Approximate radial functions

The approximate 4s and 3d radial wavefunctions of Richardsonet al. [J, chem. Physics 36, 1057 (1962)] for first-row transition-metal atoms and ions have been extended to additional electronic configurations. The results suggest several improvements in the 4s wavefunction parameters. Formulas are reported for extending the double- 3d wavefunctions over the range of atomic orbitalsd ¹ throughd ¹⁰. The results are intended for use in calculations of chemical bonding.     

Sessions of the Seminar “Algebra i Logika”

Sessions of the seminar algebra i logika     

Conical parametric scattering of a single extraordinary beam in BaTiO3 crystal

In this paper, the parametric scattering of a single extraordinary polarized beam of laser in BaTiO₃ photorefractive crystal has been investigated experimentally and theoretically. The resulting pattern consists of beam fanning, isotropic ring, and anisotropic one. Among all parts of scattering pattern, isotropic ring has not been studied as much as beam fanning and anisotropic ring, and there still are some differences in reports about it. Therefore, the study has mainly focused on this part. In this experimental configuration, isotropic ring is just visible in positive angles although the other parts of parametric scattering pattern can be visible from behind and in front of the crystal. In addition to steady state pattern in forward and backward directions, its transient behavior with the rotation of crystal has been studied. The results of experiments have been analyzed carefully, and their theoretical explanations have been presented based on the standard theory of parametric scattering in photorefractive crystals. It has been shown that this configuration corresponds to the so called parametric B-process scattering.     

General second-order scalar-tensor theory and self-tuning

Starting from the most general scalar-tensor theory with second-order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on Friedmann-Lema?tre-Robertson-Walker backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor, and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincaré invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining nontrivial cosmological solutions.     

Collisions of strings with Y junctions

We study the dynamics of Nambu-Goto strings with junctions at which three strings meet. In particular, we exhibit one simple exact solution and examine the process of intercommuting of two straight strings in which they exchange partners but become joined by a third string. We show that there are important kinematical constraints on this process. The exchange cannot occur if the strings meet with very large relative velocity. This may have important implications for the evolution of cosmic superstring networks and non-Abelian string networks.     

Ionization of aqueous toluic acids: Conductance and thermodynamics

Conductivities of aqueous solutions ofortho-, meta-, andpara-toluic acids have been measured for the concentration range 0.1–2 millimolar and at 5° intervals from 5 to 100°C. At each temperature pK _a(m) andA ₀ have been calculated using the paired ion model recently described by Fuoss. Thermodynamic parameters have been calculated for the ionization of each acid, and Walden products for the anions. Results are discussed in terms of contributions to acidity by enthalpy and entropy changes as well as by hydration of the various solute species.     

Inversion twinning in a second polymorph of the hydrochloride salt of the recreational drug ethylone

A second polymorph of the hydrochloride salt of the recreational drug ethylone, C₁₂H₁₆NO₃⁺·Cl⁻, is reported [systematic name: (±)‐2‐ethylammonio‐1‐(3,4‐methylenedioxyphenyl)propane‐1‐one chloride]. This polymorph, denoted form (A), appears in crystallizations performed above 308 K. The originally reported form (B) [Wood et al. (2015). Acta Cryst. C 71 , 32–38] crystallizes preferentially at room temperature. The conformations of the cations in the two forms differ by a 180° rotation about the C—C bond linking the side chain to the aromatic ring. Hydrogen bonding links the cations and anions in both forms into similar extended chains in which any one chain contains only a single enantiomer of the chiral cation, but the packing of the ions is different. In form (A), the aromatic rings of adjacent chains interleave, but pack equally well if neighbouring chains contain the same or opposite enantiomorph of the cation. The consequence of this is then near perfect inversion twinning in the structure. In form (B), neighbouring chains are always inverted, leading to a centrosymmetric space group. The question as to why the polymorphs crystallize at slightly different temperatures has been examined by density functional theory (DFT) and lattice energy calculations and a consideration of packing compactness. The free energy (ΔG) of the crystal lattice for polymorph (A) lies some 52 kJ mol⁻¹ above that of polymorph (B).