Mutually induced variations in dissipation and elasticity for oscillations in hysteretic materials: non-simplex interaction regimes

Self-action and effects mutually induced by oscillations interacting in hysteretic media are investigated analytically and numerically. Special attention is paid to non-simplex processes for which presence of intermediate extrema results in appearance of minor nested loops inside the main hysteretic stress-strain loop. Non-simplex regimes are typical of interaction of excitations having different frequencies and amplitudes, but comparable strain rates. It is found that, due to transition between the regimes, frequency and amplitude dependencies of the variations in elasticity and dissipation induced by one wave for another one may become non-monotonous. Either additional dissipation or induced transparency may occur in different regimes. The results obtained are important for correct interpretation of experimental data on nonlinear acoustic interactions in rocks and many other microstructured (mesoscopic) solids that are known to exhibit elastic hysteresis and memory properties.     

P-Matrix and J-Matrix Approaches: Coulomb Asymptotics in the Harmonic Oscillator Representation of Scattering Theory

The relation between the R- and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent to the usual P-matrix in the quasiclassical limit. A definition of the natural channel radius is introduced. As a result, it is shown to be possible to use a well-developed technique of R- and P-matrix theory for calculation of resonant states characteristics, scattering phase shifts, etc., in the approaches based on harmonic oscillator expansions, e.g., in nuclear shell-model calculations. The P-matrix is used also for formulation of the method of treating Coulomb asymptotics in the scattering theory in oscillator representation.     

Sapphire shaped crystals for waveguiding,sensing and exposure applications

Second half of the XX century was marked by a rapid development of sapphire shaped crystal growth technologies, driven by the demands for fast, low-cost, and technologically reliable methods of producing sapphire crystals of complex shape. Numerous techniques of shaped crystal growth from a melt have been proposed relying on the Stepanov concept of crystal shaping. In this review, we briefly describe the development of growth techniques, with a strong emphasize on those that yield sapphire crystals featuring high volumetric and surface quality. A favorable combination of physical properties of sapphire (superior hardness and tensile strength, impressive thermal conductivity and chemical inertness, high melting point and thermal shock resistance, transparency to electromagnetic waves in a wide spectral range) with advantages of shaped crystal growth techniques (primarily, an ability to produce sapphire crystals with a complex geometry of cross-section, along with high volumetric and surface quality) allows fabricating various instruments for waveguiding, sensing, and exposure technologies. We discuss recent developments of high-tech instruments, which are based on sapphire shaped crystals and vigorously employed in biomedical and material sciences, optics and photonics, nuclear physics and plasma sciences.     

Robust diode-end-pumped Nd:GdVO4 laser passively mode-locked with saturable output coupler

Passively mode-locked diode-pumped solid-state (DPSS) Nd:GdVO₄ laser by using a saturable output coupler (SOC) in stable two-mirror linear cavity design is demonstrated. The laser was pumped by low-power single laser diode without any active cooling and external optics. Robust CW mode-locked operation was obtained with a repetition of 150–250 MHz, the pulsewidth was 12 ps, the lowest threshold for CW mode-locked was 185 mW. The optimal condition is found when the laser provides the set of characteristics: low CW mode-locking threshold (～260 mW), compact size (total cavity length 60 cm), good efficiency (～20%), and very stable output. At the output power of 270 mW an average power fluctuations within ±2% for long-term operation was obtained.     

5‐Amido‐ and 5‐Amino‐Substituted Epoxyisoindolo[2,1‐a]tetrahydroquinolines and 10‐Carboxylic Acids: Their Synthesis and Reactivity

The interactions between 4‐R‐substituted 2‐furyl‐1,2,3,4‐tetrahydroquinolines (synthesized by the Povarov reaction) and a number of alkenes have been investigated. Maleic, dibromomaleic, dichloromaleic, and citraconic anhydrides, as well as acryloyl, methacryloyl, crotonyl, and cynnamoyl chlorides were used as alkene components. It was shown that the initial N‐acylation of the tetrahydroquinolines was followed by a spontaneous [4+2]‐cycloaddition of an N‐acryloyl substituent to the furan ring. It was established that the intramolecular Diels–Alder reaction of furans is reversible, occurs stereoselectively as exo‐addition, and led to target epoxyisoindolo[2,1‐a]tetrahydroquinolines with moderate yields. Oxidation and aromatization of the synthesized products were carried out.     

Electrical transport and magnetic ordering in R 2Ti3Ge4 (R=Dy, Ho and Er) compounds

New R ₂Ti₃Ge₄ (R=Dy, Ho and Er) intermetallic compounds have been synthesized and characterized by X-ray diffraction and low temperature ac magnetic susceptibility, electrical resistivity and thermoelectric power measurements were carried out. The compounds crystallize in the parent, Sm₅Ge₄-type orthorhombic structure (space group Pnma) and lanthanide contraction is observed as one moves along the rare-earth series. The changeover from paramagnetic to antiferromagnetic phase happens at low temperatures and the ordering temperature scales with the de Gennes factor. The electrical resistivity is metallic with a negative curvature above 100 K. Thermopower displays a weak maximum at temperatures less than 50 K signifying the possible phonon and magnon drag effects.     

One-pot synthesis of functionalized piperid-4-ones: a four-component condensation

The one-pot synthesis of highly substituted piperid-4-ones has been achieved. Diketene is added to a tosyl imine in the presence of TiCl(4) and MeOH, followed by 1 equiv of aldehyde to generate 2,6-disubstituted nonsymmetrical piperid-4-ones as a mixture of cis-/trans-diastereomers in good yields. This mixture of diastereomers can be converted to a single 2,6- cis-diastereomer by epimerization with K(2)CO(3).     

Description of the continuous spectrum of a three-body Coulomb system within the <Emphasis Type="Italic">J</Emphasis>-matrix approach

The contribution of the continuous spectrum of two-body Coulomb sybsystems to reaction matrix elements is studied. The respective Faddeev-Merkuriev differential equations are solved within the J-matrix approach. The differential cross sections for the double ionization of a helium atom by a direct electron impact is calculated by way of example. The results agree well with experimental data both in shape of the cross sections and in magnitude.