Experimental study and mathematical modelling of heat transfer processes in heat accumulating media

Experimental results on reversing non-stationary heat transfer are presented for filtration of an air flow through an immobile heat accumulating medium consisting of lead (D = 2.0, 3.5, and 4.5 mm) and glass (D = 3.2 mm) balls. The studied device imitated the cyclic modes of heat regeneration in the ventilation system for domestic and office rooms. Dependency between the time of flow switching and Re number was measured. The mathematical model describing heat transfer between a gas flow and an immobile layer of balls was developed. Good correspondence between the experimental data and calculation results is observed for high Reynolds numbers. For low Re numbers the effect of heat losses is considerable, and experimental time of flow switching is shorter than the calculation one. The work was financially supported by the President of the Russian Federation (Grant No. NSh 6526.2006.3), Russian Foundation for Basic Research (Grant No. 06-08-00982), Foundation “Global energy” and Program “Energy saving of SB RAS”.     

K. Schwarzschild's problem in radiation transfer theory

We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem—to be more precise the calculation of the source function within the slab—was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case (albedo=1), which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce (1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it, (2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere.     

大型空间环境模拟设备热沉设计与研究

热沉是空间环境模拟器中的重要组成部分。文中就大型热沉研制过程中有关热沉理论计算、材料选择、热沉结构等方面作了介绍。     

空间运输航天器故障诊断系统架构研究

故障诊断技术不仅是提高空间运输航天器的安全性和可靠性的重要手段,而且可以节约航天器整个寿命周期的运行维护成本,因此研究航天器故障诊断技术,特别是处理紧急故障的在轨故障检测和诊断技术是非常必要的。在分析国外航天器故障诊断系统发展趋势的基础上,提出了基于天地一体化设计思想的空间运输航天器故障诊断系统架构,阐明了设计原则,以及具体功能需求。介绍了在轨故障诊断系统和地面故障诊断系统,提出了地面故障诊断系统软件的组件模型构成。地面系统对航天器在轨故障诊断有较强的辅助作用,能有效补充故障分析、诊断、预测、处理能力。给出的系统架构对航天器故障诊断系统研制具有一定的参考价值。     

A rapidly convergent iterative solution of the non-LTE line radiation transfer problem

An iterative scheme has been developed for the solution of the non-LTE line radiation transfer problem. The method uses an approximate operator that is deliberately chosen to be local so that it can be easily extended to multidimensional geometry. The difference between the formal and approximate solutions is used as a driving term for the iterations. In one-dimensional, semiinfinite and free-standing slabs, the technique is found to be very fast, robust, and applicable to a large class of problems.     

Dictums for problem solving and approximation in mathematical acoustics: examples involving low-frequency vibration and radiation

A sequence of dictums for mathematical acoustics is given representing opinions intended to be regarded as authoritative, but not necessarily universally agreed upon. The dictums are presented in the context of the detailed solution for a class of problems involving the forced vibration of a long cylinder protruding half-way into a half-space bounded by a compliant surface (impedance boundary) characterized by a spring constant. One limiting case corresponds to a cylinder vibrating within an infinite rigid baffle, and another limiting case corresponds to a vibrating cylinder on the compliant surface of an incompressible fluid. The second limiting case is identified as analogous to that of a floating half-submerged cylinder whose vibrations cause water waves to propagate over the surface. Attention is focused on vibrations at very low frequencies. Difficulties with insuring a causal solution are pointed out and dictums are given as to how one overcomes such difficulties. Various approximation techniques are described. The derivations involve application of the theory of complex variables and the method of matched asymptotic expansions, and the results include the apparent entrained mass in the near field of the cylinder and the radiation resistance per unit length experienced by the vibrating cylinder.     

On the mathematical modelling of processes of peat firing and smoldering

Based on a mathematical model of a porous reacting medium the statement and mathematical solution are presented for a problem of the peat smoldering rise as a result of the effect of a lower seat of fire. It is found that at moderate temperatures T ≤ 750 K the firing and smoldering of the initial reagent are determined by the intensity of the external burning seat as well as by the processes of the peat drying, pyrolysis, and the oxidation reaction of the coked fixed bed. The work was financially supported by the Program of the Federal Agency for Education (Grant No. P 042242).     

Complexity analysis and mathematical tools towards the modelling of living systems

This paper is a review and critical analysis of the mathematical kinetic theory of active particles applied to the modelling of large living systems made up of interacting entities. The first part of the paper is focused on a general presentation of the mathematical tools of the kinetic theory of active particles. The second part provides a review of a variety of mathematical models in life sciences, namely complex social systems, opinion formation, evolution of epidemics with virus mutations, and vehicular traffic, crowds and swarms. All the applications are technically related to the mathematical structures reviewed in the first part of the paper. The overall contents are based on the concept that living systems, unlike the inert matter, have the ability to develop behaviour geared towards their survival, or simply to improve the quality of their life. In some cases, the behaviour evolves in time and generates destructive and/or proliferative events.     

