Phase transition in three-dimensional quantum electrodynamics at <Emphasis Type="Italic">T</Emphasis> ≠ 0

Dynamic mass generation in 3D quantum electrodynamics (QED₃) is considered at T ≠ 0. To solve the Schwinger–Dyson equation for the Matsubara electron Green’s function, the ladder approximation is used and the corresponding photonic function is taken in the Landau gauge. In this case, the instant approximation is used for the photonic function. It is established that the process of dynamical mass generation in QED₃ at T ≠ 0 is accompanied by a phase transition. Formal analogy of transitions in the coupling constant is revealed at T ≠ 0 in QED₃, at T = 0 in QED₄, and in graphene theory. Critical values of the coupling constant and temperature, calculated numerically based on an approximate analytical solution of the Schwinger–Dyson equation are of the same orders of magnitude.     

Analysis of flexible plates based on the method of averaging

The problem is solved on nonlinear bending for a rectangular plate strengthened by a unidirectional regular load-bearing assembly. Starting relationships are used in the form of Berger. An averaging method is used for differential equations in partial derivatives based on the technique of double-scale expansion. In order to evaluate the accuracy of the suggested approach an accurate solution is obtained for the problem in question in the form of a double trigonometric Fourier series.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 124–129, 1988.     

Complex lag synchronization of two identical chaotic complex nonlinear systems

Much progress has been made in the research of synchronization for chaotic real or complex nonlinear systems. In this paper we introduce a new type of synchronization which can be studied only for chaotic complex nonlinear systems. This type of synchronization may be called complex lag synchronization (CLS). A definition of CLS is introduced and investigated for two identical chaotic complex nonlinear systems. Based on Lyapunov function a scheme is designed to achieve CLS of chaotic attractors of these systems. The effectiveness of the obtained results is illustrated by a simulation example. Numerical results are plotted to show state variables, modulus errors and phase errors of these chaotic attractors after synchronization to prove that CLS is achieved.     

Application of CO2 Supercritical Fluid to Optimize the Solubility of Oxaprozin: Development of Novel Machine Learning Predictive Models

Over the last years, extensive motivation has emerged towards the application of supercritical carbon dioxide (SCCO₂) for particle engineering. SCCO₂ has great potential for application as a green and eco-friendly technique to reach small crystalline particles with narrow particle size distribution. In this paper, an artificial intelligence (AI) method has been used as an efficient and versatile tool to predict and consequently optimize the solubility of oxaprozin in SCCO₂ systems. Three learning methods, including multi-layer perceptron (MLP), Kriging or Gaussian process regression (GPR), and k-nearest neighbors (KNN) are selected to make models on the tiny dataset. The dataset includes 32 data points with two input parameters (temperature and pressure) and one output (solubility). The optimized models were tested with standard metrics. MLP, GPR, and KNN have error rates of 2.079 × 10⁻⁸, 2.173 × 10⁻⁹, and 1.372 × 10⁻⁸, respectively, using MSE metrics. Additionally, in terms of R-squared, they have scores of 0.868, 0.997, and 0.999, respectively. The optimal inputs are the same as the maximum possible values and are paired with a solubility of 1.26 × 10⁻³ as an output.     

CL-20 photodecomposition: ab initio foundations for identification of products

1,5-Dihydrodiimidazo[4,5-b:4'5'e]pyrazine, 1H-imidazo[4,5-b]pyrazine, and 1H-imidazole were considered as possible products of 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20) photodecomposition. Since we took as a reference the product obtained after CL-20 irradiation in methanol solution, the nature of intermolecular bonds between heterocycles under study and methanol molecules was analyzed in detail. Existing hydrogen bonds were found to be quite strong, so dependence of calculations results on an influence of solvent was taken into account using both the polarizable continuum model (PCM) and the supermolecular approach. Electronic spectra of 1,5-dihydrodiimidazo[4,5-b:4'5'e]pyrazine, 1H-imidazo[4,5-b]pyrazine and 1H-imidazole were simulated using time dependent density functional theory (TD-DFT) and single-excitation configuration interaction (CIS) method. We observed that TD-DFT excitation energies are lower if compared to corresponding values obtained by the CIS method. Results of calculations with PCM and the supermolecular approach are very close. It was found that differences between calculated gas phase excitation energies and those values obtained by applying solvent models increases when the number of conjugated bonds in a molecule increases. Oscillator strengths of UV bands of the considered molecules are higher in the gas phase than in modeled methanol solutions. We found that the predicted spectrum of 1H-imidazole is in close agreement with the experimental UV spectrum of the CL-20 photolysis product.     

Relativistic fermion in a spherically symmetric potential well of finite depth in a two-dimensional space

The problem of existence of bounded relativistic fermion states in a spherically symmetric well of finite depth in a two-dimensional space is investigated. The well depth critical for the appearance of standard states with energies E = m, 0, and –m is determined; moreover, cases with zero and nonzero fermion momenta are considered. Approximate analytical expressions for the critical depths of narrow and wide wells are derived which are in good agreement with the results of numerical calculations. Approximate energies of levels located on the boundaries of the upper and lower continuums and determined analytically are in good agreement with the results of numerical calculations.     

Equilibrium theory of a “soft sphere” fluid with exponential interaction

Odessa Technological Institute for Industrial Refrigeration. Translated from Zhurnal Strukturnoi Khimii, Vol. 29, No. 5, pp. 84–88, September–October, 1988.