Fractional order models for the homogenization and wave propagation analysis in periodic elastic beams

Meccanica - The advancement of manufacturing techniques has led to a rapid increase in the design and fabrication of periodic and architectured materials for a variety of dynamics and wave...     

Correction to: Involutions of Type G2 over a Field of Characteristic Two

Algebras and Representation Theory - We would like to correct two errors in our paper Involutions of type G2 over a field of characteristic 2 [2].     

Interface‐fitted moving mesh method for axisymmetric two‐phase flow in microchannels

A boundary‐fitted moving mesh scheme is presented for the simulation of two‐phase flow in two‐dimensional and axisymmetric geometries. The incompressible Navier‐Stokes equations are solved using the finite element method, and the mini element is used to satisfy the inf‐sup condition. The interface between the phases is represented explicitly by an interface adapted mesh, thus allowing a sharp transition of the fluid properties. Surface tension is modelled as a volume force and is discretized in a consistent manner, thus allowing to obtain exact equilibrium (up to rounding errors) with the pressure gradient. This is demonstrated for a spherical droplet moving in a constant flow field. The curvature of the interface, required for the surface tension term, is efficiently computed with simple but very accurate geometric formulas. An adaptive moving mesh technique, where smoothing mesh velocities and remeshing are used to preserve the mesh quality, is developed and presented. Mesh refinement strategies, allowing tailoring of the refinement of the computational mesh, are also discussed. Accuracy and robustness of the present method are demonstrated on several validation test cases. The method is developed with the prospect of being applied to microfluidic flows and the simulation of microchannel evaporators used for electronics cooling. Therefore, the simulation results for the flow of a bubble in a microchannel are presented and compared to experimental data.     

Predicting 19F NMR Chemical Shifts: A Combined Computational and Experimental Study of a Trypanosomal Oxidoreductase–Inhibitor Complex

The absence of fluorine from most biomolecules renders it an excellent probe for NMR spectroscopy to monitor inhibitor–protein interactions. However, predicting the binding mode of a fluorinated ligand from a chemical shift (or vice versa) has been challenging due to the high electron density of the fluorine atom. Nonetheless, reliable ¹⁹F chemical-shift predictions to deduce ligand-binding modes hold great potential for in silico drug design. Herein, we present a systematic QM/MM study to predict the ¹⁹F NMR chemical shifts of a covalently bound fluorinated inhibitor to the essential oxidoreductase tryparedoxin (Tpx) from African trypanosomes, the causative agent of African sleeping sickness. We include many protein–inhibitor conformations as well as monomeric and dimeric inhibitor–protein complexes, thus rendering it the largest computational study on chemical shifts of ¹⁹F nuclei in a biological context to date. Our predicted shifts agree well with those obtained experimentally and pave the way for future work in this area.     

Cytochrome P450 119 Compounds I Formed by Chemical Oxidation and Photooxidation Are the Same Species

Compound I from cytochrome P450 119 prepared by the photooxidation method involving peroxynitrite oxidation of the resting enzyme to Compound II followed by photooxidation to Compound I was compared to Compound I generated by m-chloroperoxybenzoic acid (MCPBA) oxidation of the resting enzyme. The two methods gave the same UV/Visible spectra, the same products from oxidations of lauric acid and palmitic acid and their (ω-2,ω-2,ω-3,ω-3)-tetradeuterated analogues, and the same kinetics for oxidations of lauric acid and caprylic acid. The experimental identities between the transients produced by the two methods leave no doubt that the same Compound I species is formed by the two methods.     

Konzertierte nukleophile aromatische Substitutionen

Jüngste Entwicklungen in der experimentellen und theoretischen Chemie haben zur Identifizierung einer schnell wachsenden Klasse von nukleophilen aromatischen Substitutionsreaktionen geführt, die einem konzertierten Mechanismus (cS_NAr) folgen, und nicht dem klassischen, zweistufigen S_NAr‐Mechanismus. Während klassische S_NAr‐Reaktionen auf die substantielle Aktivierung des aromatischen Ringes durch elektronenziehende Substituenten angewiesen sind, ist eine solche Aktivierung für den konzertierten Reaktionsverlauf nicht zwingend nötig.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.