Academic literature on the topic 'Δ-shell interactions'

The topological parameters of the metal-metal and metal-ligand bonding interactions in a trinuclear tetrahydrido cluster [(Cp*Co) (CpRu)2 (μ3-H) (μ-H)3]1 (Cp* = η5 -C5Me4Et), (Cp = η5 -C5Me5), was explored by using the Quantum Theory of Atoms-in-Molecules (QTAIM). The properties of bond critical points such as the bond delocalization indices δ (A, B), the electron density ρ(r), the local kinetic energy density G(r), the Laplacian of the electron density ∇2ρ(r), the local energy density H(r), the local potential energy density V(r) and ellipticity ε(r) are compared with data from earlier organometallic system studies. A comparison of the topological processes of different atom-atom interactions has become possible thanks to these results. In the core of the heterometallic tetrahydrido cluster, the Ru2CoH4 part, the calculations show no existence of any bond critical points (BCP) or identical bond paths (BPs) between Ru-Ru and Ru-Co. Electron densities are determined by the position of bridging hydride atoms coordinated to Ru-Ru and Ru-Co, which significantly affects the bonds between these transition metal atoms. On the other hand, the results confirm that the cluster under study contains a 7c–11e bonding interaction delocalized over M3H4, as shown by the non-negligible delocalization index calculations. The small values for electron density ρ(b) above zero, together with the small values, again above zero, for Laplacian ∇2ρ(b) and the small positive values for total energy density H(b), are shown by the Ru-H and Co-H bonds in this cluster is typical for open-shell interactions. Also, the topological data for the bond interactions between Co and Ru metal atoms with the C atoms of the cyclopentadienyl Cp ring ligands are similar. They show properties very identical to open-shell interactions in the QTAIM classification.

The ground state properties of light closed shell nuclei, i.e. 4He, 12C, 16O, 28Si, 32S, 40Ca and 56Ni are studied by using the channel-dependent effective two-body interactions (CDEI's). The CDEI's are generated through the lowest-order constrained variational (LOCV) calculation for asymmetric nuclear matter with the charge-dependent Av18 bare nucleon–nucleon potential. The work is performed on the harmonic oscillator basis, and the local density approximation is applied to create the relative and the center of mass dependent effective two-body potential. Unlike nuclear matter, and similar to our previous calculations with the Reid68 interaction, while the Av18 potential under binds above nuclei up J max = 2 channel, it gives ground state binding energies closer to the experimental data with respect to the Δ- Reid68 and the Reid68 potentials. There are not much difference between the results of Av18 interaction with J max = 5, and those of Reid68Day potential which has been define up to J max = 5. The different CDEI's up to J max = 5 are discussed and the results of our calculations are compared with the other theoretical approaches and experimental data. Finally, it is shown that the contributions of higher partial waves (J>2) are not very important and the two-body kinetic energy in J = 1 channel is roughly twice as that of J = 0 which is not the case for the two-body potential energy.

Abstract A series of compounds based on peroxide-cured EPDM were prepared with varying amounts of paraffinic plasticizer and carbon black. Modeling of the NMR relaxation signal was successfully carried out by either a biexponential or triexponential fitting procedure. It was found the degree of plasticization correlated directly with the average molar mass between chain entanglements (Me) calculated from the short decay constant T21. Values of Me correlated to the dynamic properties (storage modulus and tan δ) in the unvulcanized state, thus providing a measure of processability. An increase in carbon black concentration brought about a decrease in Me because of increased interactions between the filler and the polymer chain. A new parameter Mchain–filler is introduced to estimate the average molar mass between polymer chains and fillers. Compared with the chain entanglement density, the overall magnitude of this interaction appears to be weak in the mobile zone of the compound matrix. As in the case of plasticization, a relatively good correlation is obtained between Me and the dynamical properties in the unvulcanized state. Compression-set resistance is shown to directly follow the average molar mass between cross-links (Mc) before and after aging. The carbon black study results can be understood within the context of a morphological model containing different zones of chain mobility—a thin shell of immobilized chains, an intermediate zone of limited mobility, and a dominant mobile phase consisting mainly of entangled and cross-linked polymer chains.

