High-order accurate difference schemes for solving gasdynamic equations by the Godunov method with antidiffusion

A technique is proposed for improving the accuracy of the Godunov method as applied to gasdynamic simulations in one dimension. The underlying idea is the reconstruction of fluxes arsoss cell boundaries (“large” values) by using antidiffusion corrections, which are obtained by analyzing the differential approximation of the schemes. In contrast to other approaches, the reconstructed values are not the initial data but rather large values calculated by solving the Riemann problem. The approach is efficient and yields higher accuracy difference schemes with a high resolution.     

Symmetric difference schemes of componentwise splitting and equivalent predictor-corrector scheme based on the Godunov method as applied to multidimensional gasdynamic simulation

An approach is described for improving the accuracy of numerical solutions to multidimensional gasdynamic problems produced by Godunov’s schemes. The basic idea behind the approach is to construct symmetric difference schemes based on splitting with respect to spatial variables with the subsequent transformation into equivalent predictor-corrector schemes. It is shown that the computation of “large” values by solving the one-dimensional Riemann problem at the interface of two neighboring cells leads to approximation errors in Godunov’s schemes. It is proposed to reconstruct large values so as to eliminate this source of errors. The time integration step in the modified schemes is consistent with that in the one-dimensional schemes and, on spatially uniform meshes, is 2 and 3 times larger than that in Godunov’s classical schemes for two- and three-dimensional problems, respectively. The numerical results obtained for test problems confirm the improvement of the accuracy of solutions produced by the modified schemes.     

On the solvability of the tricomi problem for the Lavrent’ev-Bitsadze equation with mixed boundary conditions

We study the existence of a regular (classical) solution of the Tricomi problem for the Lavrent’ev-Bitsadze equation with mixed boundary conditions. We find conditions under which the homogeneous problem has only the zero solution and give an example in which the homogeneous Tricomi problem has a nonzero solution. We also study the solvability of the inhomogeneous Tricomi problem.     

Optimization in the class <Emphasis Type="Italic">W</Emphasis><Stack><Subscript>2</Subscript><Superscript>2</Superscript></Stack> of the boundary control by displacements at one endpoint of a string with the other endpoint being fixed

We consider the problem on the optimal boundary control of string vibrations by a displacement at one endpoint of the string with the other endpoint being fixed. The problem is studied in the space      

First experimental observations of neutron bursts under thunderstorm clouds near sea level

The connection of short-term neutron bursts near sea level with the electric and geomagnetic atmospheric fields during thunderstorms in 2009–2011 has been experimentally studied. The data from the cosmic-ray spectrograph named after Kuzmin, an electrostatic fluxmeter, and a three-component fluxgate magnetometer in Yakutsk have been analyzed. It has been shown that short-term (no longer than 4 min) neutron bursts are due to negative lightning discharges. The bursts are detected at the ground level 1–3 km below thunderstorm clouds. In this case, the neutron flux is about 4 × 10⁻³ cm⁻² s⁻¹. The minimum energy of the neutrons that are efficiently detected by the monitor is about 10 MeV. It has been found that short-term neutron bursts are detected when the electric field strength reaches a threshold value of −16 kV/m.     

Quantum computers on multiatomic ensembles in quantum electrodynamic cavity

Schemes for the construction of quantum computers on multiatomic ensembles in quantum electrodynamic cavity are considered. With that, both encoding of physical qubits on each separate multiatomic ensemble and logical encoding of qubits on the pairs of ensembles are introduced. Possible constructions of swapping (SWAP, \(\sqrt {SWAP} \)) and controlled swapping gates (CSWAP) are analyzed. Mechanism of collective blockade and dynamical elimination procedure are proposed for realization of these gates. The comparison of the scheme solutions is carried out for the construction of quantum computer at using of physical and logical qubits.     

Hydrogenation of CO2 conjugated with dehydrogenation of cyclohexane over an intermetallic catalyst

Transformations of carbon dioxide catalyzed by the hydride form of [TiFe_0.95Zr_0.03Mo_0.02]H_x, by the industrial Pt/Al₂O₃ catalyst, and by a mixture of the above materials were studied. Study of the thermal desorption of H₂ showed the presence of two forms of absorbed hydrogen, namely, the weakly bound hydrogen, which is evolved from the intermetallic structure on heating to 430 °C under Ar, and the strongly bound hydrogen (SBH), which remains in the intermetallic compound at higher temperatures (up to 700 °C). In a carbon dioxide medium, the SBH enters into selective CO₂ reduction to give CO at 350—430 °C and 10—12 atm. The selectivity of the formation of CO reaches 80—99% for conversion of CO₂ between 50—70%, the SBH being consumed almost entirely for the reduction of CO₂. In the presence of the mixed catalyst, conjugate reactions proceed efficiently; dehydrogenation of cyclohexane yields hydrogen, which is consumed for CO₂ hydrogenation.     

Oxidative dehydrogenation of N-methyl-o-phenylenediamine coordinated to the PdII and PtII atoms

The reactions of N-methyl-ortho-phenylenediamine (1) with K₂MCl₄ (M = Pd or Pt) were investigated. At the first stage, the tetraamine dicationic complexes [(C₆H₄(NH₂)(NMeH))₂M]Cl₂ were formed. Oxidation of these compounds with atmospheric oxygen in an alkaline medium afforded the neutral semiquinonediimine complexes [C₆H₄(NH)(NMe)]₂M. The structures of the {[(C₆H₄)(NH₂)(NHMe)]₂Pd}Cl₂ and [C₆H₄(NH)(NPh)]₂Pt complexes were established by X-ray diffraction analysis.     

Xylenes Alkylation with 2-(1-Adamantylimino)-5-methyl-1,3-oxathiolane

Russian Journal of Organic Chemistry -