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Chiroptical recognition of carboxylates with charge‐neutral double‐stranded zinc(II) helicates
(2023-07-30) Kalarikkal, Malavika G.; Drechsler, Christoph; Tusha, Gers; Schäfer, Lars V.; Van Craen, David
Chirality analysis of small molecules for the determination of their enantiopurity is nowadays ruled by streamlined chromatographic methods which utilize chiral stationary phases. Chiroptical probes which rely on host–guest interactions are so far overshadowed by the latter but have the benefit of depending only on common spectroscopic techniques such as CD spectroscopy to distinguish enantiomers and to quantify their ratio. Interest into this receptor-based approach is constantly rising because non-invasive high-throughput screenings with a minimal waste production can be performed. In this study we investigate the possibility to utilize metal-based containers in form of charge-neutral helicates able to recognize anions for this purpose. Key building block of the helicates are triazole units which show rotational freedom and give rise to either a meso-structure or a racemic mixture of the right- and left-handed complex. A chiroptical response of the probe is observed upon recognition of chiral mono- or dicarboxylates and chirality analysis of tartrate is conducted by CD spectroscopy.
Freezing limits for Calogero–Moser–Sutherland particle models
(2023-08-04) Voit, Michael
One-dimensional interacting particle models of Calogero–Moser–Sutherland type with N particles can be regarded as diffusion processes on suitable subsets of ℝ^N like Weyl chambers and alcoves with second-order differential operators as generators of the transition semigroups, where these operators are singular on the boundaries of the state spaces. The most relevant examples are multivariate Bessel processes and Heckman–Opdam processes in a compact and noncompact setting where in all cases, these processes are related to special functions associated with root systems. More precisely, the transition probabilities can be described with the aid of multivariate Bessel functions, Jack and Heckman–Opdam Jacobi polynomials, and Heckman–Opdam hypergeometric functions, respectively. These models, in particular, form dynamic eigenvalue evolutions of the classical random matrix models like β-Hermite, β- Laguerre, and β-Jacobi, that is, MANOVA, ensembles. In particular, Dyson's Brownian motions and multivariate Jacobi processes are included. In all cases, the processes depend on so-called coupling parameters. We review several freezing limit theorems for these diffusions where, for fixed N, one or several of the coupling parameters tend to ∞. In many cases, the limits will be N-dimensional normal distributions and, in the process case, Gauss processes. However, in some cases, normal distributions on half spaces and distributions related to some other ensembles appear as limits. In all cases, the limits are connected with the zeros of the classical one-dimensional orthogonal polynomials of order N.
Pushing the upper limit of nucleophilicity scales by mesoionic N‐heterocyclic olefins
(2023-08-04) Eitzinger, Andreas; Reitz, Justus; Antoni, Patrick W.; Mayr, Herbert; Ofial, Armin R.; Hansmann, Max M.
A series of mesoionic, 1,2,3-triazole-derived N-heterocyclic olefins (mNHOs), which have an extraordinarily electron-rich exocyclic CC-double bond, was synthesized and spectroscopically characterized, in selected cases by X-ray crystallography. The kinetics of their reactions with arylidene malonates, ArCH=C(CO2Et)2, which gave zwitterionic adducts, were investigated photometrically in THF at 20 °C. The resulting second-order rate constants k2(20 °C) correlate linearly with the reported electrophilicity parameters E of the arylidene malonates (reference electrophiles), thus providing the nucleophile-specific N and sN parameters of the mNHOs according to the correlation lg k2(20 °C)=sN(N+E). With 21
Amtliche Mitteilungen der Technischen Universität Dortmund Nr. 34/2024
(Technische Universität Dortmund, 2024-11-19)
Finite Element Simulation for Elastic and Plastic Fluids
(2024-11) Saghir, Muhammad Tayyab Bin; Damanik, Hogenrich; Turek, Stefan
In this study, we present the development of a 2D finite element solver for simulating fluids exhibiting both elastic and plastic constitutive properties. We achieve this by combining the constitutive models of the Oldroyd-B model for viscoelastic fluids and the Papanastasiou model for Bingham fluids within a single Eulerian numerical framework. Our aim within this approach is to approximate the given velocity, pressure, and elastic stresses. We employ
a higher-order finite element method for the velocity-stress approximation and a discontinuous pressure element. This specific element pair has proven highly effective for accurately capturing the behavior of both Oldroyd-B and Bingham fluids, including nonlinear viscosity functions. Our study consists of two main steps. Firstly, we validate the numerical results for each module component of the constitutives to ensure the accuracy of the approximations and calculations. This step is crucial for establishing the reliability and robustness of our approach. Subsequently, in the second step, we apply the solver to simulate elastoviscoplastic fluid behavior in a porous medium. By investigating fluid flow and deformation within this
specific context, we aim to demonstrate the capabilities and potential of our methodology.