Context. Correlations between high-precision elemental abundance ratios and the kinematics of halo stars provide interesting information about the formation and early evolution of the Galaxy. Aims. Element abundances of G 112-43/44, a metal-poor wide-orbit binary star with extreme kinematics, are revisited. Methods. High-precision studies of the chemical compositions of 94 metal-poor dwarf stars in the solar neighbourhood are used to compare abundance ratios for G 112-43/44 with ratios for stars that have similar metallicities, taking into account the effect of deviations from local thermodynamic equilibrium on the derived abundances. Gaia EDR3 data are used to compare the kinematics. Results. The X/Fe abundance ratios of the two components of G 112-43/44 agree within ±0.05 dex for nearly all elements, but there is a hint of a correlation between the difference in [X/H] and the elemental condensation temperature, which may be due to planet-star interactions. The Mg/Fe, Si/Fe, Ca/Fe, and Ti/Fe ratios of G 112-43/44 agree with the corresponding ratios for accreted (Gaia-Enceladus) stars, but Mn/Fe, Ni/Fe, Cu/Fe, and Zn/Fe are significantly enhanced, with Δ [Zn/Fe] reaching 0.25 dex. The kinematics show that G 112-43/44 belongs to the Helmi streams in the solar neighbourhood. In view of this, we discuss if the abundance peculiarities of G 112-43/44 can be explained by chemical enrichment from supernova events in the progenitor dwarf galaxy of the Helmi streams. Interestingly, yields calculated for a helium shell detonation Type Ia supernova model can explain the enhancement of Mn/Fe, Ni/Fe, Cu/Fe, and Zn/Fe in G 112-43/44 and three other α-poor stars in the Galactic halo with abundances from the literature, one of which has Helmi stream kinematics. However, the helium shell detonation model also predicts enhanced abundance ratios of Ca/Fe, Ti/Fe, and Cr/Fe, in disagreement with the observed ratios.

