Mean-field evolution of fermions with singular interaction

We consider a system of N fermions in the mean-field regime interacting though an inverse power law potential $V(x)=1/|x|^{\alpha}$, for $\alpha\in(0,1]$. We prove the convergence of a solution of the many-body Schr\"{o}dinger equation to a solution of the time-dependent Hartree-Fock equation in the sense of reduced density matrices. We stress the dependence on the singularity of the potential in the regularity of the initial data. The proof is an adaptation of [22], where the case $\alpha=1$ is treated.Comment: 16 page

Fast evaluation of solid harmonic Gaussian integrals for local resolution-of-the-identity methods and range-separated hybrid functionals

An integral scheme for the efficient evaluation of two-center integrals over contracted solid harmonic Gaussian functions is presented. Integral expressions are derived for local operators that depend on the position vector of one of the two Gaussian centers. These expressions are then used to derive the formula for three-index overlap integrals where two of the three Gaussians are located at the same center. The efficient evaluation of the latter is essential for local resolution-of-the-identity techniques that employ an overlap metric. We compare the performance of our integral scheme to the widely used Cartesian Gaussian-based method of Obara and Saika (OS). Non-local interaction potentials such as standard Coulomb, modified Coulomb, and Gaussian-type operators, which occur in range-separated hybrid functionals, are also included in the performance tests. The speed-up with respect to the OS scheme is up to three orders of magnitude for both integrals and their derivatives. In particular, our method is increasingly efficient for large angular momenta and highly contracted basis sets

A Systematic Review on Improving Health Literacy in Rural Africa Using Mobile Serious Games

Driven by an increase in the availability of cheap low-cost mobile phones and a jump in the number of telecom subscribers, the African gaming world is booming. Most importantly, it has opened an opportunity for rural communities to have an almost identical mobile phone experience than people living in urban areas. It has also opened an opportunity to leverage this high penetration of mobile devices to design mobile-based applications such as mobile serious games. The latter assists individuals living in these communities to modify, change or shape their behaviors and attitudes desirably. This paper reviews mobile serious games in healthcare education, especially those intended to improve health literacy in rural Africa. The challenges and issues encountered in the design and use of persuasive mobile games as a tool can promote behavior change among people living in the rural African communities

Cationic group VI metal imido alkylidene N‐heterocyclic carbene nitrile complexes : bench‐stable, functional‐group‐tolerant olefin metathesis catalysts

Despite their excellent selectivities and activities, Mo‐and W‐based catalysts for olefin metathesis have not gained the same widespread use as Ru‐based systems, mainly due to their inherent air sensitivity. Herein, we describe the synthesis of air‐stable cationic‐at‐metal molybdenum and tungsten imido alkylidene NHC nitrile complexes. They catalyze olefin metathesis reactions of substrates containing functional groups such as (thio‐) esters, (thio‐) ethers and alcohols without the need for prior activation, for example, by a Lewis acid. The presence of a nitrile ligand was found to be essential for their stability towards air, while no decrease in activity and productivity could be observed upon coordination of a nitrile. Variations of the imido and anionic ligand revealed that alkoxide complexes with electron‐withdrawing imido ligands offer the highest reactivities and excellent stability compared to analogous triflate and halide complexes.Deutsche ForschungsgemeinschaftProjekt DEA

Dual catalysis with an N‐heterocyclic carbene and a Lewis acid : thermally latent precatalyst for the polymerization of ε‐caprolactam

So far, the earlier reported strong correlation between basicity of an N‐heterocyclic carbene (NHC) and its reactivity in poly(ε‐caprolactam) (PA6) synthesis resulted in a substantial limitation of applicable carbenes. Here, to overcome this issue, 1,3‐dimethylimidazolium‐2‐carboxylate, an easily accessible, air and moisture‐stable NHC, was applied as thermally latent initiator. In order to compensate for its low basicity, reactivity was enhanced by the addition of both a Lewis acid and an activator to ease the initial polymerization step. The resulting mixtures of ε‐caprolactam, the CO2‐protected NHC, a Lewis acid and N‐acylazepan‐2‐one constitute homogeneous, thermally fully latent “single‐component” blends for the anionic polymerization‐based synthesis of PA6. They can be stored both in the liquid and solid state for days and months, respectively, without any loss in activity. The role of the Lewis acid as well as technical implications of the prolonged pot‐times are discussed.Projekt DEA

Transverse-mode coupling and diffraction loss in tunable Fabry-Pé rot microcavities

Wereport on measurements and modeling of the mode structure of tunable Fabry–Pérot optical microcavities with imperfect mirrors.Wefind that non-spherical mirror shape and finite mirror size leave the fundamental mode mostly unaffected, but lead to loss, mode deformation, and shifted resonance frequencies at particular mirror separations. For small mirror diameters, the useful cavity length is limited to values significantly below the expected stability range.Weexplain the observations by resonant coupling between different transverse modes of the cavity and mode-dependent diffraction loss. A model based on resonant state expansion that takes into account the measured mirror profile can reproduce the measurements and identify the parameter regime where detrimental effects of mode mixing are avoided