Minimum dissipative relaxed states in toroidal plasmas

Relaxation of toroidal discharges is described by the principle of minimum energy dissipation together with the constraint of conserved global helicity. The resulting Euler-Lagrange equation is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar-Kendall (C-K) eigenfunctions analytically continued in the complex domain. The C-K eigenfunctions are obtained as hypergeometric functions that are solutions of scalar Helmholtz equation in toroidal coordinates in the large aspect-ratio approximation. Equilibria are constructed by assuming the current to vanish at the edge of plasma. For the m=0, n=0 (m and n are the poloidal and toroidal mode numbers respectively) relaxed states, the magnetic field, current, q (safety factor) and pressure profiles are calculated for a given value of aspect-ratio of the torus and for different values of the eigenvalue λ _{r 0}. The new feature of the present model is that solutions allow for both tokamak as well as RFP-like behaviour with increase in the values of λ _{r 0}, which is related directly to volt-sec in the experiment.     

Synthesis, crystal and molecular structures, and steroechemical nonrigidity ofN-(chlorodimethylgermylmethyl)-andN-(bromodimethylgermylmethyl)-N-[(S)-1-phenylethyl]acetamides andN-(chlorodimethylgermylmethyl)-4-phenyl-2-pyrrolidone

RacemicN-(chlorodimethylgermylmethyl)-4-phenyl-2-pyrrolidone and the first optically active amide derivatives containing the asymmetrical carbon atom and the five-coordinate germanium atom,viz.,N-(chlorodimethylgermylmethyl)- andN-(bromodimethylgermyl-methyl)-N-[(S)-1-phenylethyl] acetamides, were synthesized. Their structures were established by X-ray diffraction analysis. The geometric characteristics of the trigonal-bipyramidal valence environment about the germanium atoms are compared with those of analogous enantiomeric silicon compounds and the related five-coordinate germanium compounds. The barriers to permutational isomerization of the title compounds were determined by dynamic¹H NMR spectroscopy. It was found that these barriers are higher than those of the corresponding silicon analogs. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 137–144, January, 2000.     

Mechanical stress affects glucagon fibrillation kinetics and fibril structure

Mechanical stress can strongly influence the capability of a protein to aggregate and the kinetics of aggregation, but there is little insight into the underlying mechanism. Here we study the effect of different mechanical stress conditions on the fibrillation of the peptide hormone glucagon, which forms different fibrils depending on temperature, pH, ionic strength, and concentration. A combination of spectroscopic and microscopic data shows that fibrillar polymorphism can also be induced by mechanical stress. We observed two classes of fibrils: a low-stress and a high-stress class, which differ in their kinetic profiles, secondary structure as well as morphology and that are able to self-propagate in a template-dependent fashion. The bending rigidity of the low-stress fibrils is sensitive to the degree of mechanical perturbation. We propose a fibrillation model, where interfaces play a fundamental role in the switch between the two fibrillar classes. Our work also raises the cautionary note that mechanical perturbation is a potential source of variability in the study of fibrillation mechanisms and fibril structures.     

Quantum-Chemical Study of Electronic and Steric Structure of Vinyltetrazoles: I. 2-Substituted 5-Vinyltetrazoles

The total Mulliken charges on the carbon atoms of the vinyl group, populations of S-trans-(N¹)conformers, and internal rotation energies were calculated ab initio (HF/6-31G**, MP2/6-31G**, and MP2/6-31G**//AM1) for a series of 2R-5-vinyltetrazoles (R = CH₃, C₂H₅, i-C₃H₇, t-C₄H₉, C₆H₅). The calculation results were compared to the available experimental data.     

Trichloro- and methyldichlorogermyl monochelates and dibromo- and dichlorogermyl bischelates derived from N,N-disubstituted amides of 2-hydroxycarboxylic acids

The reactions of GeCl₄, GeBr₄, and MeGeCl₃ with O-trimethylsilyl derivatives of N,N-disubstituted amides of 2-hydroxycarboxylic acids afforded pentacoordinate and hexacoordinate neutral (O,O)-mono- and (O,O)-bischelates. The reactions of glycolic acid derivatives with GeX₄ produced bischelates X₂Ge[OCH₂C(O)NR²R³]₂ 7a,c,d (X = Cl, R² = R³ = Me (a), (CH₂)₅ (c), (CH₂CH₂)₂O (d)) and 8a (X = Br). By contrast, the reactions of lactic and mandelic acid derivatives with GeCl₄ and MeGeCl₃ gave monochelates Cl₃Ge[OCH(R¹)C(O)NR²R³] (S)-9a–c (R¹ = Me) and Cl₂MeGe[OCH(R¹)C(O)NR²R³] 10a (R¹ = H), (S)-11a,b (R¹ = Me), and (S)-12a (R¹ = Ph) (R²R³ = (CH₂)₄ (b)), respectively. According to the X-ray diffraction data, the Ge atom in bischelates 7c,d and 8a has a coordination number 6, and its coordination polyhedron can be described as a slightly distorted octahedron. In monochelates (S)-9a-c, 10a, (S)-11a,b, and (S)-12a, the Ge atom has a coordination number 5, and its coordination polyhedron can be described as a trigonal bipyramid with two halogen atoms or one halogen atom and one ethereal oxygen atom in equatorial positions and the halogen atom and the amide oxygen atom in the axial positions. The bonds in the axial positions are somewhat longer than the corresponding bonds in tetracoordinate Ge compounds.     

Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl 3,0

First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions Third, we show a set of important properties of the Clifford Fourier transform on Cl_3,0 such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for Cl_3,0 multivector functions.     

Bis(O--Si)-chelate fluorobis(2-oxohexahydroazepinomethyl)silylium tetrafluoroborate,a cation-anionic complex containing a silylium ion stabilized by O→Si coordination

Russian Chemical Bulletin -     

Synthesis and structural features of new pentacoordinated monofluorosilanes containing C,O-chelate ligands based on 2-amino acid N-methylamides

Russian Chemical Bulletin - Pentacoordinated monofluorosilanes R1SO2NHCHR2C(O)N(Me)CH2SiMe2F containing moieties of N′-methyl-N-(organosulfonyl)-2-amino acid amides of glycine, alanine, and...