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The multi-wavelength outburst activity in the BL Lacertae source OJ 287 has sparked a lot of controversy about whether the source contains one or two black holes (BHs) and what characteristics of this black hole binary would be. In this article we present the results of analysis of the X-ray flaring activity of OJ 287 using the data of Swift/XRT observations. We discovered that the energy spectra in all spectral states can be adequately fit with the XSPEC BMC model (the Comptonization one). As a result we found that the X-ray photon index of the BMC model, $\Gamma$ correlates with the mass accretion rate, $\dot M$. We found the photon index $\Gamma$ to increase monotonically with accretion rate $\dot M$ from $\Gamma\sim 2$ in the intermediate state (IS) to $\Gamma\sim2.5$ the high/soft state (HSS) with subsequent saturation at $\Gamma\sim$ 2.6 level at higher luminosities. This type of behavior of the spectral index is remarkably similar to the pattern observed in a number of established stellar-mass black hole candidates. Assuming the universality of the observed pattern of the correlation between the photon index and mass accretion rate, we estimate the BH mass in OJ 287 to be around $2\times10^8$ solar masses, using the well studied BH binaries GX 339-4 and XTE J1859-226 to calibrate the model., Comment: 6 pages, 3 figures, 2 tables, submitted to MNRAS

The SPARC Toroidal Field Model Coil (TFMC) Program was a three-year effort between 2018 and 2021 that developed novel Rare Earth Yttrium Barium Copper Oxide (REBCO) superconductor technologies and then successfully utilized these technologies to design, build, and test a first-in-class, high-field (~20 T), representative-scale (~3 m) superconducting toroidal field coil. With the principal objective of demonstrating mature, large-scale, REBCO magnets, the project was executed jointly by the MIT Plasma Science and Fusion Center (PSFC) and Commonwealth Fusion Systems (CFS). The TFMC achieved its programmatic goal of experimentally demonstrating a large-scale high-field REBCO magnet, achieving 20.1 T peak field-on-conductor with 40.5 kA of terminal current, 815 kN/m of Lorentz loading on the REBCO stacks, and almost 1 GPa of mechanical stress accommodated by the structural case. Fifteen internal demountable pancake-to-pancake joints operated in the 0.5 to 2.0 nOhm range at 20 K and in magnetic fields up to 12 T. The DC and AC electromagnetic performance of the magnet, predicted by new advances in high-fidelity computational models, was confirmed in two test campaigns while the massively parallel, single-pass, pressure-vessel style coolant scheme capable of large heat removal was validated. The REBCO current lead and feeder system was experimentally qualified up to 50 kA, and the crycooler based cryogenic system provided 600 W of cooling power at 20 K with mass flow rates up to 70 g/s at a maximum design pressure of 20 bar-a for the test campaigns. Finally, the feasibility of using passive, self-protection against a quench in a fusion-scale NI TF coil was experimentally assessed with an intentional open-circuit quench at 31.5 kA terminal current., Comment: 17 pages 9 figures, overview paper and the first of a six-part series of papers covering the TFMC Program

For the maximal violation of all Bell inequalities by an arbitrary pure two-qudit state of any dimension, we derive a new lower bound expressed via the concurrence of this pure state. This new lower bound and the upper bound on the maximal Bell violation, found in [J. Phys. A: Math. Theor. 55, 285301 (2022)] and also expressed via the concurrence, analytically quantify Bell nonlocality of a pure two-qudit state via its entanglement, in particular, prove explicitly that entanglement of a pure two-qudit state is necessary and sufficient for its Bell nonlocality. By re-visiting the pure two-qubit case, we also find and rigorously prove the new results on the correlation properties of an arbitrary pure two-qubit state., Comment: Improved version, 12 pp

For a model system defined as combination of sequentially applied continuous transformations of a sphere, the question of arrangement of the parameter space around the domain of existence of the Plykin-type attractor is considered. Results of numerical calculations are presented, including charts of dynamical regimes and Lyapunov exponents on the parameter plane, as well as portraits of attractors in characteristic regions of chaotic and regular dynamics. The Plykin attractor region is determined and depicted using the computational procedure for checking hyperbolicity, which consists in analyzing angles between expanding and contracting tangent subspaces of typical trajectories on the attractor. The Plykin attractor takes place in a bounded continuous region of the parameter plane that corresponds to roughness (structural stability) of the hyperbolic dynamics. Outside that region, various types of dynamics are observed including non-hyperbolic chaos, periodic and quasiperiodic behaviors., Comment: 16 pages, 7 figures

Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies occurrence of Smale-Williams attractors in the multidimensional state space. These models can serve as a basis for design electronic generators of robust chaos within a paradigm of coupled cellular networks. One of the examples is a mechanical pendulum system interesting and demonstrative for research and educational experimental studies., Comment: 10 pages, 4 figures

We discuss two mechanical systems with hyperbolic chaotic attractors of Smale - Williams type. Both models are based on Froude pendulums. The first system is composed of two coupled Froude pendulums with alternating periodic braking. The second system is Froude pendulum with time-delayed feedback and periodic braking. We demonstrate by means of numerical simulations that proposed models have chaotic attractors of Smale - Williams type. We specify regions of parameter values at which the dynamics corresponds to Smale - Williams solenoid. We check numerically hyperbolicity of the attractors., Comment: Conference paper presented at International Scientific Conference "Scientific Heritage of Sergey A. Chaplygin: nonholonomic mechanics, vortex structures and hydrodynamics" (June 2-6, 2019, Cheboksary, Russia)

