Abstract:
In this paper a method for reliability analysis of restorable items is considered. Wepresent the model describing a variation of reliability characteristics of objects and taking intoaccount incomplete repair of operability after failure. The asymptotic solution for the intensity ofthe geometric process model is obtained. Reliability characteristics of the geometric processmodel for various distribution laws and various parameters are calculated.

Abstract:
Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schrödinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.

Process equipment placing in industrial
premises leads to essential change of room acoustic characteristics: mean
length of sound rays’ free runs, reverberation time and mean absorption factor
in a room. The changes influence distribution of the reflected sound energy in
premise volume. Failure to take account of the given circumstance results in
errors at definition of sound pressure levels and an estimation of efficiency
of building-acoustic measures of noise abatement. In the paper the results of
computer modeling of acoustic processes in premises with the process equipment
are considered and influence of the equipment on a sound absorption indoors is
analyzed. The computer simulation is carried out on the basis of the ray
tracing method with taking into account rays’ energy distribution in a room. It
is shown that such approach allows determining objectively the integral
acoustic characteristics of industrial premises, takes into account influencing
to them the room parameters, the presence and scattering characteristics of the
equipment and makes more accurate the equations putting into engineering
practice.

Abstract:
Critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. Specifically, relaxational stochastic dynamics of a non-conserved multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken Gaussian, white in time, with correlation function of the form $\propto \delta(t-t') /|{\bf k}_{\bot}|^{d-1+\xi}$, where ${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow") --- the $d$-dimensional generalization of the ensemble introduced by Avellaneda and Majda [1990 {\it Commun. Math. Phys.} {\bf 131} 381] within the context of passive scalar advection. This model can describe a rich class of physical situations. It is shown that, depending on the values of parameters that define self-interaction of the order parameter and the relation between the exponent $\xi$ and the space dimension $d$, the system exhibits various types of large-scale scaling behaviour, associated with different infrared attractive fixed points of the renormalization-group equations. In addition to known asymptotic regimes (critical dynamics of the Potts model and passively advected field without self-interaction), existence of a new, non-equilibrium and strongly anisotropic, type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the leading order of the double expansion in $\xi$ and $\epsilon=6-d$ (one-loop approximation). The scaling appears strongly anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different.

Abstract:
Infrared asymptotic behaviour of a scalar field, passively advected by a random shear flow, is studied by means of the field theoretic renormalization group and the operator product expansion. The advecting velocity is Gaussian, white in time, with correlation function of the form $\propto \delta(t-t') / k_{\bot}^{d-1+\xi}$, where $k_{\bot}=|{\bf k}_{\bot}|$ and ${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to the distinguished direction (`direction of the flow') --- the $d$-dimensional generalization of the ensemble introduced by Avellaneda and Majda [{\it Commun. Math. Phys.} {\bf 131}: 381 (1990)]. The structure functions of the scalar field in the infrared range exhibit scaling behaviour with exactly known critical dimensions. It is strongly anisotropic in the sense that the dimensions related to the directions parallel and perpendicular to the flow are essentially different. In contrast to the isotropic Kraichnan's rapid-change model, the structure functions show no anomalous (multi)scaling and have finite limits when the integral turbulence scale tends to infinity. On the contrary, the dependence of the internal scale (or diffusivity coefficient) persists in the infrared range. Generalization to the velocity field with a finite correlation time is also obtained. Depending on the relation between the exponents in the energy spectrum ${\cal E} \propto k_{\bot}^{1-\epsilon}$ and in the dispersion law $\omega \propto k_{\bot}^{2-\eta}$, the infrared behaviour of the model is given by the limits of vanishing or infinite correlation time, with the crossover at the ray $\eta=0$, $\epsilon>0$ in the $\epsilon$--$\eta$ plane. The physical (Kolmogorov) point $\epsilon=8/3$, $\eta=4/3$ lies inside the domain of stability of the rapid-change regime; there is no crossover line going through this point.

