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We present a new three-dimensional, MHD-plasma/kinetic-neutrals model of the solar wind (SW) interaction with the local interstellar medium (LISM), which self-consistently includes neutral hydrogen and helium atoms. This new model also treats electrons as a separate fluid and includes the effect of Coulomb collisions. While the properties of electrons in the distant SW and in the LISM are mostly unknown due to the lack of in situ observations, a common assumption for any global, single-ion model is to assume that electrons have the temperature of the ion mixture, which includes pickup ions. In the new model, electrons in the SW are colder, which results in a better agreement with New Horizons observations in the supersonic SW. In the LISM, however, ions and electrons are almost in thermal equilibrium. As for the plasma mixture, the major differences between the models are in the inner heliosheath, where the new model predicts a charge-exchange-driven cooling and a decrease of the heliosheath thickness. The filtration of interstellar neutral atoms at the heliospheric interface is discussed. The new model predicts an increase in the H density by ∼2% at 1 au. However, the fraction of pristine H atoms decreases by ∼12%, while the density of atoms born in the outer and inner heliosheath increases by 5% and ∼35%, respectively. While at 1 au the density of He atoms remains unchanged, the contribution from the “warm breeze” increases by ∼3%.

The role of pickup ions (PUIs) in the solar wind interaction with the local interstellar medium is investigated with 3D, multifluid simulations. The flow of the mixture of all charged particles is described by the ideal MHD equations, with the source terms responsible for charge exchange between ions and neutral atoms. The thermodynamically distinct populations of neutrals are governed by individual sets of gas dynamics Euler equations. PUIs are treated as a separate, comoving fluid. Because the anisotropic behavior of PUIs at the heliospheric termination shocks is not described by the standard conservation laws (a.k.a. the Rankine–Hugoniot relations), we derived boundary conditions for them, which are obtained from the dedicated kinetic simulations of collisionless shocks. It is demonstrated that this approach to treating PUIs makes the computation results more consistent with observational data. In particular, the PUI pressure in the inner heliosheath (IHS) becomes higher by ∼40%–50% in the new model, as compared with the solutions where no special boundary conditions are applied. Hotter PUIs eventually lead to charge-exchange-driven cooling of the IHS plasma, which reduces the IHS width by ∼15% (∼8–10 au) in the upwind direction, and even more in the other directions. The density of secondary neutral atoms born in the IHS decreases by ∼30%, while their temperature increases by ∼60%. Simulation results are validated with New Horizons data at distances between 11 and 47 au.

We investigate the role of pickup ions (PUIs) in the interaction of a periodically varying solar wind (SW) with the local interstellar medium (LISM). The analysis is performed using a 3D, time-dependent, multifluid model, where PUIs are treated as a separate fluid. The description of PUIs crossing the heliospheric termination shock utilizes results of kinetic simulations incorporated into magnetohydrodynamic (MHD) simulations. Space-time distributions of PUI properties throughout the heliosphere are presented. PUIs exhibit an intriguing behavior in the distant heliotail, where they are mostly concentrated in the vicinity of the heliopause (HP). Our simulations show that, because of the plasma mixing and MHD instabilities, PUIs created in the supersonic SW can cross the HP and enter the LISM. We find that the HP instability and solar cycle cause time-dependent variations in the flow of interstellar neutral atoms. When treated as a separate fluid, PUIs make the heliosphere slimmer, while the SW flow pattern in the heliotail exhibits enhanced variability. The simulation results are validated against in situ observations from the Voyager and New Horizons spacecraft.

The Interstellar Mapping and Acceleration Probe (IMAP) mission launched from Earth on 2025 September 24, beginning its commissioning phase as the spacecraft makes its way to Lagrange Point 1. IMAP-Hi, one of three energetic neutral atom (ENA) imagers, has improved capabilities compared to its predecessor, the Interstellar Boundary Explorer-Hi instrument, such as a wider energy coverage (∼0.4–15.6 keV compared to ∼0.5–6 keV). In this study, we aim to simulate ENA emissions from the heliosphere, at IMAP-Hi energies, with the goal of showing what ENA maps may look like when their source is affected by the presence of the Kelvin–Helmholtz instability (KHI). The KHI arises when the fast and slow solar wind meet in the heliosheath near the heliopause and create a shear flow, usually strongest at high latitudes. According to our simulation, if the KHIs are present in the heliosphere, then IMAP-Hi should be able to observe their effects on ENA emissions via long bands of enhanced ENA fluxes at high northern and southern latitudes, reaching all the way back to the tail. These bands are separated on the order of ∼15° in latitude, depending on the direction in the sky. The ENA bands are most visible at ∼2–6 keV. The presence or absence of ENA bands in IMAP-Hi observations and their orientation may not only provide important information about the structure of the heliosphere, but also guide improvements to our models, since these features differ or are not present among various simulations.

Our three-dimensional, time-dependent, multi-fluid model has been used to investigate the solar wind (SW)–local interstellar medium (LISM) interaction with pickup ions (PUIs) treated as a separate fluid. A non-zero, but fixed, angle between the Sun’s magnetic and rotation axis is adopted. The flow of the plasma mixture (thermal SW protons, PUIs, and electrons), is described by the system of ideal magnetohydrodynamic equations with the source terms responsible for charge exchange between ions and neutral atoms. Different populations of neutral atoms are governed by the individual sets of the Euler equations. As the standard Rankine–Hugoniot relations are not appropriate to describe the anisotropic behavior of PUIs at the termination shock, we use a kinetically-derived set of boundary conditions at it. We extend our previous work [1] and perform these new simulations on a Cartesian grid. This approach allows us to maintain a uniform grid resolution in all directions, without compromising resolution, at large distances from the Sun. The possibility of transition of the SW flow to a stochastic regime in the region between the termination shock and heliopause is further investigated.

— In this paper, the rate of convergence of double rational Fourier series and in particular, double trigonometric Fourier series of functions of generalized bounded variation is estimated.

In this paper, we discuss the rate of convergence of the rational Fourier series and conjugate rational Fourier series of functions of generalized bounded variation. In particular, well-known Wiener’s theorem and Siddiqi’s theorem for functions of -bounded variation are proved in more general complete rational orthogonal system and also results proved for wider class than the class functions of  bounded variation and of  p- -bounded variation.

It has been shown that sonochemical treatment in the process of Lidocaine oxidation leads to an increase in the yield of Lidocaine N-oxide (LNO) while reducing the reaction time. An ADME (absorption, distribution, metabolism, and excretion) analysis of Lidocaine and LNO was performed. According to in silico calculated ADME profile, LNO is characterized by high bioavailability, efficient absorption in the gastrointestinal tract, and slight inhibition of cytochrome P450, which is a sign of low interaction with other drugs. According to the results of the analysis of LNO interaction with the mutant p53 protein by the molecular docking method, the anticancer activity of this substance can be expected.