Keldysh Institute of Applied Mathematics

The trajectories of motion along divergence-free vector fields in the phase space of autonomous systems of differential equations are studied, along with the corresponding first-order evolutionary differential equation (the Liouville equation), which describes the shift of the argument of a given function on the phase space along the trajectories of the vector field. Finite graphs and planar domains are considered as the phase space. The absence of a global-in-time solution to the Cauchy problem for the system of differential equations leads to the absence of a transformation group of the initial data space generated by the Cauchy problem. The extension of the set of phase trajectories is associated with a skew-Hermitian extension of the differential operator defined on smooth, compactly supported functions on the phase space.It is established which skew-Hermitian extensions of the first-order differential operator are associated with deterministic extensions of the phase flow, and which are associated with stochastic extensions of trajectories through the boundary of the phase space.

Vif and Vpr are HIV-1 accessory proteins that create optimal conditions for viral replication. They are considered as potential targets for the development of therapeutic agents. Natural amino acid substitutions in these proteins have previously been associated with disease progression. The aim of this study was to analyze the genetic diversity of Vif and Vpr in HIV-1 group M clades. A total of 5286 sequences were downloaded and analyzed. For 37 clades in group M, the consensus sequences, amino acid natural variation, and clade-specific amino acid residue substitutions (CSSs) were evaluated. Structural analysis and modeling of consensus sequences were performed for subtypes A1, B, C, and D. The average conservation degree in the HIV-1 group M was 86.4% for Vif and 91.3% for Vpr. In both proteins, the lowest amino acid diversity was observed in sub-subtype A6, and the highest in subtype B. In consensus sequences, the substitutions, which might influence pathogenesis, have been determined: in Vif—22H (11_cpx, 91_cpx) and 136P (A6, 01_AE, 15_01B, 59_01B, 89_BF1, 103_01B, 111_01C, 133_A6B), in Vpr—41N (06_cpx) and 55A (B, 07_BC, 35_01D, 56_cpx, 66_cpx, 66_BF1, 71_BF1, 85_BC, 137_0107). In functional motifs, CSSs associated with changes in the chemical properties of amino acid residues were noted. These findings could be taken into account for the development of therapeutic drugs in the future. No correlation was observed between the subtypes and the spatial organization of the oligomeric structures of Vif and Vpr. Using the structural analysis and modeling, it has been shown for the first time that Vif can interact with APOBEC3G as an oligomer.

This work aims to construct a phenomenological model of a multiphase multicomponent chemically active continuous medium, within which gas–liquid satellites of the giant planets of the Solar System can comprehensively be studied. With this approach, specialized models of individual dynamic, physical, and chemical processes in the water oceans of these cosmic objects can be integrated into a single whole, i.e., this approach takes into account their complexity and mutual influence, inducing significant mutual changes. A heterogeneous continuum model has been developed for multilayer nonperfect media with the methods of multivelocity mechanics and nonequilibrium thermodynamics, accounting for the asymmetry of the pressure tensor of phase media, equilibrium chemical reactions, phase transitions, and heat- and mass-transfer processes. The generalized Stefan–Maxwell relations for multiphase mixtures, which are a system of equations of motion of individual phases with genuine inertial forces, have been first derived in terms of thermodynamics. We propose a thermodynamic technique that allows obtaining a number of algebraic relationships for transport coefficients associated with diffusion–thermal processes in a multiphase medium. The developed approach is primarily intended for mathematical modeling of the water ocean and ice crust of Saturn’s moon Enceladus, beneath the surface of which one could possibly search for extraterrestrial life in the Solar System.

The paper considers the problem of numerical modeling of nonlinear wave processes in a microwave generator with magnetic insulation, used to generate relativistic electron beams and the radiation they produce. A distinctive feature of the problem is the realistic three-dimensional geometry of the oscillator. The numerical analysis of the problem is based on a three-dimensional mathematical model involving Maxwell’s equations and the equations of motion for relativistic charged particles. The model takes into account the field emission of electrons from the cathode surface and the presence of relativistic plasma. A new numerical algorithm for solving the problem is proposed, combining explicit time-dependent schemes, the finite volume method on irregular grids, and the particle-in-cloud method. The software implementation is designed for parallel computing. To test the three-dimensional numerical approach, two relevant problems of generating relativistic electron beams in one- and two-dimensional formulations were considered. Analysis of the calculation results confirmed the reproduction of one- and two-dimensional solutions in the three-dimensional code.