination of BCP-SO₂Na and subsequent reaction with a Grignard reagent provides a new route to BCP sulfoxides. Several products were analyzed by single-crystal X-ray diffraction.     

Rapid Generation and Safe Use of Carbenes Enabled by a Novel Flow Protocol with In‐line IR spectroscopy

A powerful new continuous process for the formation and use of donor/acceptor‐substituted carbenes is described. The safety profile of diazo group transfer on methyl phenylacetate was determined including kinetic studies in batch and in flow using in‐line IR analysis. Batch work‐up and liquid chromatography were circumvented by developing an optimized liquid/liquid flow separation method providing aryl diazoacetates in high purity. Fast screening of reaction conditions in flow with in‐line IR analysis allowed rapid reaction optimization. Finally, a multistep process of diazo group transfer, extraction, separation and subsequent diazo decomposition combined with multiple X?H insertion reactions was established.     

Crystal and molecular structure of 5-benzylidene-3-acetyl-2,4-oxolandione

The title compound crystallizes in the monoclinic space groupP2₁/n (No. 14),a=14.923(2),b=4.165(2),c=18.097(2) Å,=106.40(1)°,Z=4. The structure was solved by direct methods, and refined by full-matrix least squares toR=0.048 for 1313 observed reflections. Inter- and intramolecular hydrogen bonding is observed, the latter resulting in the formation of dimers.     

High‐Frequency Fe–H Vibrations in a Bridging Hydride Complex Characterized by NRVS and DFT

High‐spin iron species with bridging hydrides have been detected in species trapped during nitrogenase catalysis, but there are few general methods of evaluating Fe?H bonds in high‐spin multinuclear iron systems. An ⁵⁷Fe nuclear resonance vibrational spectroscopy (NRVS) study on an Fe(μ‐H)₂Fe model complex reveals Fe?H stretching vibrations for bridging hydrides at frequencies greater than 1200 cm^?1. These isotope‐sensitive vibrational bands are not evident in infrared (IR) spectra, showing the power of NRVS for identifying hydrides in this high‐spin iron system. Complementary density functional theory (DFT) calculations elucidate the normal modes of the rhomboidal iron hydride core.     

On a Family of Hyperplane Arrangements Related to the Affine Weyl Groups

Let be an irreducible crystallographic rootsystem in a Euclidean space V, with ⁺ theset of positive roots. For , , let be the hyperplane . We define a set of hyperplanes . This hyperplane arrangement is significant inthe study of the affine Weyl groups. In this paper it is shown that thePoincaré polynomial of is , where n is the rank of and h is the Coxeter number of the finiteCoxeter group corresponding to .     

Height of flat tori

Relations between the height and the determinant of the Laplacian on the space of -dimensional flat tori and the classical formulas of Kronecker and Epstein are established. Extrema of the height are shown to exist, and results for a global minimum for 2-d tori and a local minimum for 3-d tori are given, along with more general conjectures of Sarnak and Rankin.