Real space and configuration space wave function in the intermediate valence problem

This paper analyses the behavior of intermediate valence compounds, from the point of view of wave functions. They are expressed in a linear combination of cellular orbitals (LCCO) basis for SCF plus correlation introduced in the configuration interaction (CI) scheme, suitable to describe the different spatial extension in real space and the correlation between different fⁿ possibilities. This allows the discussion of the large variety of interesting phenomena which arises from the changes of the f electron configuration space wave functions: fⁿ → fⁿ⁺¹ of from the changes of the electronic charge from atomic-like to the different condensed matter-like boundary conditions. In particular an analysis is included of the correspondence between the actual properties in this type of materials and the amount of atomic-like f character n_f^atomic ?n_f^total in some rare earth and actinide compounds, concluding that the experimental evidence is consistent with a large distortion of the actual f-wave functions from their atomic-like forms.     

The Kepler problem in the Snyder space

In this paper the Kepler problem in the non-commutative Snyder scenario was studied. The deformations were characterized in the Poisson bracket algebra under a mimic procedure from quantum standard formulations by taking into account a general recipe to build the non-commutative phase space coordinates (in the sense of Poisson brackets). An expression for the deformed potential was obtained, and then the consequences in the precession of the orbit of Mercury were calculated. The result could be used for finding an estimated value for the non-commutative deformation parameter.     

Hyperspin manifolds and the space problem of Weyl

A recent criticism of the claimed existence of torsion-free connections compatible with a hypermanifold structure in Finkelstein's sense is reinforced by relating the problem to the space problem of Weyl as generalized by Cartan and Freudenthal. Some historical remarks concerning the development of the latter are also included.     

Numerical solution to the plane heat-mass transfer problem in a system of focused radiation flux-liquid condensed substance film-oxidizer

The plane problem of heat and mass transfer in a focused radiation flux-liquid condensed substance film-oxidizer system is numerically solved. Peculiarities of heat and mass transfer at radiation energy absorption by a vapor-gas mixture near the liquid surface are analyzed. The influence of the radiation density distribution in a flux and the liquid and oxidizer parameters on the conditions of heat and mass transfer is assessed.     

Synchrotron radiation of charges distributed in space

We investigate characteristics of spontaneous radiation of a uniformly charged rod orthogonal to a given plane and moving such that is projection on this plane moves uniformly on a circle. It is shown that the power of radiation of such charged structure is smaller than the power of radiation of point charge of the same value and moving on the same circle. With increasing energy, the power of radiation increases slower than the power of synchrotron radiation.Institute of High Current Electrotechniques, Siberian Branch, Russian Academy of Sciences. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 23–25, January, 1993.     

Numerical modelling of the radiation efficiency of asymmetrical structures

The radiation efficiency of a structural element is required by some models in order to predict its sound insulation. A common assumption is that the radiation on both sides of the element is the same. This is not true for asymmetrical structural elements like lightweight floors consisting of a beam-supported flat board. The radiation efficiency is larger on the beam side, because the beams act as exciters and increase the pressure level in the room. These different radiation efficiencies are calculated here for a two-dimensional cross-section by using finite elements and boundary elements. The obtained preliminary results illustrate that considering a single radiation efficiency can be a source of errors and that further investigation is required in order to improve predictions.     

Inverse problem of mechanics in momentum space

The problem is solved of reproducing a spherically symmetric potential by means of the velocity vector hodograph in a classical mechanics approximation. A definite transcendental equation is obtained for the radial velocity dependence. Considered as an illustration is the problem of the Maxwell fish eye. A relativistic generalization is given. The algorithms constructed can be used to retrieve potentials possessing internal symmetries in the classical or quantum cases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 46–50, January, 1985.In conclusion, I am grateful to Prof. Yu. N. Demkov for active and stimulating interest in the research.     

Design and mathematical modelling of the space-borne far-infrared Fourier transform spectrometer for REFIR experiment

A far infrared Fourier spectrometer named REFIR (Radiation explorer in the far infrared) has been designed for space-borne observations of the atmospheric radiance in the broad spectral range 100–1000 cm⁻¹. The requirements are discussed and the adopted instrumental configuration is presented. The variability of the source and the narrow frequency bandwidth of the detectors as well as some novel features of the selected configuration require some dedicated analysis for the establishment of the instrument performances which are herewith described.