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Results of a numerical study of the laminar-turbulent transition in the boundary layer of a prolate spheroid obtained with the use of the ANSYS Fluent gas-dynamic software with an in-house developed module of the laminar-turbulent transition based on the e ^N-method are reported. Based on experimental data, a method of determining individual threshold N -factors for different transition mechanisms is proposed.

The gas-dynamic conservation laws in integral form for sections of channels which have a bend of the axis, a jump in the cross-section area or channel branching is an open system of equations. The openness problem is solved by a method based on the independence of the thermodynamic function (pressure recovery factor) on the specified geometric arguments. The mathematical model reduces to a closed system of nonlinear algebraic equations not requiring additional hypotheses and admitting a solution in explicit form for small Mach numbers.

Coupled equations are used to develop a method for solving boundary-value problems for second- and third-order equations. With the use of the factorization method, a three-point boundary-value problem for a third-order equation is reduced to a system of first- and second-order equations. In order to solve the second-order equation, a discrete problem is constructed, which is then used to solve the main problem. This method is peculiar because discrete (difference) boundary-value problems are constructed without using approximations of differential operators. The method is generalized to solve higher-order equations.

A system of two nonlinear stochastic equations is used to simulate fluctuations near a critical transition. Their interaction results in extreme fluctuations of temperature and heat fluxes with a (1/f) spectrum in critical heat and mass transfer regimes. The interaction of large and small fluctuations in the critical domain is investigated, which can make it possible to explain the physical nature of (1/f) noise and large fluctuations with power-series amplitude distribution, as well as their interaction with classical fluctuations. In the case of external periodic action on a system with interacting nonequilibrium phase transitions, the chaotic regimes characterized by unstable pulsation cycles are determined.

In this research, we use the fluid theory in an efficient way to perform a theoretical study on a divergent flux of fast electrons produced during interaction of a high-power laser beam with a cylindrical over-dense target. Cylindrical targets consisting of a low-density core with high-density cladding structures are irradiated by an ultra-intense annular laser beam. The analytical model exhibits such structures with a density gradient generating a strong spontaneous interface magnetic field that can collimate the fast electron beam and prevent electrons from escaping. The magnetic field generated by such a cylindrical target is compared with that of planar targets. The results show that cylindrical structures have a more effective potential for producing spontaneous interface magnetic fields and reducing the transverse angular distribution of the fast electron beam. Thus, they will be adequate to increase the possibility of energy transmission to the main target for a more promising fast ignition scheme in inertial confinement fusion.

The article considers the place and role of the concept of state in the context of determinist understanding in natural scientific knowledge. It is shown that without the use of this concept, determinist ideas seem to be incomplete.

The article analyses the value of the concept of independence for philosophy, pure mathematics and applied mathematics. Thus, examples from geometry and set theory demonstrate that the study of mathematical statements independent of axiomatics provided an impetus for the development both of these sciences and mathematical logic. The main attention is paid to the analysis of the use of independence in applications. As we know, the most popular applications of mathematical disciplines such as elementary probability theory and mathematical statistics often use models of independent experiments. Since formal verification of the relation of independence is labor-intensive, independence is often introduced on the basis of intuitive reasoning. The article shows the inconsistency of arguments in favor of adopting independent experiment models based on intuitive considerations, such as control of experimental conditions and a negligible correlation of random values. The author outlines the prospects for accepting independence out of pure mathematical approaches, but on the basis of philosophical principles and those of natural sciences, namely the common cause principle and the maximum entropy principle.

We argue that Anton Zeilinger’s “foundational conceptual principle” for quantum mechanics, according to which an elementary system carries one bit of information, is an idealistic principle and should be replaced by a realistic principle of contextuality. The specific properties of quantum systems arise from the impossibility of talking about them without regard to the tools of their observation/identification and, therefore, to the context in which these tools are applied. In particular, the assumption of non-locality is not required to explain quantum correlation. Correlated quantum events are interrelated in a causal way. Yet, this is not classical, but quantum causality expressed by an entangled wave function. This or that particular correlation does not arise in measurement; in measurement, it is identified in context. In contrast to Zeilinger’s principle of quantization of information, the principle of contextuality explains it realistically.

Technological progress can be described as a game called the Inventor's Dilemma which is analogous to the Prisoner's Dilemma. Two actors who independently work on creating a potentially dangerous technology are likely to continue to develop it, even if they recognize the danger and come to an agreement. The very situation, in which they are, prompts them to continue working. Thus, it is virtually inevitable that potentially dangerous technologies will appear. This means that instead of trying to prevent the emergence of such technologies we should focus on finding a way to neutralize or compensate for the negative consequences of their emergence.

The paper provides a review of Øystein Linnebo's "Thin Objects. An Abstractionist Account" and contains a brief summary of the main ideas of the chapters published in the mentioned book.