Interaction between a liquid and a cylindrical body touching a wall

An exact solution is obtained for the problem of interaction between the ideal liquid homogeneously moving at infinity and streamlining a round cylinder touching a solid wall.     

Stress analysis of a strip with a step and a crack

Stress analysis for a strip of which widths are different at the right and left handsides is carried out for before and after occurrence of a crack at a corner of a step. The strip is analyzed as a thin plate bending problem subject to transverse bending and torsion, and as a plane eleastic problem subject to bending in the plane and uniaxial tension. The rational mapping function of a sum of fractional expressions and complex variable method are used. Stress distribution and stress intensity factors are obtained.     

Calculation of a transient in a two-pole network with a thermistor

An analytical expression is derived which describes the variation of the thermistor temperature during a relay-effect transient process following an instantaneous change in the supply voltage in an R — R_T two-pole network.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 38, No. 3, pp. 465–472, March, 1980.     

Imaging a point to a line with a single spherical mirror

Methods for imaging a single point source to a line image are discussed, and a design study of single spherical mirror systems that form aberration-free line images is presented. An expression forthe ray density along the line image is derived for such systems in the cases of (i) uniform beam profiles and (ii) Gaussian beam profiles. The resulting ray density profiles are illustrated for single spherical mirror systems over a wide range of design parameters.     

Influence lines for bending under a ring load of a free shell,a shell embedded in a soft medium and a shell containing a soft core

Summary Theoretical expressions for stresses and displacements have been derived for bending under a ring load of a free shell, a shell embedded in a soft medium, and a shell containing a soft core. Numerical work has been done for typical cases with anElliot 803 Digital Computer and influence lines are drawn therefrom.

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Einflußlinien für die Biegung einer freien Schale, einer Schale in einer weichen Bettung und einer Schale mit weichem Kern

Zusammenfassung Für die Biegung einer freien Schale, einer weich gebetteten Schale und einer Schale mit weichem Kern unter einer Ringlast werden Ausdrücke für die Spannungen und Verschiebungen hergeleitet. Die Ergebnisse wurden für einige typische Fälle mit einem DigitalrechnerElliot 803 numerisch ausgewertet. Die sich ergebenden Einflußlinien wurden graphisch dargestellt.

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Nomenclature A (),B () Functions of - a, t Mean radius and thickness of the shell - E _S , _S Young's modulus andPoisson's ratio of the shell - G _c , _c Shear modulus andPoisson's ratio of the casting or core - I ₀ (r),I ₁ (r) ModifiedBessel functions of the first kind and order zero and one respectively - K ₀ (r),K ₁ (r) ModifiedBessel functions of the second kind and order zero and one respectively - p Ring load, lb/in - U, W Displacement components in the casing or core in thez andr direction - u, w Displacement components of a middle surface point in the shell - _r , _rz Radial and shearing stress components - Independent variable of infinite integrals - k [3(1–S ²)a ²/t ²]^1/4 With 13 Figures     

Analysis of a Premature Failure of a Hub from a Diesel Generator of a High-Speed Motor Ship

Failure analysis is carried out on a fractured hub obtained from a diesel generator of a high-speed motor ship. Macrofractography, microfractography, standard optical metallography, material characterization techniques, and numerical modeling were used to verify the findings of the current investigation. Cracking initiation is attributed to fretting fatigue caused by a modification performed in the vicinity of the fractured hub. Operational vibrations contributed to the propagation of the cracks as typical fatigue cracks until final fracture.     

Piercing a metallic barrier with a jet of a dilute polymer solution

Results are shown pertaining to the action of jets of dilute polymer solutions on solid barriers. The piercing of a barrier is explained by the viscoelastic properties of aggregates which, during an impact, behave like solid particles.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 25, No. 6, pp. 1090–1094, December, 1973.     

Interaction between a cylindrical shell in a fluid and a pulsating bubble

The dynamic behavior of a cylindrical fluid-immersed shell in a pressure wave initiated by a pulsating vapor-gas bubble that develops as a result of the action of laser radiation on the absorbing medium (metal) is examined experimentally and theoretically. The results of the experiments suggest that the amplitude of the shock wave that develops as a result of complete or partial vaporization of the absorbing medium is appreciably smaller than the amplitude of the waves due to pulsations of the bubble that is formed. Experimental data on the pattern of structural deformation are confirmed by calculations. The effect of load simulation on the behavior of the shell is established according to computational data.Translated from Problemy Prochnosti, No. 6, pp. 116–120, June, 1990.     

Emptying a pipe containing a fluid with a changing state of aggregation

A solution is obtained for the dynamic problem of emptying a pipe closed at one end and containing a fluid nonuniformly heated along its length, for the case in which the saturated vapor pressure of the hottest layers exceeds the ambient pressure. The solutions in quadratures in terms of the dimensionless quantities are approximated by formulas.     

