Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

Minimal kernels of Dirac operators along maps

Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels .     

An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.     

Analyzing the coexistence of DSRC and Wi-Fi networks using the Poisson line Cox process

Vehicular networks can aid in traffic monitoring, autonomous driving, and car accidents prevention. Yet, the deployment of these networks has been delayed due to the limited spectrum, especially for the case of unlicensed operations. To handle this issue, the Federal Communications Commission (FCC) proposed to permit Wi-Fi devices to operate in the 5.9 GHz band allocated to the intelligent transportation system (ITS). In a recent work, we analyzed the impact of the coexistence of dedicated short range communications (DSRC) and Wi-Fi on future DSRC network deployments by developing a stochastic geometry analytical model that considers a dynamic medium access probability (MAP) of DSRC nodes which uses carrier sense multiple access with collision avoidance (CSMA/CA). This previous work was based on the standard 2D homogeneous Poisson Point Process (PPP) model. In this work, we model the roads using the more applicable but more complex Poisson line process (PLP) Cox point process. We generate performance metrics represented through coverage probability and area system throughput, and we compare these results to our earlier work. The importance of this work is two-fold. First, it allows a further understanding of the impact of DSRC-Wi-Fi coexistence on future DSRC network deployments, and second, it highlights the effectiveness of the PLP in modeling the distribution of vehicles in an area by producing more accurate performance results.     

Molecular QTAIM Topology Is Sensitive to Relativistic Corrections

The topology of the molecular electron density of benzene dithiol gold cluster complex Au₄−S−C₆H₄−S′−Au′₄ changed when relativistic corrections were made and the structure was close to a minimum of the Born–Oppenheimer energy surface. Specifically, new bond paths between hydrogen atoms on the benzene ring and gold atoms appeared, indicating that there is a favorable interaction between these atoms at the relativistic level. This is consistent with the observation that gold becomes a better electron acceptor when relativistic corrections are applied. In addition to relativistic effects, here, we establish the sensitivity of molecular topology to basis sets and convergence thresholds for geometry optimization.     

Oxotitanium(IV) complexes of some bis‐unsymmetric Schiff bases: Synthesis,structural elucidation and biomedical applications

A number of oxotitanium(IV) complexes of the type TiOL with bis‐unsymmetric dibasic tetradentate Schiff base (LH₂) containing ONNO donor atoms have been synthesized. Mono‐Schiff base (OPD‐HNP) was prepared by the condensation of 1:3 molar ratio of 2‐hydroxy‐1‐naphthaldehyde (HNP) with o‐phenylenediamine (OPD). Dibasic unsymmetric tetradentate diamine Schiff bases were prepared by the reaction of OPD‐HNP with 2‐hydroxyacetophenone, 2‐hydroxypropeophenone, benzoylacetone, acetylacetone and ethylacetoacetate. Further, titanylacetylacetonate was reacted with these ligands to obtain their metal complexes. On the basis of analytical and physiochemical data, the formation of complexes as TiOL was suggested having square pyramidal geometry. Quantum mechanical approach also confirmed this geometry. The assessment of the synthesized ligands and their complexes showed that some behave as good inhibitors of mycelial growth against selected phytopathogic fungi but weak inhibitors against some selected bacteria. A few of them also showed antioxidant properties.