Hydraulic jumps in two-layer flow with a free surface

This paper presents a closure relation which describes hydraulic jumps in two-layer flows with a free surface over a flat bottom. This relation is derived from the momentum equations for each layer, which, subject to the condition of conservation of the total momentum and mass of each layer, become conservative in a sense. It is shown that use of this relation provides a reduction in the total energy at the jump.     

Distance-regular graphs with intersection arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} do not exist

We prove that the arrays {52, 35, 16; 1, 4, 28} and {69, 48, 24; 1, 4, 46} cannot be realized as the intersection arrays of distance-regular graphs. In the proof we use some inequalities bounding the size of substructures (cliques, cocliques) in a distance-regular graph.     

Processes in resonant domains of metal nanoparticle aggregates and optical nonlinearity of aggregates in pulsed laser fields

Optical nonlinearities in aggregates of nanoparticles formed in silver hydrosols (SHs) are studied under pico- and nanosecond pulsed laser excitation. The dependence of the nonlinear refractive index n ₂ on the degree of hydrosol aggregation is studied experimentally at the wavelength λ=1.064 μm. It is found that n ₂ changes sign when the degree of hydrosol aggregation is increased. Various physical effects occurring in resonant domains of the aggregates are analyzed using a simple physical model of two bound silver nanoparticles. The theory takes into account thermal, elastic, electrostatic, and light-induced effects. Experimental results are discussed in the context of this theory.     

New Constraints on the Axion–Photon Coupling Constant for Solar Axions

Resonance excitation of the ⁸³Kr first nuclear level (E = 9.4 keV) by solar axions formed via the Primakoff mechanism is sought. The γ- and X-ray photons and the conversion and Auger electrons arising from the excited-level relaxation are detected with a gas proportional counter of a low-background detector in the underground Baksan Neutrino Observatory. The following experimental constraint is obtained for the product of the axion–photon coupling constant and the axion mass:|g_Aγ × m_A| ≤ 6.3 × 10 ^-17 In the framework of the hadronic-axion model, this corresponds to a new axion-mass constraint of m_A ≤ 12.7 eV at 95% C.L.     

An Investigation of Signal Kinematical Region to Study Standard Model Higgs Boson Properties in the H → WW* → ℓvℓv Decay Channel in the ATLAS Experiment at the Large Hadron Collider at 13 TeV

A signal kinematical region is analyzed by the Higgs Boson Working Group (HWW) within the framework of a study of the Standard Model Higgs boson properties in the H → WW* → evεv decay channel in the ATLAS experiment on the Large Hadron Collider (LHC). The analysis is based on the full statistics of proton-proton collision data during exposures in 2015–2016 at the center-of-mass energy of 13 TeV. As compared to our previous analysis, the reconstruction software is updated and the simulation accuracy of backgrounds is improved. Events taken at low and high LHC luminosity are studied separately. In addition, the kinematics at the later stages of event selection is investigated in detail and systematic uncertainties are fully estimated. It is shown that the Monte Carlo modeling satisfactorily describes the experimental data at different selection stages. Kinematic distributions for hadron jets are studied also in the Z-boson control region, where the acquired data reach the order of ten million events. As compared to the previous investigation, the modeling accuracy of Z and background processes is noticeably improved, and events at low and high LHC luminosities are studied separately. Furthermore, all systematic uncertainties related to jets are estimated as well. As a whole, good agreement between experimental results and Monte Carlo simulation data is observed. No problems that would be caused by high luminosity are observed.

     

Difference schemes of high-order accuracy for problems with jacobi-type degeneracy

An exact and a truncated difference schemes are constructed for eigenvalue boundary-value problems for a differential equation with the same degeneracy as the Jacobi polynomial equation. The truncated scheme of rank m is shown to be accurate to (m +1)-st order. Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 67, pp. 3–15, 1989.     

Hyperbolic Models of Homogeneous Two-Fluid Mixtures

One derives the governing equations and the Rankine–Hugoniot conditions for a mixture of two miscible fluids using an extended form of Hamilton's principle of least action. The Lagrangian is constructed as the difference between the kinetic energy and a potential depending on the relative velocity of components. To obtain the governing equations and the jump conditions one uses two reference frames related with the Lagrangian coordinates of each component. Under some hypotheses on flow properties one proves the hyperbolicity of the governing system for small relative velocity of phases.     

Differential properties of the solution of a mathematical model of kinetic adsorption

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 5, pp. 698–702, May, 1989.     

Numerical solution of the mathematical model of internal-diffusion kinetics of adsorption

A numerical method is proposed for solving a nonlinear weakly singular Volterra integral equation of the second kind which arises in the study of the mathematical model of internal-diffusion kinetics of adsorption of a substance from an aqueous solution of constant and bounded volume. The efficiency of the method is demonstrated using prototype examples and in application to inverse problems of adsorption kinetics.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 63, pp. 30–38, 1987.