Dynamic stability of a spiral domain in an ac magnetic field

The dependence of the stability of a magnetic spiral domain in a film on the parameters of the film and its domain structure and on an external magnetic field is considered within a phenomenological model. The model allows one to explain a number of experimentally observed properties of dynamic spiral domains resulting from the process of self-organization of domains and domain walls in an iron-garnet film placed in an external ac magnetic field.     

Gravitation as Anholonomy

A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenböck connection. In a tetrad frame, that torsion is just the anholonomy of that frame. The infinitely many tetrad fields taking the Lorentz metric into a given Riemannian metric differ by point-dependent Lorentz transformations. Inertial frames constitute a smaller infinity of them, differing by fixed-point Lorentz transformations. Holonomic tetrads take the Lorentz metric into itself, and correspond to Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and sees the electromagnetic field strength with an additional term.     

A theoretical analysis of the TiO2/Sn doped (1 1 0) surface properties

We have used the periodic quantum-mechanical method with density functional theory at the B3LYP level in order to study TiO₂/Sn doped (1 1 0) surfaces and have investigated the structural, electronic and energy band properties of these oxides. Our calculated relaxation directions for TiO₂ is the experimental one and is also in agreement with other theoretical results. We also observe for the doped systems relaxation of lattice positions of the atoms. Modification of Sn, O and Ti charges depend on the planes and positions of the substituted atoms. Doping can modify the Fermi levels, energy gaps as well as the localization and composition of both valence and conduction band main components. Doping can also modify the chemical, electronic and optical properties of these oxides surfaces increasing their suitability for use as gas sensors and optoelectronic devices.     

Numerical solution of the Monge–Ampère equation by a Newton's algorithm

We solve numerically the Monge–Ampère equation with periodic boundary condition using a Newton's algorithm. We prove convergence of the algorithm, and present some numerical examples, for which a good approximation is obtained in 10 iterations. To cite this article: G. Loeper, F. Rapetti, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

catena‐Poly[tetra­kis(3‐phenyl­propyl­ammonium) [iodo­plumbate(II)‐tri‐μ‐iodo‐plumbate(II)‐tri‐μ‐iodo‐iodo­plumbate(II)‐di‐μ‐iodo]]

The title compound, {(C₉H₁₄N)₄[Pb₃I₁₀]}_n, crystallizes as an organic–inorganic hybrid. As such, the structure consists of a two‐dimensional inorganic layer of [Pb₃I₁₀]_n⁴ⁿ⁻ ions extending along [100]. The asymmetric unit contains two independent Pb atoms, viz. one in a general position and the other on an inversion centre. Each Pb atom is octa­hedrally coordinated by six iodide ions and exhibits both face‐ and corner‐sharing with adjacent atoms in the inorganic layer. These anionic layers alternate with 3‐phenyl­propyl­ammonium cations, which hydrogen bond to the iodides. Simple face‐to‐edge σ–π stacking inter­actions are observed between the aromatic rings that stabilize the overall three‐dimensional structure. This net structure has only been observed five times previously.     

Statistical theory for hydrogen bonding fluid system of A a D d type (I): The geometrical phase transition

The influence of hydrogen bonds on the physical and chemical properties of hydrogen bonding fluid system of A _a D _d type is investigated from two viewpoints by the principle of statistical mechanics. In detail, we proposed two new ways that can be used to obtain the equilibrium size distribution of the hydrogen bonding clusters, and derived the analytical expression of a relationship between the hydrogen bonding free energy and hydrogen bonding degree. For the nonlinear hydrogen bonding systems, it is shown that the sol-gel phase transition can take place under proper conditions, which is further proven to be a kind of geometrical phase transition rather than a thermodynamic one. Moreover, several problems associated with the geometrical phase transition and liquid-solid phase transition in nonlinear hydrogen bonding systems are discussed.     

A microspectroscopic study of the electronic homogeneity of ordered and disordered Sr2FeMoO6

Disordered Sr₂FeMoO₆ shows a drastic reduction in saturation magnetization compared to highly ordered samples, moreover magnetization as a function of the temperature for different disordered samples shows qualitatively different behaviours. We investigate the origin of such diversity by performing spatially resolved photoemission spectroscopy on various disordered samples. Our results establish that e_xtensive electronic inhomogeneity, arising most probably from an underlying chemical inhomogeneity in disordered samples, is responsible for the observed magnetic inhomogeneity. It is further pointed out that these inhomogeneities are connected with composition fluctuations of the type Sr₂Fe_1+x Mo_1-x O₆ with Fe-rich (x > 0) and Mo-rich (x < 0) regions. Dedicated to Prof J Gopalakrishnan on his 62nd birthday.     

Recyclization of Products Formed by Addition of 5-Hydrazino-2-phenyl-1,3-oxazoles Functionally Substituted in 4-Position to Aryl Isothiocyanates

Russian Journal of General Chemistry -     

Steepest Descent, CG, and Iterative Regularization of Ill-Posed Problems

The state of the art iterative method for solving large linear systems is the conjugate gradient (CG) algorithm. Theoretical convergence analysis suggests that CG converges more rapidly than steepest descent. This paper argues that steepest descent may be an attractive alternative to CG when solving linear systems arising from the discretization of ill-posed problems. Specifically, it is shown that, for ill-posed problems, steepest descent has a more stable convergence behavior than CG, which may be explained by the fact that the filter factors for steepest descent behave much less erratically than those for CG. Moreover, it is shown that, with proper preconditioning, the convergence rate of steepest descent is competitive with that of CG.This revised version was published online in October 2005 with corrections to the Cover Date.