Resistance of a sphere in a slow flow of a viscoelastic fluid

The authors have obtained an approximate solution of the problem of the resistance of a rigid sphere in a slow flow of a Maxwell viscoelastic fluid that is in good agreement with experimental data [1] for Weissenberg numbers We ≤ 0.7. It is shown that the effect of a decrease in the coefficient of resistance of a sphere in the interval 0.1 ≤ We ≤ 0.7 established experimentally is determined in full measure by the linear viscoelastic properties of the Maxwell fluid. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 6, pp. 1138–1140, November–December, 1998.     

Linear heat transfer in a flow around a cylinder or a sphere

It is shown that the relation between the Nusselt and Reynolds numbers determined by the Reynolds analogy is linear with self-similarity of the hydrodynamic resistance coefficient.Special Design and Technology Office Element, Odessa, Ukraine. translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, May–June, pp. 395–396, 1995.     

Discovering a junction tree behind a Markov network by a greedy algorithm

In our paper (Annals of Operations Research, 193:71–90, 2012) we introduced a special kind of k?1-width junction tree, called k-th order cherry tree in order to approximate a joint probability distribution. The approximation is the best if the Kullback–Leibler divergence between the true joint probability distribution and the approximating one is minimal. Finding the best approximating k?1-width junction tree probability distribution is NP-complete if 2<k<d?1, where d is the dimension of the joint probability distribution (see Karger and Srebro in 12th ACM-SIAM Symposium on Discrete Algorithms (SODA), 2001, Malvestuto in Kybernetika 48:825–844, 2012). In Broad Research in Artificial Intelligence and Neuroscience (BRAIN), special issue on complexity in sciences and artificial intelligence, pp. 40–45, 2010 we also proved that the best approximating k?1-width junction tree probability distribution can be embedded into a k-th order cherry tree probability distribution. We introduce here a greedy algorithm resulting very good approximations in reasonable computing time. We prove then that if the Markov network which encodes the conditional independences of the multivariate probability distribution fulfills some requirements then our greedy algorithm is able to find the true probability distribution. Our algorithm uses just the k-th order marginal probability distributions as input. We compare the results of the greedy algorithm proposed in this paper with the greedy algorithm proposed by Malvestuto (IEEE Trans. Syst. Man Cybern. 21:1287–1294, 1991).     

Strength analysis of a split sleeve in a pipe containing a defect

We study the decrease in the strength of a pipe containing an artificial defect. On the basis of the analytic and numerical models, we consider the influence of the structural features of a split sleeve on its load-carrying ability. We also analyze the joint operation of a sleeve and a pipe containing an artificially made axial surface defect. The results of the numerical analysis are compared with the experimental data. Translated from Problemy Prochnosti, No. 2, pp. 102–111, March–April, 2009.     

Dispersion of a solute in a Poiseuille flow of a viscoelastic fluid

Gill and Sankarasubramanian's analysis of the dispersion of Newtonian fluids in laminar flow between two parallel walls is extended to the flow of non-Newtonian viscoelastic fluids (known as Phan-Thein-Tanner (PTT)). Using a generalized dispersion model which is valid for all times after the solute injection, the diffusion coefficient K_i(t) is obtained exactly and numerically for linearized and exponential forms of the PTT fluids, respectively. The analysis leads to the novel result for K₁ and K₂(t) (which is a measure of the longitudinal dispersion coefficient of the solute). It is found that the value of K₂(t) depends on the value of Deborah number (De=a measure of the level of elasticity in the fluid) whereas the value of K₁ is constant in both cases. Finally, the effect of the Deborah number on the axial distribution of the mean concentration θ_m is investigated in detail.     

Diffusion of a dissolved gas in a flow with a stationary cavity

An exact solution is obtained for the plane problem of the diffusion of a gas from a solution into a stationary cavity behind a symmetric profile for a zero cavitation number in an ideal liquid, and its approximate generalizations are indicated.     

Sliding of a body over a melting surface at a high velocity

A mathematical model of thermal processes in the motion of one body over the melting surface of another is considered. A simple analytical solution to the problem, applicable in a wide range of velocities, is obtained.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 60, No. 6, pp. 964–968, June, 1991.     

Mixing of a jet array with a transverse stream in a channel

Universal empirical formulas are proposed for calculating, from the trajectories, the attenuation of velocity and temperature along the axis of a jet through a transverse stream in a channel.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 3, pp. 541–544, September, 1972.     

Bending of a thin plate containing a rigid inclusion and a crack

The bending of a thin infinite plate with a line crack and an arbitrarily shaped rigid inclusion is analyzed. The superposition principle is used to reduce the original formulation to two subsidiary problems. A distribution of dislocation is assumed along the crack line. The solution is obtained in an integral form by using the Green function of a point dislocation. The stress functions for both subsidiary problems are obtained by employing the rational mapping function technique. The stress intensity factors are obtained in terms of the dislocation density function. Numerical results are demonstrated for the plate containing a square rigid inclusion and a line crack.