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Streamers are ionization fronts that occur in gases at atmospheric and sub-atmospheric pressures. Numerical studies of streamers are important for practical applications but are challenging due to the multiscale nature of this discharge type. This paper introduces a spectral element method for modelling streamer discharges. The method is developed for Cartesian grids but can be extended to be used on unstructured meshes. The streamer model is based on the Poisson equation for the electric potential and the electron continuity equation. The Poisson equation is discretized via a spectral method based on the integral representation of the solution. The hierarchical Poincare-Steklov (HPS) scheme is used to solve the resulting set of equations. The electron continuity equation is solved by means of the discontinuous Galerkin spectral element method (DGSEM). The DGSEM is extended by an alternative definition of the diffusion flux. A subcell finite volume method is used to stabilize the DGSEM scheme, if required. The entire simulation scheme is validated by solving a number of test problems and reproducing the results of previous studies. Adaptive mesh refinement is used to reduce the number of unknowns. The proposed method is found to be sufficiently fast for being used in practical applications. The flexibility of the method provides an interesting opportunity to broaden the range of problems that can be addressed in numerical studies of low-temperature plasma discharges.

The influence of a supersonic projectile on a three-dimensional complex plasma is studied. Micron sized particles in a low-temperature plasma formed a large undisturbed system in the new 'Zyflex' chamber during microgravity conditions. A supersonic probe particle excited a Mach cone with Mach number M $\approx$ 1.5 - 2 and double Mach cone structure in the large weakly damped particle cloud. The speed of sound is measured with different methods and particle charge estimations are compared to calculations from standard theories. The high image resolution enables the study of Mach cones in microgravity on the single particle level of a three-dimensional complex plasma and gives insight to the dynamics. A heating of the microparticles is discovered behind the supersonic projectile but not in the flanks of the Mach cone.

The effect of micron-sized particles on a low-pressure capacitively-coupled rf discharge is studied both experimentally and using numerical simulations. In the laboratory experiments, microparticle clouds occupying a considerable fraction of the discharge volume are supported against gravity with the help of the thermophoretic force. The spatiotemporally resolved optical emission measurements are performed with different arrangements of microparticles. The numerical simulations are carried out on the basis of a one-dimensional hybrid (fluid-kinetic) discharge model describing the interaction between plasma and microparticles in a self-consistent way. The study is focused on the role of microparticle arrangement in interpreting the spatiotemporal emission measurements. We show that it is not possible to reproduce simultaneously the observed microparticle arrangement and emission pattern in the framework of the considered one-dimensional model. This disagreement is discussed and attributed to two-dimensional effects, e.g., radial diffusion of the plasma components.

A new one-dimensional fluid model for ions in weakly-ionized plasma is proposed. The model differs from the existing ones in two aspects. First, a more accurate approximation of the collision terms in the fluid equations is suggested. For this purpose, the results obtained using the Monte-Carlo kinetic model of the ion swarm experiments are considered. Second, the ion energy equation is taken into account. The fluid equations are closed using a simple model of the ion velocity distribution function. The accuracy of the fluid model is examined by comparing with the results of particle-in-cell/Monte Carlo simulations. In particular, several test problems are considered using a parallel plate model of the capacitively coupled radio-frequency discharge. It is shown that the results obtained using the proposed fluid model are in good agreement with those obtained from the simulations over a wide range of discharge conditions. An approximation of the ion velocity distribution function for the problem under consideration is also discussed.

In the present paper we discuss the lattice of reducts of $\langle \mathbb{Q}, \{$+$\} \rangle$

Thermodynamics of weakly screened (near the one-component-plasma limit) Yukawa fluids in two and three dimensions is analyzed in detail. It is shown that the thermal component of the excess internal energy of these fluids, when expressed in terms of the properly normalized coupling strength, exhibits the scaling pertinent to the corresponding one-component-plasma limit (the scalings differ considerably between the two- and three-dimensional situations). This provides us with a simple and accurate practical tool to estimate thermodynamic properties of weakly screened Yukawa fluids. Particular attention is paid to the two-dimensional fluids, for which several important thermodynamic quantities are calculated to illustrate the application of the approach., Comment: Submitted to Phys. Plasmas

The Svenonius theorem describes the (first-order) definability in a structure in terms of permutations preserving the relations of elementary extensions of the structure. In the present paper we prove a version of this theorem using permutations of sequences over the original structure (these are permutations of sequences of tuples of the structure elements as well). We say that such a permutation $\varphi$ almost preserves a relation if for every sequence of its arguments the value of the relation on an $n$-th element of the sequence and on its image under $\varphi$ coincide for almost all numbers $n.$ We prove that a relation is definable in a structure iff the relation is almost preserved by all permutations almost preserving the relations of the structure. This version limits consideration to the original structure only and does not refer to any logical notion, such as "elementary equivalence"., Comment: 9 pages

The temperature dependences of optical loss and luminescence spectra have been measured in visible and NIR spectral range for Bi-doped silica and Bi-doped germanosilicate fibers for the first time. The temperature dependence of luminescence lifetime for Si-associated active bismuth centers in germanosilicate fiber was measured. It has been revealed, that distribution of Bi3+ ions across the fiber preform is essentially different as compared to that of NIR active bismuth centers. Data received indicates that NIR-active centers are associated with the low oxidation state of bismuth ion and/or oxygen deficient center of the glass structure., Comment: 22 pages, 8 figures

Svenonius theorem reduces the problem of first-order definability to the problem of relationship between groups of permutations. In the present paper we use this approach to describe the lattice of definable relations for the structure of integer numbers with the successor relation., Comment: in this version removed buggy rational numbers section

The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical theories, algorithmic computability, Kolmogorov complexity, number theory, are discussed., Comment: In Russian. 76 pages, 6 figures