Cette thèse se focalise sur l'étude spectrale des modèles de perturbations de l'opérateur de Dirac libre en dimensions 2 et 3.Le premier chapitre de cette thèse étudie la perturbation de l'opérateur de Dirac par une grande masse M, supportée sur un domaine. Notre objectif principal est d'établir, sous la condition d'une masse M suffisamment grande, la convergence de l'opérateur perturbé vers l'opérateur de Dirac avec la condition au bord MIT bag, au sens de la norme de la résolvante. Pour se faire, nous introduisons ce que nous appelons les opérateurs Poincaré-Steklov (PS) (comme un analogue des opérateurs Dirichlet-to-Neumann pour l'opérateur de Laplace) et les analysons d'un point de vue microlocal, afin de comprendre précisément le taux de convergence de la résolvante. D'une part, nous montrons que les opérateurs PS s'intègrent dans le cadre des opérateurs pseudodifférentiels et nous déterminons leurs symboles principaux. D'autre part, comme nous nous intéressons principalement aux grandes masses, nous traitons notre problème du point de vue semiclassique, où le paramètre semiclassique est h = M^{-1}. Enfin, en établissant une formule de Krein reliant la résolvante de l'opérateur perturbé à celle de l'opérateur MIT bag, et en utilisant les propriétés pseudodifférentielles des opérateurs PS combinées aux structures matricielles des symboles principaux, nous établissons la convergence requise avec un taux de convergence de O(M^{-1}.Dans le chapitre 2, nous définissons un voisinage tubulaire de la frontière d'un domaine régulier donné. Nous considérons la perturbation de l'opérateur de Dirac libre par une grande masse M, supportée dans ce voisinage d'épaisseur varepsilon:=M^{-1}. Notre objectif principal est d'étudier la convergence de l'opérateur de Dirac perturbé lorsque M tend vers l'infini. En comparaison avec la première partie, nous obtenons ici deux opérateurs limites MIT bag, qui agissent en dehors de la frontière. Il est intéressant de noter que le découplage de ces deux opérateurs MIT bag peut être considéré comme la version confinée de delta-interaction scalaire de Lorentz de l'opérateur de Dirac, supportée sur une surface fermée. La méthodologie suivie, comme au problème précédent, porte sur l'étude des propriétés pseudodifférentielles des opérateurs PS. Cependant, la nouveauté de ce problème réside dans le contrôle de ces opérateurs en suivant la dépendance du paramètre varepsilon, et par conséquent, dans la convergence lorsque varepsilon tend vers 0 et M tend vers l'infini. Avec ces ingrédients, nous prouvons que l'opérateur perturbé converge au sens de la norme de la résolvante vers l'opérateur de Dirac couplé à une delta-interaction scalaire de Lorentz.Dans le chapitre 3, nous généralisation une approximation de l'opérateur de Dirac tridimensionnel couplé à une combinaison singulière de delta-interactions électrostatiques et scalaires de Lorentz supportée sur une surface fermée, par un opérateur de Dirac avec un potentiel régulier localisé dans une couche mince contenant la surface. Dans les cas non-critiques et non-confinants, nous montrons que l'opérateur de Dirac perturbé régulier converge au sens de la résolvante forte vers la delta-interaction singulière de l'opérateur de Dirac.Dans le dernier chapitre, notre étude porte sur l'opérateur de Dirac bidimensionnel couplé à une delta-interaction électrostatique et scalaire de Lorentz. Nous traitons dans des espaces de Sobolev d'ordre un-demi l'auto-adjonction de certaines réalisations de ces opérateurs dans divers contextes de courbes. Le cas le plus important se présente lorsque les courbes considérées sont des polygones curvilignes. Sous certaines conditions sur les constantes de couplage, en utilisant la propriété de Fredholm de certains opérateurs intégraux de frontière, et en exploitant la forme explicite de la transformée de Cauchy sur des courbes non lisses, nous établissons l'auto-adjonction de l'opérateur perturbé
This thesis mainly focused on the spectral analysis of perturbation models of the free Dirac operator, in 2-D and 3-D space.The first chapter of this thesis examines perturbation of the Dirac operator by a large mass M, supported on a domain. Our main objective is to establish, under the condition of sufficiently large mass M, the convergence of the perturbed operator, towards the Dirac operator with the MIT bag condition, in the norm resolvent sense. To this end, we introduce what we refer to the Poincaré-Steklov (PS) operators (as an analogue of the Dirichlet-to-Neumann operators for the Laplace operator) and analyze them from the microlocal point of view, in order to understand precisely the convergence rate of the resolvent. On one hand, we show that the PS operators fit into the framework of pseudodifferential operators and we determine their principal symbols. On the other hand, since we are mainly concerned with large masses, we treat our problem from the semiclassical point of view, where the semiclassical parameter is h = M^{-1}. Finally, by establishing a Krein formula relating the resolvent of the perturbed operator to that of the MIT bag operator, and using the pseudodifferential properties of the PS operators combined with the matrix structures of the principal symbols, we establish the required convergence with a convergence rate of mathcal{O}(M^{-1}).In the second chapter, we define a tubular neighborhood of the boundary of a given regular domain. We consider perturbation of the free Dirac operator by a large mass M, within this neighborhood of thickness varepsilon:=M^{-1}. Our primary objective is to study the convergence of the perturbed Dirac operator when M tends to +infty. Comparing with the first part, we get here two MIT bag limit operators, which act outside the boundary. It's worth noting that the decoupling of these two MIT bag operators can be considered as the confining version of the Lorentz scalar delta interaction of Dirac operator, supported on a closed surface. The methodology followed, as in the previous problem study the pseudodifferential properties of Poincaré-Steklov operators. However, the novelty in this problem lies in the control of these operators by tracking the dependence on the parameter varepsilon, and consequently, in the convergence as varepsilon goes to 0 and M goes to +infty. With these ingredients, we prove that the perturbed operator converges in the norm resolvent sense to the Dirac operator coupled with Lorentz scalar delta-shell interaction.In the third chapter, we investigate the generalization of an approximation of the three-dimensional Dirac operator coupled with a singular combination of electrostatic and Lorentz scalar delta-interactions supported on a closed surface, by a Dirac operator with a regular potential localized in a thin layer containing the surface. In the non-critical and non-confining cases, we show that the regular perturbed Dirac operator converges in the strong resolvent sense to the singular delta-interaction of the Dirac operator. Moreover, we deduce that the coupling constants of the limit operator depend nonlinearly on those of the potential under consideration.In the last chapter, our study focuses on the two-dimensional Dirac operator coupled with the electrostatic and Lorentz scalar delta-interactions. We treat in low regularity Sobolev spaces (H^{1/2}) the self-adjointness of certain realizations of these operators in various curve settings. The most important case in this chapter arises when the curves under consideration are curvilinear polygons, with smooth, differentiable edges and without cusps. Under certain conditions on the coupling constants, using the Fredholm property of certain boundary integral operators, and exploiting the explicit form of the Cauchy transform on non-smooth curves, we achieve the self-adjointness of the perturbed operator