The problem of constructing and classifying stationary equilibria of point vortices in the plane is studied. An ordinary differential equation that enables one to find positions of point vortices with circulations $Γ_1$, $Γ_2$, and $Γ_3$ in stationary equilibrium is obtained. A necessary condition of an equilibrium existing is derived. The case of point vortex systems consisting of $*n* + 2$ point vortices with $*n$* vortices of circulation $Γ_1$ and two vortices of circulations $Γ_2 = *a*Γ_1$ and $Γ_3 = *b*Γ_1$, where $*a$* and $*b$ *are integers, is considered in detail. The properties of polynomial solutions of the corresponding ordinary differential equation are investigated. A set of positive–dimensional equilibrium configurations is found. A continuous free parameter is presented in the coefficients of corresponding polynomial solutions. These free parameters affect the positions of the roots and hence the vortex positions. Stationary equilibrium that could be derived from each other by rotation, extension, parallel translation is considered as equivalent. All found configurations seem to be new.

The polarization switching was studied in single crystals and thin films of 2- methylbenzimidazole (MBI) obtained by evaporation method from an MBI ethanol solution. Dielectric hysteresis loops were measured in the temperature interval 290-390 K and frequency range 20-1000 Hz for different amplitudes of the electric field. The Kolmogorov β-model with account of Mertz law is used for simulation of hysteresis loops. The temperature dependence of domain wall motion activation field Ea has been obtained. Mechanisms of polarization switching in single crystals and films of MBI are discussed. In MBI films, a comparison of polarization switching for in-plane and out-of-plane electric field orientation is presented.

The canonical technique for Monte Carlo simulations in statistical physics is importance sampling via a suitably constructed Markov chain. While such approaches are quite successful, they are not particularly well suited for parallelization as the chain dynamics is sequential, and if replicated chains are used to increase statistics each of them relaxes into equilibrium with an intrinsic time constant that cannot be reduced by parallel work. Population annealing is a sequential Monte Carlo method that simulates an ensemble of system replica under a cooling protocol. The population element makes it naturally well suited for massively parallel simulations, and bias can be systematically reduced by increasing the population size. We present an implementation of population annealing on graphics processing units and discuss its behavior for different systems undergoing continuous and first-order phase transitions.

The results of the study of the impact of single-quantum magnetic flux pulses moving along the Josephson transmission lines (JTL) on the dynamics of states of qubits magnetically coupled with such lines are presented. The JTL dynamics was calculated in the frame of resistively shunted junction model with different damping coefficients. This allowed us to find the form of control current pulses (fluxon) acting on a superconducting qubit. Numerical simulations of the simplest logic operations with superconducting qubit due to calculated fluxon impact are presented.

The one-dimensional discrete Tent map is a well-known example of a map whose fixed points are all unstable on the segment [0,1]. This map leads to the positivity of the Lyapunov exponent for the corresponding recurrent sequence. Therefore in a situation of general position, this sequence must demonstrate the properties of deterministic chaos. However if the first term of the recurrence sequence is taken as a decimal fraction with a fixed number "k" of digits after the decimal point and all calculations are carried out accurately, then the situation turns out to be completely different. In this case, first, the Tent map does not lead to an increase in significant digits in the terms of the sequence, and secondly, demonstrates the existence of a finite number of eventually periodic orbits, which are attractors for all other decimal numbers with the number of significant digits not exceeding "k".

The density functional theory (DFT) is a research tool of the highest importance for electronic structure calculations. It is often the only affordable method for ab initio calculations of complex materials. The pseudopotential approach allows reducing the total number of electrons in the model that speeds up calculations. However, there is a lack of pseudopotentials for heavy elements suitable for condensed matter DFT models. In this work, we present a pseudopotential for uranium developed in the Goedecker–Teter–Hutter form. Its accuracy is illustrated using several molecular and solid-state calculations.

By the universal integrability objects we mean certain monodromy-type and transfer-type operators, where the representation in the auxiliary space is properly fixed, while the representation in the quantum space is not. This notion is actually determined by the structure of the universal R-matrix. We call functional relations between such universal integrability objects, and so, being independent of the representation in the quantum space, the universal functional relations. We present a short review of the universal functional relations for the quantum integrable systems associated with the quantum groups of loop Lie algebras.

