On Diffraction of a Sawtooth Nonlinear Wave by a Narrow Circular Aperture in a Screen

Acoustical Physics - The paper presents the experimental and theoretical studies of diffraction effects in intense acoustic beams diffracted by a narrow circular aperture in a screen. The...     

Multivalued dynamics of solutions of autonomous operator differential equations with pseudomonotone nonlinearity

We consider nonlinear autonomous operator differential equations with pseudomonotone dependence between the defining parameters of the problemand study the dynamics of all weak solutions on the positive time semiaxis. We prove the existence of a trajectory and a global attractor and study their structure. As a possible application, we consider the class of high-order nonlinear parabolic equations.     

Long-time behavior of solutions for quasilinear hyperbolic hemivariational inequalities with application to piezoelectricity problem

We consider quasilinear autonomous inclusions of hyperbolic type. The dynamics of all weak solutions defined on the positive semi-axis of time is studied. We prove the existence of trajectory and global attractors and investigate their structure. The classes of mathematical models for piezoelectric fields containing the multidimensional law are studied. The conditions of the output of each weak solution for this problem at stationary states are given. We consider as a particular case the piezoelectric model for PZT-4 piezoceramics as one of the possible applications.     

Mesoporous MgO: Synthesis,physico-chemical,and catalytic properties

Mesoporous MgO was obtained via the hydrothermal synthesis using both ionogenic and non-ionogenic surfactants as structure-directing templates. The materials prepared were characterized by SEM, BET-N₂, XRD, and TG-DTA techniques. MgO particles are spherical 20-μm aggregates of primary oxide particles well shaped as rectangular parallelepipeds. Magnesium oxide samples have the specific surface area of 290–400 m²/g and pore sizes of 3.3–4.1 nm. Their mesoporous structure remained unchanged after calcination up to 350°C. Catalytic activity of mesoporous MgO was studied in acetone condensation reaction.     

Bergeʼs maximum theorem for noncompact image sets

This note generalizes Berge?s maximum theorem to noncompact image sets. It also clarifies the results from Feinberg, Kasyanov and Zadoianchuk (2013) [7] on the extension to noncompact image sets of another Berge?s theorem, that states semi-continuity of value functions. Here we explain that the notion of a K$\mathbb{K}$-inf-compact function introduced there is applicable to metrizable topological spaces and to more general compactly generated topological spaces. For Hausdorff topological spaces we introduce the notion of a KN$\mathbb{K}\mathbb{N}$-inf-compact function (N$\mathbb{N}$ stands for “nets” in K$\mathbb{K}$-inf-compactness), which coincides with K$\mathbb{K}$-inf-compactness for compactly generated and, in particular, for metrizable topological spaces.     

Pulse signal detection in a focal area of a convergent wave front

Diffraction effects, taking place during nonlinear transformations in inhomogeneous acoustic fields, are experimentally investigated. The case of a convergent spherical wave front propagating in a uniform nonlinear medium, detection of an acoustic field in a focus, and receiving of the detected signal in the region of the initial wave front aperture are considered. A spherical piezoceramic transducer is used in the experiments as a focusing device. Broad-angle “nonlinear scattering” signals have been recorded at the experimental facility where a pulsed mode of focused transducer operation in water is implemented. The dependence of the amplitude of the signal, detected in the focal area, and its shape on the scattering direction, as well as on the distance between the focus and the receiving point, are studied.     

Picosecond X-ray plasma radiation measurements

Direct picosecond measurements of X-ray laser plasma radiation were performed with a high-speed X-ray image-converter camera (ICC). This camera operates in the single-frame mode with an exposure time ranging from 5 ns to 0.5 μs and in the streak mode with 5 × 10⁹ to 5 × 10⁷ cm/s streak velocities. Its temporal resolution in the streak mode was calculated to be about 7 ps. A plasma was created by focussing 10 ps 1 to 2 joule laser pulses onto a titanium target placed in a vacuum chamber. The halfwidth of the recorded X-ray pulses varied from 30 to 60 ps.     

Production of nitrogen oxides in a positive column of a glow-type discharge in air flow

This paper deals with the investigations of a low-current glow-type discharge in air flow as applied to the problem of nitrogen oxide production. The electrode configurations correspond to the classical coaxial plasmatron and to the so-called gliding arc. The discharge burns in a regime of constricted positive column with a typical current density from 47 to 120 A/cm² and with the related electron density from 0.53?10¹⁴ to 2.3?10¹⁴ 1/cm³. The gas temperature changes from 3000 to 3610 K. The described conditions provide a flow of NO molecules from the plasma column with the energetic cost for production of one molecule of (30–50) eV. Maximum content of NO molecules [NO]?=?4 g/m³ (3500 ppm) was obtained. In spite of a rather high gas temperature, the plasma is still nonequilibrium. The high vibrational levels of the nitrogen molecules are populated, and the main channel of the nitric oxide production is associated with the reaction in which the vibrationally excited nitrogen interacts with atomic oxygen.