The fracture energy of materials under pulse microsecond-scale loading

Based on the results of fracture in polymethyl methacrylate and a spheroplastic using a magnetic-pulse setup, the specific work of the formation of a new surface is estimated, which is similar to Griffith’s surface energy for quasi-static tests. The value obtained is greater than the corresponding value determined from the quasi-static tests by an order of magnitude and tends to increase as the loading time decreases.     

Dihalodimethyltin(IV) complexes of 2‐(pyrazol‐1‐ylmethyl)pyridine

Reaction of dichloro‐ and dibromodimethyltin(IV) with 2‐(pyrazol‐1‐ylmethyl)pyridine (PMP) afforded [SnMe₂Cl₂(PMP)] and [SnMe₂Br₂(PMP)] respectively. The new complexes were characterized by elemental analysis and mass spectrometry and by IR, Raman and NMR (¹H, ¹³C) spectroscopies. Structural studies by X‐ray diffraction techniques show that the compounds consist of discrete units with the tin atom octahedrally coordinated to the carbon atoms of the two methyl groups in a trans disposition (Sn? C = 2.097(5), 2.120(5) Å and 2.110(6), 2.121(6) Å in the chloro and in the bromo compounds respectively), two cis halogen atoms (Sn? Cl = 2.4908(16), 2.5447(17) Å; Sn? Br = 2.6875(11), 2.7464(9) Å) and the two donor atoms of the ligand (Sn? N = 2.407(4), 2.471(4) Å and 2.360(5), 2.455(5) Å). In both cases, the Sn? N(pyridine) bond length is markedly longer than the Sn? N(pyrazole) distance. Copyright © 2003 John Wiley & Sons, Ltd.     

Temperature jump induction of isomerization dynamics of alkali halide clusters

The time resolved dynamics of diffusionless cube → ring isomerization of the Na₄Cl₄ cluster was interrogated by constant energy molecular dynamics simulations, utilizing the first passage time method. The nonreactive isomerization induced by nonselective vibrational excitation is well accounted for in terms of the statistical RRK theory, opening avenues for experimental exploration of time-resolved cluster isomerization dynamics.     

Synthesis of 5-azaadenine derivatives from N-(1,2,4-triazol-5-yl)amidines

A method is proposed for the synthesis of N-substituted 5-azaadenines. The condensation of N-(1,2,4-triazol-5-yl)amidines with trichloroacetonitrile gives trichloromethyl derivatives of 1,2,4-triazolo[1,5-a]-1,3,5-triazines, which are converted by the action of primary or secondary amines into N-alkylamino- or N,N-dialkylamino-1,2,4-triazolo-[1,5-a]-1,3,5-triazines (5-azaadenines).Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 241–243, January, 1991.     

Smooth Frame-Path Termination for Higher Order Sigma-Delta Quantization

We study the performance of finite frames for the encoding of vectors by applying standard higher-order sigma-delta quantization to the frame coefficients. Our results are valid for any quantizer with accuracy ε > 0 operating in the no-overload regime. The frames under consideration are obtained from regular sampling of a path in a Hilbert space. In order to achieve error bounds that are comparable to results on higher-order sigma-delta for the quantization of oversampled bandlimited functions, we construct frame paths that terminate smoothly in the zero vector, that is, with an appropriate number of vanishing derivatives at the endpoint.     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The free Malcev superalgebra on one odd generator and related superalgebras

A base of the universal multiplicative envelope of the free Malcev superalgebra ℳ on one odd generator is constructed. Some corollaries for skew-symmetric functions and central elements in free Malcev and free alternative algebras are obtained. Moreover, a base of the Poisson-Malcev superalgebra of ℳ is constructed. As a corollary, a set of elements that spans the free alternative superalgebra on one odd generator is obtained. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 97–106, 2004.     

Inhomogeneous configurations of magnetization of ferromagnetic films with biaxial anisotropy

The system of the Landau-Lifshitz equations and magnetostatic equations for a ferromagnetic film with biaxial anisotropy and a Q-factor smaller than unity is reduced to a single scalar equation for the magnetostatic potential. Such a procedure is possible if the magnetization modulation scale in the sample considerably exceeds the characteristic magnetic length. The solutions to this equation describing inhomogeneous periodic magnetic configurations are obtained. The energy analysis of these configurations is carried out.     

Instability of Bose-Einstein condensates moving in optical lattices

We investigate the Landau damping of Bogoliubov excitations in a dilute Bose gas moving in an optical lattice at a finite temperature. Using a 1D tight-binding model, we explicitly obtain the Landau damping rate, the sign of which determines the stability of the condensate. We find that the sign changes at a certain velocity, which is exactly the same as the critical velocity determined by the Landau criterion of superfluidity. This coincidence reveals the microscopic mechanism of the Landau instability.     

Identification of dislocations and their influence on the recombination of charge carriers in gallium nitride

The relation between the density of etch pits revealed in GaN by etching in a KOH/NaOH eutectic and the density of dislocations determined by transmission electron microscopy (TEM) is studied along with the relation between the density of dislocations and the density of dark spot defects observed in GaN by microcathodoluminescence (MCL) and electron-beam-induced current (EBIC). It is demonstrated that selective etching is a reliable rapid method for the determination of the type and density of dislocations in GaN in the range 10⁶–10⁸ cm^?2, while MCL and EBIC can be used for the rapid nondestructive determination of the density of dislocations in the range 10⁶–10⁸ cm^?2. It is also found that some deep electron and hole traps are related to dislocations.