This short note is a review of the intriguing connection between the quantum Gaudin model and the classical KP hierarchy recently established in [A.Alexandrov, S.Leurent, Z.Tsuboi, A.Zabrodin, The master T-operator for the Gaudin model and KP hierarchy, Nuclear Physics B 883 (2014) 173-223]. We construct the generating function of integrals of motion for the quantum Gaudin model with twisted boundary conditions (the master T-operator) and show that it satisfies the bilinear identity and Hirota equations for the classical KP hierarchy. This implies that zeros of eigenvalues of the master T-operator in the spectral parameter have the same dynamics as the Calogero-Moser system of particles.

The quantum nuclear effects are studied in water using centroid molecular dynamics (CMD) method. The aim is the calibration of CMD implementation in LAMMPS. The calculated intramolecular energy, atoms gyration radii and radial distribution functions are shown in comparison with previous works. The work is assumed to be the step toward to solution of the discrepancy between the simulation results and the experimental data of liquid n-alkane properties in our previous works.

The subject of quasi-one-dimensional (1D) superconductivity has attracted a significant interest [1]. It has been demonstrated that in sufficiently narrow channels quantum fluctuations of the complex order parameter = ei may significantly alter the text-book attributes of superconductivity such as zero resistivity [2], persistent currents [3,4] and energy gap in excitation spectra [5,6]. The particular manifestation of quantum fluctuations corresponding to momentary nulling of the order parameter modulus and ‘slippage’ of the phase by 2 is called quantum phase slip (QPS). It has been pointed out that the QPS process, being formally equal to tunnelling of magnetic flux through a superconductor, is dual to tunnelling of a Cooper pair through an insulating layer of a Josephson junction (JJ) [7]. The observation leads to a counterintuitive effect: current-biased narrow superconducting channel governed by quantum fluctuations (QPS junction – QPSJ) demonstrates insulating behaviour – the Coulomb blockade. The objective of this paper is to experimentally study the phenomenon.

The classical Poincaré theorem (1907) asserts that the polydisk D^n and the ball B^n in C^n are not biholomorphically equivalent for *n* ≥ 2. Equivalently, this means that the Fréchet algebras O(D^n) and O(B^n) of holomorphic functions are not topologically isomorphic. Our goal is to prove a noncommutative version of the above result. Given a nonzero complex number *q,* we define two noncommutative power series algebras O_q(D^n) and O_q(B^n) which can be viewed as q-analogs of O(D^n) and O(B^n), respectively. Both O_q(D^n) and O_q(B^n) are the completions of the algebraic quantum affine space w.r.t. certain families of seminorms. In the case where 0 < *q* < 1, the algebra O_q(B^n) admits an equivalent definition related to L. L. Vaksman's algebra *C_q(B^n)* of continuous functions on the closed quantum ball. We show that both O_q(D^n) and O_q(B^n) can be interpreted as Fréchet algebra deformations (in a suitable sense) of O(D^n) and O(B^n), respectively. Our main result is that O_q(D^n) and O_q(B^n) are not isomorphic if *n* ≥ 2 and |*q*| = 1, but are isomorphic if |*q*| ≠ 1.

In a metal sample, where at least one of the dimensions is comparable with the de Broglie wavelength of conduction electrons, the quantum size effects (QSE) should be observed. QSEs manifest themselves as non-monotonic dependencies of various material properties as function of relevant dimension. QSE should be particularly noticeable in materials with charge carrier(s) effective mass less than the free electron mass. Bismuth is one of the most suitable semi-metal to observe QSE due to small effective masses and small the Fermi energy. However, bismuth has a high anisotropic energy spectrum. Hence to observe QSE which can be interpreted with reasonable accuracy, it is mandatory to fabricate single-crystal nanostructure with known orientation of crystallographic axes. In this paper several short bismuth nanowires (nanorods) were investigated, and oscillating dependence of electric resistance on effective cross section was found. Theoretical calculations provide a reasonable agreement with experiment. The quantum-size phenomena are important for operation of a wide spectrum of nanolelectronic devices.

Abstract. In a metal sample, where at least one of the dimensions is comparable with the de Broglie wavelength of conduction electrons, the quantum size effects (QSE) should be observed. QSEs manifest themselves as non-monotonic dependencies of various material properties as function of relevant dimension. QSE should be particularly noticeable in materials with charge carrier(s) effective mass less than the free electron mass. Bismuth is one of the most suitable semi-metal to observe QSE due to small effective masses and small the Fermi energy. However, bismuth has a high anisotropic energy spectrum. Hence to observe QSE which can be interpreted with reasonable accuracy, it is mandatory to fabricate singlecrystal nanostructure with known orientation of crystallographic axes. In this paper several short bismuth nanowires (nanorods) were investigated, and oscillating dependence of electric resistance on effective cross section was found. Theoretical calculations provide a reasonable agreement with experiment. The quantum-size phenomena are important for operation of a wide spectrum of nanolelectronic devices.

