Perturbations of solutions of the sinorini problem for a second-order scalar equation

Translated from Matematicheskie Zametki, Vol. 47, No. 1, pp. 115–126, January, 1990.     

The Essence of “Black Holes” for Elastic Waves in Solids with Cuspidal Sharpening

Doklady Physics - The effect of a “black hole” for elastic waves, discovered by M.A. Mironov and examined in detail by followers, is usually associated with propagation of elastic waves...     

ChemInform Abstract: A New n = 4 Layered Ruddlesden—Popper Phase K2.5Bi2.5Ti4O13 Showing Stoichiometric Hydration.

Polycrystalline K_2.5Bi_2.5Ti₄O₁₃ (I) is prepared by solid state reaction of KNO₃, Bi₂O₃, and TiO₂ (Al₂O₃ crucible, 750 °C, 16 h).     

ChemInform Abstract: YCa3(CrO)3(BO3)4: A Cr3+ Kagome Lattice Compound Showing No Magnetic Order Down to 2 K.

Polycrystalline gaudefroyite‐type YCa₃(CrO)₃(BO₃)₄ with Cr³⁺ ions (3d³, S = 3/2) forming an undistorted Kagome lattice is prepared by reaction of a stoichiometric mixture of Y₂O₃, CaCO₃, Cr₂O₃, H₃BO₃ in a KCl flux (Al₂O₃ crucible, 1000 °C, 1 d) followed by re‐grinding and further annealing (1000 °C, 2 d, 95% yield).     

Use of the energy criterion of fracture to determine the shape of a slightly curved crack

An asymptotic formula is obtained for the total-energy increment during quasistatic growth of a semiin finite crack in an anisotropic elastic plane under complex loading. It is assumed that the shear loads are much larger than the tearing loads. The shape of the slightly curved crack was determined using the Griffith criterion in two versions: global and local. It is shown, in particular, that the first version leads to an improbable result. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 119–130, September–October, 2006.     

Cospectral polymers: Differentiation via semiflexibility

We consider polymer structures which are known in the mathematical literature as "cospectral." Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics. Hence, in such approaches for cospectral graphs many mesoscopic quantities are predicted to be indistinguishable. Here we show that the introduction of semiflexibility into the generalized Gaussian structure scheme leads to different spectra and hence to distinct macroscopic patterns. Moreover, particular semiflexible situations allow us to distinguish well between cospectral structures. We confirm our theoretical results through Monte Carlo simulations.     

Ion Interactions with the Carbon Nanotube Surface in Aqueous Solutions: Understanding the Molecular Mechanisms

We study the molecular mechanisms of alkali halide ion interactions with the single‐wall carbon nanotube surface in water by means of fully atomistic molecular dynamics simulations. We focus on the basic physical‐chemical principles of ion–nanotube interactions in aqueous solutions and discuss them in light of recent experimental findings on selective ion effects on carbon nanotubes.     

Synthesis of CeO<Subscript>2</Subscript>-ZrO<Subscript>2</Subscript> hydrosols via peptization at room temperature

A procedure is developed for the synthesis of concentrated CeO₂-ZrO₂ hydrosols based on the peptization of a precipitate obtained by the hydrolysis of a cerium nitrate-zirconium oxynitrate mixture. The time intervals and optimum [H⁺]/[Me ⁿ⁺] molar ratios giving rise the formation of CeO₂-ZrO₂ hydrosols stable to aggregation with a narrow particle size distribution are established. The size, shape, density, and phase composition of the hydrosol particles are determined.     

Underwound DNA under tension: structure, elasticity, and sequence-dependent behaviors

DNA melting under torsion plays an important role in a wide variety of cellular processes. In the present Letter, we have investigated DNA melting at the single-molecule level using an angular optical trap. By directly measuring force, extension, torque, and angle of DNA, we determined the structural and elastic parameters of torsionally melted DNA. Our data reveal that under moderate forces, the melted DNA assumes a left-handed structure as opposed to an open bubble conformation and is highly torsionally compliant. We have also discovered that at low forces melted DNA properties are highly dependent on DNA sequence. These results provide a more comprehensive picture of the global DNA force-torque phase diagram.