Atom Exchange Versus Reconstruction: (GexAs4−x)x− (x=2, 3) as Building Blocks for the Supertetrahedral Zintl Cluster [Au6(Ge3As)(Ge2As2)3]3−

The Zintl anion (Ge₂As₂)^2? represents an isostructural and isoelectronic binary counterpart of yellow arsenic, yet without being studied with the same intensity so far. Upon introducing [(PPh₃)AuMe] into the 1,2‐diaminoethane (en) solution of (Ge₂As₂)^2?, the heterometallic cluster anion [Au₆(Ge₃As)(Ge₂As₂)₃]^3? is obtained as its salt [K(crypt‐222)]₃[Au₆(Ge₃As)(Ge₂As₂)₃]?en?2 tol ( 1 ). The anion represents a rare example of a superpolyhedral Zintl cluster, and it comprises the largest number of Au atoms relative to main group (semi)metal atoms in such clusters. The overall supertetrahedral structure is based on a (non‐bonding) octahedron of six Au atoms that is face‐capped by four (Ge_xAs_4?x)^x? (x=2, 3) units. The Au atoms bind to four main group atoms in a rectangular manner, and this way hold the four units together to form this unprecedented architecture. The presence of one (Ge₃As)^3? unit besides three (Ge₂As₂)^2? units as a consequence of an exchange reaction in solution was verified by detailed quantum chemical (DFT) calculations, which ruled out all other compositions besides [Au₆(Ge₃As)(Ge₂As₂)₃]^3?. Reactions of the heavier homologues (Tt₂Pn₂)^2? (Tt=Sn, Pb; Pn=Sb, Bi) did not yield clusters corresponding to that in 1 , but dimers of ternary nine‐vertex clusters, {[AuTt₅Pn₃]₂}^4? (in 2 – 4 ; Tt/Pn=Sn/Sb, Sn/Bi, Pb/Sb), since the underlying pseudo‐tetrahedral units comprising heavier atoms do not tend to undergo the said exchange reactions as readily as (Ge₂As₂)^2?, according to the DFT calculations.     

A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.     

Revealing Phosphorus Nitrides up to the Megabar Regime: Synthesis of α′-P3N5, δ-P3N5 and PN2

Non-metal nitrides are an exciting field of chemistry, featuring a significant number of compounds that can possess outstanding material properties. These properties mainly rely on maximizing the number of strong covalent bonds, with crosslinked XN₆ octahedra frameworks being particularly attractive. In this study, the phosphorus–nitrogen system was studied up to 137 GPa in laser-heated diamond anvil cells, and three previously unobserved phases were synthesized and characterized by single-crystal X-ray diffraction, Raman spectroscopy measurements and density functional theory calculations. δ-P₃N₅ and PN₂ were found to form at 72 and 134 GPa, respectively, and both feature dense 3D networks of the so far elusive PN₆ units. The two compounds are ultra-incompressible, having a bulk modulus of K₀=322 GPa for δ-P₃N₅ and 339 GPa for PN₂. Upon decompression below 7 GPa, δ-P₃N₅ undergoes a transformation into a novel α′-P₃N₅ solid, stable at ambient conditions, that has a unique structure type based on PN₄ tetrahedra. The formation of α′-P₃N₅ underlines that a phase space otherwise inaccessible can be explored through materials formed under high pressure.     

Electric-field-induced symmetry breaking of angular momentum distribution in atoms

We report the experimental observation of alignment to orientation conversion in the 7D3/2 and 9D3/2 states of Cs in the presence of an external dc electric field and without the influence of magnetic fields or atomic collisions. Initial alignment of angular momentum states was created by two-step excitation with linearly polarized laser radiation. The appearance of transverse orientation of angular momentum was confirmed by the observation of circularly polarized light. We present experimentally measured signals and compare them with the results of a detailed theoretical model based on the optical Bloch equations. The effect is odd under time reversal and should be taken into account in ever more sensitive searches for an electron electric dipole moment.     

The adsorption of a substituted benzene,the ethynyl-trifluoro-toluene on Si(100)-2 × 1

The adsorption of 3-ethynyl-trifluoro-toluene (ETFT) on Si(100)-2 × 1 surface in ultra high vacuum is studied in the low coverage regime, through a joint experimental and theoretical approach. The STM images of both filled and empty states revealed few distinct adsorption configurations. On the basis of Density Functional Theory (DFT) calculations the STM images were simulated and three main adsorption configurations were identified, with a predominance of di-sigma bonded species that leave the benzene ring unreacted. A discussion of the reactivity of the reconstructed silicon surface towards benzene derivatives is proposed by comparing the adsorption of ETFT close related molecules, like styrene and phenylacetylene.     

Chern–Simons,Wess–Zumino and other cocycles from Kashiwara–Vergne and associators

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as \(p= \langle F, F\rangle \) where F is the curvature 2-form and \(\langle \cdot , \cdot \rangle \) is an invariant scalar product on the corresponding Lie algebra \(\mathfrak g\). The descent for p gives rise to an element \(\omega =\omega _3+\omega _2+\omega _1+\omega _0\) of mixed degree. The 3-form part \(\omega _3\) is the Chern–Simons form. The 2-form part \(\omega _2\) is known as the Wess–Zumino action in physics. The 1-form component \(\omega _1\) is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components \(\omega _1\) and \(\omega _0\). Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara–Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to \(\omega _1=C(F)\). Furthermore, the component \(\omega _0\) is related to the associator \(\Phi \) corresponding to F. It is surprising that while F and \(\Phi \) satisfy the highly nonlinear twist and pentagon equations, the elements \(\omega _1\) and \(\omega _0\) solve the linear descent equation.     

High average power large-pitch fiber amplifier with robust single-mode operation

Ytterbium-doped large-pitch fibers with very large mode areas are investigated in a high-power fiber amplifier configuration. An average output power of 294?W is demonstrated, while maintaining robust single-mode operation with a mode field diameter of 62?μm. Compared to previous active large-mode area designs, the threshold of mode instabilities is increased by a factor of about 3.     

On a metric for the class of compact convex sets

A distance function, defined in [12], for the class of compact convex sets inn-space is introduced in a new way, and some of its properties are developed. This concept is compared with some traditional distance functions for convex sets.     

Predictor-corrector algorithm for solvingP *(κ)-matrix LCP from arbitrary positive starting points

A new predictor-corrector algorithm is proposed for solvingP _*(κ)-matrix linear complementarity problems. If the problem is solvable, then the algorithm converges from an arbitrary positive starting point (x ⁰,s ⁰). The computational complexity of the algorithm depends on the quality of the starting point. If the starting point is feasible or close to being feasible, it has -iteration complexity, whereρ ₀ is the ratio of the smallest and average coordinate ofX ⁰ s ⁰. With appropriate initialization, a modified version of the algorithm terminates in O((1+κ)²(n/ρ ₀)L) steps either by finding a solution or by determining that the problem has no solution in a predetermined, arbitrarily large, region. The algorithm is quadratically convergent for problems having a strictly complementary solution. We also propose an extension of a recent algorithm of Mizuno toP _*(κ)-matrix linear complementarity problems such that it can start from arbitrary positive points and has superlinear convergence without a strictly complementary condition. The work of this author was supported in part by NSF, Grant DMS 9305760 and by an Oberman fellowship from the University of Iowa Center for Advanced Studies.