Cesium ordering and electron localization-delocalization phenomena in the quasi-one-dimensional diphosphate tungsten bronzes: Cs1‒xP8W8O40

We present a structural investigation of the family of quasi-one-dimensional (quasi-1D) conductors, which exhibit intriguing charge transport properties where, for x small, the conductivity exhibits a crossover from a semiconducting to a metallic like regime when the temperature decreases. In these materials the double zig-zag chains, together with the diphosphate groups, delimit channels which are partially filled with the ions. It is found, from an X-ray diffuse scattering investigation, that at room temperature the ions are locally ordered on a lattice of well-defined sites in the channel direction and not ordered between neighboring channels. These ions form 1D incommensurate concentration waves whose periodicity depends on the stoichiometry. In upon cooling, the intrachannel order increases significantly, and an interchannel order between the 1D concentration waves develops. But, probably because of kinetic effects, no tridimensional (3D) long range order of the ions is achieved at low temperature. The 3D low-temperature local order has been determined and it is found that the phase shift between the concentration waves minimizes their Coulomb repulsions. This local order is increasingly reduced as the Cs concentration diminishes. We interpret the intriguing features of the electrical conductivity in relationship with the thermal evolution of the Cs ordering effects. We suggest that in , for x small, a localization-delocalization transition of the Anderson type occurs due to the thermal variation of the Cs disorder. When x increases, the enhancement of the disorder leads to a localization of the electronic wave function in the whole temperature range measured. Finally, and probably because of the disorder, no charge density wave instability is revealed by our X-ray diffuse scattering investigation. Received: 10 October 1997 / Received in final form: 11 December 1997 / Accepted: 16 December 1997     

Undecidability of the elementary theory of groups of measure-preserving transformations

The undecidability of the elementary theory of the automorphism group for a Lebesgue space is proved. It is shown that arithmetic can be interpreted in this theory. The technique of proof can be carried over to certain other groups. Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 414–420, March, 1998. The author wishes to thank the participants of the seminar on dynamical systems headed by D. V. Anosov, R. I. Grigorchuk, and A. M. Stepin as well as the participants of the Kolmogorov seminar of the Mechanics and Mathematics Department of Moscow State University for discussion of this work. The author is also indebted to N. K. Vereshchagin and A. M. Stepin for support and valuable remarks as well as to V. V. Ryzhikov for setting the problem and for his assistance.     

Synthesis of Al–Cr decagonal quasicrystal nanoparticles and their temperature of phase transformation to stable crystal phase

The synthesis of Al–Cr single quasicrystal (QC) nanoparticles of the decagonal phase was achieved by introducing an advanced gas flow evaporation method. By obtaining successive electron diffraction patterns for single-QC nanoparticles, the phase transformation temperature of a single-QC nanoparticle was determined to be 700 °C. It was also determined that part of the QC nanoparticle decomposed into hex-Al₈Cr₅ and Al during the phase transformation. Since the grain growth did not occur during the phase transformation in the present experiment, the inherent phase transformation temperature could be measured.     

The use of DSC in describing the structure evolution of an AlZnMg alloy

Summary The potential of DSC in suggesting modifications of thermal treatments of Al alloys to increase mechanical properties is described. Significant results can be obtained from calorimetric evolution after a series of annealings, even without a direct observation of the microstructure. The role of a reference baseline is discussed. The Guinier-Preston (GP) zones formation, dissolution or transformation is followed, and their relevance for the microhardness increase is shown, for an AlZnMg alloy of technical interest. Multi-stage thermal treatments have been confirmed to be beneficial. A secondary precipitation occurs at room temperature after annealing at temperatures at which primary precipitation is almost complete.     

Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model

A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.     

Normal forms of quadratic bose operators

We construct a proper canonical transformation that reduces the quadratic Bose operator to a direct sum of finite-dimensional quadratic operators each of which can be reduced by a finite-dimensional canonical transformation to one of the standard forms corresponding to the standard forms of real quadratic Hamiltonians. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 69–90, January, 1997.     

Bounds for the expectation of the kth root of a random variable

Exact bounds for the mean value of a fractional moment, such as the sample standard deviation, are considered. These bounds are compared with those found by summation techniques applied to computer extended series. An expansion involving an arbitrary parameter is introduced, and now best bounds are found by optimization. There are applications to bounds for a certain class of quadrature problem.     

Backlund Transformation and Exact Solution to Kadomtsev-Petviashvili Equation with Variable Coefficients

By using the homogeneous balance principle, we derive a Backlund transformation (BT) to (3+1)-dimensionaI Kadomtsev-Petviashvili (K-P) equation with variable coefficients if the variable coefficients are linearly dependent. Based on the BT, the exact solution of the (3+1)-dimensional K-P equation is given. By the same method, we derive a BT and the solution to (2+1)-dimensional K-P equation. The variable coefficients can change the amplitude of solitary wave, but cannot change the form of solitary wave.     

The effect of stiffness in wormlike micelles

The effect of stiffness in a 2D living polymer system is investigated by Monte-Carlo simulation in a canonical ensemble. As the flexibility decreases, the mean chain contour length decreases and goes through a local maximum. The mean end to end square distance shows a non-monotonic behaviour due to the coil-to-rod transition and the decrease in chain contour length. Near the maximum of chain ordering in the bulk, the chain length distribution adapts itself to increase the configurational entropy. With the parameters used in this simulation, it seems that the effect of the stiffness for high stiffness is to decrease as in the isotropic case, since the ordering decreases again. Received: 16 September 1997 / Revised: 27 June 1998 / Accepted: 29 June 1998     

On the classical solution of SO(3) gauge theory and ’t Hooft-Polyakov monopole

It is shown that the ansatz for the asymptotic (r → ∞) gauge fields used by ’t Hooft in the study of monopoles in SO(3) electroweak theory is not unique.