Synthesis and Crystal Structure of Fluoride K2(Ta0.9I0.1)F7 with the Micro-Isomorphic Substitution in the Ta Cationic Position

Crystallography Reports - Fluoride crystals K2(Ta0.9I0.1)F7 (sp. gr. Р21/c) complementary to the K2TaF7 and K2NbF7 fluoride family have been obtained by hydrothermal synthesis. Their...     

Synthesis and Crystal Structure of New Indium Iodate (K<Subscript>0.6</Subscript>Na<Subscript>0.4</Subscript>Ba)In[IO<Subscript>3</Subscript>]<Subscript>6</Subscript>

Crystals of new indium iodate (K_0.6Na_0.4Ba)In[IO₃]₆ were prepared by the hydrothermal synthesis. The unit-cell parameters are a = 11.3984(3) Å, с = 11.3817(3) Å, sp. gr. R3?. The chemical formula of the compound was derived from the structure determination and refinement with anisotropic displacement parameters to R = 0.0284. In the structure the InO₆ octahedra share vertices with six umbrella-like [IO₃]–groups typical of iodates and form isolated 3?-symmetric charged \(\rm{In[IO_{3}]_6^{3-}}\) clusters. Large Ba, K, and Na cations occupy a common site on a threefold axis due to the isomorphous substitution and compensate the charge of the clusters. The new structure extends the family of the recently discovered alkali-metal and barium iodates containing Ti and Zr atoms in octahedral sites. The iodate K₂Ge[IO₃]₆ containing Ge atoms in the centers of octahedra is the parent compound of this structural family.     

Single-Crystal Synthesis and Structures of Rb-Boroleucite Rb(BSi2)O6 and Boropollucite Cs(BSi2)O6 at 293 and 120 K

Crystallography Reports - The structures of Rb-boroleucite Rb1.0(B0.333Si0.667)3O6 and boropollucite Cs0.87(B0.290Si0.710)3O6 were studied using single crystals, which were prepared under...     

Aromatic and Antiaromatic Pathways in Triphyrin(2.1.1) Annelated with Benzo[b]heterocycles

Understanding of the aromatic properties and magnetically induced current densities of highly conjugated chromophores is important when designing molecules with strongly delocalized electronic structure. Linear extension of the triphyrin(2.1.1) skeleton with an annelated benzo[b]heterocycle fragment modifies the aromatic character by extending the electron delocalization pathway. Two-electron reduction leads to an antiaromatic triphyrin(2.1.1) ring and an aromatic benzo[b]heterocycle subunit. Current-density calculations provide detailed information about the observed pathways and their strengths.     

Interchange-turbulence-based radial transport model for SOLPS-ITER: A COMPASS case study

Mean-field plasma edge transport codes such as SOLPS-ITER heavily rely on ad-hoc radial diffusion coefficients to approximately model anomalous transport. Such coefficients are experimentally determined and vary between different machines, and also depend on the operational regime and plasma location within the same device. Therefore, to match experimental data the modeller is required to manually tune several free parameters in expensive simulations, and the code's predictive capabilities are significantly downgraded. As a solution, a new model has been developed for SOLPS-ITER, solving an additional transport equation for the turbulent kinetic energy k, derived by consistently time-averaging the Braginskii equations, and including a diffusive closure for the anomalous particle flux. This closure model relates the anomalous diffusion coefficient to the local k value. The resulting equation structure and its closure are inspired by TOKAM2D isothermal interchange turbulence simulation results. Within this model, fewer and hopefully more universal free parameters are retained, thus improving the code's predictive capabilities. The new model has been tested on a COMPASS case for which upstream plasma profiles were available. Experimental data and a reference solution, obtained by matching the profiles through manual tuning of radial diffusivities, have been used to estimate the parameters of our new transport model. A ballooned particle diffusivity profile is retrieved by the new radial transport model, thanks to the proposed interchange drive. The obtained upstream profiles qualitatively agree with the experiment and prove the new model is a promising first attempt to be further refined.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Contribution of the surface dipole moment and the contact potential-induced disjoining pressure to the stress balance at a three-phase contact

The contact between three insulators results in a set up of contact potentials related to the adsorbed dipole moment at each surface. The produced electric field applies force (disjoining pressure) on each interface. This disjoining pressure is a long-ranged force (1/distance²) which is proportional to the difference between the dielectric permittivities of the phases on the two sides of the interface and, for small angles, to the square of the contact angle. The contact potential leads to a logarithmic perturbation of the profile of the three-phase contact zone.     

An Anionic Amido-Substituted Seven-Vertex Siliconoid Cluster

The silanide [Si₄{N(SiMe₃)Dipp}₃]⁻ ( 1 ) transforms into the anionic siliconoid cluster [Si₇{N(SiMe₃)Dipp}₃]⁻ ( 2 ) with four unsubstituted silicon atoms as a contact ion pair with [K([18]crown-6)] in C₆D₆ at room temperature within five weeks. Anion 2 was investigated by natural population analysis and visualization of intrinsic atomic orbitals. Magnetically induced current-density calculations of 2 revealed two distinct strong diatropic vortices that sum up in one direction and create a strongly shielded apical silicon atom in 2 .     

Existence and Asymptotic Behavior of Positive Solutions of Neutral Impulsive Differential Equations

In this article, we consider first-order neutral impulsive differential equations with constant coefficients and constant delays. We study the asymptotic behavior of eventually positive solutions of these equations and establish necessary and sufficient conditions for the existence of such solutions. __________ Published in Neliniini Kolyvannya, Vol. 8, No. 3, pp. 304–318, July–September, 2005.     

On the maximal regular subsemigroups of ideals of order-preserving or order-reversing transformations

We characterize the maximal regular subsemigroups of the ideals of the semigroup of all order-preserving transformations as well as of the semigroup of all order-preserving or order-reversing transformations on a finite ordered set.