Abstract:
The problem of anomalous scaling in magnetohydrodynamics turbulence is considered within the framework of the kinematic approximation, in the presence of a large-scale background magnetic field. The velocity field is Gaussian, $\delta$-correlated in time, and scales with a positive exponent $\xi$. Explicit inertial-range expressions for the magnetic correlation functions are obtained; they are represented by superpositions of power laws with non-universal amplitudes and universal (independent of the anisotropy and forcing) anomalous exponents. The complete set of anomalous exponents for the pair correlation function is found non-perturbatively, in any space dimension $d$, using the zero-mode technique. For higher-order correlation functions, the anomalous exponents are calculated to $O(\xi)$ using the renormalization group. The exponents exhibit a hierarchy related to the degree of anisotropy; the leading contributions to the even correlation functions are given by the exponents from the isotropic shell, in agreement with the idea of restored small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in the odd correlation functions : the skewness factor is slowly decreasing going down to small scales and higher odd dimensionless ratios (hyperskewness etc.) dramatically increase, thus diverging in the $r\to 0$ limit.

Abstract:
Critical behaviour of a fluid, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. As a simplified model, relaxational stochastic dynamics of a non-conserved scalar order parameter, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken Gaussian, white in time, with correlation function of the form $\propto \delta(t-t') /|{\bf k}_{\bot}|^{d+\xi}$, where ${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to the distinguished direction (``direction of the flow''). It is shown that, depending on the relation between the exponent $\xi$ and the space dimensionality $d$, the system exhibits various types of large-scale self-similar behaviour, associated with different infrared attractive fixed points of the renormalization-group equations. Existence of a new, non-equilibrium and strongly anisotropic, type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the second order of the double expansion in $\xi$ and $\epsilon=4-d$ (two-loop approximation). The most realistic values of the model parameters (for example, $d=3$ and the Kolmogorov exponent $\xi=4/3$) belong to this class. The scaling behaviour appears anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different.

Abstract:
Problem statement. Power objects (heat and power plants, district heat plants, and boiler plants)are located within the precincts of the settlements and are sources of elevated noise levels. Thereuponthere is a necessity of estimation of a noise conditions in the premises of thermal power stationsand in the territories adjoining to them. The process of formation of noise conditions in thethermal power station premises is a difficult multiple process, which requires sophisticated mathematicalmodels for its description. The existing methods do not provide obligatory accuracy ofcalculations. The development of the new methods is required.Results. The new combined method of noise calculation in industrial premises of the thermalpower stations is proposed. The method is based on the principles of division of glassy and diffusivecomponents of the reflected energy and their calculation, accordingly, with the help of a methodof tracing and a statistical energy method. The total condensation of sound energy in imputedpoints is determined by the power summation of all the components. For the method implementationa computer model is elaborated.Conclusions. The method proposed and the computer model of its implementation provide the solutionof problems of noise estimation in the premises of the thermal power stations and in the adjoiningareas. The accuracy of the calculations is sufficient for an objective estimation of noise andfor development of the measures on its reduction.

Abstract:
Stochastic quantization is used to derive exact equations, connecting multilocal field correlators in the phi^3 theory and gluodynamics. Perturbative expansion of the obtained equations in the lowest orders is presented.

Abstract:
Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a non-conserved order parameter. The second one is the strongly non-equilibrium reaction-diffusion system, known as Gribov process and equivalent to the Reggeon field theory. The turbulent mixing is modelled by the Kazantsev-Kraichnan "rapid-change" ensemble: time-decorrelated Gaussian velocity field with the power-like spectrum k^{-d-\xi}. Effects of compressibility of the fluid are studied. It is shown that, depending on the relation between the exponent \xi and the spatial dimension d, the both systems exhibit four different types of critical behaviour, associated with four possible fixed points of the renormalization group equations. The most interesting point corresponds to a new type of critical behaviour, in which the nonlinearity and turbulent mixing are both relevant, and the critical exponents depend on d, \xi and the degree of compressibility. For the both models, compressibility enhances the role of the nonlinear terms in the dynamical equations: the region in the d-\xi plane, where the new nontrivial regime is stable, is getting much wider as the degree of compressibility increases. In its turn, turbulent transfer becomes more efficient due to combined effects of the mixing and the nonlinear terms.