The article considers Chaplygin sleigh on a plane in potential well, assuming that an external potential force is supplied at the mass center. Two particular cases are studied in some detail, namely, a one-dimensional potential valley and a potential with rotational symmetry; in both cases the models reduce to four-dimensional differential equations conserving mechanical energy. Assuming the potential functions quadratic, various behaviors are observed numerically depending of the energy, from those characteristic to conservative dynamics (regularity islands and chaotic sea) to strange attractors. This is another example of nonholonomic system manifesting these phenomena (similar to those for Celtic stone or Chaplygin top), which reflects a fundamental nature of these systems occupying intermediate position between conservative and dissipative dynamics., Comment: 10 pages, 7 figures

We consider a self-oscillator whose excitation parameter is varied. Frequency of the variation is much smaller then the natural frequency of the oscillator so that oscillations in the system are periodically excited and decay. Also a time delay as added such that when the oscillations start to grow at a new excitation stage they are influenced via the delay line by the oscillations at the penultimate excitation stage. Due to a nonlinearity the seeding from the past arrives with a doubled phase so that oscillation phase changes from stage to stage according to chaotic Bernoulli-type map. As a result, the system operates as two coupled hyperbolic chaotic subsystems. Varying the relation between the delay time and the excitation period we affect a coupling strength between these subsystems as well as intensity of the phase doubling mechanism responsible for the hyperbolicity. Due to this, a transition from non-hyperbolic to hyperbolic hyperchaos occurs. The following steps of the transition scenario are revealed and analyzed: (a) an intermittency as alternation of long staying near a fixed point at the origin and short chaotic bursts; (b) chaotic oscillations with often visits to the fixed point; (c) plain hyperchaos without hyperbolicity after termination visiting the fixed point; (d) transformation of hyperchaos to hyperbolic form., Comment: 13 pages, 11 figures

We discuss Hamiltonian model of oscillator lattice with local coupling. Model describes spatial modes of nonlinear Schr\"{o}dinger equation with periodic tilted potential. The Hamiltonian system manifests reversibility of Topaj - Pikovsky phase oscillator lattice. Furthermore, the Hamiltonian system has invariant manifolds with dynamics exactly equivalent to the Topaj - Pikovsky model. We demonstrate the complexity of dynamics with results of numerical simulations. We also propose two dissipative models close to Topaj - Pikovsky system.

The two-mode even and odd coherent states and two-mode squeezed correlated state are discussed. Photon distribution functions, means, dispersions, Fano factor for even and odd coherent states and squeezed correlated state are calculated. The photon distribution function for two-mode squeezed correlated state is obtained. The tomograms of two-mode even and odd coherent states and squeezed correlated states are investigated within the framework of a symplectic tomography scheme. It is shown that the phenomenon of entanglement appears in the system. Two different measures of entanglement are employed., Comment: based on materials of the report at International Workchop on Quantum Optics 2003, Sankt-Peterburg, Russia

A system of $N$ rotators is investigated with a constraint given by a condition of vanishing sum of the cosines of the rotation angles. Equations of the dynamics are formulated and results of numerical simulation for the cases $N$=3, 4, and 5 are presented relating to the geodesic flows on a two-dimensional, three-dimensional, and four-dimensional manifold, respectively, in a compact region (due to the periodicity of the configuration space in angular variables). It is shown that a system of three rotators demonstrates chaos, characterized by one positive Lyapunov exponent, and for systems of four and five elements there are, respectively, two and three positive exponents (`hyperchaos'). An algorithm has been implemented that allows calculating the sectional curvature of a manifold in the course of numerical simulation of the dynamics at points of a trajectory. In the case of $N$=3, curvature of the two-dimensional manifold is negative (except for a finite number of points where it is zero), and Anosov's geodesic flow is realized. For $N$=4 and 5, the computations show that the condition of negative sectional curvature is not fulfilled. Also the methodology is explained and applied for testing hyperbolicity based on numerical analysis of the angles between the subspaces of small perturbation vectors; in the case of $N$=3, the hyperbolicity is confirmed, and for $N$=4 and 5 the hyperbolicity does not take place., Comment: 20 pages, 5 figures

For a Chaplygin sleigh moving in the presence of weak friction, we present and investigate two mechanisms of arising acceleration due to oscillations of an internal mass. In certain parameter regions, the mechanism induced by small oscillations determines acceleration which is on average one-directional. The role of friction is that the velocity reached in the process of the acceleration is stabilized at a certain level. The second mechanism is due to the effect of parametric excitation of oscillations, when the internal moving particle is comparable in mass with the main platform, and, as occurs, a necessary condition for the acceleration is presence of friction. The parametric instability and the resulting acceleration of the sleigh turn out to be bounded if the line of oscillations of the moving mass is displaced from the center of mass. The steady-state regime of motion is in many cases associated with a chaotic attractor; accordingly, the motion of the sleigh turns out to be similar to the process of random walk on a plane.