Quasi-3D model for calculation of radiation leakage currents in modern submicron SOI MOSFET structures is proposed. Instead of the fully 3D modeling is proposed to solve two tasks: 2D modeling of the traditional MOSFET cross-section and 3D modeling of the side parasitic transistor. The radiation-induced leakage current simulation in the 0.35 μm SOI MOSFET structure with taking account ionizing radiation with a dose of up to 500 krad was simulated. The results of the simulation show that in comparison with the traditional fully 3D modeling, which requires 11 hours of computer time, the computer time for the IdVg characteristic was reduced to 71 minutes (i.e. the computer time decreased by 9 times).

In the recent work by Gusakov, Kantor & Ofengeim [Phys. Rev. D 96, 103012 (2017)] a new method to calculate the quasistationary evolution of magnetic field in the core of a neutron star was proposed. Here we further develop it, focusing on a simple case of neutron-proton-electron (npe) core composition with purely poloidal magnetic field B. We find that the meridional flow of the npe-fluid can be unexpectedly large. We estimate the typical timescale τ of the field evolution due to dragging of the magnetic field lines by this flow and show that τ can be as small as ∼ (100 — 1000) yr for magnetars with B ∼ 1e16 G.

We extend concept of local simulation times in parallel discrete event simulation (PDES) in order to take into account architecture of the current hardware and software in high-performance computing. We shortly review previous research on the mapping of PDES on physical problems, and emphasise how physical results may help to predict parallel algorithms behaviour.

Molecular modelling is used to calculate transport properties and to study relaxation of liquid n-triacontane (C30H62). The problem is important in connection with the behavior of liquid isolators in a pre-breakdown state. Two all-atom models and a united-atom model are used. Shear viscosity is calculated using the Green–Kubo formula. The force fields are compared with each other using the following criteria: the required time for one molecular dynamics step, the compliance of the main physical and transport properties with experimental values. The problem of the system equilibration is considered. The united-atom potential is used to model the n-triacontane liquid with an initial directional orientation. The time of relaxation to the disordered state, when all molecules orientations are randomized, are obtained. The influence of the molecules orientations on the shear viscosity value and the shear viscosity relaxation are treated.

Data analysis in fundamental sciences nowadays is an essential process that pushes frontiers of our knowledge and leads to new discoveries. At the same time we can see that complexity of those analyses increases fast due to a) enormous volumes of datasets being analyzed, b) variety of techniques and algorithms one have to check inside a single analysis, c) distributed nature of research teams that requires special communication media for knowledge and information exchange between individual researchers. There is a lot of resemblance between techniques and problems arising in the areas of industrial information retrieval and particle physics. To address those problems we propose Reproducible Experiment Platform (REP), a software infrastructure to support collaborative ecosystem for computational science. It is a Python based solution for research teams that allows running computational experiments on shared datasets, obtaining repeatable results, and consistent comparisons of the obtained results. We present some key features of REP based on case studies which include trigger optimization and physics analysis studies at the LHCb experiment.

The paper considers programs and devices of augmented reality, examines the general environments and methods of software development and the rationale for their selection. The work describes in detail the operating principle of the software, the pattern recognition algorithm, the UML class diagram, the UML usage diagram, and the architecture of the 3D rendering engine and a description of its operation. An example of practical application of software with pattern recognition is offered. The paper examines the impact of virtual reality on human health, as well as the problem of assimilation of educational material in preschool education. To solve the problem, various algorithms for the program are proposed. Based on the conducted studies, it was decided to create the software for the experiment on the basis of developed algorithms for preschool education. The results of the work can be used for further research in the field of expanded reality, for new developments in this field and improvement of the quality of education.

The aim of this work is the software implementation of three image scaling

algorithms using parallel computations, as well as the development of an application with a

graphical user interface for the Windows operating system to demonstrate the operation of

algorithms and to study the relationship between system performance, algorithm execution

time and the degree of parallelization of computations. Three methods of interpolation were

studied, formalized and adapted to scale images. The result of the work is a program for

scaling images by different methods. Comparison of the quality of scaling by different methods

is given.