Statistical Theory of the Phonon Drag Force Acting on a Conduction Electron

Within the framework of microscopic fluctuation-dissipation theory, we obtain the stochastic equation describing the Brownian motion of an electron in the phonon field of the crystal lattice. An expression for the Green’s function of the phonon field is found in general form and for the case of linear phonon-variable interaction of an electron with the phonon field with allowance for the potential screening of crystal-lattice nuclei. An expression for the phonon drag acting on a conduction electron in the lattice field is found and analyzed with allowance for the interaction. Frequency dependence of the coefficient of the phonon drag acting on a conduction electron is studied and the contribution of the electron-phonon interaction to the effective mass of a charge carrier is determined.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 3, pp. 249–268, March 2005.     

Evidence for internal resistive barriers in a crystal of the giant dielectric constant material: CaCu3Ti4O12

Complex impedance spectra were obtained on a crystal of CaCu₃Ti₄O₁₂ (CCTO) from 289 to 456 K. As in the case of ceramic CCTO, these spectra can be interpreted as arising from a conducting material containing insulating barriers. This is then further evidence for the existence of planar defects within crystals of CCTO that act as insulating barriers and produce the large dielectric constant through a space charge mechanism.     

Survivability in IP-over-WDM Networks: WDM Lightpath Protection versus IP LSP Protection

This article compares the performance of WDM lightpath protection and IP LSP protection schemes for IP-over-WDM networks. A mathematical formulation of the maximum throughput problem is presented and analytical expressions for recovery time are derived for both schemes. The throughputs and recovery times are analyzed and compared. Results show that the IP LSP protection scheme presents higher throughputs then WDM lightpath protection. The IP LSP protection scheme, providing individual IP LSP protection has, however, scalability problems. This scheme presents high recovery times when a failure affects many lightpaths and many hops are allowed for the primary routes of IP LSPs.     

Closed-form solutions for a rectangular layer with central crack under anti-plane shear stress

We consider the problem of determining the stress distributionin a finite rectangular elastic layer containing a Griffithcrack which is opened by internal shear stress acting alongthe length of the crack. The mode III crack is assumed to belocated in the middle plane of the rectangular layer. The followingtwo problems are considered: (A) the central crack is perpendicularto the two fixed lateral surfaces and parallel to the othertwo stress-free surfaces; (B) all the lateral surfaces of therectangular layer are clamped and the central crack is parallelto the two lateral surfaces. By using Fourier transformations,we reduce the solution of each problem to the solution of dualintegral equations with sine kernels and a weight function whichare solved exactly. Finally, we derive closed-form expressionsfor the stress intensity factor at the tip of the crack andthe numerical values for the stress intensity factor at theedges of the cracks are presented in the form of tables.     

Synthesis, X-ray diffraction study, and ionic conductivity of new AB2O6 pyrochlores

The oxides A(Ti_0.5Te_1.5)O₆ (A = K, Rb, Cs, Tl), A(Ti_0.5W_1.5)O₆ (A = Rb, Cs, Tl), and Cs(B_0.5W_1.5)O₆ (B = Zr, Hf) have been obtained as polycrystalline powders giving X-ray diffraction patterns characteristic of defect cubic pyrochlores, space group (No. 227), Z = 8. The best discrepancy R factors, from 0.0265 for Rb(Ti_0.5Te_1.5)O₆ to 0.0554 for Cs(Zr_0.5W_1.5)O₆, were obtained for the B cations randomly distributed at 16(d), A ions at one quarter of 32(e), and oxygen atoms at 48(f) positions. A linear relationship is observed between the a unit cell parameters and the ionic radii of the A cations, as well as the average ionic radii of the B atoms. The results of electrical resistivity measurements for A(Ti_0.5Te_1.5)O₆ (A = K, Rb, Cs, Tl) are given.     

Reaction of 3,3,3-trifluoropropene-1 with bromoform and methylene bromide

The radical telomerization of 3,3,3-trifluoropropene with bromoform and methylens bromide has been studied. The nature of the products with bromoform depends substantially on the method of initiation. In the presence of Fe(CO)₅ + DMF, telomers of CHBr₂(CH₅₂CHCF₃)_nBr are formed, while with initiation with benzoyl peroxide other compounds are also formed that contain two, three, or four bromine atoms per molecule. To elucidate the formation of these products a reaction scheme is proposed that involves rearrangement of CHBr₂CH₂CH(CF₃)CH₃CHCF₃ radicals to CBr₂CH₂CH(CF₃)CH₂CH₂CF₃ radicals.Deceased.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2558–2562, November, 1989.